1 Econ 500 Microeconomic Review Deman What these notes hope to o is to o a quick review of supply, eman, an equilibrium, with an emphasis on a more quantifiable approach. Deman Curve (Big icture) The whole point of a eman curve is to fin the relationship between the price of a goo an the quantity that consumers wish to purchase (the quantity emane). Why oes it matter? First off, a soli unerstaning of supply an eman is generally necessary to have an economic unerstaning of the worl aroun you. Secon, an as important, if firms have knowlege of the eman curve facing their firm, they will have the ability to make more informe pricing an output ecisions. These ecisions that will irectly affect the firm s profitability. This will be particularly true of firms with pricing power (monopoly power). For even more backgroun, rea the tetbook. I am going to assume that you have some unerstaning of the st Law of Deman. The st Law of Deman states, ceteris paribus (holing other relevant factors constant), as the price of a goo falls, the quantity eman of that goo increases. Basically, it states that eman curves are ownwar sloping. Interpretations of the Deman Curve There are two ifferent ways you can interpret the information given in a eman curve. Horizontal Interpretation of Deman Curve - this is the interpretation of the eman curve you are most likely familiar with. The iea here is to pick a price, then move (horizontally) over to the eman curve. For eample, if the price of a Hona Accor is $,000, the quantity emane of Hona Accors might be 450,000. That is, if the price is $,000, consumers will wish to purchase 450,000 cars. Likewise, if the price of a Hona Accor is $0,000, the quantity emane might be 500,000. See the graph below. The reason we call this the horizontal interpretation shoul be apparent. ACCORD $,000 $0,000 Deman 450, ,000 Q ACCORD Vertical Interpretation of Deman Curve this will be less familiar, an will come in hany when iscussing consumer surplus, an later when we iscuss price iscrimination an other pricing strategies. The iea here is to pick a quantity, then move (vertically) up to the eman curve. We sometimes call the result the height of the eman curve. See the picture below.
2 Econ 500 Microeconomic Review Deman For instance, if the height of the eman curve facing a specialize pizza store at Q = 0 is $7, this means that the most a consumer will be willing to pay for the 0 th pizza is $7. Likewise, if the height of the eman curve at Q = 5 is $3, this means the most a consumer will be willing to pay for the 5 th pizza is $3. IZZA $7 $3 Deman 0 5 Q IZZA As elue to above an in the previous footnote, price iscrimination is a strategy where firms will try to charge ifferent customers ifferent prices. If the firm can come up with a way to charge the first consumer $7 an the other consumer $3, it will earn more revenue than if it charges a price of $7 (only the st consumer will purchase the pizza) or a price of $3 (both consumers purchase the goo). Of course, we coul use either interpretation on a eman curve, epening in which type of problem we are intereste. We coul have aske what is the most a consumer will be willing to pay for the 450,000 th or the 500,000 th Hona Accor. 3 Likewise, we coul ask how many pizzas that consumers will wish to purchase at a price of $3 or $7. 4 Which interpretation we choose oes not change the unerlying eman curve. As you progress, you will fin it makes more sense to use one interpretation or the other epening on the problem we are ealing with. This consumer woul be willing to purchase the 0 th pizza for any price less than $7, but will not pay any price higher than $7. We sometimes call the height of the eman curve the marginal benefit, marginal value, or marginal willingness to pay. If you recall the ifference between an iniviual consumer s eman curve an the market eman curve, we are iscussing the market eman curve in this case. We know that iniviual s eman curves are ownwar sloping. Iniviually, you woul be willing to pay more for the 0 th pizza then you woul for the 5 th pizza. Are you still hungry? However, when we look at the market (overall) eman curve for a prouct, we have combine every person s iniviual eman curve. The consumer who was willing to pay $7 for the 0 th an the consumer who was willing to pay $3 for the 5 th pizza are likely to be ifferent people, a point we shall revisit when we iscuss price iscrimination. 3 Some consumer woul be willing to pay $,000 for the 450,000 th Hona Accor an some other consumer woul be willing to pay $0,000 for the 500,000 th Hona Accor. In this case, I am very sure these are ifferent consumers. Do you know anyone who owns 50,000 Hona Accors? 4 Hopefully not surprisingly, the answers here are 5 an 0, respectively.
3 Econ 500 Microeconomic Review Deman Ceteris aribus Conitions for Deman Curves Thus far, we have glosse over the st Law of Deman an the ceteris paribus conitions for eman. Some more very eep backgroun that you shoul have learne before... If, we were intereste in the important factors etermining the number of cars sol, surely the price of cars woul be important. This is eactly what we hope to capture with a eman curve. A eman curve illustrates how the quantity of cars consumers wish to purchase changes as the price of cars changes, holing other relevant factors constant. 5 On the other han, many other things (asie from the price of cars) affect the number of cars people wish to purchase. We call these other things eman shifters or ceteris paribus conitions for eman. In orer to raw a eman curve (to isolate the relationship between the own price of a car an the quantity emane of cars), we must hol the ceteris paribus conitions constant. On the other han, when one of these ceteris paribus conitions changes, we must shift the eman curve in the appropriate irection. What are these eman shifters or ceteris paribus conitions for the eman for cars? Just to name a few: rice of gasoline / insurance / tires, price of trucks / bicycles / public transportation, incomes of consumers, quality an characteristics of cars, epectations about future car prices, More in the net section... Mathematical Epressions of Deman Curves The following section borrows heavily from Baye s Chapter, an uses the notation therein. We can learn something from mathematicians. Here is what they woul write: Q = f (,, M, H ) y What oes it mean? It means the quantity emane of goo X ( Q ) is a function of, or epens on, the price of goo X ( ) the price of relate goos ( y ), the income level of consumers ( M ) an other stuff ( H ). In fact, we can get even more specific about the form of the relationship. While it is not necessarily the case, we often moel eman curves as being linear. 6 If so, we can write out a very simple numerical epression of a eman curve. For eample: Q = 00 y + 6M 5 If you recall from your previous economics classes, in this case, we woul call the price of the car the own price. The own price is the price of the goo for which we are rawing the eman curve. 6 A linear eman curve is one with a constant slope of the eman curve. Mathematically, this means the power (eponent) on the term is (implicitly). We will focus on linear eman curves in this class. As an eample of a non-linear eman curve, consierq = 00 + M. y 6 3
4 Econ 500 Microeconomic Review Deman We will call this a eman function. The eman function contains a whole slew of information. First off, suppose you were tol to raw the eman curve for goo X. You woul pull out a piece of graph paper, label the vertical ais, the horizontal aisq, an then you woul be stuck. 7 In fact, you cannot raw the eman curve without knowing the values of y an M, which are the ceteris paribus conitions for eman. Suppose you were tol that M = 0 an the point where you coul raw it. 8 Q = 00 y + 6M Q = 00 (30) + 6(0) Q = = 00 Q y = 30. In that case, you coul simplify the eman function to Now, your eman function is epresse with only Q an. You can graph it, which we will o in a bit. Before oing this, though, let us take an asie on the inverse eman function. Asie Inverse Deman Function It turns out it will save us some trouble to fin what is calle the inverse eman function. To fin the inverse eman function, simply start with the eman function, an solve it for. In the case where M = 0 an y = 30, we start with: = 00 Q Now we just o the algebra. You can take whatever steps get you to the en. I will begin by aing to both sies: Q Then subtract + = 00 Q from both sies: = 00 Q An multiply both sies by : 7 Why not label itq? You coul. Eventually, we will have the quantity of goo X supplie, as well, so often we will just be lazy an label itq. 8 It is just a coincience in this case that the last two terms in the eman function cancel out. This will not always be the case. See also below the eamples for when M an y change. 4
5 Econ 500 Microeconomic Review Deman = 00 Q Why have I one this? First off, you will see in a secon that it is now very easy to fin a secon point on our eman curve. In aition, this epression will come in hany when we fin the marginal revenue curve for the firm. Graphing the Deman Function Recall from out eman function thatq = 00. By plugging in = 0 in the epression above, we fin that Q = 00. This is one point on our eman curve. In fact, this is the horizontal intercept of the eman curve. We also solve for the inverse eman function, fining that = 00 Q. By plugging in Q =0, we fin that =00. It turns out this is the vertical intercept of the eman curve. Because we have a linear eman function, to raw the line, we nee only fin two points on the line, which we have just one. ut these two points on a graph, connect the ots, an we are finishe. See below. X $00 D 00 Q X 5
6 Econ 500 Microeconomic Review Deman Shifting the Deman Curve What if M increases from $0 to $0? What happens to the eman curve? From a mathematical perspective, we can just plug an chug. But we woul also like to go back to the intuitions as well. First the math Q = 00 y + 6M Q = 00 (30) + 6(0) Q = = 60 (compare this to = 00 ) Q Q When we change the eman function, we will also get a new inverse eman function. Taking the same steps as before (but leaving out the eplanation of these steps), we get: Q = 60 Q + = 60 = 60 Q = 30 Q Now, we raw the new eman curve. From the eman function, I see that setting epression above results in in =30. Now we stick these new points on our graph paper. = 0 in the Q = 60. From the inverse eman function, I see that setting Q = 0 results Below is a picture with the original eman curve ( M = $0) labele D 0 an the new eman curve ( M = 0) labele D. We see immeiately what has happene is that the eman curve has shifte to the right because of the increase in income. We call a rightwar shift of the eman curve an increase in the eman curve. 9 Likewise, we call a leftwar shift of the eman curve a ecrease in the eman curve. Again, any change in a ceteris paribus conitions shifts the eman curve. That is, a change in anything but the own price, causes a shift in the eman curve. 9 Why is this calle an increase in the eman curve? From the horizontal interpretation of the eman curve, notice that at any (an every) price, there is a larger quantity emane on the new eman curve than there is on the ol eman curve. 6
7 Econ 500 Microeconomic Review Deman X $30 $00 D 0 D Q X Some eercises, you ask? Start with original eman curve an M = $0 an if M fell to $5? 0 y = $30. What woul happen to the eman curve Start over at the original values. What woul happen if the price of goo Y fell to $0? Start over at the original values. What woul happen if the price of goo Y rose to $40? More on Ceteris aribus Conitions In our original eman shift, an increase in M from $0 to $0 results in an increase in the eman for the goo. That is, an increase in income has lea to an increase in income. In fact, this tells us that goo X is a normal goo. But we also want to hone your intuition. We can make preictions about what happens to the eman curve without knowing anything about the actual mathematics of the eman curve. Now is the time for a review of our ceteris paribus conitions. Our focus will be on how changes in our ceteris paribus conitions shift the eman curve. 0 The eman curve ecreases (shifts left). The new vertical intercept woul be $40 an the new horizontal intercept woul be 70. The eman curve increases (shifts right). The new vertical intercept woul be $40 an the new horizontal intercept woul be 0. The eman curve ecreases (shifts left). The new vertical intercept woul be $60 an the new horizontal intercept woul be 80. 7
8 Econ 500 Microeconomic Review Deman Generally speaking, the ceteris paribus conitions can be classifie into a few major groups. rice of Relate Goos Substitutes an Complements.. Income of Consumers Normal or Inferior Goos 3. Epectations of Future rices 4. Other Stuff rices of Relate Goos Complements are things that are use together. The classic eample is peanut butter an jelly. In the car eample, cars an gas an cars an insurance woul be complements. Substitutes are alternatives. The classic eample is butter an margarine. In the car eample, car an trucks an are substitutes an cars an public transportation woul also be substitutes. Substitutes You ten to know them when you see them, but the efinitions are as follows: Goos A an B are calle substitutes, if, when the price of goo A changes, the quantity emane (eman curve) for goo B changes in the same irection. Say we eamine Coke an epsi, which are substitutes. If the price of Coke increases, the eman for epsi will increase. Why? Because people will substitute from rinking Coke (whose price has increase) to rinking epsi. When the price of Coke rises, at each an every price of epsi (the horizontal interpretation of a eman curve), there will be a larger quantity emane of epsi on the new eman curve than the original eman curve. The change in the price of coke has cause the eman curve for epsi to shift to the right (an increase in eman). In the car eample, if the price of trucks rise, the eman for cars will increase (shift right). If the price of public transportation falls, the eman for cars will ecrease (shift left). Ha two ugly errors here Complements Goos A an B are calle complements, if, when the price of goo A changes, the quantity emane (eman curve) for goo B changes in the opposite irection. Consier ink cartriges an printers. If the price of ink cartriges increases, the eman for printers will shift to the left, or ecrease. Why? eople will realize the overall cost of printing will have increase, an thus will cut back on their printer purchases In the car eample, an increase in the price of gas will ecrease the eman for cars. A ecrease in the price of car insurance woul increase the eman for cars. The Numerical Eample Recall our original epression of the eman function: 8
9 Econ 500 Microeconomic Review Deman Q = 00 y + 6M Believe it or not, that epression tells us if the goos X an Y are complements. How can you tell? For every $ increase in the price of goo Y, the quantity emane of goo X falls by units. This means the price of goo Y an the quantity emane of goo X are changing in the opposite irection. From this, we can conclue the goos are complements. In fact, it is the sign (not the magnitue) on the y term that tells us this. In this case, we have y in the epression (the sign is negative), inicating complements. If for eample, the eman function were instea Q = y + 6M then X an Y woul be substitutes. 3 Not convince? Go back to the eample where the y ecrease to $0. What happene to the eman curve for cars? What happene to the eman curve when y increase to $40? Income Normal Goos Goo A is calle a normal goo, if, when the incomes of consumers changes, the quantity emane (eman curve) for goo A changes in the same irection. Eamples of normal goos inclue Saints tickets, steak inners, SUVs, almost everything else. An increase in the incomes of Saints fans will increase the eman for Saints Tickets (shift right). A ecrease in the incomes of SUV consumers will ecrease the eman for SUVs (shift left). Inferior Goos Goo A is calle an inferior goo, if, when the incomes of consumers changes, the quantity emane (eman curve) for goo A changes in the opposite irection. Eamples of inferior Goos inclue Ramen Nooles, SAM, Ma Dog 0/0, use unerwear. An increase in the incomes of consumers will ecrease the eman for Ramen Nooles (shift left). A ecrease in the incomes of consumers will increase the eman for SAM (shift right). 3 If you are wonering about the meaning of the magnitue of the coefficient on the y term, that is a goo thing to woner. The magnitue of the coefficient inicates how closely relate the goos are. A large coefficient (in absolute value or further from zero) inicates the goos are closely relate. If we consiere the eman for epsi, substitutes for epsi that might be inclue are the price of Coke an the price of orange juice. But the eman for epsi will be more sensitive to the price of Coke than the price of orange juice. Thus, we woul epect a larger coefficient on COKE then OJ, even though both woul be positive. More when we get to elasticities. 9
10 Econ 500 Microeconomic Review Deman The Numerical Eample The logic is the same as above. A positive coefficient on the M (in this case we have6 M ) in the eman function inicates that a one unit increase in income leas to a 6 unit increase in the quantity emane of goo X. This is consistent with a normal goo. A negative coefficient on the M term in the eman functions inicates inferior goos, as M an the eman curve for goo X change in the opposite irection. 4 Not convince? See the eample above about M increasing from $0 to $0 or the eercise ecreasing from $0 to $5. Epectations of Future rices Quite simple. When people epect prices to fall in the future, the (current) eman falls. eople elay their purchases. When people epect prices to rise in the future, the (current) eman rises. eople try to act ahea of the price increases. This becomes interesting for firms that regularly scheule sales. On the one han, the sale itself woul ten to increase purchases (while the sale occurs) accoring to the st Law of Deman. On the other han, if people epect the sale, they may curtail their purchases in the perio leaing up to the sale. Automakers with their moel year-en closeout? Last-year's fashions? The harback version of a book before the paperback comes out? Microsoft Vista? Dollar movie theaters? Everything Else I o not min writing notes, but I o not want to write forever! Many other things can shift a eman curve. Consumer Surplus The height of the eman curve tells us the maimum amount a consumer is willing to pay for a unit of the goo. But very selom oes this consumer actually pay this amount. If there is a gap between the two, we call this gap consumer surplus. Consumer Surplus = Amount consumer is willing to pay - the amount they ha to pay Can we fin this are graphically? We can. From the vertical interpretation of a eman curve, we know that the height of a eman curve at some quantity tells us the maimum amount a consumer was willing to pay. If we compare this to the price on the graph, we have consumer surplus. Let s go back to the pizza eample, only we will a in some aitional information an assume the price of pizza is $. We can calculate the consumer surplus enjoye for each iniviual unit of pizza consume. 4 Again, the magnitue etermines how sensitive consumption of that goo is to changes in income. Consier Kraft Mac & Cheese an restaurant meals. I believe both Mac & Cheese an restaurant meals are normal goos, an thus both will have positive coefficients on M in their respective eman functions. I woul also epect the coefficient on M in the eman function for Mac & Cheese to be close to zero, while the coefficient on M in the eman function for restaurant meals to be larger. When people win the lottery, they o not a bunch more Mac & Cheese than they use to, but people likely o buy a bunch more restaurant meals than they use to. More when we get to elasticities. 0
11 Econ 500 Microeconomic Review Deman For eample, at Q = 5, the height of the eman curve is $, while the price is $, so consumer surplus is $0 ($ - $ = $9). The iea is this consumer is getting a eal. They woul have pai $0 more than they ha to. The larger the consumer surplus, the larger is the welfare (happiness) of consumers. At Q = 0, the eman curve tells us the consumer is willing to pay $7, while the price is only $, leaving consumer surplus of $6. It shoul be easy for you to calculate consumer surplus on the 5 th pizza. 5 IZZA $ $7 $3 $ Deman Q IZZA Aing consumer surplus up for each iniviual unit of the goos gets very teious. Fortunately there is a calculus trick. In general, if you want to a up the total consumer surplus for consuming Q units (where Q can be any quantity), simply a up the entire area that is () uner the eman curve, () above the price that consumers pay, an (3) out to the quantity Q. See the picture below. This will come in very hany when we talk about price iscrimination. As a firm, wouln t you want to try to charge everyone the maimum they are willing to pay? 5 Consumer surplus is $, as the consumer is willing to pay (the height of the eman curve) $3, while the price is $. Consumer surplus is $3 - $ = $.
13 Econ 500 Microeconomic Review Supply Supply Curve (Big icture) The whole point of a supply curve is to fin the relationship between the price of a goo an the quantity that firms wish to prouce (the quantity supplie). I am going to assume that you have some unerstaning of the st Law of Supply. The st Law of Supply states, ceteris paribus (holing other relevant factors constant), as the price of a goo rises, the quantity supplie of that goo increases. Basically, it states that supply curves are upwar sloping. Interpretations of the Supply Curve There are two ifferent ways you can interpret the information given in a supply curve. Horizontal Interpretation of Supply Curve - this is the interpretation of the supply curve you are most likely familiar with. The iea here is to pick a price, then move (horizontally) over to the supply curve. For eample, if the price of a car is $,000, the quantity supplie of cars might be 450,000. That is, if the price is $,000, firms will wish to prouce 450,000 cars. Likewise, if the price of a car is $4,000, the quantity supplie might be 500,000. See the graph below. The reason we call this the horizontal interpretation shoul be apparent. CAR $4,000 Supply $, , ,000 Q CAR Vertical Interpretation of Supply Curve again, less familiar, an will be iscusse in greater etail when it comes to cost curves. Just as the eman curve illustrate the highest price a consumer woul be willing to pay, a supply curve illustrates the lowest price a firm woul be willing to accept to prouce the goo. The iea here is still to pick a quantity then move (vertically) up to the supply curve. We sometimes call the result the height of the supply curve. See the picture below. For instance, if the height of the supply curve facing a specialize pizza store at Q = 0 is $5, this means that the least a firm will be willing to accept to prouce the 0 th pizza is $5. This proucer woul be willing to prouce the 0 th pizza for any price above $5, but will not prouce for any price less $5. The height of the supply curve is calle the marginal cost of proucing, a term we will return to in our iscussion of cost curves.
14 Econ 500 Microeconomic Review Supply Likewise, if the height of the supply curve at Q = 5 is $9, this means the least a firm woul be willing to accept for the 5 th pizza is $9. IZZA Supply $9 $5 0 5 Q IZZA An as was case for eman, we can use either interpretation of a supply curve, epening in which type of problem we are intereste. We coul have aske what is the least a firm woul have been willing to accept to prouce the 450,000 th or the 500,000 th car. 3 Likewise, we coul ask how many pizzas that firms will wish to purchase at a price of $5 or $9. 4 Which interpretation we choose oes not change the unerlying supply curve. As you progress, you will fin it makes more sense to use one interpretation or the other epening on the problem we are ealing with. Ceteris aribus Conitions for Supply Curves Thus far, we have glosse over the st Law of Supply an the ceteris paribus conitions for supply. Some more very eep backgroun that you shoul have learne before... If, we were intereste in the important factors etermining the number of cars prouce, surely the price of cars woul be important. This is eactly what we hope to capture with a supply curve. A supply curve illustrates how the quantity of cars that firms wish to prouce changes as the price of cars changes, holing other relevant factors constant. 5 If you recall the ifference between an iniviual firm s supply curve an the market supply curve, I want to be iscussing the market supply curve in this case. We know that iniviual s supply curves are upwar sloping. When we look at the market (overall) supply curve for a prouct, we have combine every firm s iniviual supply curve. It may or may not be the case that the firm that was willing to prouce the 0 th unit for $5 is the same firm that is willing to prouce the 5 th pizza. More later 3 Some firm woul be willing to prouce the 450,000 th car for $,000 an some firm (coul be the same firm or a ifferent firm) woul be willing to prouce the 500,000 th car for $4, Hopefully not surprisingly, the answers here are 0 an 5, respectively. 5 If you recall from your previous economics classes, in this case, we woul call the price of the car the own price. The own price is the price of the goo for which we are rawing the supply curve.
15 Econ 500 Microeconomic Review Supply On the other han, many other things (asie from the price of cars) affect the number of cars firms wish to prouce. We call these other things supply shifters or ceteris paribus conitions for supply. In orer to raw a supply curve (to isolate the relationship between the own price of a car an the quantity supplie of cars), we must hol the ceteris paribus conitions constant. On the other han, when one of these ceteris paribus conitions changes, we must shift the supply curve in the appropriate irection. What are these supply shifters or ceteris paribus conitions for the supply of cars? Just to name a few: rice of steel / wages of workers, price of trucks, technology of proucing, epectations about future car prices. More in the net section... Mathematical Epressions of Supply Curves We revisit our friens the mathematicians. Here is what they woul write: Q s = f (,, W, H ) r s What oes it mean? It means the quantity supplie of goo X ( Q ) is a function of, or epens on, the price of goo X ( ) the price of technologically relate goos ( r ), the price of inputs (W ) an other stuff ( H ). 6 While it is not necessarily the case, we often moel supply curves as being linear. 7 very simple numerical epression of a eman curve. For eample: If so, we can write out a s Q = r 5W We will call this a supply function. The supply function contains a whole slew of information. If you were tol to raw the supply curve for goo X, again you woul pull out a piece of graph paper, label the vertical ais, the horizontal ais Q, an woul be stuck. 8 In fact, you cannot raw the supply curve without knowing the values of r anw, which are the ceteris paribus conitions for supply. 6 Why W for the price of inputs? One of the main inputs that firms use is labor, an the price of this input is calle a wage. In short, W is to remin us of wages. Baye s tetbook slips once an uses W to refer to wages. Also, the items in H, the other stuff, will be ifferent things for supply curves than they were for eman curves. 7 A linear supply curve is one with a constant slope of the supply curve an therefore the power (eponent) on the term is (implicitly). We will focus on linear supply curves in this class. As an eample of a non-linear supply curve, consier Q 3 = 70 + W. s r 5 3 3
16 Econ 500 Microeconomic Review Supply Suppose you were tol that W = 8 an you coul raw it. s Q = 70 + r 5W 3 s Q = 70 + (5) 5(8) 3 s Q = s = 0 + Q 3 r = 5. You coul simplify the supply function to the point where Now, your supply function is epresse with only Q an as unknowns. Asie Inverse Supply Function You guesse it, you can solve for an inverse supply function. Not as useful as the inverse eman function, but it will help a bit on the graphing. To fin the inverse supply function, simply start with the supply function, an solve it for = 5, we start with: s Q = s. In the case where W = 8 an Now we just o the algebra. You can take whatever steps get you to the en. I will begin by subtracting 0 from both sies: s Q 0 = 3 Then multiply each sie by 3. 3 Q 60 = s An then just rearrange the terms: = s Q Graphing the Supply Function s A bit trickier than eman functions in most cases. Recall from out supply function thatq = s By plugging in = 0 in the epression above, we fin that Q = 0. This is one point on our supply curve. In fact, this is the horizontal intercept of the supply curve. s s We also solve for the inverse supply function, fining that = Q. By plugging in Q =0, we fin that = -60. Technically, this is the vertical intercept of the supply curve. But is any firm going to pay their customers $60 for their prouct? There is no such thing as a negative price. Let s look at what we have on a graph thus far. r 8 s Why not label itq? You coul. Eventually, we will combine the eman curve an supply curve, an thus we will just lazy an label itq. 4
17 Econ 500 Microeconomic Review Supply X Supply -$60 0 Q X However, as you can see, this information still helps us out in rawing the picture. But as we hinte at above, only the portion of the supply curve in the positive quarant (with positive price an positive quantity) is going to be relevant. Se we ll en up iscaring that lower (otte) portion of the supply curve. X $40 Supply 0 00 Q X Sometimes is helps to throw in one more point. You ll see above, I ve chosen Q = 00, at ranom, an stuck that on the graph as well. If we plug in Q = 00 to the inverse supply function, we see: = s Q = (00) = 40 5
18 Econ 500 Microeconomic Review Supply Shifting the Supply Curve What if W ecreases from $8 to $4? What happens to the supply curve? First the math, then the intuition. s Q = 70 + r 5W 3 s Q = 70 + (5) 5(4) 3 s Q = s 40 + s Q = 3 (compare this to Q = ) When we change the supply function, we will also get a new inverse supply function. Taking the same steps as before (but leaving out the eplanation of these steps), we get: s Q = s Q 40 = 3 s 3 Q 0 = s = 0 + Q 3 Now, we raw the new supply curve. From the supply function, I see that setting = 0 in the epression s s above results in Q = 40. From the inverse supply function, I see that setting Q = 0 results in =-0. s Not much help there. So let me stick in Q = 00 in the inverse supply function an I ll get Now we stick these new points on our graph paper. = 80. Below is a picture with the original supply curve (W = $8) labele S 0 an the new supply curve (W = 4) labele S. We see immeiately what has happene is that the supply curve has shifte to the right because of the ecrease in wages. Just as we i with eman curves, we call a rightwar shift of the supply an increase in the supply curve. 9 We call a leftwar shift of the supply curve a ecrease in the supply curve. Again, any change in a ceteris paribus conitions shifts the supply curve. That is, a change in anything but the own price, causes a shift in the supply curve. One more note: having iscusse both eman curves an supply curves at this point, it is worth noting that most changes affect only the eman curve or the supply curve. There are separate lists of ceteris paribus conitions for eman an ceteris paribus conitions for supply. A change in wages will shift the supply curve, but not the eman curve. A change in the income of consumers will shift the eman curve, but not the supply curve. However, every so often something comes about that shifts both the supply curve an the eman curve, but these are fairly rare. 0 9 Why is this calle an increase in the supply curve? From the horizontal interpretation of the supply curve, notice that at any (an every) price, there is a larger quantity supplie on the new supply curve than there is on the ol supply curve. 0 An eample might be the iscovery of AIDS in the market for prostitution. This woul affect both suppliers of prostitution services an the customers of prostitution services. Epectations about future prices will also affect both supply an eman. 6
19 Econ 500 Microeconomic Review Supply X S 0 S $40 $ Q X Some eercises, you ask? Start with original supply curve an W = $8 an rose to $? r = $5. What woul happen to the supply curve if W Start over at the original values. What woul happen if the price of the relate goo ( ) fell to $? Start over at the original values. What woul happen if the price of the relate goo ( ) rose to $8? 3 More on Ceteris aribus Conitions In our original supply shift, a ecrease in W from $8 to $4 resulte in an increase in the supply for the goo. That is, a ecrease in an input price has le to an increase in supply. But we also want to hone your intuition. We can make preictions about what happens to the supply curve without knowing anything about the actual mathematics of the supply curve. Now is the time for a review of our ceteris paribus conitions. Our focus will be on how changes in our ceteris paribus conitions shift the supply curve. r r The supply curve ecreases (shifts left). The new vertical intercept woul be = $0 an the new s horizontal intercept woul also be Q = 0 (the supply curve starts at the origin). 00 woul be another point. = $300 an The supply curve increases (shifts right). The new vertical intercept woul be -$84 an the new s Q = horizontal intercept woul beq = 6. s s = $6 an Q = 00 woul be another point. 3 The supply curve ecreases (shifts left). The new vertical intercept woul be -$4 an the new s s horizontal intercept woul be Q = 4. = $58 an Q = 00 woul be another point. 7
20 Econ 500 Microeconomic Review Supply Generally speaking, the ceteris paribus conitions for Supply can be classifie into a few major groups. Input rices. rices of Technologically Relate Goos (substitutes an complements in prouction) 3. Epectations of Future rices 4. Other Stuff Input rices With input prices, a mi of the vertical interpretation of the supply curve an the horizontal interpretation of the supply curve is necessary. Consier, as we i above, a ecrease in wages, one of the firm s input prices. That is, consier a ecrease in an input price. It stans to reason that a firm woul now be willing to accept a lower price to prouce the goo. Why? We know a firm, broaly speaking, won t prouce a goo unless it covers it costs. Because the cost of prouction is ecreasing, the firm can accept a lower price (an still cover it costs). For eample, if the height of the ol supply curve at some quantity Q was $, an now wages fall, the firm might accept $ to prouce the Q th unit of the goo. More generally, because the height of the supply curve tells us the lowest price a firm will accept to prouce a goo, a ecrease in an input price will cause the supply curve to shift own, vertically. 4 See the picture below. X Supply Supply Q Q X But as soon as we see this picture, we want to go back to the horizontal interpretation of supply curve. When we iscuss increases in supply or ecreases in supply, we want you think of these as changes as shifts to the right or left (not up or own). So if you were presente with the picture shown below (the same two supply curves), an you were force to escribe it using the horizontal interpretation of a supply curve, hopefully you woul conclue there has been a shift to the right of the supply curve, which we call an increase in supply. 4 If you are comfortable interpreting supply curves as marginal cost curves, than all we are saying is the marginal cost of prouction is reuce at each level of output. The supply curve (marginal cost curve) shifts own vertically. 8
21 Econ 500 Microeconomic Review Supply X Supply Supply Q Q X At the en of the ay, a ecrease in an input price leas to a rightwar shift of the supply curve (an increase in supply). An increase in an input price leas to a shift to the left of the supply curve (a ecrease in supply). Don t believe me? Go back to the eample above where we change the wage from $8 to $4. You ll see we ha a rightwar shift of the supply curve. Finally, for an increase in an input price, o the eercise where I suggeste an increase in the wage from $8 to $. More eamples? What happens to the supply curve for pizza if there is a ecrease in the price of tomato sauce? 5 What happens to the supply curve for cars if there is an increase in the price of steel? 6 rices of Technologically Relate Goos Technological Complements Technological complements are things that are prouce together. Let s imagine for epositional purposes that every time a onut is prouce, a onut hole is also prouce. Another eample woul be that at a slaughterhouse, every time a cow is slaughtere, there is both beef an a hie prouce. Any situation in which a byprouct is involve woul be an eample of technological complements. The main iea is that prouction of the one goo might be influence by the price of the other, because the prouction of both goos is linke. A more formal efinition: Goos A an B are calle technological complements, if when the price of goo A increases, the quantity supplie of Goo B changes in the same irection. Eamples: If the price of onut holes increases, the firm will react by increasing the quantity supplie of onuts (increase in supply). 5 The supply curve increases (shifts right). 6 The supply curve ecreases (shifts left). 9
22 Econ 500 Microeconomic Review Supply If the price of beef ecreases, a firm woul ecrease the quantity of hies it will prouce (ecrease in supply). Technological Substitutes Technological substitutes are alternative proucts. General motors can use its equipment to prouce compact cars or SUVs. A onut shop coul prouce crème fille onuts or anishes. Goos A an B are calle technological substitutes, if when the price of goo A increases, the quantity supplie of Goo B changes in the opposite irection. Eamples: If the price of SUVs ecreases, General Motors will increase the quantity supplie of compact cars (increase in supply). The logic here is that because the equipment is capable of proucing both, proucing SUVs will be less relatively less lucrative, an thus the firm will switch to proucing compact cars. Soun familiar? If the price of anishes increases, a onut shop will ecrease its quantity supplie of onuts (ecrease in supply). Now proucing anishes will be more lucrative, so the firm will substitute from proucing onuts to anishes. The Numerical Eample Recall our original epression of the supply function: s Q = 70 + r 5W 3 Recall that r inicates the price of the relate goo. Are goos X an the relate goo technological substitutes or technological complements? Again, it will come own to the sign on the This means if r increases by $, Q will fall by units. 7 s r term. In this case, the coefficient on the r term is -. This is consistent with technological substitutes, as the price of the one goo an the quantity supplie of the other goo are moving in the opposite irection. Not convince? Go back to the eercise of changing r from $5 to $ an then changing $8. Confirm that the changes in the supply curve are what you epect. Epectations of Future rices r from $5 to When suppliers epect prices to fall in the future, current supply will increase. Firms will attempt to sell their proucts at the high current price. 7 If you are thinking that the magnitue of the coefficient tells you how closely technologically relate the two goo are you are correct. The larger the size of the coefficient (in absolute value, further from zero) the more technologically relate the two goos. An of course, a positive coefficient on the r term woul inicate technological complements. 0
23 Econ 500 Microeconomic Review Supply When firms epect prices to rise in the future, the current supply ecreases. Firms will hol back prouction. One etail here take for eample the secon situation in which firms epect prices to rise in the future. While we say that current supply will ecrease, we coul be a bit more precise. What is likely to happen is that firms will continue to prouce goos, but will not sell as many of these goos toay, instea choosing to accumulate inventories, which they then epect to liquiate when prices rise in the future. In this regar, when we say supply, we are talking about those proucts that are brought to market, not the quantity of goos that are manufacture. 8 You may also have notice that if firms hol back prouction toay in anticipation of future prices, this act itself may cause prices to increase now. More later Everything Else I like writing notes more last week Many other things can shift a supply curve. roucer Surplus My hope is that you can anticipate everything that is forthcoming here. The height of the supply curve tells us the minimum amount a proucer is willing to accept to prouce a unit of the goo. But selom oes this proucer actually get pai this amount. If there is a gap between the two, we call this gap proucer surplus. roucer Surplus = Amount proucer actually is pai - the minimum amount they woul have accepte From the vertical interpretation of a supply curve, we know that the height of a supply curve at some quantity tells us the minimum amount a proucer was willing to accept. If we compare this to the price on the graph, we have proucer surplus. Let s go back to the pizza eample, an assume the price of pizza is $. At Q = 5, the height of the supply curve is $, while the price is $, so consumer surplus is $ ($ - $ = $). The iea is that the proucer is getting a eal. They woul have accepte $ for the goo, but they receive $. If this $ souns something like profit, you re on the right track. 9 At Q = 0, proucer surplus is $ - $5 = $7. It shoul be easy for you to calculate proucer surplus on the 5 th pizza. 0 8 Not all firms have this option. For eample, Domino s pizza can not prouce pizzas in August, an sell them in September. 9 If you are comfortable with interpreting supply curves as a marginal cost curve, proucer surplus is the ifference between an marginal costs, sometimes calle operating profit. 0 roucer surplus is $3, as the proucer is willing to accept (the height of the supply curve) $9, while the price is $. roucer surplus is $ - $9 = $3.
24 Econ 500 Microeconomic Review Supply IZZA Supply $ $9 $5 $ Q IZZA Just as before, aing proucer surplus up for each iniviual unit of the goos gets very teious. We ll use the same calculus trick. In general, if you want to a up the total proucer surplus for proucing Q units (where Q can be any quantity), simply a up the entire area that is () above the supply curve, () below the price that suppliers receive, an (3) out to the quantity Q. See the picture below. roucer Surplus Supply Q Q
25 Econ 500 Microeconomics Review Equilibrium Markets an Equilibrium Market a process or location in which equilibrium is establishe an the otherwise inconsistent aspirations of emaners an suppliers are reconcile. Equilibrium - an outcome or state that will ten to persist unless isturbe by a change in one or more of the ceteris paribus conitions. Is the equilibrium price H? I bet you guys know the rill, but as long as we ve wanere own this path, we may as well waner a bit more. Let s combine a supply curve (firm behavior) with a eman curve (consumer behavior) an see if we can t see how things play out. Basically, what is the equilibrium price an quantity we will observe? Let s try out H. At this price, we fin out how much suppliers want to prouce by looking at their supply curve (Q S ), an how much emaners want to consume by looking at the eman curve (Q D ). At this price, Q S > Q D. This is calle an ecess quantity supplie or surplus. Suppliers woul like to supply more than emaners want to purchase (suppliers an emaners aspirations are not consistent). Suppliers will not be able to sell all that they wish to at this high price. The surplus will cause ownwar pressure on price. As price falls, two things happen simultaneously. Suppliers esire to prouce less as price lowers, an emaners esire to purchase more as price lowers. This causes the size of the surplus to ecrease. The ownwar pressure on price will continue until the equilibrium price is reache an there is no longer a surplus. rice Supply H L Deman Is the equilibrium price L? Q D Q S Q D Q S Quantity Let s try L. At this price, we again fin out how much suppliers want to prouce by looking at their supply curve (Q S ), an how much emaners want to consume by looking at the eman curve (Q D ). At this price, Q D > Q S. This is calle an ecess quantity emane or shortage. At this low price, many consumers want to purchase the prouct, but suppliers will not be willing to prouce as much as consumers esire (the aspirations of suppliers an emaners are inconsistent). This will cause upwar pressure on price. As the price rises, two things simultaneously happen. Suppliers esire to prouce more as price rises, an emaners esire to purchase less as price rises. These two factors cause the size of the shortage to ecrease. This upwar pressure on price will continue until the equilibrium price is reache an the shortage isappears entirely.
26 Econ 500 Microeconomics Review Equilibrium The equilibrium price is * Let s try *. Refer to the picture below. At *, emaners want to purchase Q* units. At *, suppliers want to supply Q* units. Everyone who is willing to pay * can buy all the goos they want. Everyone who is willing to supply goos at * is supplying what they want. Everyone s aspirations are consistent an everyone is happy. Let s all hol hans an sing. No one wants to change their behavior, hence an equilibrium. rice Supply * Deman Q* Quantity * an Q* are the equilibrium price an equilibrium quantity. Equilibrium occurs where the supply curve intersects the eman curve. In other wors, at the equilibrium price, quantity supplie equals quantity emane. There is neither a shortage, nor a surplus - we say that the market clears. Even if we fin the market price temporarily away from the equilibrium price, these pressures will cause the price to ten to return to equilibrium price. This is why we say equilibrium will ten to persist unless there is a change in a ceteris paribus conition. Comparative Statics Fining equilibrium prices an quantities are nice, but the most useful thing we ll get out of supply an eman analysis will be what we call comparative statics. Basically, we change a ceteris paribus conition for some goo then we see what impact this will have on the equilibrium price an quantity of that goo. You can think of comparative statics eercises as a four part process. As your get more comfortable, you ll breeze through these without oing them step by step.. Start in initial equilibrium (raw an initial S & D curve to start). Change one or more of the ceteris paribus conitions 3. Eamine the impact on eman or supply (shift the appropriate curve) 4. Eamine new equilibrium (compare)
27 Econ 500 Microeconomics Review Equilibrium Eamples of Comparative Statics Suppose we are looking at the market for oranges. The initial equilibrium is ( 0, Q 0 ). There is an increase in income. Oranges are a normal goo. This causes an increase in eman (eman curve to shift to the right). At the original price, 0, there is now an ecess quantity emane, putting upwar pressure on the price. The new equilibrium will be (, Q ). Both equilibrium price an quantity will increase. rice S 0 D D Q 0 Q Quantity Now, suppose unusually col weather occurs in Floria, estroying some of the orange crop. This causes a reuction in the supply of oranges (supply curve shifts left). The initial equilibrium is ( 0, Q O ). The new equilibrium is (, Q ). The equilibrium price will increase an the equilibrium quantity will ecrease. rice S S 0 D Q Q 0 Quantity What if more than one curve shifts? Suppose we are looking at the market for prostitution. Suenly, AIDS is evelope. What happens to the prostitution market? Again, the initial equilibrium is ( 0, Q O ). AIDS ecreases the eman for prostitution, as well as ecreases the supply of prostitution. The new equilibrium is (, Q ). You can think of AIDS as a sort of increase in the cost of proucing prostitution services. rostitutes will nee to be pai a higher price to incur the risk of contracting AIDS. ROSTITUTION S S 0 D D Q Q 0 Q ROSTITUTION 3
28 Econ 500 Microeconomics Review Equilibrium As it is rawn, the price oes not appear to have change. However, the change in price is ambiguous. This can be seen two ways. First, take the two changes one at a time. Change Effect on Effect on Q Decrease in supply increases ecreases Decrease in eman ecreases ecreases Total ambiguous ecreases The other way this can be shown is to use supply an eman shifts of ifferent magnitues. Draw this with a large eman curve shift an a small supply curve shift. Check your answer. Now raw it again with a large supply curve shift an a small eman curve shift. Compare. You shoul see that in one case the price rises, while in the other case, the price falls. In general, if you simultaneously change both a ceteris paribus conition for both supply an for eman, either the irection in the change of price or the irection of the change in quantity will be ambiguous. What about the math? If we ha a eman function an a supply function, can we solve for the equilibrium price? The answer is yes. Hurray! Here is how. We note above that the equilibrium price was the price where quantity emane is equal to quantity supplie. The nice thing is the eman function tells us what quantity emane will be at various prices, while the supply function tells us what quantity supplie will be at various prices. By setting quantity emane equal to quantity supplie an solving for the price, we can etermine the equilibrium price. Once we o this, we can plug the equilibrium price back into the eman function (or the supply function) to etermine the equilibrium quantity. Let s o an eample with our hopefully now familiar eman function an supply function. Recall we starte with: Q = 00 y + 6M then assume that M = 0 an Q = 00 On the supply sie, we starte with: s Q = r 5W then assume that W = 8 an = 0 + s Q 3 y = 30, which resulte in: r = 5, which simplifie to: Now, set quantity emane equal to quantity supplie, an solve for. 4
29 Econ 500 Microeconomics Review Equilibrium Q = Q 80 = = () = 96 = 5 3 = 3 Can we be sure we are correct? Let s inee confirm that at a price of $96, the quantity emane is equal to the quantity supplie. Q Q 00 = = ( 96) = ( 96) = = = s = = Inee, the quantity eman equals quantity supplie. One last thing we can o is to check the graph. Visually, our answer looks reasonable. X $40 $00 $96 D Q X 5
30 Econ 500 Microeconomics Review Elasticity of Deman, Marginal Revenue Elasticities Why? Why shoul we bother with elasticities? As we learn a bit more economics, one of the things we woul like to o is to try to be more specific. If you think back to your first microeconomics course, we were happy with you telling us simply in what irection the price an quantity will change. As we progress, we will still want to know in what irection the price an quantity will change, but in aition, we like to know how much the price an quantity will change. Elasticities enable us to answer these questions. Is it a big change in price or a small one? Further, an perhaps more importantly, a firm s pricing ecisions will be irectly influence by the elasticity of eman for the prouct it is selling. Elasticities What are they? All elasticities will be a measure of sensitivity. The (own) price elasticity of eman measures how sensitive quantity eman is to changes in (own) price. The (own) price elasticity of supply measures how sensitive quantity supplie is to changes in (own) price. The income elasticity of eman measures, you guesse it, how sensitive eman is to changes in income. The cross price elasticity of eman measure how sensitive quantity emane is to a change in the price of a ifferent goo (a substitute or complement). The net step is to come up with a classification of what is sensitive an what is insensitive. Consier the eample below: Suppose a $ increase in the price of gas leas to a 500 gallon ecrease in gas sol. Now, suppose a $ increase in the price of a BMW leas to a 500 fewer BMW cars to be sol. Which of these is a big quantity response? Even though both changes involve an increase of $ an a reuction in quantity of 500, my feeling is that car change is etremely sensitive, while the gas is not so sensitive. The point here is that measuring changes is ollars an units sol might not be appropriate. $ is a big eal for gas, but not for cars. erhaps measuring the changes in percentages woul give us a better iea? This is in fact how elasticities are measure. In general, an elasticity is the percentage change in one variable resulting from a % increase in another. (Own) rice Elasticity of Deman (Own) rice Elasticity of Deman is efine as the percentage change in quantity emane of a goo resulting from a % increase in its price. E Q, % Q = % You shoul rea this as the percentage change in quantity emane of goo X ivie by the percentage change in price of goo X. The notation means change in. Of course, because eman curves are ownwar sloping, the elasticity of eman will always be a negative number. An increase in price (positive enominator) will lea to a reuction in quantity emane (negative numerator), giving us a negative value of E Q,. Likewise, a ecrease in price (negative enominator) will lea to an increase in quantity emane (positive numerator), an again result in a negative value of E Q,. Since the elasticity of eman is always negative, people often strip off the negative sign an talk about the absolute value of elasticity. If someone ever tells you the elasticity of
31 Econ 500 Microeconomics Review Elasticity of Deman, Marginal Revenue eman is, what they really mean to say is that the absolute value of the elasticity of eman is. No matter how you slice it, we ll all know that this really means is that E, = -. Categorization of rice Elasticity of Deman Values We ll want to classify eman curves into three categories. Q When you think of elasticities, think of sensitivities. The (own) price elasticity of eman is a measure of how sensitive the change in quantity emane is to a given size price change. If a eman curve is inelastic, this means that change in quantity emane is relatively insensitive to changes in price. If a eman curve is elastic, this means that the change in quantity emane is relatively sensitive to changes in price. Let s be a bit more formal: E Q, >, elastic a % in price will lea to a more than % in quantity emane E Q, =, unit elastic a % in price will lea to an eactly % in quantity emane E Q, <, inelastic a % in price will lea to an less % in quantity emane Also, there are some etreme elasticity values. E Q, =, perfectly elastic a % in price will lea to an infinite reuction in quantity emane E Q, = 0, perfectly inelastic a % in price will lea to no change in quantity emane Check out Baye for pictures of the eman curve for these etreme cases, flat an vertical, respectively. Are price elasticities the same thing as slopes of eman curves? No. To see this, we can look at the efinition of elasticities, o some rearranging, an you ll see why. First, we nee to back to 6 th grae an remember how to calculate percentage changes. Remember a percentage change in just the change in the value ivie by the original value. So we have: Q % Q = an Q % = Thus, we can rewrite the elasticity formula, plug in the above efinitions, an then o a little rearranging: Q % Q Q Q = E = = Q, EQ % Q E Q,, Q The first term ( ) is constant along a linear eman curve an equal to the inverse of the slope of the eman curve. The secon term ( ) changes as we move along a linear eman curve. On the Q uppermost portion of a eman curve, will be relatively high an Q relatively low, resulting in Q
32 Econ 500 Microeconomics Review Elasticity of Deman, Marginal Revenue being a large number. On the lower portion of a eman curve, will be relatively low while Q is relatively high, resulting in being a low number. Therefore, as we move along a linear eman curve Q the elasticity of eman will change from 0 to negative infinity. How about an eample? Eample Suppose you were tol a eman curve was escribe by the equationq = 8. I ve rawn the eman curve below. Ignore the slope calculation for just a secon if you can. In this case, an you shoul confirm, the inverse eman function is = 4. Q 4 3 Slope = Rise Run = Q 4 = = Q Now, go an calculate the slope using the graph. The slope is (see picture above). You ll notice it s easy to grab the slope from the inverse eman function, as it is just the coefficient onq. Suppose I aske you to calculate the elasticity of eman at five ifferent spots along the eman curve, specifically where = 4, = 3, =, =, an = 0. You no oubt consult your notes an write own the formula for the elasticity of eman. Q E Q, = Q Q Now, hopefully your remember the first term ( curve an remains constant along a eman curve. ), has something to o with the slope of a eman You coul stare at the eman curve, Q = 8, an note that a one ollar increase in price leas to a Q two unit reuction in Q, an thus conclue that = =. + This eample is very close, but not eactly the same as one in Baye s book. 3
33 Econ 500 Microeconomics Review Elasticity of Deman, Marginal Revenue Or you coul stare at the inverse eman function, = 4 Q, an note that a unit increase in Q + leas to a ½ unit ecrease in leaing you again to conclue that = =. Or you might have calculate the slope of the eman curve as an took the inverse. Any way you o Q it, you ll conclue that =. Now you just nee anq. To figure out Q for each, it is more convenient to use the eman curve. BecauseQ = 8, it is pretty easy to plug an chug... When = 4, Q = 8 (4) = 0 When = 3, Q = 8 (3) = When =, Q = 8 () = 4 When =, Q = 8 () = 6 When = 0, Q = 8 (0) = 8 Finally, put it all together: Q = 4, Q = 0 = 3, Q = =, Q =4 =, Q = 6 = 0, Q = 8 E E E E E Q = Q Q, Q 4 = = 0 3 = =, = Q Q Q = = 4, = Q Q Q = = 6, = Q Q Q 0 = 8, = Q = Q perfectly elastic elastic unit elastic inelastic perfectly inelastic Notice that as the price increase (as you move up a eman curve), the eman curve becomes more elastic. As price ecreases (as you move own a eman curve), the eman curve becomes more inelastic. Some intuition on this point is in orer. As the price increases, people will look for alternatives. When the price of gas is $.00, a 0% increase in the price of gas might lea to a small reuction in the quantity emane of gas. But at a price of $4.00, there might now be more viable alternatives than before, an thus we might see a larger change in quantity emane. None of us were biking to work when gas was $.00 a gallon, but some of us were when gas was $4.00 a gallon. The higher the price, the more sensitive consumers will be. You, of course, will get the same answers if you use the inverse eman function, you ll just have to o more algebra. Try it. It will get ol quick. 4
34 Econ 500 Microeconomics Review Elasticity of Deman, Marginal Revenue It looks like the point where eman is unit elastic is half way along the eman curve (the mipoint of the eman curve). In fact it is. You can take it on faith, an that s fine. If you like algebra, you let me know an I can sen you a proof. 3 See the graphs net page. E = Q, 4 E = 3 Q, E = Q, 3 E = 0.33 Q, E = 0 Q, Q In general, E = (perfectly elastic) Q, elastic E Q, = (unit inelastic) at the mipoint of the eman curve inelastic E Q, = 0 (perfectly inelastic) Q Why o some goos have elastic eman curves while other inelastic eman curves? Reasons why goos ten to have elastic eman curves:. The goo have many available substitutes Kellogg s Corn Flakes. The goo is a large fractions of consumer s buget appliances 3. The goos in an input into a prouct that is itself has an elastic eman curve computer components Reasons why goos ten to have inelastic eman curves:. The goo has few available substitutes / unique features Britany Spears albums. The goos is a small fraction of a consumer s buget table salt 3. Comparisons amongst substitutes are ifficult oor to oor proucts 4. Consumers pay only a fraction of the full price of a prouct health care 5. The consumer is committe to using the prouct your printer s ink jet cartriges Which woul be more sensitive to change in price the eman curve for Kellogg s Corn Flakes or the eman curve for all cereal? 3 No one has ever taken me up on that offer. 5
35 Econ 500 Microeconomics Review Elasticity of Deman, Marginal Revenue The answer is Kellogg s Corn Flakes. If the price of all cereals increase, people woul cut back on cereal, but consumers are limite because the price of all cereals have increase. They coul switch to having pancakes for breakfast, but not all people woul. The quantity of cereal consume woul fall, but not very ramatically. On the other han, if only the price of Kellogg s Corn Flakes increase, we epect a large reuction in quantity emane of Kellogg s Corn Flakes, as consumers woul substitute to any number of breakfast cereals, or even pancakes. In short, there are more substitutes for Corn Flakes specifically than cereal in general. The elasticity of eman for Miller Lite will be more elastic that the elasticity of eman for beer, which will be more elastic than the eman for beverages. Another way of stating this iea is that bran elasticities are higher (more elastic) than inustry elasticities. Relationship between inverse eman curves an marginal revenue You nee to be familiar with how to go from an inverse eman function to a marginal revenue curve. Recall that marginal revenue is the aitional revenue associate with a one unit increase in prouction. Inverse Deman Function: = a bq Total Revenue = * Q = ( a bq ) * Q Total Re venue Q = aq bq Marginal Revenue = ( ) = a bq For those of you who are calculus incline, marginal revenue is the erivative of total revenue with respect to quantity. For those of you who are not calculus incline, o not fret, you can use the shortcut metho escribe below. A few things to notice... The marginal revenue curve has the same vertical intercept (a) as the eman curve oes. The slope of the marginal revenue curve is twice the slope of the eman curve, or more simply the MR curve is twice as steep as the eman curve. The marginal revenue curve intersects the horizontal ais where a Q = which is half way b between the origin an where the eman curve intersects the horizontal ais a Q =. b Marginal revenue can be negative. In general, the picture will look like this: 6
36 Econ 500 Microeconomics Review Elasticity of Deman, Marginal Revenue D MR Q I want everyone to be able to come up with the equation of the MR curve given the inverse eman function (or for that matter the eman function). Notice that = a bq an that MR = a bq. For those of you who aren t calculus incline, to transform an inverse eman function to a marginal revenue function, you just have to change the coefficient on the Q term. 4 See the eamples below. Eamples: Inverse Deman Function: = Q Total Revenue = * Q = ( Q ) * Q = Q Q Total Re venue = 4Q Q Marginal Revenue = ( ) You shoul sketch both the eman function an the marginal revenue function. You shoul fin the eman curve intersects the vertical ais where = $ an the horizontal ais where Q = 6. You shoul also fin that the marginal revenue curve intersects the vertical ais where MR = $ an the horizontal ais where Q = 3, an then continues along into negative values. If you were given an inverse eman function = Q, the marginal revenue function woul be MR = 4 7Q. If you were given a eman curve ofq = 4, you have to first transform the eman function into an inverse eman function, an then use the trick. In this case, you fin an inverse eman function of = Q an MR = Q If you are not sure, graph them. 4 Be sure that you are using the inverse eman function when you o this trick. 7
37 Econ 500 Microeconomics Review Elasticity of Deman, Marginal Revenue What is the relationship between Marginal Revenue an Total Revenue? Marginal revenue is the etra revenue associate with a one unit increase in prouction. The calculus incline shoul realize that MR is the slope of the total revenue function. Others on t nee to worry. Let s start at Q = 0 (the upper most point on the eman curve). At Q = 0, MR is positive, meaning that proucing another unit will increase total revenue. However, we can see that MR is getting smaller as we increase output (though for the time being it is still positive). Thus we know that total revenue is increasing, but increasing at ecreasing rate. Eventually (at the mipoint of the linear eman curve), MR = 0. This means total revenue is neither rising nor falling. Total revenue has reache a peak. For all aitional units, MR < 0, this means total revenue will fall as we prouce aitional units of output. We can combine this information, an the fact that we know revenue is $0 when we sell zero units (the vertical intercept of the eman curve) an the fact that we know revenue is 0 when price is zero (the horizontal intercept of the eman curve) to raw the following picture. Total revenue is maimize where MR = 0, which just so happens to be the spot where the elasticity of eman is equal to - (unit elastic). This is no coincience. Those of you who like calculus can note we are setting the erivative of the total revenue function to zero to fin out where total revenue is maimize. Others nee not worry. A B C (mipoint) D E Deman MR Q Total Revenue Q Given an inverse eman function = 8 3Q, coul you calculate MR? Coul you then fin the quantity that will have the largest total revenue? Hint: what is the value of marginal when total revenue is at its maimum? What is the quantity where this occurs? What is the price at this quantity? What is value of total revenue at this quantity? 5 5 If = 8 3Q, then MR = 8 6Q. MR = 0 when total revenue reaches it maimum. Setting MR = 0 8 6Q = 0 Q = 3. To fin whenq = 3, use the inverse eman curve. = 8 3 = 8 3(3) = 8 9 = $9. Q TR = * Q = $9*3 = $ 7. If you 8
38 Econ 500 Microeconomics Review Elasticity of Deman, Marginal Revenue What is the relationship between elasticity of eman an total revenue? If a firm or manager knew what their whole eman curve looke like, it woul be easy for the firm to calculate marginal revenue an elasticities. Often, though, firms will not have information on their entire eman curve, but will have a pretty goo iea about the elasticity of eman for their prouct. What if you only know the elasticity? What coul you say about what happens to total revenue if price changes? An easy thing you shoul be able to o is tell me what happens to total revenue when there is an increase in price when eman is elastic, when eman is unit elastic an when eman is inelastic. If you combine the picture above with the picture on the mile of page 5 of these lecture notes, you have the whole story. For instance, you know on the upper half of the eman curve, eman is elastic. You also know that if you raise price (move from B to A), total revenue is ecreasing. On the lower half of the eman curve, eman is inelastic. You see from the picture above if you raise price (moving from E to D), total revenue is increasing. An finally, if you are right in the mile of the eman curve, eman is unit elastic. You know if you make a very small change in price at point C, there is no change in revenue. You might try an figure out what is going on for price ecreases for each of inelastic, elastic, an unit elastic. Confirm your answers in the chart below. rice Decrease rice Increase Deman Elastic TR TR Deman Unit Elastic no TR no TR Deman Inelastic TR TR One More Nice Formula Some smart people have tol us that a way you can write the epression for marginal revenue is as follows. We will likely come back to this when we iscuss firms with pricing power. For fun, plug in + E MR = EQ Q Then plug in a value of Finally, plug in a value of Q,, E, = - an see what the formula tells you. 6 E, that is inelastic, say Q E, that is elastic, say Q get bore, you coul calculate revenue at Q =0,,, 3, 4, 5, 6 an confirm the picture looks like the one I ve rawn (it will). You fin revenue woul be $0, $5, $4, $7, $4, $5, an $0, respectively. 6 It tells you that MR = 0 when E Q, =, a point we alreay iscusse in rawing the MR curve. 7 It tells you that MR = -0.5 *, which means that MR is less than zero, a point we alreay iscusse in rawing the MR curve 8 It tells you that MR = 0.67 *, which means that MR is less than, but positive, again a point we iscusse in rawing the MR curve. 9
39 Econ 500 Microeconomics Review Elasticity of Deman, Marginal Revenue This is really just another look at how MR various along ifferent spots on a eman curve. The reason your tetbook points it out is, later, this formula will be use to come up with a very simple pricing rule for firms with market power. It turns out that a firm s mark-up over MC will be a function of its elasticity. The more inelastic the eman curve, the higher the mark-up. More later Other Elasticities By far, the most important elasticity we will eal with is the price elasticity of eman, there are other elasticities that come in hany. I ll just list them here. Check Baye for more. We ll come back as appropriate. See also page of these notes. Cross rice Elasticities Income Elasticities Avertising Elasticities Own rice Elasticity of Supply 0
40 Econ 500 Microeconomic Review Cost Curves The goal for this set of notes is to figure out the basic shape of cost curves. Ultimately, I want you to be able to unerstan the ATC, AVC, an MC curves. To o that, we have to o what seems like a ton of backgroun. To know what the MC curve looks like we will nee to know what the marginal prouct of labor curve looks like. To know the marginal prouct of labor curve looks like we will nee to talk about prouction functions. Therefore, the first part will work on the marginal prouct of labor. Once we get there, we will put that asie an work on cost curves. You will see when we bring back the marginal prouct rouction Functions The prouction process, broaly speaking, is converting inputs into outputs. We general call inputs the factors of prouction. Most tetbooks label them labor, capital, an materials. Some tetbooks will a lan to the list. Labor is human effort, physical or mental. Capital is things that are use to ai in the prouction of goos an services. Eamples are builings, elivery fans, factories, hammers, cranes, computers, cash registers, etc. Materials are inputs into prouction that are not capital. See below for an eample. McDonals will convert labor (workers), capital (builing, grill, cash registers), an materials (beef, buns, cheese) into cheeseburgers. General Motors will convert labor (workers), capital (assembly lines, forklifts, tools), an engines, tires, an healights to prouce cars. For McDonals the output is cheeseburgers, for GM the output cars. Net, we nee a way to escribe the technology of proucing. We o this with something calle a prouction function. The tetbook efinition is below: A prouction function inicates the highest output level (q) that a firm can prouce for every specifie combination of output. To simplify, we will assume that a firm only uses two inputs of prouction - capital an labor. The notation will be: q = F(K,L) where: q represents output prouce by the firm K represents capital L represents labor All this means is that the amount of output prouce by the firm is a function of (epens on) how much capital the firm uses an the amount of labor the firm uses. If you know you were going to hire 5 units of labor an 0 units of capital, you coul plug them in a prouction function an it woul spit out how much output the firm coul prouce. You can think of a prouction as a escription of the technology the firm has it its isposal. If a firm is to acquire better technology, the same amount of input will result in more output, an the firm will have a new prouction function to escribe this new technology. Most of the time we will simply raw prouction functions, but we will take care to make sure they have the shape that best fits the real worl. Later we may use Q to represent inustry level output. Both Baye an Besanko will use capital Q. It will not be an issue here.
41 Econ 500 Microeconomic Review Cost Curves Short run vs. Long Run: If we took a look at capital an labor in general, it seems reasonable to me that one of these inputs is more variable than the other. If McDonals wante to prouce twice as many burgers tomorrow as they i yesteray, it seems sensible to suggest that McDonals woul want to use both more labor an more capital. Think about how McDonals might be able to a labor. They can call in a few etra workers who ha the ay off or maybe can have folks work overtime. This seems oable. However, if the firm wants to a capital, will they be able to o it overnight? Remember that for McDonals, capital is the builing, cash registers, grills, etc. Can McDonals quickly increase the amount of capital they have available? Not so easy. We think it takes a significant amount of time for firms to increase the amount of capital they have available. As such, we will want to istinguish between what we call the short run an the long run. The short run is the perio of time in which at least one input is fie (can not be varie). We assume the amount of capital is fie, while the amount of labor is variable. Basically, in the short run, you are stuck with the amount of capital you have. The long run in the perio of time that is sufficiently long enough so that all inputs are variable. It will vary from inustry to inustry. A firm will be able to change the amount of capital they have in the long run. If it takes McDonals one month to increase the size of their restaurant, then the long run for McDonals is one month. If you think of the Lucky Dog hotog cart inustry, it seems like the long run woul only be maybe only a week you coul increase the capital stock in this inustry quickly (a hot og cart). For a nuclear power plant, it takes a very long time to change the size of a nuclear power plant. Lots of permits, regulation, elaborate construction, etc. The long run for nuclear power might be ten years. rouction in the Short Run: Let us irect our focus on the firm s ecisions in the short run. The first insight to have is that because we are assuming there are only two inputs, capital an labor, an because we are talking about the short run, the amount of capital is fie by assumption. Therefore, the only way the firm can prouce more output in the short run is to vary the amount of labor. This will make the firm s ecision quite simple ecie how much output they want to prouce an hire the corresponing amount of labor. But let s not get ahea of ourselves Consier the numerical eample below of a short run prouction function below. It is clippe from another tetbook. Ignore the last two columns for a moment. Notice that the secon column remins you that the amount of capital is fie in the short run. As the firm changes the amount of labor, the firm will be able to prouce iffering amounts of output. Labor (L) Capital (K) Output (q) Average rouct (q / L) Marginal rouct ( q / L) Below is a picture of the prouction function.
42 Econ 500 Microeconomic Review Cost Curves 0 00 Output (q) F(K,L) Labor (L) Some important measures: As it turns out, we will fin it useful to take a look at the prouction function an calculate some quantities. First the efinitions: A L = Average rouct of Labor = q / L = output per unit of labor M L = Marginal rouct of Labor = ( q / L) = aitional output prouce by each aitional unit of labor The average prouct of labor is just what it souns like a measure of the average prouctivity of labor. For instance, if 08 units of output are prouce with 9 units of labor, then the average amount of output prouce per unit of labor is units. This one will not be too important for us. An if you remember your Econ, I woul bet you coul guess what the marginal prouct of labor is. The marginal prouct of labor is the aitional output prouce by each etra unit of labor. More on this in a bit. This one will be important for us. Go back an look at the last two column of the table above. Make sure you can calculate the marginal prouct of labor. Things to note about the shape of the prouction function: It is important you unerstan what is going on insie our hypothetical firm an how this relates to the shape of the prouction function, an thus the marginal prouct of labor. Consier a McDonals with a fie amount of capital a certain size grill, a certain number of tables, cash registers, an builing size. Now imagine this McDonals with only one worker. Think of how many burgers this worker can prouce. This worker woul have to take care of all of the tasks at the restaurant, grilling, taking orers, cleaning up the tables, etc. Hiring this first worker woul enable some etra burgers to be prouce, but perhaps not many. However, hiring a secon or thir worker woul enable much output to occur. erhaps now one worker coul take care of the cash register, another the grill, another cleaning up the restaurant. In fact, the aitional output prouce by the n an 3 r unit of labor might be quite high compare to the first. 3
43 Econ 500 Microeconomic Review Cost Curves But eventually, hiring aitional workers will enable only a small number of etra units of output to be prouce. How many etra burgers woul be prouce by sticking the 43 r worker in the McDonals? Not much, if any. In fact, it is possible that hiring another worker may lea to less output being prouce. The Marginal rouct of Labor Curve The marginal prouct of labor is the etra output prouce by an etra unit of labor. Notice in the eample, an consistent with our story, the marginal prouct of labor increases for the first couple of units of labor. erhaps this is because of the specialization of the employees escribe above. But also notice as more an more workers are hire, the marginal prouct of labor begins to iminish an eventually becomes negative. This concept has a special name - the law of iminishing marginal returns. The law of iminishing marginal returns states as we hire more an more of one input, holing other inputs constant, the marginal prouct of the variable input will eventually ecrease. In our case (the short run), the amount of capital is fie an the amount of labor is variable. Thus, as we hire more an more labor, holing the amount of capital constant, the marginal prouct of labor ecreases. It is very important that you unerstan that the reason for this is not that the 7 th or 0 th worker is hire is any less skille that the st worker. We have implicitly assume that all units of labor are equally skille. This has nothing to o with the quality of labor. The reason for the iminishing marginal prouct of labor is that the restaurant is becoming more crowe. You can t fit 8 workers aroun a grill, nor can three workers work on the same cash register. More precisely, with a fie amount of capital at the restaurant, hiring aitional units of labor means that each worker has less capital to work with. If the restaurant becomes so crowe, aing another worker may cause even more less output to be prouce workers just bumping to each other. It has everything to o with the quantity of labor. Simply put, a worker s marginal prouct of labor will epen on the amount of capital they have at their isposal. With a fie amount of capital, aing labor necessarily means that each worker has less capital at their isposal. Drawing the ictures of the M L curve: Obviously, given the chart above, you coul simply calculate the M L an raw the picture from those figures. But you woul miss out on an insight or too. I have rawn the pictures below. The biggest thing we want to notice right now is that the marginal prouct of labor curve first increases, then ecrease. It is an upsie-own U shape curve. 4
44 Econ 500 Microeconomic Review Cost Curves 0 00 Output (q) F(K,L) Labor (L) ML Output (q) Labor (L) ML Technically, the marginal prouct of labor is the slope of the prouction function. A bit more intuitively, it is the etra output that each unit of labor enables to be prouce. Notice, at low levels of output, the prouction function is getting steeper; therefore, the marginal prouct of labor is increasing. Eventually, the slope of the prouction function ecreases, an hence the marginal prouct of labor ecreases. Also notice at q = 8, the prouction function is neither increasing nor ecreasing, an therefore the marginal prouct of labor is zero. Finally, aing more labor (past Q = 8) will cause output to fall, leaing to a negative marginal prouct of labor. It seems with this prouction function, the maimum slope occurs at q = 3. 5
45 Econ 500 Microeconomic Review Cost Curves Firms Cost Curves Ok so having figure out what the marginal prouct of labor curve looks like, we will stick that in our back pocket an work on iscussing the costs of firms. A couple of important istinctions Economic Costs vs. Accounting Costs: The big ifference between the way accountants calculate costs an the way that economists calculate costs is that accountants o not inclue non-eplicit opportunity costs. The most common misse opportunity costs are the entrepreneur s time an the opportunity cost of the capital involve in the business. Let us run through the some quick stylize eamples. Consier a proprietor running a pizza restaurant an assume this proprietor oes not pay himself or herself a salary. If yearly total revenue were $0,000, while the eplicit (accounting) costs of prouction were $90,000, then the accountant woul calculate accounting profit of $30,000. The economist woul be certain to a in the opportunity cost of the proprietor s time. If this iniviual coul have earne $40,000 a year elsewhere, then the opportunity cost of time is $40,000. Economic costs therefore woul inclue the $90,000 eplicit costs an the $40,000 opportunity cost, for a total of $30,000. The economist woul conclue economic profits in this case were -$0,000. This calculation is suggesting that proprietor woul be better serve working elsewhere. Suppose a business involves $40,000 of capital that is alreay pai for. Suppose that yearly revenue is $,000, while eplicit accounting costs are $0,000. The accountant may calculate a profit of $,000 in this case. But again, we nee to be careful to inclue the opportunity costs, this time the opportunity cost of capital. If the market interest rate was 0%, then instea of having the $40,000 worth of capital investe here, the capital have been investe elsewhere (or simply sol an the money coul sit in the bank). With a 0% interest rate, this amount of capital woul have earne $4,000 yearly. The economist woul inclue this opportunity cost, an thus woul calculate an economic profit of -$000. Sunk Costs vs. Recoverable Costs: Once a ecision is mae, an is totally irreversible, it shoul be ignore. Costs that have been incurre, an cannot be recovere, are calle sunk costs. The ol epression - It s a sunk cost, get over it - is right on. Consier the purchase of a specialize piece of equipment that has no value to any other business. Once the equipment is purchase, the costs are sunk. They cannot be recovere. There is some ate where you can no longer get a refun on your tuition ollars from NSU. After you cross that ate, the amount spent on tuition is a sunk cost. A ifferent tetbook takes you through an interesting eample about how a firm is consiering relocating. Say it spens $50,000 to purchase an option (the legal right to buy the builing) at a price of $500,000. Regarless of whether this builing is purchase, the $50,000 spent on the option is non-refunable. It is a sunk cost. Now, suppose a secon builing is locate that is similar an costs $55,000. Someone might argue that because if the first builing is purchase, a total of $550,000 will have been spent, an because the secon builing costs only $55,000, it makes sense to purchase the secon builing. But this reasoning is fallacious. The $50,000 was spent, cannot be recovere, an therefore is irrelevant in future ecisionmaking. Going forwar, an ignoring this cost, the ecision shoul be mae to purchase the builing that costs only $500,000. 6
46 Econ 500 Microeconomic Review Cost Curves The lesson here is to ignore the sunk costs, an focus on the incremental costs (the costs going forwar). Have you ever hear someone say in the mile of a crappy movie, Since we have alreay pai for the movie, we shoul stay. Might this person be making a mistake? Shouln t the ecision be base on the benefit of watching the rest of the movie, an the costs of watching the movie? Aren t the epenitures on the ticket sunk? Or how about walking into a bar an opening a beer, then saying, Since I bought the beer, I shoul finish it before leaving. I am pretty sure once you goober on your beer, it is a sunk cost. Does your beer have any resale value? It is unrecoverable. As such, whether your stay to finish your beer or leave shoul be base on the benefits of consuming the beer (going forwar) an the cost of rinking the beer (going forwar), but the $ you spent on the beer is now irrelevant. Fie Costs vs. Variable Costs: This one is pretty easy. Some costs change epening on how much output is prouce, while other costs o not change epening on how much output is prouce. Fie costs (FC) are costs that o not vary with the level of output. Eamples woul inclue monthly rent, a fee pai to a security monitoring company, the salary of the manager. Variable costs (VC) are costs to o vary with the level of output. If you prouce more pizzas, you will nee to hire more labor, buy more cheese, an more tomatoes. Therefore, labor, cheese, an tomatoes are variable costs. Notice that some types of labor can be fie costs, while other types of labor can be variable costs. Your tetbook also points out that some costs that are fie in the short run are variable in the long run. erhaps you have agree upon a fie salary for your manager. But in the long run, if you prouce more output, it may be the case that the manager has to work more hours an will eman a higher salary. In this case, in the long run, the salary pai to the manager is a variable cost. Eamples: Software Development izza Restaurant University Computer Harware Fie Costs Variable Costs Sunk Costs Large evelopment Small costs of costs inepenent of uplication of software how many copies relatively small prouce Large rent, proprietor s time, kitchen equipment, chairs an tables Huge builings, IT infrastructure, library Small nee some place to assemble the computers, but not very specific technology Relatively low labor, materials, ingreients Small university can hire ajunct professor cheaply Large processors, memory, components, assemblers Large - once software is evelope, these epenitures are sunk Very few kitchen equipment, tables an chairs, can be sol. Main sunk cost may be long term nonrefunable lease Very large woul anyone buy orms, ol library books? Small Lemonae Stan Low carboar sign High lemons, sugar Low carboar sign? 7
47 Econ 500 Microeconomic Review Cost Curves Marginal, Average, an Total Costs: So often, we preach that it is always marginal stuff that matters in economics class. Here is one notable eception. To figure out what firms will be up to in both the short run an the long run, we have to keep track of what is going on with both marginal costs an average costs. Going back to our istinctions above, the first important relationship is simple. Costs are either fie or variable. Total Costs (TC) = Variable Costs (VC) + Fie Costs (FC) Net, we will work on marginal cost. As you know, marginal cost is just the change in total cost associate with a one-unit increase in output. So you will see below that MC = TC / q. But because TC = VC + FC, an because fie costs on t change when we alter then output level, another way we can write MC is to note that MC = VC / q MC = TC / q = VC / q Average Costs: All of the average costs measures are calculate the same way. Take some measure of total cost, an ivie by the quantity of output prouce. Your book is a bit sloppy about how it abbreviates average total costs. Sometimes it will use ATC an sometimes it will use AC (average costs). Average Total Costs: Average Fie Costs: Average Variable Costs: ATC = TC / q AFC = FC / q AVC = VC / q Eample: At this point, mechanically, you shoul be able to calculate this whole mess of a table, given the first two columns. Remember that fie costs o not change with the level of output. Output FC VC TC MC AFC AVC ATC See the answers at the en of these notes. 8
48 Econ 500 Microeconomic Review Cost Curves What etermines short run costs: Keep in min that in the short run, the amount of capital is fie. If the firm is to prouce more output, it must hire more labor. What then etermines the marginal cost of proucing? The important factors will be the wage rate (the cost of hiring labor) an the marginal prouct of labor (how much output that labor can prouce). For instance, if the market wage is $5 in one situation an $8 in a secon situation, marginal cost will be lower in the first. Also, if the marginal prouct of labor is high in one situation (one etra unit of labor prouces many aitional units of output) an lower in a secon situation (one etra unit of labor prouces fewer aitional units of output), the marginal cost will be lower in the first. If we continue with this logic, we can figure out that when the ML curve is rising, the MC curve will be falling. When the M L curve is falling, the MC cost curve will be rising. That is, because the M L curve is upsie-own U shape, the MC will be U-shape. Still unconvince? We are cheating a bit, but we can get the basic iea by looking back at our prouction function. Let us assume that the going wage that has to be pai to a unit of labor is $30, regarless of how many units of labor the firm hires. We can calculate the etra cost per unit prouce by figuring out how many etra things we get (M L ) for each $30 increase in costs. Labor (L) Output (q) Marginal rouct ( q / L) Aitional Labor Costs Something retty Close to MC $30 $3.00 / unit ($30 / 0) 30 0 $30 $.50 / unit ($30 / 0) $30 $.00 / unit ($30 / 30) $30 $.50 / unit ($30 / 0) $30 $.00 / unit ($30 / 5) $30 $.3 / unit ($30 / 3) For you people who like math We know that marginal cost is equal to the change in variable costs for a given change in output. However, the change in variable costs is simply equal to the market wage multiplie by the change in the amount of labor hire. MC = VC / q = w L / q But if you remember from our iscussion of prouction functions, q / L = M L. Therefore, you can conclue that MC = w / M L Thus, if M L is first increasing then ecreasing, the MC will be first ecreasing, then increasing. 9
49 Econ 500 Microeconomic Review Cost Curves ictures of Cost Curves (Short Run) Your tetbook raws the picture of total costs, (total) fie costs, an (total) variable costs, but I o not think it as much. I woul focus on the picture with MC, ATC, AVC, an AFC. I think the best way to go about unerstaning this picture is to attack the curves in the following orer: MC, then AVC, then AFC, an finally ATC. While you can o these mechanically, an simply graph them in the numerical eample, there are few more insights to gain from scratching your hea about them. Marginal Cost marginal cost is typically U-shape. Why? When we talke about prouction functions, we tol a story about how the marginal prouct woul initially increase for a while, then (eventually) ecrease. Since marginal costs moves in the opposite irection of the marginal prouct of labor, it will be the case that MC first ecreases, then increases. Average Fie Costs fie costs are some set figure, say $50. As more an more output is prouce, average fie costs continually ecrease. Check the eample above. Notice that AFC ecreases rapily for the first few units of output, an while AFC continues to ecrease, the AFC flattens out consierably. This is what people are talking about when they iscuss spreaing out the overhea. Average Variable Costs a test analogy. If your last test score is higher than your average test score, your average will be rising. If your last test score is lower than your average, the average will be falling. But the average will not be rising quite as rapily. If MC > AVC, AVC will be rising. If MC < AVC, AVC will be falling. Because MC is falling at low output levels, it will be below AVC an thus AVC will be falling at low levels of output. When MC begins to rise, eventually it will be above AVC, an thus AVC will be rising at high levels of output. As a result, AVC will be U-shape as well. The lowest level of AVC will occur at the spot where the AVC curve bumps into the MC curve. Average Total Costs I think the best way to think about the ATC as coming from aing up the AVC an AFC curve. Because TC = FC + VC, then it is the case that ATC = AFC + AVC. We have alreay figure out what the AVC curve looks like, an what the AFC curve looks like, so we just a them up. At low levels of output, AFC is high, so the ATC will be much larger than AVC. At high levels, we know that AFC is low, an thus the ATC curve will be very close to AVC curve. As output increases, the ATC curve will get closer an closer to AVC. 0
50 Econ 500 Microeconomic Review Cost Curves The picture: MC AFC AVC ATC What to notice? Notice that then MC < AVC, AVC is falling an when MC > AVC, AVC is rising. Notice where MC = AVC, AVC is at its minimum. Notice that when MC < ATC, ATC is falling, an when MC > ATC, ATC is rising. Notice where MC = ATC, ATC is at its minimum. Notice at low levels of output, AVC an ATC are far apart (as AFC are high). Notice at high levels of output, AVC an ATC are close together (as AFC are low). What is Net? We will take a look at firm s ecisions net. Given some assumptions about the structure of the inustry (competitive, monopolistic, etc), we will moel how firms behave. We will also look at how firm ecisions iffer in the long run. What shoul I rea? If you were only going to rea one, I woul rea Baye on this one. Besanko Cost Curves are iscusse at the beginning of the primer. You will see a bit more emphasis on the long-term there than in these notes. Also, the notation will be just a bit ifferent. Baye Chapter 5. Rea the beginning an the en. Chapter 5 begins with prouction functions, which will be similar to what you see above. I o not think the mile portion, starting with the subsection Algebraic Forms of rouction Functions is as important as the things I have iscusse above. (It covers isocost lines an isoquants nothing wrong with it but we are time constraine). Start reaing again when you get to the section The Cost Function. The notation is a pinch ifferent, but I think you will be ok.
51 Econ 500 Microeconomic Review Cost Curves Answers to Eample in Notes Output FC VC TC MC AFC AVC ATC
52 Econ 500 Microeconomics Review - erfectly Competitive Firms erfectly Competitive Markets We turn our attention to perfectly competitive markets. To be sure, this is a tetbook ieal. There are few if any markets that are perfectly competitive. Nonetheless, it will be useful to eamine. Competitive Market Assumptions. Many buyers an sellers. Some books simply say firms are small relative to the market. The iea is that each firm is a small portion of the overall market. If that one firm prouces a little more or a little less, the market price will not change. As a result, each iniviual firm acts as though the price is beyon their control.. Homogenous proucts. Homogeneous means that proucts are ientical firm A s prouct is a prefect substitute for firm B s prouct. As an eample, consier gasoline or sugarcane. Amoco gas is just about the same as B gas, just like Farmer Joe s sugarcane is just about the same as Farmer John s sugarcane. All # pencils are alike. Because proucts are homogenous, a single firm can not raise their price above the market or competitive price. If the firm i, consumers fin a suitable alternative at any number of other firms, an thus the firm whose price ha increase woul lose most or all of its business. Shoes woul be an eample of a heterogeneous prouct one firm s shoes are not eactly the same as the others. A firm will have more pricing leeway in this case as one firm s prouct may not be a perfect substitute for another. This woul not be a perfectly competitive market. 3. No transaction costs. No taes, waiting in line, etc. 4. erfect information. Consumers are well informe about the availability of goos an their prices, as are rival firms. 5. Free entry an eit. This is very important for the long run ynamics. This means there are no special costs that make it ifficult for a new firm to enter into an inustry, nor are their special costs that make it ifficult for an eisting firm to leave the inustry. We will see that if entry is free, if the inustry is earning unusually high profits, new firms will quickly enter the inustry. If eit from the inustry is free an the inustry is earning unusually low profits, eisting firms will eit the inustry. Restaurants woul be a goo eample of an inustry where entry an eit are easy. Nuclear power plants (eit an entry), airlines (entry), rug companies (entry), an cemeteries (eit) woul be eamples of businesses where have a more ifficult time entering or eiting. A bit on the goals of the firm We assume that firms maimize profits. Is it true? I will tell you a story about a company my brother worke for clearly we can come up with eamples of actions managers take that o not maimize profits. But we certainly know that firms o not minimize profits. A particular instance where people often claim managers are not maimizing profits is the case of large corporations. The problem here is that managers of the firm own little if any of the firm, an thus may not have much incentive to maimize profits. Nonetheless, if managers stray too far from the ieal, they will be replace. At the en of the ay, assuming firms maimize profits is a useful assumption in trying to preict behavior. rofit Maimization You may remember from your Econ class that a perfectly competitive firm chooses to prouce where = MC, or you might have learne that a price taking firm chooses to prouce where MR = MC. Both of these are true. The reason is because that for a price taking competitive firm, MR =. Why? Because the price taking firm takes the price as given, the eman curve facing an iniviual firm is a horizontal line at the prevailing market price. If the market price is $0, the firm acts as though it can sell
53 Econ 500 Microeconomics Review - erfectly Competitive Firms all it wants at a market price of $0. A consequence of this fact is that the marginal revenue curve of a competitive firm is also a horizontal line at the market price. Quantity rice Total Revenue Marginal Revenue 0 $0 $0 -- $0 $0 $0 $0 $0 $0 3 $0 $30 $0 4 $0 $40 $0 5 $0 $50 $0 On the right, we picture the overall market eman curve; on the left we picture the situation facing one iniviual firm. If for whatever reason the prevailing market price was 0, then each iniviual firm woul face a horizontal eman curve (an marginal revenue) curve locate at 0. (I believe in class we i this the other way aroun it makes no ifference). S = mr 0 D q Q Choosing Output in the Short Run If the firm is to prouce, the firm will operate where = MC (or MR = MC). It turns out there are three relevant cases we will want to iscuss. We will also assume that all fie costs are sunk, an that all firms have ientical costs.
54 Econ 500 Microeconomics Review - erfectly Competitive Firms High rice: First, consier the case where is high. If the firm is to prouce, it will choose to prouce where = MC (or MR = MC). In the graph below, it is labele q*. ($ per unit) MC $5 $ ATC AVC = MR q* = 0 q We can illustrate profits graphically. If for instance, = $5, an ATC = $, this means there is an average profit of $4 per unit. If we knew that say 0 units were prouce, we woul know in this case that total profit was $80. Graphically, this area is epicte above. Shae in the area between an ATC an from q = q* to q = 0. This firm is earning positive economic profits. > ATC, so the firm is earning enough to cover variable costs an fie costs. The firm will of course continue to operate. More generally, if > ATC, firms will continue to operate. Meium rice: Now, consier the case where the price is meium. Again, if the firm is to prouce, it will prouce where = MC, or MR = MC. In the picture below it is labele q*. If ATC is $0, while = $6, the firm is losing $4 per unit. Because 8 units are being prouce, profits are -$7. This firm is earning negative economic profits the firm is losing money. The losses are shae in the graph below. The question is, shoul the firm prouce 8 units, or shoul it shut own? If the firm prouces nothing (shuts own), it still has to pay its fie costs, because they are sunk. How much are fie costs? Recollect that ATC = AVC + AFC. Therefore, the gap between ATC an AVC is AFC. In this eample, ATC = $0, AVC = $4, so AFC are $6. Since 8 units are being prouce, we can Any price where intersects the MC curve where > ATC. Any price so that intersects the MC curve where is between AVC an ATC. 3
55 Econ 500 Microeconomics Review - erfectly Competitive Firms calculate total fie costs are $08 ($6 * 8 = $08). If the firm shuts own, then it will have no variable costs, no revenue, an will have pai its fie costs of $08, an thus profit woul be -$08. If the firm prouces 8 units, as we note above, the profit level is -$7. While the firm is losing money by proucing overall, it will lose less money by proucing. It shoul not shut own. In fact, in any case where > AVC, price will be enough to cover the variable costs an still cut into the fie costs. The firm shoul continue to operate. More generally, as long as > AVC, the firm will prouce (at least in the short run.) 3 ($ per unit) MC $0 ATC AVC $6 $4 = MR q* = 8 q 3 If you are thinking that the fie costs can be ignore because they are sunk, you are correct. So long as the price is enough to cover the variable costs, the firm will want to operate. 4
56 Econ 500 Microeconomics Review - erfectly Competitive Firms Low rice: Finally, consier a "low" price. 4 Again, if the firm is to prouce, it will prouce where = MC, or MR = MC. In the picture below it is again labele q*. ($ per unit) MC ATC $3 AVC $4 $ = MR q* = q If the firm is to prouce, it will prouce unites. Say price is $, AVC is $4, an ATC is $3, shoul the firm operate? Note that the gap between ATC an AVC is $9, which means that AFC must be $9. Because units are being prouce, this again makes fie costs $08 (of course the same as we ha above -- fie costs are fie). If the firm shuts own, we know the firm s profits are -$08. If the firm prouces units, it will lose $ a unit, an because units are being prouce, the firm s profits are -$3. This loss is shae above in re. Clearly it is better for the firm to shut own, because price is not even high enough to cover variable costs. It is better to lose $08 than to lose $3. More generally, if < AVC, the firm will shut own. Is there a concise combination of this information the firm s short run supply curve? Yes. We now know that if the firm is going to operate, it will operate where = MC (or MR = MC). We also know in the short run, the firm will operate as long as the > AVC. If you imagine trying every possible price, an connect the ots, you fill fin that the firm s short run supply curve is the portion of the firm s MC curve above AVC. See the picture below the firm s supply curve is the thick black line. So after all that, we know where a firm s short run supply curve comes from. 4 Any price where intersects the MC where < AVC. 5
57 Econ 500 Microeconomics Review - erfectly Competitive Firms ($ per unit) MC ATC AVC Firm s Short Run Supply Curve q What happens as we transition to the long run? High rice: Keep in min when we ae up costs, we inclue the opportunity cost of the proprietor s time an the opportunity cost of capital. If we en up with economic profit equal to eactly zero, that means price is just high enough to cover all costs, variable costs an fie. The proprietor is earning fair or normal return for their time. The capital investe is earning a fair or normal rate of return on its investment. The capital coul not earn more elsewhere. 5 With > ATC, in the short run, firms will be earning positive profits (economic profits above 0). A positive economic profit means that firms in this inustry are earning profits better than in other inustries. Capital in this inustry is earning a higher return than capital in other inustries, sometimes calle an above normal return. As a result, we will epect new firms to be attracte to this inustry. In short, there will be entry. Entry will increase output in the inustry an rive own price. How low must prices go until there is no longer an incentive to enter the inustry? rices must fall until economic profits are zero. At what price are economic profits zero? Where = ATC. rice will be just high enough to cover fie an variable costs. Likewise, price will be just high enough so that capital earns a fair or normal rate of return. In the long run, entry will occur until economic profits are riven to zero an price is riven to the minimum of the ATC curve. Meium rice: We have assume all of our fie costs are sunk. For eample, if the firm s only fie costs was a lease that was signe for say a year, the moment this lease is signe it woul be a sunk cost as it is not recoverable. In the meium price case, price is high enough to cover variable costs, but only some, not all of the firms fie costs. If the time comes to sign a lease for net year, woul the firm o it? That is, if the fie costs 5 Remember that even though economic profits are 0, accounting profits will be greater than 0. 6
58 Econ 500 Microeconomics Review - erfectly Competitive Firms are not sunk, shoul the firm stay in business? Shoul the firm continue to operate if it will be earning negative economic profits? The answer is no. Net year s lease is not a sunk cost; it is avoiable. The firm will not want to continue operating at a loss. Some firms will shut own. In short, eit will occur. Firms will leave, inustry output will ecrease, an prices will rise. How high must price increase until there is no longer an incentive for firms to eit? Again, price must rise until economic profits return to zero. At what price are economic profits zero? Again, where = ATC. In the long run, eit will occur until price rises to the level where economic profits are zero. Again, price will be riven to the minimum of the ATC curve. Low rice: Not much to say here. At this price, because the firm shuts own immeiately, there is obviously eit from the inustry. Eit will occur, price will rise, an firms will continue to eit until economic profits are zero an is at the minimum of the ATC curve. Below is a picture of a firm operating where economic profits are zero. ($ per unit) MC ATC AVC = MR q* q Big icture Keep in min what we ve assume. There are many firms, proucing a homogeneous prouct, an importantly entry an eit are easy. Ask yourself if they are realistic in real worl situations. ick your favorite inustry. Are there are large number of firms in each inustry? Do they prouce homogenous proucts? Is entry an eit easy? If not, our moel won t o such a great job preicting behavior. It is really only a starting point. If there are a small number of firms, firms may be able to charge prices above the competitive level, or perhaps collue or otherwise behave strategically. If ifferent firms prouce ifferentiate proucts, each firm may be able to charge ifferent prices, as a perfect substitute is not available for each firm s prouct. As a result, they will have more latitue in pricing. If entry an eit are not easy, economic profits coul persist for long perios of time. 7
59 Econ 500 Microeconomics Review - erfectly Competitive Firms Also, we have implicitly assume that firms all have the same costs. If a firm has a cost avantage, it will be able to prouce at a lower cost, will sell more output than other firms, an will earn aitional profits. If a firm has a cost isavantage, it will struggle to say in business. We will start to work on net is what happens as the number of firms ecreases this makes firm behavior much more fun an much more strategic. What shoul I rea? Chapter 8 in Baye. The primer in Besanko. 8
60 Structure / Conuct / erformance The Structure / Conuct / erformance paraigm is a bit of an outate way to escribe the ifferences across market structures an the resulting performance of the firms an inustries. It is nice because it introuces some variables an ways to categorize the conitions facing ifferent inustries. We first focus on Structure trying to escribe the ifferences across firms. Structure Market Structure factors such as number of firms that compete in a market the relative size of the firms (concentration) technological an cost conitions eman conitions ease at which firms can enter / eit the inustry. Different firms have ifferent structures an these affect managerial ecision marking. See Table 7- in Baye for ifferences in sales for biggest firms in various inustries. Structure: Concentration Two main measures of concentration C 4 an the HHI. C 4 = Four firm concentration ratio S = sales of the largest firm S = sales of n largest firm S 3 = sales of 3 r largest firm S 4 = sales of 4 th largest firm S T = total sales of all firms in the inustry (incluing 5 th thru N th largest firms) C 4 = (S + S + S 3 + S 4 ) / S T Alternatively, C 4 = w + w + w 3 + w 4 w = market share of largest firm w = market share of n largest firm w 3 = market share of 3 r largest firm w 4 = market share of 4 th largest firm C 4 ranges from 0 to. With a large number of (small) firms, C 4 is close to zero. With a small number of (large) firms, C 4 is close to one. With four or fewer firms, C 4 =. See Table 7- in Baye: Goo C 4 HHI Breakfast Cereals Breweries Milk 05 Jewelry 3 8 Reay-mie concrete 7 9
61 HHI = Herfinahl-Hirschman Ine HHI = 0,000 * Σw i HHI squares the market shares of each firm an as them up. It inclues all firms whereas c 4 contains only 4. The multiplication of this sum by 0,000 serves to ensure the number is not a ecimal. HHI ranges from 0-0,000. 0,000. An inustry with a single firm (monopoly) woul have an HHI of Eample: Three firms, with sales of $0, $0, an $30, respectively. Firm s market share is $0 / $50 = 0. Firm s market share is $0 / $50 = 0. Firm 3 s market share is $30 / $50 = 0.6 HHI = 0,000 * ( ) = 0,000 * ( ) = 0,000 * 0.44 = 4400 For a comparison, C 4 in this case woul be C 4 = = The Department of Justice antitrust guielines use HHI. Caveats with both measures Don t inclue imports consier beer. With many importe beers available to consumers, the beer inustry is likely much more competitive than calculate with just the omestic ata. National, not regional or local in some cases, a regional HHI or C 4 might be more appropriate. For instance, if there was one gas station in each state, an we assume each station or state was the same size, each gas station woul have a national market share of 0.0, making the C 4 = 0.08, leaing us to think the market was very competitive. However, if there were only one gas station in each state, each station woul have much monopoly power. rouct efinitions what shoul we inclue when we calculate the HHI for soft rinks? Coke an epsi shoul be in. Shoul we inclue root beer, fruit rinks, bottle water, gin? It is ifficult. You can actually make a living o this. Inustry efinitions how o we classify firms? Uncle Sam has come up with SIC (Stanar Inustry Classification) coes, but they aren t perfect, but helpful. Rea Baye if you are intereste. Structure: Technology Labor intensive technologies: accounting, econ lectures Capital intensive technologies: ship builing, auto manufacturing In some inustries, a firm might have superior technology than competitors oil rilling In other inustries, all firms might have ientical technology as their competitors restaurants When Besanko reports HHI, they on t multiply by 0,000. So in Besanko, the HHI ranges from 0 to.
62 Structure: Deman Conitions General eman conitions Broaly speaking, we sometime see low eman or can support only a few firms. My business iea: Wrinkle in Time. In other cases, eman is sufficiently large that it can support many firms. In such cases, niche firms can eist. Comic book stores? Scarf stores? Information available to consumers: rices: Use Cars vs. Flights, Sushi vs. Mrs. aul s fish sticks Elasticity of Deman Bran vs. prouct elasticities Elasticity of eman for Marlboros is ifferent from elasticity of eman for cigarettes Rothschil Ine: provies a measure of sensitivity to price of prouct group as a whole relative to the sensitivity of quantity emane of a single firm R = E T / E F E T = elastiticity for the total market E F = elasticity for the prouct of an iniviual firm Rothschil ranges from 0 to. If R = firm s elasticity same as the market eman curve If R = 0, firm s elasticity much larger than the market eman curve If R = 0.0, a firm s eman curve is 0 times more sensitive that the inustry level elasticity. See Baye Table 7.3 Goo E T E F R Foo Tobacco Apparel aper Agriculture Structure: otential for Entry Barriers to Entry Eplicit Costs Capital requirements atents you can t uplicate Lipitor until its patent runs out in 0 years Economies of Scale the efficient scale of prouction might be very large (autos?) making it ifficult for new firms to achieve this scale. This isn t unrelate to capital requirements. More later on barriers to entry
63 Conuct Having ealt with the observable ifferences in the characteristics of firms (structure), we turn out attention to the firm s conuct. What o they o? How much o they mark-up their proucts? Do they merge with other firms? Do they spen on avertising? On R&D? The bigger here is the pricing behavior. Conuct: ricing Behavior Lerner ine ifference between an MC as a fraction of the price L = MC The Lerner ine (L) tells us how much the mark-up is as a fraction of the price of the goo. The Lerner ine varies from 0 to. If = MC, as it woul be in a perfectly competitive inustry, L = 0. If is much larger than MC, say = $00 an MC = $, the Lerner woul be L = 0.99, very near one. Alternatively, we coul solve for the price as a function of the marginal cost. So let s solve for. MC MC MC L = L = L = ( L ) = MC MC MC = = = MC L L L Thus, = MC L. So now price is epresse as a function of the MC of proucing an mark-up factor. L, which is calle the Eamples: When = $5 an MC = $4, L = MC 5 4 = = 0. 5 = = L =.5 So we can think of the mark-up as being 0% of the price, or can think of the price as being 5% higher than MC (from the mark-up factor of.5). I think the latter is more intuitive.
64 When = $ an MC = $, MC L = = = 0.5 = = =. L So here we can think of the mark-up as being 50% of the price, or can think of the price as being 00% higher than MC (from the mark-up factor of ). Again, I think the latter is more intuitive. See Table 7.5 in Baye for more real worl eamples. L MUF Foo Tobacco Leather Conuct: Integration & Merger Behavior Vertical Integration: Various states in the prouction of a single prouct are carrie out a single firm: A car company coul buy steel, makes engines, make boies, put them together, an therefore buils cars. Alternatively, it coul buy engines, buy boies, an put them together. The reason for vertical integration is transaction costs. An eample woul be that General Motors once bought Fisher Boy arts. Instea of buying car boies from Fisher, GM bought Fisher. Horizontal Integration: Merging of the prouction of similar proucts into a single firm. The reasons for horizontal integration are economies of scale or score or to enhance market power. But is market power increases, the HHI increases, an this market power is potentially ba for consumers. So our Uncle Sam has come up with some antitrust guielines: 800 = highly concentrate, block mergers that increase more than 00. <000 = unconcentrate, you can merge if you want >000, <800 = weight cost savings vs. anti-competitive An eample woul be the merger of AT& T / Cingular, specifically their cellular ivisions. Conglomerate Merger: Integration of prouct lines into a signal firm of non-relate final proucts. The reason for conglomerate mergers is sometime sai to be the ability to smooth revenues by iversifying into prouct lines. I fin that argument a bit sketchy. An eample woul be the merger of RJR (a tobacco company) with Nabisco (a foo / snack company). Conuct: Research an Development, Avertising Inustries an firm iffer in the amount of research an evelopment they choose. For rug companies, lots of research, while for cereal companies not so much. Both o a lot of avertising. See Table 7-6 in Baye. R & D Avertising rofits Bristol-Myers-Squib AT&T
65 &G (Soaps & Cosmetics) Kellogg erformance The last chuck on the Structure Conuct erformance paraigm is to evaluate the effect on overall profits an social welfare. Managers are surely interest in how profitable the inustry is, but economist always like to worry about is the right amount of output is prouce an if the gains from trae are maimize. We ll aress profits as we go, but not worry so much about the efficiency consierations. Check out profits as a percentage of sales in the last column of Table 6. Structure Conuct erformance - Critique Shoul we buy this whole Structure Conuct erformance train of logic? Some o. They believe in the Causal view. Others suggest is it is more complicate, believing in the Feeback view. I think the feeback folks are right. But it s not so far off that you can t learn anything from it. An if you compare it to what the folks that espouse the 5-Forces view say, it oesn t seem all that far off. Causal View: Structure causes conuct. If we have a small number of firms (concentrate), this causes market power for the firms, resulting in high prices, high profits, an low social welfare (not enough being prouce). Feeback View: Not a one-way street. The conuct of firms can leas to changes in concentration, which then loops back aroun to the conuct of firms. All of these items are interrelate. 5-Forces View: Growth an sustainability of profits are affecte by: () entry () power of input suppliers (3) power of buyers (4) inustry rivals (5) substitutes an complements
66 Market Structures Having iscusse all this, we net turn to classify market structures. We can classify firms an inustries into 4 broa groups. We ve alreay talke about perfect competition. We can quickly know off monopolies. We ll come back to monopolistic competition later. An we ll get into oligopoly shortly, using our game theory skills. erfect Competition: Firms / Buyers: Many firms, many buyers Technologies: Firms have access to same technologies roucts: Homogeneous Market ower: Firm has no market power (no firm can alter p, q, or quality) C 4 an R: C 4, R, ten to be close to zero. Eample: corn farming ricing / Output Rule: = MR = MC Barriers / Entry: In the long run, entry will occur, zero economic profits, = min of ATC in LR Bottom line: Ignore your rivals, take market price as given, entry / eit until zero profits. Monopoly Firms / Buyers: One firm that is a sole proucer, many buyers Technologies: One firm n/a roucts: One firm - n/a Market ower: Large market power (no competition) C 4 an R: C 4 =, R = Eample: local utility ricing / Output Rule: Restrict output, charge prices above MC. MR = MC. Barriers / Entry: ositive economic profits, > ATC. Bottom line: No rivals, pick a spot on the eman curve, positive profits Monopolistic Competition Firms / Buyers: Many firms, an many buyers Technologies: Firms can have access to same or ifferent technologies roucts: Heterogeneous (ifferentiate) Market ower: Firms have some market power C 4 an R: C 4 close to 0, R close to 0 Eample: Chili s ricing / Output Rule: Restrict output, charge prices above MC. MR = MC. Barriers / Entry: No barriers to entry. ositive economic profits will lea to entry. Bottom line: Ignore rivals? ick a spot on the eman curve, epect entry if profitable **Avertising: Convince consumers their bran is better or even ifferent Oligopoly Firms / Buyers: A few large firms ominate the market, many buyers Technologies: Firms can have access to same or ifferent technologies roucts: Homogeneous or heterogeneous Market ower: Firms have substantial market power C 4 an R: C 4 an R large (close to ). Eample: Airlines, Auto Manufacturers, Aerospace ricing / Output Rule: Restrict output, charge prices above MC. MR = MC. But interepenent. Barriers / Entry: Barriers to entry, positive economic profits Bottom Line: strategy is important mutual interepenence can t ignore rivals - moels **Bertran, Cournot
67 Monopoly Why no competitors? a. Economies of scale - LRAC ecline as output increases. b. Economies of scope - big firms access to capital at lower cost. c. Cost Complementarities core competencies. atents an Other Legal Barriers Nee not be big firms small town movie theater, gas station Firm s eman curve is market eman curve Free to charge any price but consumers ecie how much to purchase Choose any spot on the eman curve Clear Traeoff between an Q. ricing for Monopoly. Why is MR less than price? Econ style. rice Quantity Total Revenue Marginal Revenue $0 $0 $0 $9 $8 $8 $8 3 $4 $6 $7 4 $8 $4 $6 5 $30 $ $5 6 $30 $0 $4 7 $8 -$ $3 8 $4 -$4 But we know how to o math from before: Q = 00 or = 00 ½ Q Use inverse eman curve. Because = 00 ½ Q, MR = 00 Q Now, set MR = MC. Say MC = $40 an is constant. MR = MC 00 Q = 40 Q = 60 Finally, stick back into the inverse eman curve to fin the price. See picture below. = 00 ½ Q = 00 ½ * 60 = = $ MC D MR 00 Q
68 More generally, with a typical cost curve. Graphically, first fin the quantity where MR = MC. Then scoot up to the eman curve to etermine the maimum amount the consumer is willing to pay. rofit maimizing rate of output MC ATC ATC D MR Q* Q By the way, if you on t believe that choosing that quantity is the right one, pick another spot on the eman curve, shae in the bo for profits, an see if it s bigger than the one above. It won t be. Not the profit maimizing rate of output MC ATC ATC D MR Q WRONG Q
69 Econ 500 Game Theory Intro to Game Theory Game theory is the theory of strategic behavior. Its evelopment is largely relate to military applications, but game theory is now etensively utilize by those stuying economics, management, political science, an even biology an genetics. Broaly speaking, players (participants) are place in strategic situations calle games. layers are given choices they can take, rules (when they can take them), an evelop certain courses of actions (strategies). The game is then playe, an players either win or lose, or receive some payment (payoffs). For eample, in the prisoner s ilemma, the payoffs will the number of years in prison Bonnie an Clye serve. In most games, the payoffs will be profits of some hypothetical firm. While games can have more than two players, we will focus on games with only two participants. Some games are simultaneous people make their choices at the same time (e.g. rock, scissors, paper). Other games are sequential people take turns (e.g. tic, tac, toe). Most games we ll look at are one-shot games games that are playe only once, while other games are repeate games games that are playe more than once with the same opponents. Solution Methos Depening on how far you go in game theory, there are number of ifferent ways to solve games. Nash equilibrium - One of the most simple is calle a Nash equilibrium. A Nash equilibrium is calle an equilibrium because no player wishes to change his or her strategy. Each person is making the best response to their opponent s strategy an these strategies are consistent. Some games have what are calle pure Nash equilibria. An eample of a game of this type is the prisoner s ilemma. See below. Some games have no (pure) Nash equilibrium. These games are often solve with a metho calle mie strategy equilibrium. In these games, some sort of ranomness is involve. An eample of this type of game is the employee monitoring game. See below. Some games have multiple Nash equilibrium. Determining which of the multiple Nash equilibrium will occur in a simultaneous game is a ifficult problem. An eample of this type of game is the prouct choice game. What you will see is that when these games become sequential (taking turns) they become easy to solve. Backwars Inuction Backwars inuction is a way to solve sequential games (players take turns). The iea is surprise to work backwars. The sequential games we will consier will be solve by backwars inuction. The solutions we ll get are special cases of Nash equilibrium calle sub-game perfect equilibria. By going backwars, we are effectively able to eliminate strategy combinations that woul not occur. There are others ways to solve more comple games, but we will not get there. We are just scratching the surface. The games you will see, say on an eam, will be similar to those here. We will focus on Nash equilibrium an backwars inuction.
70 Econ 500 Game Theory risoner s Dilemma First off, note that this particular formation of the prisoner s ilemma wasn t iscusse in class. This classic game theory eercise is calle the prisoner s ilemma. The story is just what it souns like two criminals are put in separate cells an have been accuse of committing a crime (which they have committe). They cannot communicate an will make their ecisions simultaneously. It is a one-shot game. If both confess, they both will go to prison for 5 years. If neither confesses, they will be charge with a lesser crime an each go to prison for years. The prosecutor offers a plea bargain to each if one confesses an the other oes not, the one who confesses gets a break only one year in prison while the one who oes not gets a long sentence, going to prison for 0 years. When this might as first glance seem like tetbook BS, this will be very much relate to when we iscuss pricing an output ecisions for in an oligopolistic ecision. After you rea about Bertran Oligopoly, come back. An we ll see a bunch of eamples below. The game can be epresse in the following chart: Bonnie Confess Don t Confess Confess Bonnie: 5 years Clye: 5 years Bonnie: 0 years Clye: years Clye Don t Confess Bonnie: years Clye: 0 years Bonnie: years Clye: years Bonnie s strategy choices are reflecte in the rows of the game. Clye s strategy choices are reflecte in the columns of the game. Each of the four shae boes represents a combination of Bonnie s strategy an Clye s strategy. For instance, if Bonnie chooses not to confess an Clye chooses to confess, we en up with Bonnie going to prison for 0 years an Clye going to prison for year. Solving the risoner s Dilemma / Best Responses / Dominant Strategies Where you shoul always start when looking for the solution to a game is to look for ominant strategies. A ominant strategy is the case where one player s best response oes not epen on their opponent s strategy. First, what is Bonnie s best response if Clye chooses to confess? If (Clye confesses an) Bonnie chooses to confess, she goes to prison for 5 years. If (Clye confesses an) Bonnie chooses not to confess, she goes to prison for 0 years. Clearly, Bonnie will wish to confess. That is, when Clye chooses to confess, Bonnie s best response is to confess. Net, what is Bonnie s best response if Clye chooses not to confess? If (Clye oes not confess an) Bonnie chooses to confess, she goes to prison for year. If (Clye oes not confess an) Bonnie chooses not to confess, she goes to prison for years. The game we use in class is later in these notes, labele as the Cartel / ricing game. Sometimes stuents think that games must have either no players or both players with ominant strategies. As you saw in the assignment, a game can be such that only player has a ominant strategy.
71 Econ 500 Game Theory Again, Bonnie will wish to confess. That is, when Clye chooses to confess, Bonnie s best response is to confess. In this case, we say Bonnie has a ominant strategy. Her best response (confess) oes not change epening on what strategy her opponent chooses. Whether Clye chooses to confess or Clye chooses not to confess, we fin that Bonnie s best response is to confess. We woul epect Bonnie to Confess. You shoul now work through what Clye s best responses are. What is Clye s best response if Bonnie chooses to confess? What is Clye s best response if Bonnie chooses not to confess? Does Clye have a ominant strategy? If so, what is it? 3 Solving the risoner s Dilemma / Nash Equilibrium Back to the iea of a Nash equilibrium. At this point, you will hopefully be incline to think that the solution to this game is that both Bonnie an Clye confess. In fact, if both players have ominant strategies, the Nash equilibrium (outcome of the game) will be both play their ominant strategy. It is instructive, however, to confirm that Bonnie confesses, Clye confesses is in fact a Nash equilibrium. If so, neither player will have an incentive to change their strategy. Let s check. Given that Bonnie is choosing to confess, is Clye making his best response by confessing? Yes. Does he want to change his strategy? No. Given that Clye is choosing to confess, is Bonnie making her best response by confessing? Yes. Does she want to change her strategy? No. Neither wants to change an their strategies are consistent. Thus, the Nash equilibrium of this game is for both to confess. Both will confess, an both will spen 5 years in prison. Now, at this point hopefully you re yelling wait a minute. If they both ha chosen not to confess, they woul both go to prison for only years. True. Why can t they pull it off? Suppose for a secon that Bonnie was reasonably convince that Clye will cooperate an keep his mouth shut. 4 What shoul she o at this point? She will again want to take the plea an rat him out. Her best response is to confess. The same goes for Clye. Regarless of what their opponent oes, they are better off confessing. In a prisoner s ilemma type game, there will be a powerful iniviual incentive to confess ( cheat ), even though what is best for the group ( cooperate ) is for everyone to keep their mouth shut. This type of situations shows up all the time in the real worl. rovision of public goos, stuying for eams, an importantly cartels (pricing ecisions) all can be though of as prisoner s ilemma situations. I trie to put my money where my mouth was in class one time with unergrauates 80% of them actually playe the Nash equilibrium strategy when playing for etra creit points. 3 You shoul have foun that Clye also has a ominant strategy to confess. We epect Clye to confess. 4 We mean cooperate from the point of view of Bonnie an Clye (not cooperate as in cooperating witness). 3
72 Econ 500 Game Theory The risoner s Dilemma as a repeate game The analysis above assumes that this game is what we call a one-shot game a game playe only once. The problem with the prisoner s ilemma is that it is ifficult to get cooperation in the face of the selfinterest of the participants. If this game is playe repeately, however, we get a much more interesting story. If Bonnie an Clye know each other, have been in this situation many times in the past, an have always kept their mouth shut, it is quite likely that trust may factor into the game an we might see both keep their mouth shut (both on t confess). However, one interesting aspect of this part of the story is that when we know that the game is in its last perio, there is no tomorrow an cooperation is very unlikely. That is cooperation inuce by repeate games can break own when the en is known. See the en of these notes. rouct Choice Game Here is one we in t talk about in class. You shoul try it out. The story here is two breakfast cereal companies are thinking of introucing a new cereal. One is a crispy cereal an the other is a sweet cereal. Check out the payoffs (profits) in the table below. The game has been set up so the firms on t care which prouct they prouce, so long as both firms on t introuce the same prouct. The iea is there isn t enough room in the market for two new crispy cereals or two new sweet cereals. The firms make their ecisions simultaneously without communicating. Firm Crispy Crispy Firm : -5 Firm : -5 Sweet Firm : 0 Firm : 0 Firm Sweet Firm : 0 Firm : 0 Firm : -5 Firm : -5 First check for ominant strategies. What is Firm s best response if Firm chooses crispy? What is Firm s best response if Firm chooses sweet? Choose sweet Choose crispy Does Firm have a ominant strategy? No. Their best response changes epening on their opponent s strategy. What is Firm s best response if Firm chooses crispy? What is Firm s best response if Firm chooses sweet? Choose sweet Choose crispy Does Firm have a ominant strategy? No. Their best response changes epening on their opponent s strategy. Since we on t have any ominant strategies, we ll have to work harer to come up with the solution to this game. While a brut force metho, you can always check manually to see if a certain combination is a Nash equilibrium. Let us try out a couple. Then we ll show you an easier way. 4
73 Econ 500 Game Theory ossibility # - Firm chooses crispy, Firm chooses crispy: Is it a Nash equilibrium? To fin out, check to see if each player is making the best response to their opponent s strategy. Given that firm chooses crispy, is Firm s best response to choose crispy? The answer is no. Firm woul want to change their strategy. That is enough to tell you this is not a Nash equilibrium, but let s pile on. Given that firm chooses crispy, is Firm s best response to choose crispy? The answer is no. Firm woul want to change their strategy. Again, this is not a Nash equilibrium. ossibility # - Firm chooses sweet, Firm chooses crispy: Is it a Nash equilibrium? Again, to fin out, check to see if each player is making the best response to their opponent s strategy. Given that firm chooses sweet, is Firm s best response to choose crispy? Yes. They on t want to change their strategy. Given that firm chooses crispy, is Firm s best response to choose sweet? Yes. They on t want to change their strategy. Neither wants to change. Firm choosing sweet an Firm choosing crispy is a Nash equilibrium. You try out the other two possibilities. ossibility #3 - Firm chooses sweet, Firm choosing sweet ossibility #4 - Firm chooses crispy, Firm chooses sweet 5 In this game, there are two Nash equilibria both involve one firm choosing crispy an the other firm choosing sweet. How o we know which one will happen? In a strict game theory sense, we on t. But let s go outsie the game an think about the real worl. This is a game about coorination. What might we epect the firms to o in this case? erhaps one firm will sen out a press release that says they are introucing a sweet cereal. This woul be an inication to the other firm that they shoul choose sweet. Might this have something to o with trae group meetings? 6 Technically, the press release woul have change the game from a simultaneous move game to a sequential game. More in a bit. For now all we can say is that we have a coorination problem. Asie: Is there an easier way to fin Nash Equilibria? There is. ut yourself in the shoes of Firm for a moment. Now, suppose you know Firm was going to choose crispy. ut a circle aroun your best response. (I ve labele this.) Now, suppose you know Firm was going to choose sweet. ut a circle aroun your best response. (I ve labele this.) Now, put yourself in the shoes of firm for a moment. Imagine you know Firm is going to choose crispy. ut a circle aroun your best response. (I ve labele this 3.) Now imagine you know Firm is going to choose sweet. (I ve labele this 4.) ut a circle aroun your best response. If you have a combination of strategies that has two circles (one inicating player s best response an the other inicating player s best response), that combination of strategies is a Nash Equilibrium. See below. 5 ossibility 3 is not a Nash Equilibrium, while ossibility 4 is a Nash Equilibrium 6 This game is similar, but not eactly the same as the coorination game between the husban an wife involving the opera an theatre. See below. 5
74 Econ 500 Game Theory Firm Crispy Crispy Firm : -5 Firm : -5 Sweet Firm : 0 Firm : 0 4 Firm Sweet Firm : 0 Firm : 0 Firm : -5 Firm : -5 3 You shoul try out this trick on the prisoner s ilemma game above. Confirm the Nash equilibrium is for both to confess. This is a bit quicker that trying them all out. Beach Location Moel You an a competitor plan to sell stuff on a beach that is 00 yars long. The left sie of the beach is labele 0; the right sie of the beach is labele 00. Customers on the beach are sprea evenly across the beach an will choose the closest venor because each venor s prouct is assume to be ientical. Each venor chooses where to locate. What is the Nash equilibrium of the game? To write own the game chart for this game woul take a very long time. You coul locate at 0,,, 3,, 98, 99, 00, as coul your opponent. However, you can solve this game pretty simply. Consier you locating at 5 an your opponent locating at 6. Is this a Nash equilibrium? Given you are locate at 5, is it your opponent s best response to locate at 6? Yes. You will capture all the customers locate from 0 to 5 (those customers on the far left of the beach) but your opponent will capture all the customers from 6 to 00 (everyboy else) an enjoy toasty profits. Given that your opponent is locate at 6, is it your best response to be locate at 5? No. You be better to move to 7, an thereby capture all the customers from 7 to 00, leaving your opponent to serve only those customers from 0 to 6. Therefore, you locating at 5 an your opponent locating at 6 is not a Nash equilibrium. If you were at 7, your opponent woul want to move to 8. If your opponent were as 8, you want to move to 9. An so on The only Nash equilibrium to this game is for both of you to locate as close to the center of the beach as possible. Only then woul neither of you have an incentive not to move only then woul you have a Nash equilibrium. Tetbook BS? Why are fast foo restaurants, gas stations, car ealerships, an hospitals (?) locate right net to each other? It might be zoning, but it might be game theory. The implications for politics are clear an important. If the ots below are George Bush, Ralph Naer, at Buchannan, an Al Gore, which ot is which? Why weren t Ralph an at nominate? After the primary is over, which way shoul George Bush move? Which way shoul Al Gore move? Does an incumbent presient that oesn t face a serious primary challenger have an avantage? Liberal Conservative 6
75 Econ 500 Game Theory Employee Monitoring Game The story here is the workers can either work har (work) or be lazy (shirk). The manager can either check up on the employee to see if they are working (monitor) or not (on t monitor). When we i this in class we use W an L, but we just as well can use an -. If the manager monitors a worker that was alreay working, the worker wins an the manager loses (wastes time monitoring an employee that was working). If the manager monitors a worker that was shirking, the workers loses an the manager wins. If the manager oesn t monitor a worker that was working, the manager wins an the employee loses (the worker coul have gotten away with shirking). Lastly, if the manager oesn t monitor a worker that wasn t working, the manager loses an the employee wins. All this boils own to the foiling game: Manager Work Monitor Manager: - Worker: Don t Monitor Manager: Worker: - Worker Shirk Manager: Worker: - Manager: - Worker: First, check for ominant strategies. You ll fin there is none. Do the circle trick or write them out. What is the manager s best response if the worker works? What is the manager s best response if the worker shirks? What is the worker s best response if the manager monitors? What is the worker s best response if the manager oesn t monitor? Don t monitor Monitor Shirk Work Now, check for Nash equilibrium. There are none. Don t believe me? ick any combination, for eample, the worker monitors an the worker works. Is it a Nash equilibrium? Given the worker is working, manager s best woul be on t monitor the manager woul want to change their behavior. You ll fin if you pick any other combination, it too, will not be a Nash equilibrium. How then o we solve the game? What woul be the outcome? The best answer here is that the boss shoul ranomly monitor the worker. If the worker knows when the boss will be monitoring, the monitoring won t be effective. However, if the worker oesn t know the boss will be monitoring, the effort level may increase all the time. When ranomness is involve, the solution is calle a mie strategy equilibrium (as oppose to a pure strategy equilibrium). You on t nee to remember the terminology, but it might help to have the iea of the solution of the game. What oes this have to o with the real worl? I argue that monitoring employees is pretty real worl. Lance Armstrong, we ll be having a rug test net week. DUI checkpoints? Auiting theory? oker? Bluffing all the time is a ba iea. But so is not bluffing all the time. 7
76 Econ 500 Game Theory rouct Choice, Revisite Another new one we in t iscuss in class. Thus far, games have been playe simultaneously. You can have more fun if players take turns (sequential games). Revisit the cereal game, only this time let s have the firm take turns. To make things a bit more interesting, let s suppose the sweet cereal prouct is more esirable (higher profits) than the crispy prouct. However, if both firms introuce the same prouct, both will lose money. Check out the payoffs an game below. The numbers in the payoffs are again profits. With sequential games, we have to be more careful about who is choosing when. We start on the left. First firm chooses. Then firm chooses. If firm chooses crispy, firm s choices are given on the upper portion of the game tree. If firm chooses sweet, firm s choices are given on the lower portion of the game tree. crispy Firm : -5, Firm : -5 crispy Firm chooses sweet Firm : 0, Firm : 0 Firm chooses sweet crispy Firm : 0, Firm : 0 Firm chooses sweet Firm : -5, Firm : -5 To solve sequential games, work backwar (use backwars inuction). If Firm fins it self on the upper portion of the game (if firm has chosen crispy), what will they o? They will choose sweet (0 in profits rather than -5). If Firm fins it self on the lower portion of the game (if firm has chosen sweet), what will they o? They will choose crispy (0 in profits rather than -5). A goo way to solve these games is to bol the choices we epect firm to make an basically eliminate choices we on t epect firm to make. We bol in the ones they will make an ignore the others. See below. 8
77 Econ 500 Game Theory crispy Firm : -5, Firm : -5 crispy Firm chooses sweet Firm : 0, Firm : 0 Firm chooses sweet crispy Firm : 0, Firm : 0 Firm chooses sweet Firm : -5, Firm : -5 Now, given that firm anticipates firm s choices, firm will choose sweet (knowing firm will react by choosing sweet), resulting in firm earning 0 in profits. (If instea, firm ha chosen crispy, firm woul have chosen sweet, an firm woul have earne only 0 in profits.) See below. crispy Firm : -5, Firm : -5 crispy Firm chooses sweet Firm : 0, Firm : 0 Firm chooses sweet crispy Firm : 0, Firm : 0 Firm chooses sweet Firm : -5, Firm : -5 The outcome of the game will be Firm chooses sweet, firm chooses crispy. In fact, we say that Firm choosing sweet an firm choosing crispy is a sub-game perfect equilibrium. Notice the first mover avantage. By choosing first, Firm ensures 0 in profits (by choosing the lucrative prouct). This is why there is sai to be a first-mover avantage. Real worl? Firms that are the first to introuce proucts may reap rewars. Ipos? See Besanko. (In)Creible Threats Suppose Firm tol firm that no matter what firm ecie, firm was going to introuce the sweet cereal. Firm woul be trying to convince firm that it woul prouce sweet cereal, in hope that firm woul introuce the crispy cereal. If successful, firm woul get the 0 in profits instea of 0. 9
78 Econ 500 Game Theory Woul the threat be creible, however? That is, woul firm believe that Firm woul carry through on its threat? robably not. Because if firm chose sweet, firm woul be face with choosing crispy an earning 0 in profits or choosing sweet an losing 5 in profits. It is very unlikely firm woul o this. The threat is not creible. 7 Therefore, Firm shoul again choose sweet. I am always remine of the horrifying roa trips I took when my mother threatene to turn this car right aroun if I in t stop throwing twizzlers at my sister (usually about 600 miles from home). Those threats were not creible. I wish they were - I have thrown more twizzlers. See the assignment. Sub-game erfect Equilibrium It is pretty har to come up with a goo efinition of a sub-game perfect equilibrium. One tetbook suggests it is a Nash equilibrium where no player can improve at any stage of the game. I m not sure there is much value in wrangling over the efinition. Here is what is important, though. If you use backwars inuction, an have each player choose optimally in any sub-game (any ecision that they might possible face), the result of oing backwars inuction is a sub-game perfect equilibrium, an an outcome that is highly likely. Infinitely Repeate Games Thus far, we have seen a number of prisoner s ilemma style games where the cheating outcome prevaile even though there was a cooperative outcome that woul have been better for the participants. However, this has occurre in one-shot games. We like to change the story now by having the same players repeately interact with one another. When we play repeate games, we assume that the game is playe once a time perio (once a year). Time perio 0 refers to the current perio, time perio refers to the perio year from toay, an so on. As I m sure you know, ollars in the future are not the same as ollars toay, so we ll have to ivie by a iscount factor. Firms will want to maimize the iscounte present value of payoffs to the firm. Letting π stan for the payoff, i stan for the interest rate, an subscripts numbering the year, we have: V π = π i π + π ( + i) ( + i) ( + i) ( + i) T π 4 π T It also turns out there is a math trick the formula for perpetuity. As long as the payments are the same amount, the first payment comes one year from toay, an the payments are repeately infinitely (forever), the formula for the present value simplifies: 8 7 If somehow Firm coul become the first mover an introuce the sweet cereal before firm ecie, that woul be a ifferent story in fact a ifferent game an not the game being playe here. 8 If you check Baye s book, they give you a slightly ifferent formula. They are assuming the first payment + i is coming toay (t = 0). In that case, the formula is V = π which is foun by taking i epression I have, aing π, an simplifying. 0
79 Econ 500 Game Theory V π π π π π = = + i 3 4 ( + i) ( + i) ( + i) i Trigger Strategy We know that when prisoner s ilemma games are playe as one-shot game, the Nash equilibrium is for each player to cheat. But with repeate games, folks might o better. In orer to iscuss trigger strategies, you might fin it is helpful to translate your game s options into cooperating an cheating. In the contet of the prisoner s ilemma proper (two people locke up in separate cells), cooperating was to not confess while cheating was to confess. In the contet of the cartel game, cooperating was choosing the high price while cheating was choosing the lower prices. With repeate games, there is a possibility the players can o better than repeately choosing to cheat. One such possibility is a trigger strategy. The basic iea of trigger strategy is to choose the cooperative strategy so long as your opponent also plays the cooperative strategy. If, however, at any time your opponent plays the non-cooperative strategy, this triggers you to switch to the cheating strategy, forever. You never return to the cooperative strategy. Figuring Out If Trigger Strategies Are rofitable: Begin by assuming that each player has agree to play the trigger strategy. Is it an equilibrium? That is, oes anyone have the incentive to change his or her strategy? Either you can continue to play the cooperative strategy, or you can cheat. If you continue to play the cooperative strategy, you will repeately get the payoff associate with the cooperative outcome. If you cheat, you will receive a larger payoff toay (how much?), but you will receive a lower payment in the future (how much lower?) Therefore, if the trigger strategy is going to work (if we are to successfully leave the outcome where both players cheat), the iscounte present value of the cooperative outcome forever must be higher than the present value of the one-time gain from cheating an the cheating outcome forever after that. See the assignment, an later the solutions. Repeate Games with a known en I upe you folks a bit on the assignment. It is sai that with repeate games, if the en perio of the game I known with certainty, the game can unravel to the etent that neither player will ever cooperate. The reason cooperation works in the infinitely repeate game is because there is a cost to cheating. When someone eviates from the trigger strategy, they receive the one-time game from oing so. But the eviation results in the loss of all the incremental payments that woul have occurre if they cooperate instea of cheate. That is, they lose the ifference between the present value of the cooperative outcome forever an the present value of the cheating outcome forever. With low enough iscount rates, the cooperative outcome can occur.
80 Econ 500 Game Theory Consier a game that will be playe eactly 5 times. You might think that a trigger strategy might work. But consier the incentives in the 5 th (last perio). 9 In the 5 th perio, there is no future. There is no cost to cheating, as there is no future cooperation to consier. At this point, the game is a one-shot game, an each will cheat in the 5 th perio. But now, consier what happens in the 4 th perio. Given that each player knows the other will cheat in the 5 th perio, is there any cost to cheating in the 4 th perio? Again there is no future an there is no cost to cheating in the 4 th perio. So each player will then cheat in the 4 th perio. An then the 3 r perio. An it continues on up to the st perio. So the story is, in a game with a known en, cooperation is very unlikely to occur. This cause much iscussion in class. Some of you on t buy it suggesting that cooperation might occur. You might be right. However, I will say this. The trick on sequential games is to go backwars. What I can say is that the subgame perfect equilibrium in a repeate game with known en is to cheat every perio (in the contet of a trigger strategy). Does this have anything to o with firms firing employees who give their two weeks notice? If you are not offene by somewhat crue han gestures, click on the link below to see my t-shirt. Way too much buil up for you to be impresse now. Don t forget about T. My t-shirt iea Repeate Games with unknown en This bit originally appeare as an announcement on BB. Something that came up after class - regaring the result that some of you in't like about repeate games with known ens. The story on the repeate games was that if the last perio is known, each player will have the incentive to cheat in the last perio, an thus have the incentive to cheat in the perio before that, an so on, until the game unravels an each person cheats throughout. Remember, to solve sequential games, you nee to work backwars. The sub-game perfect equilibrium is to cheat the whole time. A caveat. A game theoretician woul tell you that this is the equilibrium in the game. As I sai, my unergrauates ten to cooperate for a while, but they usually pull the trigger before the last perio. I'm not convince that people woul unravel to the etent to which the game theory guys say they woul. But nonetheless, the iea is meaningful. An maybe some time, we can talk about tit-for-tat. But I igress... On to the new part... There is another way to get cooperation without having the game infinitely repeate you might fin appealing. Instea of playing the game once a year for ever an ever, we can imagine a situation where we play toay, an there is a probability (less than one) that we play again tomorrow. So instea of Coke an epsi being aroun forever, we can say there is a probability that the two companies will be aroun tomorrow an play again. That means there is a probability they will be aroun the year after that. So long as there is a sufficiently high probability that the game will be playe again, we can get cooperation. Repeating, even if we know there is say a % chance the game will not be playe net perio, 9 In game theory notation, the last perio is usually inicate by a T (a capital T). Don t forget this point if you look at my t-shirt!
81 Econ 500 Game Theory we can still get cooperation. The reason this make sense is because with a probabilistic en to the game, the players on't *know* eactly when the game will en (until after it actually ens). When they are in the last perio, they on't *know* they are in the last perio. An thus they can't cheat in the last perio. erhaps that is more realistic an more intuitive that thinking of infinitely repeate games. I on't like thinking about infinite amounts of times. Coke an epsi won't be aroun until the en of time, but there is a very high probability they will both be aroun tet time. The iscounting we ha in our problem / ( + i) isn't that much ifferent from the probability the game will continue. In fact, instea of having to calculate the iscounte present value of the future games, we coul instea just calculate the epecte value of the future payments - the payments multiplie by the probability they occur. They are both numbers less than one, an as we go out further into the future, they are going to be raise to higher an higher powers. Just as when the interest rate rises it makes players less likely to cooperate (because it "shortens" the future or makes those future payments less valuable), when the probability the game will *not* be repeate increases (it "shortens" the epecte future or makes those future games less likely), players will be less likely to cooperate. As the probability the game will en becomes (the probability the game continues is zero), we are back to a one-shot game an cheating becomes certain in (the only) first perio. That tibit is actually iscusse in Baye's book if you want to take a closer look - but I shoul probably have talke about that in class tonight. 3
82 Econ 500 Game Theory Appeni More Games You ve Seen Baggage Rea the intro to Baye s Chapter 0, then his commentary on the answer at the en of Chapter 0. The basic iea is that it woul be goo for the inustry to limit carry-ons to epeite the boaring process, but if one airline took action unilaterally, they likely be penalize. This is a stanar prisoner s ilemma game. Cooperating is to aopt tighter stanars, while cheating is to stick with the current stanars. Airline A Current Current A: 0 B: 0 Tighter A: -5 B: 5 Airline B Tighter A: 5 B: -5 A: B: You shoul confirm that the Nash equilibrium is for both airlines to choose current. How can cooperation occur? Airlines call up the FAA an ask them to enforce cartel or cooperation by manating that all airlines have the tight stanar. Tetbook BS? Many of the most effective cartels we know in the Unite State (where other cartels are illegal) are actually enforce by government. The American Meical Association restricts the number of octors, increasing wages of octors. The city of New Orleans restricts the number of taicab by requiring a license (an limits the number), increasing wages of cabbies. Major League Baseball restricts the number of teams, increasing ticket prices. Restrictions on shrimp catches? rouct Quality Also clippe out of Baye. Consumer Low Quality Don t Buy C: 0 F: 0 Buy C: -0 F: 0 Firm High Quality C: 0 F: -0 C: F: Confirm that Nash equilibrium is Don t Buy, Low Quality, an again we have a prisoner s ilemma game. How can we get cooperation? If the game is repeate. The temptation is for the firm to take the one-time game for cheating. Any behavior that reuces this gain from cheating woul make cooperating more likely. We know from before low iscount rates will help. But there are other things, outsie the game, that are pertinent. Might this be where firms avertise an create bran name capital? Spen lots of money on signs? Don t these actions serve as ways to increase their cost of cheating? 4
83 Econ 500 Game Theory Cartel, ricing Game In class, our original presentation of the prisoner s ilemma game use these payoffs. Firm A Last things Low Low A: 0 B: 0 High A: -0 B: 50 Firm B High A: 50 B: -0 A: 0 B: 0 Go watch the princess brie for yet another lesson on game theory. Recall that scene about which glass of wine has the poison? Secon, if you haven t, rea Baye s chapter 0. It occurre to me about 3 hours into writing these notes I have just recreate the chapter, an one so less thoroughly than Baye.. Finally, if you have some more time, rea Besanko, Chapter 7. He has a lot to say about commitments an threats. If you are intereste in managerial strategy proper, you ll like it. 5
84 Econ 500 Oligopoly Moels (Cournot, Bertran) Strategic Interactions between Firms Thus far, we have looke mostly at two etreme cases. On the one han, we ha perfect competition. Firms took the market price as given an acte as though they coul sell as much as they wante at the market price. In some regar, a firm in t have to pay much attention to what its rivals were oing. On the other han, we looke at monopolists. By efinition, they ha no rivals. Again, a monopolist in t have to worry about what its rivals were oing either. What we will o net is take a look oligopoly a situation where there is a small number of firms. Here, strategic interactions between firms will be important. Cournot Duopoly Moel Assumptions: Two Firms (Duopoly) Barriers to Entry Decisions are mae on the basis of prouction Of course, the market price will epen on total prouction (of both firms) Each firm will treat the other firm s output level as given when eciing what to prouce Decisions are mae simultaneously roucts can be homogeneous or heterogeneous Suppose the overall market inverse eman is given by = 30 Q. Q = Q + Q. That is, the total quantity of output prouce is the sum of the output that is prouce by firm (Q ) an the output prouce by firm (Q ). For the moment, we imagine that both firms marginal cost of proucing is 0. (MC = MC = 0). What we want to o first is come up with Firm s reaction function. It will tell us how firm will react to various output levels firm will choose. Below I will walk you through how to fin it. We will fin a few spots on the reaction function. Then we will connect the ots. Keep in min, we are just figuring out best responses. We re oing game theory. oint #: Suppose Q = 0. In this case, Firm has the whole market eman curve to itself. The firm will act like a monopolist. We know how to answer this question from before. You coul rewrite the eman curve = 30 Q. If = 30 Q, then MR = 30 * Q. The firm sets MR= MC. In this case, MC = 0. Setting MR = MC (or MR = MC ) gives us: 30 Q = 0 Q = 30 Q = 5. So, if Q = 0, firm will choose Q = 5. Firm s best response to firm proucing nothing is to prouce 5 units.
85 Econ 500 Oligopoly Moels (Cournot, Bertran) 30 5 D oint # MR 5 30 MC Q Suppose Q =. We have to o some thinking here. If Firm has alreay prouce units, the price never be higher than $9 ( = 30 Q = 30 = $9). If firm were to prouce 0, the price woul be $9. If firm were to prouce, the price woul fall to $8. If firm were to prouce, the price woul fall to $8. If firm were to prouce 9 units, the price woul fall to $0 (there woul be 30 total units prouce). It as though firm s eman curve is the market eman curve, scoote over by the unit firm has prouce. The epression for this eman curve is = 9 Q MR D D MC Q But now, the firm is a monopolist with this remaining portion of the eman curve. What oes the firm o? Set MR = MC. MR = 9 * Q. MR = MC 9 * Q = 0 * Q = 95 Q = 4.5 So if Q =, firm one chooses Q = 4.5. Notice, that as a result of Q increasing by unit, Q ecreases by 0.5 units. Or state ifferently, firm s best response to firm increasing their prouction by unit is to reuce their prouction by half a unit.
86 Econ 500 Oligopoly Moels (Cournot, Bertran) oint #3 We coul keep going forever. This one we in t talk about in class. Suppose Q = 5. If Firm has alreay prouce 5 units, the price will never be higher than $5 ( = 30 Q = 30-5 = 5). If firm were to prouce 0, the price woul be $5. If firm were to prouce, the price woul fall to $4. If firm were to prouce 5, the price woul fall to zero (there woul be 30 total units prouce) MR D D MC Q It as though the firm s eman curve is the market eman curve, scoote over by the 5 units that firm has prouce. The epression for this eman curve is = 5 Q. But again, the firm is a monopolist with this remaining portion of the eman curve. MR = 5 * Q. What oes firm wish to o? MR = MC 5 * Q = 0 * Q = 5 Q = 7.5 So if Q = 5, firm one chooses Q = 7.5. oint #4 Another we in t talk about in class, but a nice point. Suppose Q = 30. If firm has alreay prouce 30 units, the price has alreay been riven own to 0. Firm will not want to prouce at all. So if Q = 30, Q = 0. Firm s reaction function. ut it all together. It seems like we have been going on for ays, but we can finally raw a picture of Firm s reaction function. The reaction function is a curve (or algebra) that tells us how Firm woul react to various quantities that Firm woul prouce. We connect the ots on the 4 points we foun above. It turns out it is a nice straight line. Watch the labels on the aes. Q on the horizontal, Q on the vertical. In fact, there is an algebraic epression as well. I ll show you how in a page or two. Q = 5 ½ * Q A very common mistake is to label the vertical ais on t o this! 3
87 Econ 500 Oligopoly Moels (Cournot, Bertran) It seems Firm s reaction function starts (when Q = 0) with Firm acting like a monopolist, an then ecreases by a ½ unit for every etra unit of output firm prouces, until firm prouces so much output that firm no longer wants to prouce. Don t lose track of the enpoints! Q Firm is riven out of the market by firm 30 Firm s reaction function 6 5 Firm is a monopolist with the whole eman curve Q What about Firm s reaction function? Same rill. If Q = 0, Firm reacts by acting like a monopolist. Thus, Q = 5. If Q =, Firm acts as though its eman curve is = 9 Q. It acts like a monopolist with the remaining eman curve an chooses Q = 4.5. If Q = 5. Firm acts as though its eman curve is = 5 Q. It acts like a monopolist with the remaining eman curve an chooses Q = 7.5. If Q = 30. Firm chooses Q = 0. Déjà vu, anyone? Connect the ots. We can epress this algebraically as well: Q = 5 ½ Q. Firm s reaction function starts with the monopoly level of output an ecreases ½ a unit for every one etra unit Firm prouces. We graph it on the same graph with Firm s reaction function below. 4
88 Econ 500 Oligopoly Moels (Cournot, Bertran) Q 30 Firm s reaction function 5 Equilibrium 0 Firm s reaction function Equilibrium Q So know we know how each firm reacts to the other, but what will happen? Suppose Firm assumes Firm will prouce some ranom amount, say 3 units? Firm s reaction function says Firm will want to prouce 3.5 units: Q = 5 ½ * Q = 5 ½ * 3 = 3.5. Now if Firm s optimal response to firm proucing 3.5 is to prouce 3 units, we have ourselves equilibrium. But what oes Firm want to o if Firm prouces 3.5? Q = 5 ½ * Q = 5 ½ * 3.5 = 8.5 So this is not an equilibrium. What oes Firm want to o now given Firm is proucing 8.5? Q = 5 ½ * Q = 5 ½ * 8.5 = But what oes Firm want to o now that firm is choosing 0.875? Q = 5 ½ * Q = 5 ½ * = 9.56 We re getting closer an closer. If you keep going, you ll fin there is only one spot where each firm s reaction is consistent what that of the other firm. You ll get closer an closer to the points where the reaction functions intersect, which happens to be where Q = 0 an Q = 0. This will be the equilibrium. Take a look at the picture above. Notice, Firm s reaction function says if Q = 0, then firm will choose Q = 0: Q = 5 ½ * Q = 5 ½ * 0 = 0 Firm s reaction function says if Q = 0, then firm will choose Q = 0. Q = 5 ½ * Q = 5 ½ * 0 = 0. It is a Nash Equilibrium because each firm is making the preferre response to what the other firm is oing, an their responses are consistent with one another. The outcome of the Cournot Moel is always foun where the reaction functions intersect. 5
89 Econ 500 Oligopoly Moels (Cournot, Bertran) Can you fin the numerical answer? Once you have the reaction functions, you stick one into the other, o the algebra, an you can fin the answer. In this case, Q = 5 ½ * Q. Q = 5 ½ * Q. Start with Firm s reaction function Q = 5 ½ * Q. Now substitute in for Q Q = 5 ½ * Q = 5 ½ * (5 ½ * Q ) Q = 5 ½ * 5 + ¼ * Q ¾ * Q = 7.5 Q = (4/3) * 7.5 Q = 0 Now, use Firm s reaction function to fin Q. Q = 5 ½ * Q = 5 ½ * 0 = 5 5 = 0 What else can we o? If you keep in min that the reaction function is basically forme by connecting the ots between (i) the level of output the firm woul choose if it were a monopolist - an - (ii) the level of output that rives own below MC you can figure out lots of stuff. Suppose Firm s MC increases to $ MC MR D Q 6
90 Econ 500 Oligopoly Moels (Cournot, Bertran) What woul happen if firm prouce nothing? Firm woul again act like a monopolist MR = MC 30 * Q = 0 Q = 0 Q = 0 So now if Q = 0, Q = 0 How much woul Firm have to prouce now to rive Firm out of the market? If price gets own to MC, there will be no profit for Firm. Where oes the eman curve run into the MC curve? At Q = 0. So now, if Q = 0, firm chooses Q = 0. Compare the new reaction function to the ol reaction function. As a result of an increase in Firm s MC, the reaction function shifts (in a parallel fashion) towars the origin. In fact, it is still the monopoly output minus ½ a unit for every unit firm prouces. See picture below. Q 30 0 Firm s reaction function (ol) Firm s reaction function (new) Q Finally, stick put both firms together, an you can see the results of Firm s MC increasing (while Firm s remains the same). You sell that Firm will en up proucing less, while firm will en up proucing more. See picture below. This shoul jive with your intuition the firm with a cost avantage shoul capture a larger share of the market than the firm with a cost isavantage. Q 30 Firm s reaction function Equilibrium (new) 5 Equilibrium (ol) Firm s reaction function 5 30 Q 7
91 Econ 500 Oligopoly Moels (Cournot, Bertran) What are other changes I can make? By similar logic you shoul be able to confirm: A ecrease in Firm s MC of proucing will shift Firm s reaction function away from the origin. An increase in Firm s MC of proucing will shift Firm s reaction function towars the origin. A ecrease in Firm s MC of proucing will shift Firm s reaction function away from the origin. An increase in the eman for the prouct will shift both firms reaction functions away from the origin. A ecrease in the eman for the prouct will shift both firms reaction functions towars the origin Things for later How oes the overall profit level of the two firms at the Cournot equilibrium compare to the profit level if the firm was a monopoly? If the firms were competitive? We ll o this with the net eample. Bore? Figure out the answer to eactly how much output will be prouce after Firm s MC increases to 0. What is epression for Firm s new reaction function? Firm s reaction function is unchange. Just stick in Firm s reaction function into Firm s new reaction function an solve for Q. Then use firm s reaction function to fin Q. You shoul fin Q = 3.33 an Q = 3.67, an = $3. Aing MC to Cournot -- an a Shortcut Suppose we use the same eman curve we use in the previous lecture, but now go from having no marginal costs to a situation in which each firm has positive marginal costs. Suppose we now have: = 30 Q MC = MC = $0 Now the question is how much will each firm prouce? You coul go through the whole process in eveloping each firm s reaction function. First we assume Q = 0 an then ask what firm will prouce. Firm will of course act like a monopolist an set MR = MC. Because = 30 Q, MR = 30 Q, an setting MR = MC gives us 30 Q = 0. Doing the math leas us to Q = 0. An on an on we go If Q = 0, Q = 0 But it turns out, thankfully, there is a short cut. Suppose we more generally epress the inverse eman curve as follows: = a b * Q Also, let c represent the marginal cost of proucing for firm an c represent the marginal cost of proucing for firm. In our current case, a = 30, b =, c = 0, an c = 0. See the footnote below for another eample, which is worke out to the bitter en. If the inverse eman curve were given by = 60 3Q an MC = $6 an MC = $8, than a = 60, b = 3, c = 6, an c = 8. 8
92 Econ 500 Oligopoly Moels (Cournot, Bertran) You coul show that firm s reaction function is: a c Q = * Q b An firm s reaction function is: a c Q = * Q b I ll write this info own on the test for you. It looks like a mess, but it is not that complicate. We foun before that for every one unit firm prouces, firm will want to prouce ½ a unit less. That is the secon term in firm s reaction function. We also know that if firm prouces nothing, firm will act like a monopolist with the whole eman curve. But what is a c? It is the amount of output firm will prouce if it is a monopolist. In the b current case it is 30 0 = 0. So all that epression is telling you is that firm s reaction function is firm s monopoly level of output less ½ a unit for each unit the other firm prouces. The logic woul be eactly the same to figure out firm s reaction function. Solving for the equilibrium level of output If you plug an chug, you ll fin: a c 30 0 Q = * Q = * Q = 0 * Q b (Firm s reaction function) a c 30 0 Q = * Q = * Q = 0 * Q b (Firm s reaction function) Once you get to the point where you have each firm s reaction function, you can solve for the equilibrium level of output by plugging in Firm s reaction function into firm s reaction function. First write own firm s reaction function. Because Q = 0 ½ * Q, we can substitute 0 ½ * Q in for Q. 3 Q = Q Q = 0 Q = 5 = 4 3 * Q Q = *(0 4 Q * 5 = 6.67 * Q ) Be careful on the math here. A common mistake is to get the sign wrong on the ¼ Q. Now use Firm s reaction function to fin Q. Q 0 = * Q = 0 * 6.67 = = 6.67 After you rea the rest of these notes, you shoul be able to confirm that Q = 9 ½ * Q, Q = 7 ½ * Q. Q = 7.33, Q = 3.33, Q = 0.67, = 8, Rev = 05.33, Cost = 44, rofit = 6.33, Rev = 93.33, Cost = 60, rofit = eople who like math this is a system of two equations with to unknowns. There are many ways to solve this system. They will all yiel the same result. 9
93 Econ 500 Oligopoly Moels (Cournot, Bertran) Now, we can fin a couple of other bits of information: If Q = 6.67, an Q = 6.67, Q = = 30 Q = = $6.67. Firm s revenue = * Q = $6.67 * 6.67 = $. Firm s costs = c * Q = 0 * 6.67 = $66.67 Firm s profits = $. - $66.67 = $44.44 Firm s revenue = * Q = $6.67 * 6.67 =$. Firm s costs = c * Q = $0 * 6.67 = $66.67 Firm s profits = $. - $66.67 = $44.44 Total profit of both firms (inustry) = $88.88 Want some practice? See the previous footnote. What happens if = 60 3Q, MC = $6, an MC = $8. The answers are in the footnote. How oes this compare to a perfect cartel? If the firms forme a perfect cartel, together they woul have agree to act as a monopolist an ivvie up the profits. In this case, Q = 0, = 0, revenue = $00, costs = $00, profit = $ They on t get cartel profits, but competition oesn t rive own profits to zero either. If they split prouction own the mile, each firm coul prouce 5, so each firm earns revenue of $00, has costs of $50, an profits of $50. 0
94 Econ 500 Oligopoly Moels (Cournot, Bertran) Bertran Duopoly Now, a ifferent moel of oligopoly calle the Bertran Moel. Again, looking a the strategic interactions between firms. This one is much easier to solve, as you ll see in a secon. First, the assumptions: Two Firms (Duopoly) Barriers to entry Decisions are mae on the basis of price (compare this to Cournot) Of course, the market price will epen on total prouction Each firm will treat the other firm s price as given (compare this to Cournot) Decisions are mae simultaneously roucts are homogeneous or heterogeneous Consumers will purchase only from the low-price proucer 4 Before you continue, go back to the top of these notes an compare the assumptions here for the Bertran moel to those of the Cournot moel. erhaps a goo eample of an inustry characterize by Bertran woul be two gas stations on the same corner of some intersection. The signs tell consumers the prices of gas they can clearly see which firm is offering the lower price. It seems at least somewhat reasonable (more later) that consumers will fin the two stations gas as homogeneous an thus will buy gas from the station offering the lowest price. Now, consier = 30 Q, MC = MC = $0. Let s consier a case where the goos are completely homogeneous. 5 What is the equilibrium? Suppose you rival firm chooses a price of $0. 6 What is your best response? By the assumptions of the moel, by choosing a price of $9.99, you will capture the entire market an earn large profits. Recall that we ve assume that all consumers will purchase from the low price provier. You woul have a powerful incentive to unercut your rival s price. But is this an equilibrium? What woul your rival s best response be to you charging $9.99? They woul wish to charge $9.98. An so on How low can the price go? The equilibrium of the game is for each firm to choose a price equal to MC. Why? If you were charging $0, an your rival was charging $0, neither of you woul have an incentive to change your price. This is a Nash Equilibrium. If your rival was charging $0, if you increase your price to $0.0, you woul lose all of your business, so clearly there is no incentive to o so. If your rival was charging $0 an you lowere your price to $9.99, you woul capture all of the business, but you woul be losing money as < MC. There in no incentive to lower your price. (You be earning 0 economic profits at $0.00) Therefore, the equilibrium of the game is for each firm to choose = MC. 4 If proucers choose two ifferent prices, the low-price proucer will capture the entire market an the high-price proucer will sell nothing. If they choose the same prices, we assume the firms will split the market evenly. 5 I think you ll be able to work through the basic implications of how the moel woul be ifferent if there were not true after you rea these notes. 6 A bit ifferent starting point than in class. It oesn t matters so much, but let s start with a price of $0, which is what a collusive cartel woul like to pull off.
95 Econ 500 Oligopoly Moels (Cournot, Bertran) What else can we figure out for the Bertran Moel? Because firms will be charging = MC ($0), we can figure out how much output will be prouce. = 30 Q 0 = 30 Q Q = 0 When both firms are charging the same price, we assume the firms split the market evenly. Because 0 total units are being prouce, Q = 0, Q = 0. Firm s revenue = * Q = $0 * 0 = $00.00 Firm s costs = c * Q = $0 * 0 = $00.00 Firm s profit = $00 - $00 = $0 Firm s revenue = * Q = $0 * 0 = $00.00 Firm s costs = c * Q = $0 * 0 = $00.00 Firm s profit = $00 - $00 = $0 Total profit of both firms = $0 This is a moel where consumers are very prince sensitive an firms compete intensely on the basis of price. It takes only two firms competing to rive own prices to the perfectly competitive level. Big icture Take this moel, an any other moel, with a grain of salt. Go back to the assumptions an consier the implications if they on t match the real worl. The point of the Bertran moel is with very price sensitive consumers an easy information about prices, there woul be healthy price competition. However, one of the assumptions is that all consumers will choose the firm with the lowest price. That is, if one gas station charges $.83 per gallon an the other charges $.8, the secon station will capture all the business. Is that realistic? What woul happen if the secon gas station oesn t have enough capacity to capture all the market, perhaps because it oesn t have enough pumps causing people to have to wait in line? Woul the first firm lose all of its business? Of if one station was on the other sie of a busy street? What woul happen if the goos each firm was selling weren t perfectly homogeneous (perfectly substitutable)? Might this eplain why firms that might be subject to Bertran conitions willingly unergo costs to ifferentiate their proucts? What if these firms play a repeate game? That is, they play this game ay after ay after ay? Are they more likely to resist the temptation to reuce prices? All of these changes woul lessen the cutthroat nature of the price competition an woul likely result in higher prices, lower output levels, an higher profit levels. Nonetheless, the moel is suggestive.
96 Econ 500 Oligopoly Moels (Cournot, Bertran) Comparisons One of the reasons we went through the math of the Cournot Moel with = 30 Q an MC = MC = $0 was so that we coul compare all three moels (cartel, Cournot, Bertran) given the same eman curve an ientical costs conitions. = 30 Q, MC = MC = $0 (Monopoly) = 0 Q = 0 Inustry profit = $00.00 erfect Cartel = 0 Q = 0 Inustry profit = $00.00 Cournot = 6.67 Q = 3.33 Inustry profit = $88.88 Bertran = 0 Q = 0 Inustry profit = $0 (Competition) = 0 Q = 7 Inustry profit = $0 While Cournot isn t a perfect cartel, it clearly results in a relatively high price, a relatively low quantity, an relatively high profits. Bertran, with just two firms competing vigorously on the basis of price rives own prices to competitive levels. What shoul I rea? You might rea Baye for the verbal escription of Cournot, but they go crazy with isoprofit curves that on t a anything. I stick with my notes. Baye takes you through reaction functions for the Bertran moel with ifferentiate (non-homogeneous) proucts if you are aventurous. Besanko iscusse both, but oes so in a cursory fashion. 3
97 Econ Bunling Bunling Bunling is the practice of selling two or more goos as a package. The eamples an figures for this set of notes are clippe right out of the tetbook. The story is about MGM, which when it istribute the films Gone With the Win (GWW) an Getting Gertie s Garter (GGG), it sol them as a bunle. The numbers in the table below will represent each theatre s reservation price for each film the maimum amount they woul be willing to pay (for the right to show the firm at their theatre). Eample - bunling oesn t increase revenue GWW GGG Theatre A $000 $4000 Theatre B $0000 $3000 Sell films separately GWW: GGG: rice = $,000, Q = (only theatre A), Revenue = $,000. rice = $0,000, Q = (both theatres), Revenue = $0,000. If the firm was to charge a single price, it will charge $0,000. rice = $4,000, Q = (only theatre A), Revenue = $4,000. rice = $3,000, Q = (both theatres), Revenue = $6,000. If the firm was to charge a single price, it will charge $3,000. Combine, the stuio woul enjoy revenue of $6,000. Bunle the films (sell as package) Now consier bunling the goos that is, selling a package of the two movies. GWW GGG Bunle Theatre A $,000 $4,000 $6,000 Theatre B $0,000 $3,000 $3,000 It stans to reason that Theatre A woul be willing to pay $6,000 ($,000 + $4000) for a bunle, while theatre B woul be willing to pay $3,000 ($0,000 + $3,000). Bunle: Comparison rice = $6,000, Q = (only theatre A), Revenue = $6,000 rice = $3,000, Q = (both theatres), Revenue = $6,000. If the theatre were to bunle the movies, the stuio woul enjoy revenue of $6,000. In this case, bunling oesn t increase revenue. The stuio collects the same revenue whether it bunles at a price of $3,000, or sells GWW for $0,000 an GGG for $3,000 (separately). Each results in $6,000 of revenue.
98 Econ Bunling Eample - bunling increases revenue GWW GGG Theatre A $0000 $4000 Theatre B $000 $3000 Sell films separately GWW: GGG: rice = $,000, Q = (only theatre B), Revenue = $,000. rice = $0,000, Q = (both theatres), Revenue = $0,000. If the firm was to charge a single price, it will charge $0,000. rice = $4,000, Q = (only theatre A), Revenue = $4,000. rice = $3,000, Q = (both theatres), Revenue = $6,000. If the firm was to charge a single price, it will charge $3,000. Combine, the stuio woul enjoy revenue of $6,000. Bunle the films (sell as package) Now consier bunling the goos that is, selling a package of the two movies. GWW GGG Bunle Theatre A $0,000 $4,000 $4,000 Theatre B $,000 $3,000 $5,000 Theatre A woul be willing to pay $4,000 for a bunle, while theatre B woul be willing to pay $5,000. Bunle: Comparison rice = $5,000, Q = (only theatre B), Revenue = $5,000 rice = $4,000, Q = (both theatres), Revenue = $8,000. If the theatre were to bunle the movies, the stuio woul enjoy revenue of $8,000. In this case, bunling increases revenue above what woul be earne by charging a single price. Here, bunling increase revenue by $000. Why oes bunling work here an not in the previous eample? In the first eample, the reservation prices of the theatres were positively correlate. Theatre A was willing to pay more for both movies than was Theatre B. In the secon eample, the reservation prices of the theatre were negatively correlate. Theatre A was willing to pay more for GGG, but it was Theatre B that was willing to pay more for GWW. It is easier to see the negative correlation graphically that to escribe it verbally. We raw a picture, an put a persons (theatre s) reservation price for goo (R ) on the horizontal ais an the reservation price for goo (R ) on the horizontal ais. Then we can see if these reservation price combinations are positively or negatively correlate.
99 Econ Bunling First eample unprofitable to bunle positively correlate Secon eample profitable to bunle negatively correlate R R $,000 $0,000 $,000 $0,000 $3,000 $4,000 R $3,000 $4,000 R Again, if it is the case that person with the higher reservation one goo is the person with the lower reservation price of the other goo, it will be profitable to bunle. Consier cable or satellite TV. Here you purchase a bunle. The channel I woul pay the most for is ESN my reservation price is high for ESN. I on t much care for A&E my reservation price is low. But Dish Network oesn t know this. I also bet it is the case that people who really like A&E on t really care for ESN. Dish Network oesn t have to figure out who is who, just charge a bunle price. Where, then, o we epect to see bunling? We epect bunling in situations where consumers have heterogeneous eman curves an where firms can t fin an easy way to price iscriminate. (If Dish Network knew I really like ESN, it might tell me that ESN costs $3 a month). In the theatre eample, perhaps some theatres will cater to a crow that woul like GWW, while other theatres will cater to a crow that likes GGG, but the theatre can t tell which is which. The more closely negatively correlate are the reservation prices, the more profitable bunling will be as a pricing strategy. When you get to the tetbook, you might enjoy the section calle bunling in practice. Mie Bunling We often see in the real worl, not only bunling, but a situation where the bunle is available but the goos are sol separately as well. This is calle mie bunling. Consier the following situation with four customers whose reservation prices for two goos are picture below. 3
100 Econ Bunling R c = 0 A B C 30 c = 30 0 D R There is a lot going on there. We have four customers, an their reservation prices are perfectly negatively correlate. We ll confirm below, but (pure) bunling will be more profitable than charging a single price. We are also aing costs of prouction to the mi. The graph above inicates that marginal cost of proucing goo is (constant an) equal to $0, while the marginal cost of proucing goo is (constant an) equal to $30. Sell goos separately: Goo : = $90, Q = Revenue = $90, Costs = $0, rofit = $60 = $60, Q =, Revenue = $0, Costs = $40, rofit = $80 = $50, Q = 3, Revenue = $50, Costs = $60, rofit = $90 (maimum profit) = $0, Q = 4, Revenue = $40, Costs = $80, rofit = -$40 Goo : = $90, Q = Revenue = $90, Costs = $30, rofit = $60 (maimum profit) = $50, Q =, Revenue = $00, Costs = $60, rofit = $40 = $40, Q = 3, Revenue = $0, Costs = $90, rofit = $30 = $0, Q = 4, Revenue = $40, Costs = $0, rofit = -$80. Total profit from selling goos separately is $50 (when = $50, = $90) ure Bunle: = $00, Q = 4, Revenue = $400, Costs = $00 (the bunle costs $50 to prouce), rofit = $00 As epecte, pure bunling increase profits, as reservation prices are negatively correlate. Mie Bunle: Offer both a bunle an the goos separately. = $89.95, Q =, Revenue = $89.95, Cost = $0, rofit = $69.95 = $89.95, Q =, Revenue = $89.95, Cost = $30, rofit = $59.95 Bunle = $00, Q =, Revenue = $00, Costs = $00, rofit = $00 Total profit from mie bunling is $9.90 ($ $ $00). Notice this is higher than the profits from pure bunling. 4
101 Econ Bunling Why the Etra rofits? Where o the etra profits from mie bunling come form? Take a look at consumer D. Uner pure bunling, the consumer woul pay $00 for the bunle. Recall the consumer s reservation price for goo is $90, while their reservation price for goo is $0. The marginal cost of proucing goo, which is involve in proucing the bunle, is $30, an ecees the reservation price for goo. It is almost as though the consumer is purchasing the bunle an (nearly) throwing away goo. If the firm were to offer goo separately, at a price just below $90 (so the consumer has just a small amount of consumer surplus ), they coul collect all the surplus on goo an avoi proucing goo. Doing so causes the firm to lose $0.05 in revenue (they woul have gotten $00 from the bunle), but saves $0 in costs. This causes profits to increase by just less than $0. Intuitively, the firm oesn t want to spen money proucing the goo if the consumer will throw it away. Likewise, the firm will target consumer A to purchase only goo. Consumer A has a very low reservation price of goo, one which is less than the marginal cost of proucing goo. The firm will be better off offering a price just below consumer A s reservation price of goo ($89.95) an selling only goo to consumer A. It costs the firm a bit $0.05 of revenue again (they woul have gotten $00 from the bunle), but saves $30 in costs by not having to prouce goo, which is almost thrown away. This causes profits to increase by just less than $0. R c urchase only goo. R > c, but R < c. urchase bunle reservation price of each goos ecees cost of proucing urchase only goo. R > c, but R < c. c D R More eamples of bunling? Cable, etra value meals at McDonals, buffets, option packages on cars (I ha to buy the CD player to get the sun roof), tuition at universities (I woner how much you woul pay for Econ 3 sol separately), halloween cany variety packs, season ticket packages, etc. What shoul I rea? You ve got to stick with my notes here neither or your books like this iea. When the bunle is price at $00, the consumer is left with no consumer surplus. If the single goo was price at eactly $90, the consumer woul also be left with no consumer surplus. The consumer woul be inifferent between buying the bunle or buying the single goo. By lowering the price to $89.95, we have given the consumer surplus of $0.05, which (hopefully) ensures the consumer will purchase the single goo, not the bunle. (In a practical setting, maybe more than a nickel woul be require.) 5
102 Econ Notes on st an n Degree rice Discrimination st Degree rice Discrimination The iea of first-egree price iscrimination is to charge every customer his or her eact reservation price. For this reason, st egree price iscrimination is sometimes calle perfect price iscrimination. If pulle off successfully, the consumer will have no consumer surplus this is because each consumer has pai his or her entire reservation price. As a practical matter st egree price iscrimination is relatively unlikely to be observe in the real worl. This is because the firm must be able to ientify the reservation price of each consumer eactly. This requires a ton of information. That being sai, it is a bit more likely to be observe when consumers purchase only a single unit of the goo (as oppose to a situation in which the typical consumer purchase multiple units of the goo more below). Eample: To simplify the interpretation of the eample below, let us go ahea an assume that each customer purchases only one unit of the goo. Therefore, ifferent spots on a market eman curve represent ifferent consumer s reservation prices. 3 Check out the table below, an the picture that follows the table. Each epicts the same information. Consier first the table. By saying at = $9, Q =, what this means is that there is one consumer who is willing to pay no more $9 for a unit of the goo. Look at the graph an fin that ot on the eman curve that represents that consumer. Back to the table. By saying at = $8, Q =, we can iscern there is a secon consumer who is willing to pay no more than $8 for a unit of the goo. An of course, a ot on the eman curve represents that consumer in the graph. By saying at = $7, Q = 3, we can figure there is a thir consumer who is willing to pay no more than $7 for a unit of the goo. An another ot. rior to learning about price iscrimination, we woul have given the firm only the option to charge all customers the same price. They coul charge everyone $9, everyone $8, everyone $7, an so on. If the price was $9, the firm woul sell, if the price was $8, the firm woul sell, an at a price of $7, the firm woul sell 3. In fact, you coul calculate MR, an fin the optimal price the firm woul charge uner these conitions. In fact, you efinitely shoul o this. 4 If you ve forgotten, consumer surplus is the gap between the amount consumers are willing to pay (their reservation price) an the amount they have to pay. If a consumer is charge their reservation price, consumer surplus is zero. It is helpful to consier situations where st egree price iscrimination occurs (or firms attempt to o so). Eamples inclue car salespersons, accountants (thing ta return preparation fees), attorneys, etc. It shoul be reasonable clear in the case of accountants an lawyers why these professionals might have a large amount of information about the consumers reservation price. 3 While the interpretation changes just a bit, the basic story is unchange even if you consier the situation where the firm is charging one customer ifferent prices for multiple units of the goo. More below 4 While the math oesn t come out nice here, the firm will prouce 4 units an charge a price of $6. Why Q = 4? At Q = 4, MR > MC, so surely the firm woul prouce the 4 th unit an you be incline to think the firm woul prouce more. But we know the firm will not prouce the 5 th unit because MR < MC (MR
103 Econ Notes on st an n Degree rice Discrimination Now on to st egree price iscrimination. If, an it is a big if, the firm coul ientify which consumer was which that is, if the firm coul ientify the reservation price of each consumer when they walke up to the store, the firm coul increase revenue by charging each consumer their reservation price. So what is the optimal pricing strategy uner these conitions, given the numerical eample below? Q MC $ $9 $0.5 $8 $0.50 $7 3 $0.75 $6 4 $ $5 5 $.5 $4 6 $.50 $3 7 $.75 $ 8 $ $ 9 $.5 Or equivalently, the graphical epiction? D Q MC The answer is to charge the st consumer $9, the secon consumer $8, the 3 r consumer $7, an so on. Where oes the firm stop? Where the price is equal to MC. The firm coul charge the 7 th consumer (Q = 7) a price of $3, which still ecees MC ($.75). Doing so woul increase the firm s profit level by $.5. Notice on the 8 th unit, = $ an MC = $, so proucing this unit will not increase profits, but we ll say go ahea an prouce this last unit. = $ an MC = $.5). Let s not worry about proucing half units here perhaps we are ealing with tables (as oppose to gallons of milk that are ivisible). With Q = 4 an = $6, total revenue is $6 * 4 = $4, total costs is $0.5 + $ $ $ = $.50, an profit = $.50.
104 Econ Notes on st an n Degree rice Discrimination You shoul also be able to see why the firm woul not want to sell to the 9 th consumer at a price of $. 5 Given that we ve settle on Q = 8, we just a up revenue (an then costs) by aing up the iniviual prices on each unit (an then iniviual marginal costs on each unit). Total Revenue is $9 + $8 + $7 + $6 + $5 + $4 + $3 + $ = $44 Total cost is $0.5 + $ $ $ + $.5 + $.50 + $.75 + $.00 = $9 rofit = $44 - $9 = $35 Notice, compare to the firm that charges only one price, the firm has higher profits uner st egree price iscrimination. That is, st egree price iscrimination is profitable. Also note, each consumer has no consumer surplus. Finally, the firm prouces more than a firm that charges only one price. Real Worl Difficulties As mentione in a previous footnote, this woul be ifficult to pull off ue to the informational requirements. The firm woul nee to know each customer s reservation price. An yet, it is a nice starting point for our analysis, an it is the ieal to which firms strive to achieve. Reucing consumer surplus to zero results in the highest possible profit level for the firm. But even though the information requirements are heroic, this is to a large etent, what car salespersons try to o. The more information firms have about the reservation prices of consumers, the more likely they will be to pull this off. Accountants that have just prepare a ta return have some serious information on how much their customer is able to pay. Estate planning lawyers? Don t wear your Role when you go to buy a car. Financial ai offers? How o they know what families can pay? Getting a bit more realistic, given their limite information, firms will try to approimate st egree price iscrimination. We ll focus on n egree an 3 r egree price iscrimination net these are not as profitable as perfect ( st egree price iscrimination), but are still more profitable that charging a single price. Before we get into these, let s take a step back. There are at (at least) two ways in which a firm coul st egree price iscriminate. Case # Each customer purchases one unit of the goo, an thus ifferent customers have ifferent reservation prices, an firm attempts to charge each customer their reservation price. This is what we assume at the beginning of these notes, to simplify the interpretation. (Recall we consier a case where a consumer purchase only one unit of the goo.) Thus, each ot on the eman curve represente a ifferent consumer. Case # Consumers are ientical, but they have ifferent reservation prices for ifferent quantities of goos. Consier electricity. You might be willing to pay more for the st unit of electricity (to run your refrigerator) than you woul for the X th unit of electricity (to run your hair ryer). The firm coul attempt to charge your (ifferent) reservation price for each iniviual unit (e.g. $4 for the st unit of electricity, $3.50 for the n unit,, $0.0 for the X th unit of electricity). In that case, the chart, an the ots on the eman curve reflect that one consumer s ifferent reservation prices for ifferent units of the goo. When the firm can t quite pull off case #, but has some information on ifferent customer s ifferent willingness to pay, but can only separate customers roughly into two groups with ifferent elasticities, we 5 Of course, = $ an MC = $.5, so proucing this unit woul reuce the firms profit by $.5.
105 Econ Notes on st an n Degree rice Discrimination call this imperfect form (yet still profitable) of price iscrimination 3 r egree price iscrimination. You ve alreay one the math on that one. When the firm can t quite pull off case #, but has some information on the average customer s ifferent willingness to pay for varying units, we call this imperfect form (an yet still profitable) of price iscrimination n egree price iscrimination or block pricing. 3 r Degree rice Discrimination See the notes on 3 r egree price iscrimination n Degree rice Discrimination Again, the iea here is to charge an average (or representative) consumer ifferent prices of ifferent units of the goo. This is sometimes calle block pricing, an it really not much ifferent from a bulk iscount. In aition to the general ifficulties with knowing reservation prices, even if the firm coul o this perfectly, the firm woul literally have to charge ifferent prices of each unit of the goo. The list of prices on your power bill woul be very long. So the iea is to set up some blocks some segments where the price changes. There will be separate prices for separate blocks, but not a separate price for each an ever unit. 6 My impression is that, an this will bother you folks some in preparing for an eam, that there is no har an fast rule where to select these blocks or for that matter, how many of them there shoul be. Nonetheless, the iea will be to use information on the eman curve when etermining the prices for a given size block. This gets a lot trickier with non-ientical consumers. However, you ll get the main iea from the eample below. Say I split the eman curve in to blocks of size. What woul be the best price for the st two units? The eman curve (see the chart or graph above) tells me to sell units, the price can be no higher than $8. To sell 4 units, the price can be no higher than $6. To sell 6 units, the price must be no higher than $4. To sell 8 units, the price must be no higher than $. So the firm coul offer the following pricing scheme: $8 for the st two units, $6 or the net units, $4 for the net units, an $ for the net units. 7 If it oes so, the firm woul sell 8 units. Total revenue = $8 * + $6 * + $4 * + $ * = $40 Total cost is = $0.5 + $ $ $ + $.5 + $.50 + $.75 + $.00 = $9 rofit = $3 rofit is better than charging a single price, but not as goo as perfect price iscrimination. 6 Another way the firm coul pull this pricing strategy off woul be to offer say a -pack of coke for $.50 per can, a 6-pack of coke for $0.50 per can, a -pack of coke for $0.33 per can. When we combine the elements of Case # an Case #, this pricing strategy can also separate costumers that purchase infrequently vs. those that purchase frequently. However, to make a point about the traeoff between profits an the number of blocks, Coke oesn t want to offer the 7-pack, 8-pack, 9-pack, 0-pack, etc. T comes in the single roll, the 4-pack, but there is no 3-pack. 7 Or say $6 for a -pack, $8 for a 4-pack, $36 for a 6-pack, $40 for an 8-pack.
106 Econ Notes on st an n Degree rice Discrimination The firm capture much, but not all of the consumer surplus. See the picture below, where revenue is shae. (With st egree price iscrimination, revenue woul have been all of the area below the eman curve) D Q MC You coul try out figuring out the optimal prices for blocks of 3 units. You ll have to be a bit careful on the 3 r block. More While the math gets tougher with non-ientical consumers, you o see a goo bit of this pricing scheme out there in the real worl. Electricity is price this way, we o see 6-packs an -packs with ifferent prices (though there is an element there of separating ifferent types of consumers there). If you get a chance (not on the test), rea about two-part pricing in your book. This is the scheme where firms capture consumer surplus by charging an entry-fee an then a per-unit fee. Both can etract some consumer surplus. Eamples here inclue country-club memberships (yearly fee + green s free) an even cover charges at bars. Instea of changing the price of a beer on Friay night, they charge a cover charge on Friay night to etract some consumer surplus. What shoul I rea? Baye iscusses this in Chapter.
107 Econ 500, rice Discrimination Shortcuts A ricing Rule of Thumb Many times, a firm won t have an estimate of the entire eman curve, but they will have a pretty goo iea of their elasticity, an have a pretty goo iea of the marginal cost of proucing. If so, they can come up with an optimal price. How woul a firm know its elasticity? This coul be from trail an error, past eperience, feel, or perhaps something like an iea of a Rothschil ine an an inustry level elasticity. Some economist types have one some math for us. They ve foun out that + E MR = EF F Where E F is the firm level elasticity. It seems like its out of thin air, but it really is just math. We know something alreay about how the elasticity of eman changes along a linear eman curve. You really know what is going on. Remember a picture similar to this from the notes on elasticities? E = (perfectly elastic) Q, elastic E Q, = (unit inelastic) at the mipoint of the eman curve inelastic E Q, = 0 (perfectly inelastic) MR Q When the elasticity for the firm is - (the mipoint of the eman curve), we know that MR = 0. We can confirm from our formula above: + E F + MR = = = EF If the elasticity is -, we have: 0 = + E F + MR = = = 0.5* E = F So MR is half as large as price. Let s keep scooting up the eman curve. If the elasticity is -0, we have: + E F MR = = = 0.9* E = F 0 0 So MR is 90% of price. Keep scooting If the elasticity if -00 (very near the vertical intercept), we have: 0
108 Econ 500, rice Discrimination + E F MR = = = 0.99* E = F Now, we know for firms with market power (monopolists, monopolistic competition), that these firms set MR = MC. + E MR = EF Now solve for. + E EF F F = MC EF = MC = MC + E F Ok that is important. EF = MC + E F is our pricing rule of thumb. It says that the price selecte by an optimizing firm with market power is a simple mark-up over MC, where the mark-up epens on only one thing the elasticity of eman at the firm level. Again, if you know your firm s MC an know the elasticity, you can set optimal prices without having to hire an economic consultant to estimate the whole eman curve. Let us apply it. Suppose E F = -. In this case, the firm shoul charge a price ouble its marginal cost: E F = MC MC = MC = * MC E = + F + Suppose E F = -4. In this case, the firm shoul charge a price 33% above its marginal cost: E F 4 4 = MC MC = MC =.33* MC E = + F Keep this in min when we later iscuss price iscrimination. In the secon case, where the eman is more elastic (more sensitive to prices), firms charge a lower price (a smaller mark-up). Technically, this works for perfectly competitive firms as well. A perfectly competitive firm faces an infinitely elastic eman curve for their prouct. If you plug in infinitely (or a super large number not quite as big as infinite), you ll fin that MR =, eactly what we foun for a perfectly competitive firm. Not sure you notice, but this formula oesn t work well when the absolute value of the firm level elasticity is less than one (e.g. -0.5). But recall, a firm will never choose a spot where the eman curve is inelastic. We know this because if the firm were to raise the price, it woul increase revenues an ecrease costs (less woul be purchase), thus increasing profits. It will not stop until the eman curve becomes at least unit elastic (MC = 0) an likely until the elasticity is elastic (so long as MC > 0).
109 Econ 500, rice Discrimination st Degree rice Discrimination [Insert Discussion of st Degree rice Discrimination Here] 3 r Degree rice Discrimination 3 r Degree rice Discrimination involves charging ifferent prices to ifferent customers even though the marginal cost of serving these customers is the same. The iea is that ifferent groups of consumers might have ifferent sensitivities to price (ifferent elasticities of eman). If so, it might be wise to increase the price to the consumers who are more insensitive to price an reuce the price to the consumers who are more sensitive to prices. In fact, we will show that using 3 r egree price iscrimination will lea to higher profits for firms that using this pricing strategy. Eamples: Classic eamples are business travelers vs. leisure travelers when it comes to airline tickets. Who is less sensitive to prices? Business travelers are. Who pays higher prices? Business travelers. Another classic eample is senior citizen (or stuent) iscounts at the movie theatre. As seniors (stuents) are more sensitive to prices, they will pay lower prices than aults. Requirements to 3 r Degree rice Discriminate To successfully pull off this type of price iscrimination, the firm nees to have three characteristics: () it must have some market power (it is not a perfectly competitive firm) () it must be able to separate consumers into groups (that have ifferent price elasticities of eman) (3) it must be able to prevent resale amongst groups The economics of this one aren t that tough. Suppose I tol you there were two groups, call them group an group. Suppose you in t know anything about these two groups ecept the fact that the marginal revenue you woul get from selling an etra unit to group was $7, while the marginal revenue you woul get from selling an etra unit to group was $3. Is the firm choosing wisely? No. If the firm was to sell one less unit to group, the firm woul lose $3. But if the firm sol one more unit to group, the firm woul gain $7. Costs woul be unchange, because the firm is still proucing the same number of units. But switching a unit of the goo from the low MR group to the high MR group woul increase revenue (an profits). Of course, any time this situation was true (where MR MR ), the firm woul have the incentive to rearrange output between the two groups. Thus, eventually, the firm will want to choose where the marginal revenue of both groups is equal. That is, the firm shoul choose where MR = MR. Now, suppose we ve solve this problem, so MR = MR = $7, but MC is only $3. What shoul the firm o in this case? rouce more output for both groups. When shoul the firm stop overall? When MR = MR = MC. Eventually, we will be looking of a situation where MR = MR = MC. Long Drawn Out Numerical Eample of 3 r Degree rice Discrimination Suppose one firm is the only firm that sells tickets for a concert (it has market power). Suppose market research has ientifie that stuents an professors have ifferent eman curves (ifferent elasticities of eman). How shoul the firm price to take avantage of price iscrimination? Suppose we know that the eman curve for stuents is given by: 3
110 Econ 500, rice Discrimination Q S = 00 4 S An the eman curve for professors is given by Q = 500 Suppose the MC of selling tickets to both groups is 0. What are the optimal prices for the firms to charge the two groups? The firm shoul fin a spot where MR = MR = MC. Because the MC of servicing each group are equal, the firm will en up at setting MR = MC an MR = MC. 3 First, for the stuents. Start with the eman curve. Then figure out the inverse eman curve an MR. Q = S S = 00 S Q S 00 4 Q 4 S S = = 50 4 Q S That is the inverse eman curve. Now we can fin MR by multiplying the coefficient on Q by : MR = 50 S Q S Now set MR = MC : S S 50 Q S Q = 50 Q Q S S S = 0 = *50 = 00 lug this value into the inverse eman curve to fin the price: S = 50 4 QS = 50 *00 4 = 50 5 = 5 Now calculate revenue: REV S = S * QS = 5*00 = 500 Now for the professors. Again start with the eman curve an fin the inverse eman curve: Q = = 500 Q 500 Q = = Q 3 Because MR an MR are both equal to MC, we know MR = MR. 4
111 Econ 500, rice Discrimination Now use the inverse eman curve to fin MR: MR = 00 5 Q Set MR = MC 50 Q = 0 Q = 00 5 Q Q 5 = *00 = 50 lug into the inverse eman curve to fin the quantity: = 00 Q 5 = 00 * 50 5 = = 50 Calculate revenue: REV = * Q = 50*50 =,500 So overall, by selling to the group separately, we collect $5,000 worth of revenue, $,500 coming from professor an $500 coming from professors. Notice we charge a higher price ($50) to professors than we o to stuents ($5). Can this be isplaye graphically? Yes, with a bit of a trick. We have two eman curves an two marginal revenue curves, so the picture can get pretty crowe, so we ll use the trick of flipping over one set of curves. Start with stuent eman. It is rawn on the right sie of the graph below. Imagine flipping over the eman curve an marginal revenue curve to the left sie of the graph. If you only ha the left sie, you still what is going on.. 50 Q D 00 MR MR D 00 Q 5
112 Econ 500, rice Discrimination 50 Q D 00 MR 00 Now, we ll leave stuents on the left sie (backwars) an raw the professors eman curve on the right sie of the graph an the MR curve for professors as well Q S MC S D S 00 MR S MR 50 D 500 MC Q Fining the answer graphically is much easier. MR = MC for professor occurs at Q = 50. rofessor will pay a price of $50. MR = MC for stuents occurs at Q = 00. Stuents pay a price of $5. Notice that even though the groups of consumers are paying ifferent prices ($50 an $5), at the quantities ultimately selecte by the firm, MR for each group is equal ($0 in both groups). Is 3 r Degree rice Discrimination more profitable than charging a single price? What we have one thus far is show what price an quantity the firm will charge each group if it chooses to price iscriminate. What we nee to show is that if the firm price iscriminates, it will have higher profits than it oes if it oes not price iscriminate. This is a bit more involve. Aing together eman curves: If the firm can charge only one price, we have to a the two eman curves together. Let s let the letter T represent the total quantity emane (or market quantity emane). At prices above $50, though, tickets will be sol only to professors. In this case, the market eman curve woul be given by Q T = T, which is simply the same eman curve we ha for professors, only it is relabele. Of course, the inverse eman curve woul be given by T = 00 (/5) * Q T an the MR curve woul be given by MR T = 00 (/5) * Q T. 6
113 Econ 500, rice Discrimination At prices below $50, we must a the eman curves together, as both stuents an professor will be purchasing tickets. Here, a bit of a math trick. We take the professor eman curve Q = an the stuents eman curve Q S = 00 4 S an a them together. Because we are charging both groups the same price, we relabel using T to enote the total. As crazy as it seems, that gives you the epression for the overall eman curve. Q = Q + Q = = T S T T T Don t believe me? Let s confirm this fact. Let s first plug an chug assuming the formula is right (it is). rices of $0 an $50 seem interesting. I ll also try out $5, an also $6. Why $6? By comparing what happens at $6 to what happens at $5, we can see what happens when the price increases by $. T = 0, Q T = 700 T = 5, Q T = 475 T = 6, Q T = 466 T = 50, Q T = 50 An because it will come in hany, let s plug an chug for each price on the stuent an professor eman curve S = 0, Q S = 00 = 0, Q = 500 T = 0, Q T = = 700 S = 5, Q S = 00 = 5, Q = 375 T = 0, Q T = = 475 S = 6, Q S = 96 = 6, Q = 370 T = 0, Q T = = 466 S = 50, Q S = 0 = 50, Q = 50 T = 0, Q T = = 50 Notice, at each price, is you simply a up Q S an Q, you o get what our formula says. In fact, all our formula i was a up the quantities. An one more thing to make us feel like the aing up trick is working. When increases by $ (e.g. from $5 to $6), the stuents purchase 4 fewer units. When increases by $ (e.g. from $5 to $6), the professor purchase 5 fewer units. Doesn t it stan to reason that when increases by $, the total quantity sol (so long as we re on the lower portion of the eman curve) will fall by 9 units? Souns right to me. Isn t that eactly what the epression Q T = T tells us? D T 9 = 700 T Q T D S D A If we solve for the inverse eman function here, we get 700 Q 7
114 Econ 500, rice Discrimination T T 700 QT = 9 9 = Q 9 T So now, we have two chunks of the eman curve: the upper part (just the professors), for prices above $50, an the lower part (where both professors an stuents are purchasing tickets). At prices above $50, the relevant MR curve woul be the one base on the professors eman curve only But at prices below $50, the relevant MR curve woul be the one base on aing up the two eman curves. 00 MR 500 D D T 700 Q D T MR T D 700 Q Combing this information, the effective MR curve is the combination of the upper portion of the re marginal revenue curve (professor s eman) an the lower portion of the blue marginal revenue curve (the combine eman curve). Finally, we set this MR curve to MC, which is 0. We o en up on portion of the eman curve below $50, where the firm is selling to both professors an stuents. 8
115 Econ 500, rice Discrimination MR T D T MC Q 700 Back to the math... Now that we know the firm will operate where < $50, we know the important MR curve for the will be the one on the lower portion of the market eman curve (where < $50). Because we know the eman curve, we can use our stanar trick of multiplying the coefficient on Q by to fin MR: T = Q T MR = T Q T Setting MR = MC : T T Q T Q = Q Q T T T = 9 = *77.78 = Net, stick into the inverse eman curve to get price (using the combine curve): T = QT = *350 9 = = Finally calculate revenue: REVT = T * QT = 38.88*350 = 3,608 9
116 Econ 500, rice Discrimination Big icture Stuff Notice with a single price, the firm collects only $3,608, while when price iscriminating, the firm collecte $5,000. In both cases there are 350 units of prouction as well (so it is not a sneaky consequence of having MC = 0). rice iscrimination is more profitable. But on t forget about the conitions. The firm must be able to ientify groups with ifferent elasticities. Also notice that the two ifferent groups may feel ifferently about how they feel about price iscrimination. If there is only one price charge, everyone pays $ There woul be a lot of tickets sol to professors, but not so many stuents buying tickets. With price iscrimination, the price pai by stuents ecreases to $5, which is goo for stuents, thus more stuents will en up going to the show. However, the price pai by professors increases to $50, not so goo for professors, an fewer professors will en up going to the show. rofessors woul prefer there is no price iscrimination, while stuents are mae better off. Don t forget that the firm has to be able to prevent resale. If the firm offers a iscount to one group, an can t prevent people buying at the iscounte price an reselling to the other group, it won t make sense to price iscriminate. Airlines o this with your name on the ticket. The ivie consumers into groups by requiring Saturay night stays an giving iscounts to those who book travel far in avance (both not likely to be easy for business travelers). Movie theatres make stuents an seniors whip out the IDs. They also print stuent or senior on the tickets so that other can t use these tickets. Why oesn t it work at Blockbuster? 0
117 Econ Notes on Signaling Here is what I have one. I have starte with the notes I give to my Econ stuents when I iscuss averse selection. At the en of the ay, I want you to focus on the signaling moel, but also have a general unerstaning of the asymmetric information. Let me translate signaling will efinitely be on the final, while general asymmetric information / averse selection Econ stuff is just backgroun. Asymmetric Information Econ Style Typically, even when we haven t been very eplicit about it, we have been assuming that both buyers an sellers in a market have the same information about the quality of the proucts they have been buying an selling. However some situations arise where the buyers an sellers have asymmetric information one party knows more about the quality, say, of a goo that is being sol. The classic eample is a use car. The seller of the use cars knows more about the car than the potential buyers. They know if the car is a goo car (a plum ) or a ba car (a lemon ). What are the implications of asymmetric information? Suppose buyers are willing to pay $4000 for a plum an $000 for a lemon. Suppose buyers assume that if they buy a car, there is a 50/50 chance they will get a plum, a 50/50 chance they will get a lemon. Without knowing what type of car they will get, they might be willing to pay perhaps $3000 for a use car. Now, suppose you re selling a car. You see the going price for use cars is $3000. Are you more likely to offer your car up for sale if it is a plum or if it is a lemon? $3000 is a goo price for a lemon, but not such a goo price for a plum. Other owners of cars woul be making similar calculations. When you go out an look at the types of car that will be on the market at this price o you epect that there will be an equal number of plums an lemons? In fact, we woul epect a large number of lemons an just a few plums (if any). Lemon owners will jump at this price, while plum owners will be less willing to sell their cars. erhaps it will be an 80% lemon, 0% plum split. This is calle averse selection. The cars available for sale on the use market will be an averse group (isproportionately lemons). Will consumers (who though they ha a 50% change of getting a plum) be willing to pay $3000 now? Now there is an 80% chance they will en up with a lemon an only a 0% change they will en up with a plum. Since there is a smaller chance they will get a goo car, the price they will be willing to pay will fall, say to $400. This price will fall may further eacerbate the averse selection problem at a price of $400 even more plum owners to hol back their cars for sale. Eventually, it coul get to the point that many (if not all) of the cars on the use markets will be lemons. So what s the point? With asymmetric information about the quality of cars, we woul epect a isproportionately large number of lemons in the market for use cars. The lemons rive the goo cars out of the use market. The use cars for sale are an averse selection (of all use cars). How o we solve the problem Econ Style How o owners of plums convince sellers that they have a plum? How about offering a money back guarantee? Or a warranty where you agree to pay for repairs? Sellers of a lemon woul not fin these options esirable. While the seller woul receive the plum price, buyers woul realize the car is a plum. The owner woul have to pay for the repairs or give the money back to the consumers. How about paying for epert information? You coul have an epert, in this case a mechanic, take a look at the car an try to etermine the quality. Often people log (an keep receipts) for regular maintenance for the car. You can call up carfa an see if the car has been involve in an accient. In this case, folks are actually literally searching for information to reuce the asymmetric information problem. Information is valuable. Finance types if it bothers you, I am assuming buyers are risk-neutral for simplicity.
118 Econ Notes on Signaling Can reputation (bran names) solve the problem Econ Style? You coul go to a use car ealer who has a reputation at stake. If this ealer sells a bunch of lemons at high prices (claiming they are plums), soon everyone aroun town will know he is a isreputable ealer. Might this be why people who buy cars from strangers through the newspapers seem to often en up with crappy cars? Does a one-time seller of a use car in the newspaper have a reputation at stake? (It is a prisoner s ilemma type game, but a repeate game.) If you think about this further, it oesn t make sense to avertise unless you are a high quality seller. Say you avertise that you sell only plums on your use car lot. If you o in fact to o, consumers will fin plums an be willing to pay high prices for cars. The money you ve spent avertising can be thought of as investment in reputation. If you continue to sell high quality cars, this investment is effective. However, if you avertise an prouce low quality goos, consumers will realize an stop buying cars from you. The money you have spent on avertisement is no longer valuable. Avertising then, can be a signal to potential consumers that you are a high quality proucer. The same goes with signs an Chinese restaurants. The nature of the restaurant business is that it is reasonable easy to close a restaurant in one place an start a new restaurant another place (low sunk costs). So why o I like to eat at Chinese restaurants with big signs outsie the restaurant? If the Chinese restaurant has a big sign that has the name of their restaurant an Thiboau on the sign, I know that this sign has no value if they go out of business an try to set up a new restaurant own the roa. The sign is an investment in their name bran, an it is specific to Thiboau an the name of the restaurant. If they start serving awful foo, that sign is no longer valuable. Whatever money was spent on the sign is lost (the sign is a sunk cost). Given that, woul a firm that was a fly by night operation, epecting to be out of business in 3 months, choose to spen $6000 on a fancy sign? No. Those firms that are spening on signs are signaling quality, as again, it makes no sense to invest money in a low quality reputation. Therefore, you shoul avoi restaurants with carboar signs in the winows! The more epensive the sign, the better, the more specific it is to the current location (says Thiboau), the better it is. Might this be why banks usually have super fancy lobbies? Other eamples of where reputation is important? EBay (why have the system of seller ratings?) Lawyers? An on t forget the en-perio problems. Another Eample (Insurance) Econ Style In the case of use cars, the buyer ha less information than the seller of the car. In this eample, we will have the buyers having more information than the sellers. Consier the market for malpractice insurance. Suppose there are two types of octors, both of whom are consiering purchasing meical malpractice insurance. On type (Dr. Hibbar) is a low-risk octor, who will not have many claims. The secon type (Dr. Nick) is a high-risk octor, who will have many claims. Suppose the insurance companies can t tell who is who. That is, the buyers of insurance (Dr. Nick an Dr. Hibbar) have more information than the insurance companies about what type of octors they are. Suppose Dr. Nick s claims will average $30,000 a year, while Dr. Hibbar s claims will average $4,000 a year, an they both know this. Now, suppose the insurance company sells insurance at a premium of $7,000. I have chosen this amount for if they both buy insurance, the insurance company will collect enough in premiums ($34,000) to just cover the claims (basically we are ignoring the aministrative costs). But if the company charges this price how will the insurance company o?
119 Econ Notes on Signaling The answer is not very well. Dr. Hibbar will not buy the insurance, while Dr. Nick will. The insurance company will collect $7,000 but pay out $30,000 in claims. The insurance company has averse selection issues all of the octors that buy the insurance will be risky octors. What must happen to the premiums? In this case, they must rise to $30,000. It is again calle an averse selection issues because all of the insure octors will be risky octors an averse group. Just as lemons rove plums out of the use car market, the risky octors rove the low-risk octors out of the insurance market. There again is an effort to acquire valuable information on the part of insurance companies. This eplains why your car insurance company is very intereste in collecting information on your riving recor. Your claim history, accients, an speeing tickets will provie companies information about whether you are a low risk river or a high-risk river. Of course, car insurance companies (an meical insurance companies) will charge ifferent prices to ifferent rivers (octors) epening on what they think of your risk profile. But again, the problem arises because of the fact that rivers (octors) have more information about their characteristics than the insurers. More eamples of averse selection Econ Style When lening money, people who are less likely to pay are require to pay higher interest rates. Suppose a lener is fining that they are not oing well at the current interest rate they are not collecting enough to cover the losses on the non-payers. It seems logical to raise interest rates. But wait - coul there be an averse selection problem here? Does averse selection have anything to o with why bloo banks on t pay people for bloo? What woul happen if one price were charge to everyone for meical insurance, regarless of whether they were a smoker or not? Who woul buy insurance? Is there an averse selection problem? Might this be the one of the reasons why insurance is typically offere through your employer? What are the os that everyone who works at Nicholls State is a smoker? Shoul you be ma at the price you pay if you are not a smoker? Or just very healthy? I wrote a blog post once about where some parents of teenagers might willingly put cameras in cars that recore what their kis were up to. Might *not* volunteering to have a vieo camera be put in your car an recor your riving convey information to your insurance company? Use baseball players? If the team that the player is currently playing for is willing to sell the player, shoul you be worrie? The research on this one suggest that pitchers who change teams (are sol ) spen more time on the isable list than pitchers who on t change teams. For simplicity, I am assuming that there is no legal requirement that octor s buy malpractice insurance. 3
120 Econ Notes on Signaling Signaling Econ 500 style One important eample of asymmetric information is when firms ecie which employees to hire. In this case, firms have less information about how prouctive workers might be than the potential employees o. Clearly, if workers just ask potential employees if they are prouctive or not, all but the most honest (or most foolish) will say they are very prouctive. Because it is costly to hire an train workers, an because it might be several months before the firm can truly tell which employees are truly prouctive, it will not pay the firm to hire workers iniscriminately. We nee another solution. The question becomes - is there something that potential employees can o to signal to firms that they are prouctive employees? Consier what happens when you are looking for a job. You can fill out a resume, get recommenation letters, an o some research on the firm. Think about what happens when it is time for an interview. You make sure you ress nicely. This is a signal, but not a very goo one. While prouctive workers will ress nicely, it is easy for less prouctive workers to ress nicely as well. Wearing flip-flops will ensure you will not be hire, but ressing nicely is not enough. We nee something else. One possibility is that employees coul signify that they are highly prouctive by completing college. Let us eplore this iea an make some assumptions to make it more etreme. Suppose for a secon that you o not learn anything of value by going to college, which I hope is a ubious assumption. Is it possible that going to college can make sense if you o not learn anything while you are there? State a bit ifferently, is it possible that going to college coul simply serve as a signal to perspective employees that you are a prouctive employee? Imagine that the firm comes up with a rule that is uses to try to etermine the quality of applicants. The firm assumes that anyone who complete four years of college will be a highly prouctive employee (an will pay this worker a high wage), while the firm assumes that anyone who i not complete four years of college is less prouctive (an will pay this worker a low wage). At the en, we will come back an check to see that the firm s rule matches the facts. This last step will be very important. Let us throw some numbers at this problem. Suppose there are two types of employees. Group I employees are not as prouctive as Group II employees are. Of course, employees know whether they belong to Group I or Group II, but firms cannot tell to which group potential employees belong. Group I Marginal rouct (per year) = unit Group II Marginal rouct (per year) = units rice of rouct = $0,000 rice of rouct = $0,000 Value of Goos rouce (per year) = $0,000 Value of Goos rouce (per year) = $0,000 Career Length = 0 years Career Length = 0 year Value of Goos rouce (career) = $00,000 Value of Goos rouce (career) = $00,000 One possibility is simply to average the two types an pay workers $5,000 a year. This woul be goo for Group I workers but no so goo for Group II workers. In fact, the firm might have an averse selection problem only Group workers woul want to work for the firm. Why? 3 Now, consier using college as a signal. Suppose these ifferent types of workers have ifferent costs of completing four years of school. Both groups pay tuition an fees, have an opportunity cost of going to college, but both groups also have a 3 This is just like a $3000 price for a car. One group fins the price (or wage) esirable, the other oes not. 4
121 Econ Notes on Signaling psychic cost of going to school (think of all the unpleasant parts of going to college). erhaps Group II workers breeze through college an can complete four years of college in four actual years. erhaps Group I workers struggle, have to repeat classes, it takes seven years to complete four years of college, or they just islike oing homework more than Group II worker. To make things concrete, suppose we have the figures below. Group I Group II Cost of completing each year of school = $40,000 Cost of completing each year of school = $0,000 Given the set up, we can compare the costs an benefits of going to college. Workers know that if they complete four years of college, they will have signale to firms they are prouctive workers an will get the higher wage. Recollect that we have assume there is no benefit to going to school ecept that completing four years of school convinces firms that the worker is a prouctive one. If a worker completes four years, then, the firm will assume the employee is highly prouctive, an pay the worker the high wage of $0,000 a year. The employee will earn $00,000 over the course of their career with the firm. If the worker completes less than four year of school, the firm will assume the worker is not prouctive, an will pay the worker the low wage of $0,000 a year. The worker will earn $00,000 over the course of their career with the firm. Combing these two facts, the benefit of attening 4 years of school will be $00,000, whether the worker is truly prouctive or not. Keep in min the benefit of going to college is the aitional earnings that the worker gets ($00,000 - $00,000). It is the gap between the wage pai to Group II an the wage pai to Group I. 4 The cost of going to college epens on whether you are a Group I worker or if you are a group II worker. The cost of completing four years of college if you are a Group I worker is $40,000 for each year for a total of $60,000. Does it make sense, then, for Group I workers to go to college? Shoul the worker incur $60,000 worth of costs for $00,000 worth of etra earnings? No. In fact, Group I workers will not go to college. Now check the math for a Group II worker. The cost of completing four years of college if you are a group II worker is $0,000 for each year for at total of $80,000. Does it make sense for Group II workers to go to college? Shoul the worker incur $80,000 worth of cots for $00,000 worth of etra earnings? Yes. In fact, Group II workers will go to college. So take a step back. Recall the firm use college as a signal. It assume that workers that i not go to college were Group I workers an workers that i go to college were Group II workers. This is just what happens. Group I workers o not go to college an Group II workers o go to college. The firm sees a worker that has not gone to college, assumes they are a Group I worker, an the firm is correct. The firm sees a worker that has gone to college, assumes they are a Group II worker, an the firm is correct. The firm s assumptions are correct. Thus, college can serve as a signal. Is this real or just tetbook BS? Surely, you learn something valuable in college. However, almost as surely, part of what is happening with you going to college is that you are signaling to perspective employers that you are prouctive. How am I so sure? eople who complete four years of college in the 4 Completing the st, n, or 3 r year of schooling has no benefit specifically because we have assume that nothing is learne in college. In this eample, the only reason to go to college is to signal to firms that you are prouctive. Because the firm thinks worker that complete four years of college are prouctive, three years has no benefit. Likewise, by the same argument, there is no reason to complete the 5 th or 6 th year of college. 5
122 Econ Notes on Signaling real worl earn much more than people who complete three years of college. Is this because the classes you take your senior year are super valuable? On the other han, is that completing college inicates that you are smart, iligent, thorough, able, motivate, etc? Can you raw a picture? Yes. On the vertical ais, we have the costs an benefit of going to college. Again, keep in min that the benefit of attening college is the aitional wages you get ($00,000 - $00,000). An also, recall because the only reason we go to school is to sen signals, there is not benefit for any schooling beyon the four years. Group I Group II Costs, Benefits Costs Costs, Benefits $60,000 Costs > Benefits (no college) Benefits > Costs (go to college) Costs $00,000 Benefits $00,000 $80,000 Benefits 4 Years Complete 4 Years Complete Of course, notice for the Group workers, the costs of college ecee the benefits of going to college. For Group workers, the benefits of college ecee the costs of college. Eample where signaling oes *not* work Let s start with the same initial set up. 5 Group I Marginal rouct (per year) = unit Group II Marginal rouct (per year) = units rice of rouct = $0,000 rice of rouct = $0,000 Value of Goos rouce (per year) = $0,000 Value of Goos rouce (per year) = $0,000 Career Length = 0 years Career Length = 0 year 5 In class, I presente this material in a ifferent orer. The first case in your class notes will correspon to the secon eample here (signaling oes not work). The secon case in your class notes (salvage signaling by making folks get an MBA) appears briefly in page 8 of these notes. Finally, the first case in these notes (signaling oes work) i not appear in your class notes. If the pictures help, raw them, but they are not necessary to unerstan or tell the story. 6
123 Econ Notes on Signaling Value of Goos rouce (career) = $00,000 Value of Goos rouce (career) = $00,000 But now, let us change the cots of going to college Group I Group II Cost of completing each year of school = $0,000 Cost of completing each year of school = $0,000 Again, consier the possibility that a firm will believe that everyone who has compete four years of college is a group II (highly prouctive employee). Is this an equilibrium situation? The cost to Group I folks of completing four years of college is now $80,000, while the benefit is $00,000. They will go to college. The cost to Group II folks of completing four years of college is now $40,000, while the benefit is $00,000. They will go to college. Now, everyone goes to college, so when the firm hires college eucate workers (an assumes they are group II workers), they will often be wrong. This is not an equilibrium. The firm woul be hiring low prouctivity workers (an paying them high prouctivity wages. The firm woul be isappointe, an woul quickly revise its hiring ecisions. Signaling oes not work here. See the net section for a more general iscussion of the characteristics of an effective signal. The picture for this case is illustrate below. Group I Group II Costs, Benefits Costs, Benefits Benefits > Costs (go to college) Costs Benefits > Costs (go to college) $00,000 $80,000 Benefits $00,000 Benefits $40,000 Costs 4 Years Complete 4 Years Complete What is in a goo signal? For signaling to work, it has to been less costly for prouctive workers to make the signal to the firm than it is for less prouctive workers to make the signal to the firm. In the first eample (where signaling worke), it worke because it was sufficiently tougher (more costly) for less prouctive workers to sen the signal that for more prouctive workers to sen the signal. The signal has to be something that only highly prouctive workers fin they want to engage in. Group II 7
124 Econ Notes on Signaling people wante to go to college, Group I people i not want to go - because it was too costly for them to sen the signal. In the secon eample (where signaling i not work), it i not work because it was too easy for the low prouctivity workers to sen the signal. Both groups wante to sen the signal. This is like ressing nicely at the interview. Both groups will make the signal, so it oes not help firms separate workers into groups. What might be other signals? Working long hours or staying late at work. It might be less costly for a prouctive employee to work 0 hours a ay, perhaps because the prouctive worker is better at what they o or enjoys their work more than a less prouctive worker. Do you think using fancy paper for resumes can be use by workers to inicate they are highly prouctive workers? Can we salvage signaling in the secon eample? Go back up to the costs an benefits of going to college. Even in the secon eample, it is more costly for low ability workers to go to college ($0,000 per year of school) than for high ability workers. If we wante to salvage signaling, how about just making a hiring rule base on competing more than 4 years of schooling? Suppose instea the firm assumes that workers that have 6 years of schooling are high prouctivity workers. Will this work? 6 What shoul I rea? Just my notes here 6 Now, the benefit of attening si years of school is $00,000 for each group. The cost of attening si years of schooling for Group I workers is $0,000 (they won t atten) an the cost of attening si years of schooling for Group II workers is $60,000 (they will atten). Firms will assume that those that have complete si years are Group II workers an they will be correct. It is an equilibrium situation. Has attening college gotten easier in the last 30 years? Does that eplain why are getting an MBA right now? 8
125 Econ 500 Notes Training On-the-Job Training General training refers to the creation of skills or characteristics that are equally usable in all firms an inustries. Eample woul inclue learning to rive a truck, general accounting an bookkeeping knowlege, math skills, computer skills, using Microsoft Wor. Specific training refers to the creation of skills or characteristics that can be use in only the particular firm that provies the training. Eamples woul inclue specific information about the pharmaceutical trials for Viagra for someone who is a sales rep for Viagra. If you go to some other company an start selling ail, this knowlege is no longer valuable. Detaile knowlege of a proprietary computer system that is only use by one firm, or working on lecture notes for a class that is only offere by one college. There is an element of tetbook bs with this istinction. It is ifficult to come up with an eample that is 00% specific or 00% general. Knowlege of Microsoft oweroint skills strikes me as being very general skills an yet, if you work as a rug ealer, I m not sure you ll be making bullet point presentations for your promotional materials. Driving a truck seems general, but if you are working for a watchmaker, are those truck riving skills valuable? One certainly coul suggest that in learning info about Viagra trials, likely a very specific skill, there might be a portion of this learning process that applies to the ail, rugs in general, sales in general, etc. I wouln t isagree. Nonetheless, we fin it useful to make the istinction. To iscuss the economics of training, we have to introuce one more bit of aitional terminology. We call the firm s marginal revenue prouct (MR) the increase in firm s total revenue associate with employment of a given worker. Think of it as the value of the workers prouctivity. A simple eample first Suppose hiring 3 workers at McDonals enables 0 burgers an hour to be prouce. Suppose hiring a 4 th worker (one more worker) enables 5 burgers an hour to be prouce. This workers marginal prouctivity, the etra output prouce by the firm when the worker is hire, is 5 etra burgers. If these burgers can be sol for $ a piece, the value of the workers prouctivity is $0 per hour. Thus for this 4 th worker, we say the MR is $0 per hour. More generally, the iea is that firms hire workers to make stuff. The firm then sells that stuff. The value to the firm of hiring the worker is ollar amount of the stuff that worker prouces. It is base on the prouctivity of workers an the price of the goo being prouce. In general, firms will have to offer a wage equal to MR, or they will have a ifficulty attracting workers. General Training First, consier the prouctivity path of a worker with no training. If they receive no training, their prouctivity will never change (MR U ). The firm will have to offer them a wage that is commensurate with their prouctivity; else the worker will go to another firm that oes (W U ). As a result, both the wage of the worker an the time path of their MR will be flat across time. Net, consier the prouctivity path of a worker who unergoes general training (MR T ). During the training perio, the workers prouctivity will fall because time that previously was being use for proucing will now be use to learn new skills. The worker will have their nose in a book or be in a classroom instea of being on the line or proucing. After the training perio, however, the worker will We just skippe over about a month of labor economics class there, there are eceptions, etc. It turns out that firms will hire labor until the wage = MR, so only for that last unit of labor hire, will the wage equal the MR. If you are thinking it is impossible for the firm to earn profits if workers are always pai the value of what they prouce, I suppose I ought to note that the MR will ecee the wage for all units but the last unit of labor. If you are intereste, come talk to me.
126 Econ 500 Notes Training have more skills an thus be more prouctive. See the picture below. MR is first lower than a worker who unerwent no training, but after the training perio ecees the MR of a worker that unerwent no training. This is not the har part to figure out. What we want to figure out is what wages shoul be offere to these employees. You nee to think backwars. Start in the post-training perio an then figure out what to o in the training perio. There seems to be two sensible possibilities. One possibility is for the firm to pay for training. The firm will pay the worker a wage above their prouctivity level uring the training perio an will then recoup the training costs in the post-training perio by offering a wage below their prouctivity level. The firm woul pay for training, but woul also receive the rewars for the training. The other possibility is for the worker to pay for training. The worker will accept a lower wage in the training perio, one that reflects the iminishe prouctivity level, an then will receive a higher wage in the post-training perio. In this case, the worker pays for the training, but woul also receive the rewars for the training. So, what happens to wages of a worker who unergoes general training (w T )? Since the training the worker receives in general, it is valuable to all employers. Can the firm get away with paying the worker a wage that is less than their MR after the training? The answer is no, because the worker woul be able to go to another firm that will. As a result, the firm will fin it has to pay the worker commensurate with their skill level after the training. The firm knows that the workers prouctivity will be lower uring the training perio. Given that the firm won t be able to recoup the investment in the post-training perio, will the firm come out ahea if it pays workers a wage that ecees their prouctivity in the training perio? The answer is no. So the firm will only pay workers that level of their (lower) prouctivity uring the training perio. The firm oes not pay for training it all. Think of this reuction in wages as equivalent to taking the workers off the clock when they are learning general skills at work. The worker pays for training by having to accept a lower wage uring the training perio. 3 From the employee s perspective, the traeoff is lower wages uring the training perio in echange for higher wages in the post-training perio. Therefore, on-the-job training is just like an investment from the perspective of the iniviual. 4 See the picture on the net page. If the firm pai workers a wage that eceee their prouctivity in the training perio, an then pai workers equal to their prouctivity in the post-training perio, the firm woul fin it woul have a lot of young workers (who woul unergo the training perio) an then leave the firm to work somewhere else. This woul be an epensive proposition for the firm. 3 While writing up these notes, I kept thinking of big 6 consulting firms, where young workers o gain the on-the-job training. Might these workers pay for the training by having to work many hours an yet not receive (irect) compensation commensurate with that level of eperience? 4 I m sure you all appreciate that college is an investment the costs come up from through tuition, the opportunity cost of time, etc, an the benefits come in the future through higher wages. You ve been rille to o the math on investment ecisions throughout your acaemic careers, an the insight labor economists have is that schooling ecisions are no ifferent. What perhaps some of you han t appreciate before this lecture (though I bet many of you ha) is that on-the-job training can be viewe the same way. If the skills are valuable enough, it may be wise to invest in accepting a lower wage if the prospect of future wage growth, by way of on-the-job training, eists. This is the opposite of the iea of a ea en job an one you shoul consier in both your career ecisions, an in hiring an wage offering ecisions you might make as a manager.
127 Econ 500 Notes Training Specific Training Start again with someone who oes not unergo training. Their prouctivity (MR U ) an their wage (w U ) will both be flat, just as before. Net, consier the prouctivity path of a worker who unergoes specific training (MR T ). Just as before, uring the training perio, the workers prouctivity will fall. Just as before, after the training perio, the worker will have more skills an thus be more prouctive. See the picture below. MR is first lower than a worker who unerwent no training, but after the training perio ecees the MR of a worker that unerwent no training. So far, the story is the same as with general training. Net, consier what happens to wages of a worker who unergoes specific training (w T ). Since the training the worker receives is specific, it is valuable to only the present employer. Can the firm get away with paying the worker a wage that is less than their MR after the training? The answer is yes, because if the worker trie to go to another firm, they woul be treate as an untraine worker at the new firm (the training they have is not valuable to this new firm). The current firm (the one oing the training) can pay them the same wage that it woul pay an untraine worker after the training. 5 But if the worker will not receive a higher wage in the future, will they agree to accept a lower wage uring the training perio? Certainly not. They will have to be pai just as much as they woul have earne if they were an untraine worker. Therefore, the wages traine workers will receive follows the same path of the wages that untraine workers receive (no ecrease uring the training perio, but no increase after in the post-training perio). So with specific training, it is the firm that pays for the training. Think of it as being as if workers are on the clock while they are learning the specific skills. 5 If the employee threatene to go to a new firm ue to higher wages, the threat woul be increible.
128 Econ 500 Notes Training The investment ecision is being mae from the firm s point of view. Shoul the firm spen the money up front on training in echange for the benefits of more prouctive workers? We ll epan on this question below. But of course, the firm will wish to o so if the benefits ecee the costs. One more twist on specific training Consier the incentives of the firm proviing the specific training above. It pays the cost of training up front an gets the benefits (the gap between MR an wages) in the future (post-training perio). It shoul be intuitive that as the length of post-training perio increases, it is more likely the investment will be profitable for the firm. If firms are constantly training new workers, an those workers for whatever reason leave immeiately, it woul be all costs an no benefits. The firm may want to o something to improve retention an reuce turnover. One thing it coul o is offer a slight wage increase after the training perio. Now the worker woul have an aitional incentive to say, as they woul be earning a slightly better wage at the current firm than they coul earn at another firm. This is calle an efficiency wage. It woul reuce the gap between the MR an wage (the benefit to the firm of oing the training) per perio, but may increase the average amount of time an employee woul stay (mean that gap woul be enjoye by the firm for a larger number of perios). Therefore, it wouln t be inconsistent, even with the general iea that the firm oesn t have to offer the employers a higher wage that the firm might want to offer the employees a higher wage after training. See the picture on the net page. The iea of an efficiency wage is a bit more general. Any time you offer an employee a higher wage than they coul earn elsewhere, they employee has an etra incentive to stay at the current firm. If training, teams, etc, are important, it might make sense to o this. Google Henry For an $5 a ay wage for a famous eample of an efficiency wage reucing turnover.
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