Chapter 1: Supply, Demand and Elasticity

Transcription

1 Chapter 1: Supply, Demand and Elasticity Section 1: Supply and Demand (Source: In the context of supply and demand discussions, demand refers to the quantity of a good that is desired by buyers. An important distinction to make is the difference between demand and the quantitiy demanded. The quantity demanded refers to the specific amount of that product that buyers are willing to buy at a given price. This relationship between price and the quantity of product demanded at that price is defined as the demand relationship. Supply is defined as the total quantity of a product or service that the marketplace can offer. The quantity supplied is the amount of a product/service that suppliers are willing to supply at a given price. This relationship between price and the amount of a good/service supplied is known as the supply relationship. When thinking about demand and supply together, the supply relationship and demand relationship basically mirror each other at equilibrium. At equilibrium, the quantity supplied and quantity demanded intersect and are equal. In the diagram below, supply is illustrated by the upward sloping blue line and demand is illustrated by the downward sloping green line. At a price of P* and a quantity of Q*, the quantity demanded and the supply demanded intersect at the Equilibirum Price. At equilibrium price, suppliers are selling all the goods that they have produced and consumers are getting all the goods that they are demanding. This is the optimal economic condition, where both consumers and producers of goods and services are satisfied. The Law Of Demand Very simply, the law of demand states that if all other factors remain constant, if a good's price is higher, fewer people will demand it. As the price of that good goes down, the quantity of that good that the market will demand will increase. In the diagram below, you see this relationship. At price P1, the quanity of that good

2 demanded is Q1. If the price of this good were to be decreased to P2, the quantity of that good demanded would increase to Q2. The same is true for P3 and Q3. When prices move up or down (assuming all else is constant), the quantity demanded will move up or down the demand curve and define the new quantity demanded. The Law Of Supply After understanding the law of demand, the law of supply is simple, it's effectively the inverse of the law of demand. The law of supply states that as the price rises for a given product/service, suppliers are willing to supply more. Selling more goods/services at a higher price means more revenue. In the diagram below, you can see that as the price shifts from P1 to P2, the quantity supplied of that good shifts from Q1 to Q2. The movement in price (up or down) causes movement along the supply curve and the quantity demanded will change accordingly.

3 Section 2: Computations with Supply and Demand Curves Example 1: Suppose the demand function for pumpkins is D(q) = q, and the supply function for pumpkins is S(q) = q. D(q) and S(q) are the prices, in dollars per ton, and q is the amount of pumpkins, in tons. a) Sketch a graph of D(q) and S(q) on the same grid b) Calculate D(300) and S(300) and explain what they mean, and place these points on the graph Solution: a) the two functions are shown below. Notice the demand function is downward-sloping, and the supply curve is upward-sloping D(q) 500 S(q) b) To calculate D(300) and S(300), replace q with 300 and compute: The demand: D(300) = (300) = 460. This means, when there are 300 tons of pumpkins available, the price is $460 per ton. (or, at $460, 300 tons of pumpkins will be sold) The supply: S(300) = (300) = 250.

4 This means, when quantity is 300, the price is $250 per ton. This means when the price is $250, the farmers (the suppliers in this case) are willing and/or able to produce 300 tons of pumpkins. These points are shown on the graph below: Notice that, at the same quantity, the prices are different. The point (300, 460) represents the buyer s perspective. In other words, at $460, buyers are willing to buy 300 tons. The other point, (300, 250), represents the seller s perspective. In other words, at $250, sellers are willing to produce 300 units. Example 2: A politician complains about the high price of pumpkins and the greedy pumpkin farmers. He proposes a new law: Henceforth, the maximum price for pumpkins shall be $200 per ton. The population cheers but what happens as a result? Solution: Let s start with the demand curve: if price is set at $200 per ton, what will be the quantity demanded? Solve the equation: Set the demand equation equal to 200: q = 200 Subtract 700 from each side: -0.8q = -500 Divide by -0.8: q = 200 If the price is set at $200, then customers will demand 625 tons of pumpkins.

5 Now, let s look at the supply equation: Set the supply equation equal to 200: q = 200 Subtract 100 from each side: 0.5q = 100 Divide by 0.5: q = 200 At $200, producers are only willing or able to produce 200 tons of pumpkins. These points are shown on the graph below: Notice that we have a small problem: People want 625 tons of pumpkins, but the farmers only produced 200 tons we have a shortage! How did this happen? When the price is artificially set too low, then producers are unable or unwilling to produce. Only the most efficient farmers could produce pumpkins cheaply enough to make a profit at $200 per ton, so not many pumpkins were grown. This is a natural consequence of the supply curve. How to fix this problem? Remove the price control, and allow the price to increase. Then more farmers are willing and/or able to produce more pumpkins at the higher price.

6 Section 3: Equilibrium As we saw from the pumpkin example, when prices are too low, then the supply is too low. On the other hand, if prices are too high, then the number of pumpkins sold decreases. Is there a point where supply and price balance out? The answer is yes, and it is called the equilibrium point. Definition: the Equilibrium Point is the point where the demand and supply functions intersect. It occurs where D(q) = S(q) Example 3: Suppose the demand and supply functions for pumpkins is D(q) = q and S(q) = q. D(q) and S(q) are the prices, in dollars per ton, and q is the amount of pumpkins, in tons. Find the equilibrium point. Solution: The equilibrium point can be visually estimated where q is a little bit higher than 450 tons, and the price is little higher than 300 dollars per ton D(q) 500 S(q) Equilibrium Point To find a more precise solution, set the demand and supply equations equal to each other: D(q) = S(q) q = q Subtract 100 from each side, and 0.8 to each side: 600 = 1.3q Divide by 1.3 and round off: = q

7 What is the price? Just plug into either the supply or demand function: D( ) = ( ) = Answer: the equilibrium point is at ( , ), which means when quantity is tons, the price will be $ per ton.

8 Section 4: Price elasticity of demand (PED) From Wikipedia, the free encyclopedia Definition PED is a measure of responsiveness of the quantity of a good or service demanded to changes in its price. The formula for the coefficient of price elasticity of demand for a good is: The above formula usually yields a negative value, due to the inverse nature of the relationship between price and quantity demanded, as described by the "law of demand". For example, if the price increases by 5% and quantity demanded decreases by 5%, then the elasticity at the initial price and quantity = 5%/5% = 1. Determinants The overriding factor in determining PED is the willingness and ability of consumers after a price change to postpone immediate consumption decisions concerning the good and to search for substitutes ("wait and look"). A number of factors can thus affect the elasticity of demand for a good: Availability of substitute goods: the more and closer the substitutes available, the higher the elasticity is likely to be, as people can easily switch from one good to another if an even minor price change is made; There is a strong substitution effect. If no close substitutes are available the substitution of effect will be small and the demand inelastic. Percentage of income: the higher the percentage of the consumer's income that the product's price represents, the higher the elasticity tends to be, as people will pay more attention when purchasing the good because of its cost; The income effect is substantial. When the goods represent only a negligible portion of the budget the income effect will be insignificant and demand inelastic Necessity: the more necessary a good is, the lower the elasticity, as people will attempt to buy it no matter the price, such as the case of insulin for those that need it. Duration: for most goods, the longer a price change holds, the higher the elasticity is likely to be, as more and more consumers find they have the time and inclination to search for substitutes. When fuel prices increase suddenly, for instance, consumers may still fill up their empty tanks in the short run, but when prices remain high over several years, more consumers will reduce their demand for fuel by switching to carpooling or public transportation, investing in vehicles with greater fuel economy or

9 taking other measures. This does not hold for consumer durables such as the cars themselves, however; eventually, it may become necessary for consumers to replace their present cars, so one would expect demand to be less elastic. Breadth of definition of a good: the broader the definition of a good (or service), the lower the elasticity. For example, Company X's fish and chips would tend to have a relatively high elasticity of demand if a significant number of substitutes are available, whereas food in general would have an extremely low elasticity of demand because no substitutes exist. Brand loyalty: an attachment to a certain brand either out of tradition or because of proprietary barriers can override sensitivity to price changes, resulting in more inelastic demand. Who pays: where the purchaser does not directly pay for the good they consume, such as with corporate expense accounts, demand is likely to be more inelastic. Elasticities of demand are interpreted as follows: Value Descriptive Terms Ed = 0 Perfectly inelastic demand - 1 < Ed < 0 Inelastic or relatively inelastic demand Ed = - 1 Unit elastic, unit elasticity, unitary elasticity, or unitarily elastic demand - < Ed < - 1 Elastic or relatively elastic demand Ed = - Perfectly elastic demand A decrease in the price of a good normally results in an increase in the quantity demanded by consumers because of the law of demand, and conversely, quantity demanded decreases when price rises. As summarized in the table above, the PED for a good or service is referred to by different descriptive terms depending on whether the elasticity coefficient is greater than, equal to, or less than 1. That is, the demand for a good is called: relatively inelastic when the percentage change in quantity demanded is less than the percentage change in price (so that Ed > - 1); unit elastic, unit elasticity, unitary elasticity, or unitarily elastic demand when the percentage change in quantity demanded is equal to the percentage change in price (so that Ed = - 1); and relatively elastic when the percentage change in quantity demanded is greater than the percentage change in price (so that Ed < - 1). Selected price elasticities Various research methods are used to calculate price elasticities in real life, including analysis of historic sales data, both public and private, and use of present-day surveys of customers' preferences to build up test markets capable of modeling such changes. Alternatively, conjoint analysis (a ranking of users' preferences which can then be statistically analysed) may be used. Though PEDs for most demand schedules vary depending on price, they can be modeled assuming constant elasticity. Using this method, the PEDs for various goods intended to act as examples of the theory described above - are as follows. For suggestions on why these goods and services may have the PED shown, see the above section on determinants of price elasticity. Cigarettes (US)[41] -0.3 to -0.6 (General) -0.6 to -0.7 (Youth) Alcoholic beverages (US)[42] -0.3 or -0.7 to -0.9 as of 1972 (Beer) Rice[48] (Austria) (Bangladesh) (China) (Japan) (US)

10 -1.0 (Wine) -1.5 (Spirits) Airline travel (US)[43] -0.3 (First Class) -0.9 (Discount) -1.5 (for Pleasure Travelers) Livestock -0.5 to -0.6 (Broiler Chickens)[44] Oil (World) -0.4 Car fuel[45] (Short run) (Long run) Medicine (US) (Medical insurance)[46] -.03 to -.06 (Pediatric Visits) [47] Cinema visits (US) (General)[46] Live Performing Arts (Theater, etc.) -0.4 to -0.9 [49] Transport (Bus travel US)[46] (Ford compact automobile)[50] Soft drinks -0.8 to -1.0 (general)[51] -3.8 (Coca-Cola)[52] -4.4 (Mountain Dew)[52] Steel -0.2 to -0.3[53] Eggs -0.1 (US: Household only),[54] (Canada),[55] (South Africa) Practice Problems for Elasticity of Demand Example 4: Recently, the price of avocados increased by 5%. As a result, 4% fewer were sold. What is the elasticity of demand? Is this elastic or inelastic? Solution: Using the formula, % changein quantity 0.04 E= 0.8 % changein price 0.05 Answer: The elasticity is This is inelastic, meaning the quantity sold is not too sensitive to changes in price. When calculating elasticity, sometimes you must calculate the percentage change yourself. However, when computing elasticity, use a modified percent formula, that uses the midpoint as the base: percent change = new amount old amount midpoint of the amounts Example 5: Yesterday, the price of envelopes was $3 a box, and Julie was willing to buy 10 boxes. Today, the price has gone up to $3.55 a box, and Julie is now willing to buy 8 boxes. Is Julie's demand for envelopes elastic or inelastic? What is Julie's elasticity of demand? Is it elastic or inelastic?

11 Solution To find Julie's elasticity of demand, we need to divide the percent change in quantity by the percent change in price. Step 1: find the % Change in Quantity: the quantity decreased from 8 to 10. The midpoint is 9. new amount old amount percent change = midpoint of the amounts 9 9 Step 2: find the % Change in Price: the price increased from $3.00 to $3.55. The midpoint is new amount old amount percent change = midpoint of the amounts Step 3: find the Elasticity E = (-0.222)/(0.1679) = 1.32 (rounded off) Answer: The elasticity is Julie's elasticity of demand is elastic, meaning she the quantity she will buy is sensitive to price changes. Example 6: Which of the following goods are likely to have elastic demand, and which are likely to have inelastic demand? Home heating oil Pepsi Chocolate Water Heart medication Oriental rugs Solution Elastic demand: Pepsi, chocolate, and Oriental rugs Inelastic demand: Home heating oil, water, and heart medication

12 Section 5: Price elasticity of supply From Wikipedia, the free encyclopedia In economics, price elasticity of supply (PES) is an elasticity defined as a numerical measure of the responsiveness of the supply of a given good to a change in the price of that good. Calculation Price elasticity of supply is a measure of the sensitivity of the quantity of a good supplied in a market to changes in the market price for that good. Per the law of supply, it is posited that at a given price and corresponding quantity supplied in a market, a price increase will also increase the quantity supplied. PES is a numerical measure (coefficient) of by how much that supply is affected. Mathematically: In other words, PES is the percentage change in quantity supplied that one would expect to occur after a 1% change in price. For example, if, in response to a 10% rise in the price of a good, the quantity supplied increases by 20%, the price elasticity of supply would be 20%/10% = 2. Interpretation If the law of supply holds, an upward-sloping supply curve would result from this. As a ratio of two percentages, the price elasticity is not tied to any specific units. However, the exact value can yield more inferences about the good in question. When the coefficient is less than one, the supply of that good can be described as inelastic; when the coefficient is greater than one, the supply can be described as elastic. An elasticity of zero indicates that quantity supplied does not respond to a price change: it is "fixed" in supply. Such goods often have no labor component or are not produced, limiting the short run prospects of expansion. If the coefficient is exactly one, the good is said to be unitary elastic. The quantity of goods supplied can, in the short term, be different from the amount produced, as manufacturers will have stocks which they can build up or run down. Determinants Availability of raw materials: for example, availability may cap the amount of gold that can be produced in a country regardless of price. Likewise, the price of Van Gogh paintings is unlikely to affect their supply. Length and complexity of production: Much depends on the complexity of the production process. Textile production is relatively simple. The labor is largely unskilled and production facilities are little more than buildings - no special structures are needed. Thus the PES for textiles is elastic. On the other hand, the PES for specific types of motor vehicles is relatively inelastic. Auto manufacture is a multi-stage process that requires specialized equipment, skilled labor, a large suppliers network and large R&D costs. Time to respond: The more time a producer has to respond to price changes the more elastic the supply. Supply is normally more elastic in the long run than in the short run for produced goods, since it is generally assumed that in the long run all factors of production can be utilised to increase supply, whereas in the short run only labor can be increased, and even then, changes may be prohibitively costly. For example, a cotton farmer cannot immediately (i.e. in the short run) respond to an increase in the price of soybeans because of the time it would take to procure the necessary land. Excess capacity: A producer who has unused capacity can (and will) quickly respond to price changes in his

13 market assuming that variable factors are readily available. Inventories: A producer who has a supply of goods or available storage capacity can quickly increase supply to market. Various research methods are used to calculate price elasticities in real life, including analysis of historic sales data, both public and private, and use of present-day surveys of customers' preferences to build up test markets capable of modelling such changes. Alternatively, conjoint analysis (a ranking of users' preferences which can then be statistically analysed) may be used. Graphical representation It is important to note that elasticity and slope are, in the most part, unrelated. Thus, when supply is represented linearly, regardless of the slope of the supply line, the coefficient of elasticity of any linear supply curve that passes through the origin is 1 (unit elastic). The coefficient of elasticity of any linear supply curve that cuts the y- axis is greater than 1 (elastic), and the coefficient of elasticity of any linear supply curve that cuts the x-axis is less than 1 (inelastic). Likewise, for any given supply curve, it is likely that PES will vary along the curve. Selected Supply Elasticities Heating Oil 1.57 (Short Run) [11] Gasoline 1.61 (Short Run) [11] Tobacco 7.0 (Long Run) [11] Housing (Long Run) [11] Cotton 0.3 (Short Run) [12] 1.0 (Long Run) [12] Steel 1.2 (Long Run, from Minimills) [13]

14 Section 6: Power functions Definition: a Power function is a function with the form f(x) = kx p Where k and p are nonzero constants. In realistic settings, the domain of the function (the x) is usually restricted to positive numbers. Here are some examples of power functions: f(x) = 3.2 x 0.4 H(t) = 489 t -1/2 D(q) = 4 q 2 Graphs of power functions The basic shape depends on the power, p. Example 7: Graph f(x) = 3x 1.5 Set up an Excel sheet and make a scatterplot: A B 1 x f(x) =3*A2^1.5 f(x)

15 As you can see, the curve is bent slightly upward. Since the exponent is greater than 1, the function is increasing, but also the rate of increase is increasing. This type of shape is called concave up. For all power functions, if the power is greater than 1, then the curve is always concave up. Example 8: A cost function is C(q) = q 0.25 Make a graph of this function. Solution: Again, set up an Excel sheet and make a scatterplot A B 1 x f(x) = *A2^0.25 f(x) This is a fairly typical cost function. As quantity increases, according to economy of scale, the costs per unit start to decrease. So the cost function, although it is still increasing, is increasing at a slower rate. This type of shape is called concave down. Any power function, where the power is between 0 and 1, is always concave down. Example 9: A demand function is D(q) = 326 q Make a graph of the demand function Solution: You know the drill: A B 1 x f(x) =326*A2^(-0.45)

16 The parentheses around the exponent are not essential, but sometimes Excel is fickle with negative numbers. So just to be safe, put the negative numbers inside parentheses. f(x) Anytime the power is negative, the function will decrease. However, as q gets larger, the function decreases at a slower and slower rate. This shape is also called concave up. Summary Power Example direction Shape Picture Negative H(t) = 489 t -1/2 Decreasing Concave up Between 0 and 1 f(x) = 3.2 x 0.4 Increasing Concave down Greater than 1 D(q) = 4 q 2 Increasing Concave up

17 Derivatives of Power Functions The power rule (the derivative of cx n is ncx n-1 ) applies for all values of n, so it applies to all power functions. Example 10: A cost function is C(q) = q What is the marginal cost? Solution: The 32 drops out, then multiply the power (0.78) times the coefficient (3.4). then decrease the power by 1 ( = -0.22): Answer: MC(q) = 2.652q -0.22

18 Section 7: Solving Power Function Equations Like most equations, the procedure is to do something to both sides of an equation that will undo a particular operation. For instance: Solve x + 5 = 8 Solve 3 x = 20 add -5 to both sides to undo the addition take log of both sides to undo the exponentiation The way to solve a power function is usually to take the reciprocal power of each side. Example 11: Solve x 2 = 25 Solution: The procedure would be to find the square root of each side of this equation. But we want a method that would work for any power function. So, the reciprocal of 2 is ½. So we ll take each side to the ½ power. (remember that ½ power is equivalent to square root) ( x 2 ) 1/2 = (25) 1/2 On the left side of the equation, 2 times ½ equals 1, so the left side becomes x 1, which is just x. That s the nice thing about reciprocals! You always get 1. x = 5 (normally, plus or minus 5, but we re only interested in positive numbers for solutions) Answer: x = 5 Now for a tougher one: Example 12: Solve 67 x = 38.9 Solution: first, divide both sides by 67: x = 38.9/67 x = Answer: x = then, take both sides to the 1/(-0.45) power (the reciprocal of -0.45) (x ) 1/(-0.45) = ( ) 1/(-0.45) On the left side, we ll have x 1. The right side will take some serious calculatorbutton-pushing: ^(1/-0.45) = Example 13: Suppose a demand function for steel is D(q) = 23q -2.1, and the supply function for steel is S(q) = 12q a) Use Excel to graph both b) Find the equilibrium point. Solution: To set up an Excel sheet, you will need three columns:

19 A B C 1 Q D(q) S(q) In cell B2, enter the demand function, which is =23*A2^(-2.1) In cell C2, enter the supply function, which is =12*A2^(0.45) Then copy the formulas down, and you ll see: A B C 1 Q D(q) S(q) Select all three columns and select Insert>Scatterplot: We can visually estimate the equilibrium point to be about (1.5, 14). To get a more precise answer, solve D(q) = S(q): Set the equations equal to each other: 23q -2.1 = 12q Divide both sides by 12: q -2.1 = q 0.45 Divide both sides by q = q 2.55 Take the 1/2.55 power of both sides: /2.55 = q Compute and round off: q =

20 If we go back to our spreadsheet, and enter for q, then we see that supply and demand are equal at that point (except for rounding): A B C 1 Q D(q) S(q) Answer: the equilibrium point is approximately (1.3, 13.5)

21 Chapter 1 Practice Problems Practice with Supply and Demand Curves 1. Suppose the supply and demand functions for oranges are D(q) = q and S(q) = q, where prices are in dollars per pound and q is in pounds. a) Sketch a graph of both functions on the same grid. b) Calculate D(200) and S(200) and explain what these mean. Then locate the points on the graph c) if the price was $1 per pound, what would be the quantity demanded, according to the demand function? d) if the price was $1 per pound, what would be the quantity supplied, according to the supply function? e) if the price was $1 per pound, would this indicate a shortage or a surplus? f) Find the equilibrium point 2. Suppose the supply and demand functions for apples are D(q) = q and S(q) = q, where prices are in dollars per pound and q is in pounds. a) Sketch a graph of both functions on the same grid. b) Calculate D(300) and S(300) and explain what these mean. Then locate the points on the graph c) if the price was $1 per pound, what would be the quantity demanded, according to the demand function? d) if the price was $1 per pound, what would be the quantity supplied, according to the supply function? e) if the price was $1 per pound, would this indicate a shortage or a surplus? f) Find the equilibrium point Practice with Elasticity 3. Suppose that last year the price of a movie ticket was $9, and this year the price is $9.50. As a result, the number of tickets sold decreased from 45,000 to 41,000. a) What is the percent change in the quantity sold? (remember to use the midpoint as the base) b) What is the percent change in the price? (remember to use the midpoint as the base) c) Calculate the elasticity of demand d) Based on your answer from part (d), is the demand for movie tickets elastic or

22 inelastic? 4. Suppose the price of tomatoes increased from $2.50 per pound to $3.50 per pound. As a result, tomato growers decided to plant more tomato plants this year, and the supply of tomatoes increased from 56,000 tons to 61,000 tons. a) What is the percent change in the quantity produced? b) What is the percent change in the price? c) Calculate the elasticity of supply d) Based on your answer from part (d), is the supply of tomatoes elastic or inelastic? 5. The elasticity of demand for a product is E = What is the effect on demand of: a) A 3% price increase? b) A 3% price decrease? 6. The elasticity of demand for a product is E = 2. What is the effect on demand of: a) A 3% price increase? b) A 3 % price decrease? 7. The elasticity of demand for peaches is 1.49 (Estimated by the USDA). Explain what this number tells you about the effect of price increases on the demand for peaches. Is the demand elastic or inelastic? Explain factors that contribute to the elasticity of peaches. 8. The elasticity of demand for potatoes is 0.27 (Estimated by the USDA). Explain what this number tells you about the effect of price increases of potatoes. Is the demand elastic or inelastic? Explain factors that contribute to the inelasticity of potatoes. 9. Would you expect the demand for heated toilet seats to be elastic or inelastic? Why? 10. There are many brands of smart phones. Assuming the quality of each brand is similar, would you expect the elasticity of demand to be elastic or inelastic? Why? 11. If there is only one telephone company that services a city, would the demand be elastic or inelastic? Why? 12. The demand curve for a product is D(q) = 75-4q. Find the elasticity of demand when quantity changes from q = 8 to q = The demand curve for a product is D(q) = 90-10q. Find the elasticity of demand when quantity changes from q = 4 to q = 6. Practice with Power Functions 14. Compute the following without a calculator: a) 64 2/3 b) 81 3/4 c) 16 1/2 d) 32-2/5 e) 9-1/2

23 15. Compute the following without a calculator: a) 64 1/3 b) 16 3/4 c) 25 1/2 d) 32-3/5 e) 36-1/2 16. Compute the following with a calculator, and round to 3 digits after the decimal point: a) b) c) Compute the following with a calculator, and round to 3 digits after the decimal point: a) b) c) Convert each expression to radical form: a) 2/3 x b) 3q 1/2 19. Convert each expression to radical form: a) 3/4 x b) 3q 1/3 20. A cost function is C(q) = q 0.452, where q is in thousands and costs are in millions. a) Compute the cost of producing 30,000 units. b) What is the fixed cost? c) Use Excel to make a table and graph of this cost function. Start with q = 0 and end with q = 50, using increments of 5. d) What is the marginal cost function? e) What is the marginal cost when q = 10? Include units with you answer. f) Is the marginal cost increasing or decreasing? How do you know? 21. A cost function is C(q) = q 0.494, where q is in thousands and costs are in millions. a) Compute the cost of producing 20,000 units. b) What is the fixed cost? c) Use Excel to make a table and graph of this cost function. Start with q = 0 and end with q = 50, using increments of 5. d) What is the marginal cost function? e) What is the marginal cost when q = 10? Include units with you answer. f) Is the marginal cost increasing or decreasing? How do you know? 22. Solve the following equations, and round the answer to 3 digits after the decimal point: a) 34 = x 2.7 b) = 4.2q Solve the following equations and round the answer to 3 digits after the decimal point:

24 a) 37 = x 2.2 b) 24.8 = 6.2q Suppose the demand function for gummy bears is D(q) = 3.4q -0.6, and the supply function for gummy bears is S(q) = 2.1q 1.2 a) Use Excel to graph both on the same scatterplot b) Solve for the equilibrium point 25. Suppose the demand function for sunglasses is D(q) = 19.56q -0.24, and the supply function for sunglasses is S(q) = 3.45q 0.81 a) Use Excel to graph both on the same scatterplot b) Solve for the equilibrium point, rounded to 2 digits after the decimal point Answers to Selected Exercises 1a) 1.5 (200, 1.6) 1 (200, 1.1) b) D(200) = 1.6. This means at $1.60, 200 pounds of oranges would be sold. S(200) = 1.1, which means at $1.10, 200 pounds of oranges would be supplied c) 500 lb d) lb e) shortage; buyers want 500 lb, suppliers only produce lb f) (300, 1.4). 300 lb of oranges, selling for $1.40 per pound. 3a) 9.3% b) 5.4% c) -1.7 d) elastic 5a) 1.5% decrease b) 1.5% increase 7) elastic. People will stop buying peaches if the price gets too high because there are substitutes available and it's not a necessity. 9) elastic, because it is not a necessity 11) low, since the consumers have no other choice 13) quantity increases from 4 to 6 (40% increase, using the midpoint, 5, as the base) and price decreases from 50 to 30 (50% decrease, using the midpoint, 40, as the base). Therefore elasticity is 40/50 = a) 4 b) 8 c) 5 d) 1/8 17a) b) c) a) 4 x 3 b) 3 3 q 21a) million dollars b) 18 million dollars

25 c) 1 A q (thousands) B C(q) (millions) d) MC(q) = q e) million dollars per thousand units f) decreasing, because the cost function is concave down 23a) b) b) (5.22, 13.16)