Practice Problem Solutions PAI723 Professor David Popp Fall 2013

Transcription

1 Practice Problem Solutions PAI723 Professor David Popp Fall Using supply and demand diagrams, illustrate the effect on the equilibrium price and quantity sold of cars when: a) the rates for auto insurance double b) imports from Japan are banned c) Lee Iacocca is elected President, and declares that all cars must be sold for at least $50,000. (Assume that $50,000 is above the current market price for cars.) The purpose of this problem is to get you thinking about how demand and supply curves are affected by outside influences, and to help you distinguish between shifts of a curve versus a movement along a curve. a) P P0 P1 S Increasing the rates for auto insurance will decrease the demand for cars, since cars and insurance are complements. Demand shifts in, so both the equilibrium price and quantity fall. Note that supply does not shift. Rather, the new equilibrium results from a movement along the supply curve. D D Q1 Q0 Q b) P P1 P0 S S A ban on imports causes the supply curve to shift in, since fewer cars are available at any given price. As a result, the equilibrium quantity falls, and the equilibrium price rises, since fewer cars are available. Note that demand does note shift. Rather, we move along the demand curve to find the new equilibrium. D Q1 Q0 Q

2 2 c) P $50,000 P * Excess Supply S In this case, neither curve shifts, since nothing has happened to change preferences (the demand curve) or the amount suppliers are willing to provide (the supply curve). This is simply a case of an excess supply resulting from an artificially high price floor. At a price of $50,000, quantity demanded is less than quantity supplied. D QD Q * QS Q 2. Suppose that the demand for chocolate ice cream cones is given by QD =12-2P. The supply of ice cream cones is QS = 4P. a) Find the price and quantity of ice cream cones, assuming that the market is competitive. b) Due to concerns over the supply of chocolate (it's true!), the government levies a tax of $0.50 per chocolate ice cream cone. Compute the quantity of ice cream cones after the tax, the price paid by consumers, and the price paid by producers. c) Who bears the bigger economic burden - consumers or producers? What does this tell you about the relative elasticities of suppliers and demanders of chocolate ice cream cones? d) Calculate the deadweight loss of the tax. a) The supply and demand of chocolate ice cream cones is: Q = 12-2P (demand) Q = 4P (supply) To find equilibrium, we find the intersection of supply and demand: 12 2P = 4P 12 = 6P P = 2 Next, we plug this answer into either the supply or demand equation to find the equilibrium price: Q = 12 2(2) Q = 4(2) Q = 12 4 or Q = 8 Q = 8 To graph the equilibrium, we first need to solve the equations for P, since P will be on the y-axis of the graph. This gives us: P P = 6 Q/2 (demand) P = Q/4 (supply) The graph for this market is: 6 D S Q

3 3 b) Recall from class that a tax requires us to shift either the supply curve or demand curve in. Note that your results will be the same no matter which one you choose. For example, let s shift the supply curve. P D 12 Q S S The supply curve shifts in by the amount of the tax. That is because at any given price, suppliers now receive $0.5 less, with the remainder going to the government. This is the supply curve faced by consumers. Algebraically, P 0.5 = Q/4 P = Q/ We subtract $0.5 because P is the price consumers pay (We know this because we ll be finding the intersection of this curve with the original demand curve). Suppliers get to keep this price less the $0.50 tax. Graphically, note that the y-intercept of the graph has shifted up by the amount of the tax. We begin by finding the new equilibrium. Equate the new supply curve with the old demand curve. Q/ = 6 Q/2 3Q/4 = 5.5 Q = 7.33 With a quantity of 7.33, consumers pay: P C = 6 (7.33)/2 = $2.33 (from the demand curve) PC = $2.33. However, $0.5 goes to the government, leaving $1.83 for suppliers. Note that we can also get this off the old supply curve (1.83 = 7.33/4). We use the old supply curve because what we are interested in is what suppliers are willing to supply after the tax has been paid. Note that we could have gotten the same result by shifting the demand curve. In this case, the demand curve shifts in. For any P purchase, consumers must give $0.5 to the government. Suppliers receive P 0.5 dollars. Thus, the new demand curve represents the demand curve faced by suppliers. Algebraically, P+0.5 = 6 Q/2 P = 5.5 Q/2. (We add $0.5 because P is the price 6 suppliers get. Consumers pay that plus the $0.50 tax.) S Graphically, note that the y-intercept of the graph has 2.33 shifted down by the amount of the tax D D 12 Q We begin by finding the new equilibrium. Equate the new demand curve with the old supply curve. 5.5 Q/2 = Q/4 3Q/4 = 5.5 Q = 7.33 With a quantity of 7.33, suppliers get: P S = (7.33)/4 (from the supply curve) PS = $1.83 In addition, $0.50 goes to the government, so that consumers pay $2.33 for ice cream. Note that we can also get this off the old demand curve (2.33 = 6 (7.33)/2). We use the old demand curve because what we are interested in is the total that consumers must pay, including the tax. c) The bigger burden of the tax is borne by consumers. The price for consumers rose by $0.33. The price received by suppliers fell by just $0.17. This says that demand is more inelastic for consumers than producers. d) The deadweight loss is the shaded triangle on the graph above.it has a height of 0.5 (the tax) and base of 0.67 (8 7.33). Thus, deadweight loss = 0.5(0.5)(0.67) = $0.17.

4 4 3. The market for semiskilled labor can be represented by the following supply and demand curves: L D = 32,000 4,000w L S = -8, ,000w, where L = millions of person hours per year, and w = the wage in dollars per hour. a) Calculate the competitive market equilibrium price and quantity. What impact does a minimum wage of $4.25 per hour have on the market. Illustrate. b) The government is contemplating an increase in the minimum wage to $5 per hour. Calculate the impact of the new minimum wage on the quantity of labor supplied and demanded. c) Calculate producer surplus (the laborers surplus) before and after the proposed change. Comment on the net effect of the proposed change upon workers as a whole and upon individual workers. d) Is this policy efficient from an economist s point of view? a) We find the equilibrium by equating supply and demand: 32,000-4,000w = -8, ,000w 40,000 = 10,000w w = $4.00 per hour Substitute this into either supply or demand to get: L = 16,000 million person hours. w 8.00 Excess Supply S To see the effect of the minimum wage, plug the minimum wage into both the labor supply and labor demand to find the value at a wage of $4.25. L S = -8, ,000(4.25) = 17,500 L D = 32,000 4,000(4.25) = 15,000 Since labor supply is greater than labor demand, there is an excess supply of 2,500 million person hours of labor. This represents unemployment ,000 17,500 16,000 D L To graph the result, we first need to solve for w to find the y- intercepts. We get: w = L D and w = L S b) An increase in the minimum wage will increase unemployment: L S = -8, ,000(5) = 22,000 L D = 32,000 4,000(5) = 12,000 There is now an excess supply of labor equal to 10,000.

5 5 c) To find the producer surplus, refer to the graph at the right. Recall that producer surplus is the area above the supply curve and below the prevailing price. When the minimum wage is $4.25, producer surplus is equal to areas DEGHI. To find the areas of these, we ll need to find the wage that workers will supply 12,000 units at and the wage at which they will supply 15,000 units. These are $3.33 and $3.84, respectively. To proceed, first find the values for the area o f each of these shapes. We can then add them together to get the appropriate surpluses. w A C B F D E G I H S D = ( )(12,000) =$4,920 E = ( )(15,000 12,000) = $1,230 G = ( )(12,000) = $6,120 H = 0.5( )(15,000 12,000) = $765 I = 0.5( )(12,000) = $12, ,000 15,000 D L The producer surplus is the sum of these, or $25,035. With a minimum wage of $5, the producer surplus is BDGI. Workers lose E and H, because fewer jobs are available. However, they gain area B, because those that are working get a higher wage. The value of area B is: B = ( )(12,000) = $9,000 Producer surplus, the sum of areas BDGI, is $32,040. Note that producer surplus increases for those that are able to still find jobs. However, not everyone is able to take advantage of the increase. Employment falls by 3,000 million person hours. The unfortunate people who lose their job would be better off without the minimum wage increase, since they cannot partake in the newly increased producer surplus. d) The increased minimum wage is not efficient. There is a loss of consumer surplus. Areas B and C are consumer surplus at a minimum wage of $4.25. With a minimum wage of $5, B goes to producers (workers), and C is lost. It becomes part of deadweight loss. In addition, areas E and H, which are producer surpluses at a minimum wage of $4.25, also become deadweight loss. The total deadweight loss increases from area F under the old minimum wage to areas CEFH with the new minimum wage. Since deadweight loss has increased, the policy is not efficient.

6 6 4. Concerned about the behavior of his own teenage children, the governor of a large Southern state is considering policy to help reduce consumption of alcoholic beverages. His advisors have suggested a new tax, the Tax Against Beer (TAB). While beer is currently taxed, this tax would increase the overall tax on beer, and would have the effect of raising the price of beer by 10%. You are given the following information, and asked to calculate the effect of the tax on both consumption of alcoholic beverages and on government revenue. Price elasticity of demand for alcoholic beverage: -0.4 Number of alcoholic beverages currently consumed per year: l,000,000 a) By how much will consumption of alcoholic beverages fall after the tax is imposed? b) Will government revenue increase or decrease after the tax is imposed? How do you know this? c) How might your answers to (a) and (b) vary if looking at the long-run, rather than the immediate effect? a) For this problem, we simply use the elasticity formula: % Q % P We are given the percent change in price (10%) and the elasticity. Thus, we can calculate the change in quantity: Quantity will fall by 4%. % Q % Q ( 0.4)(0.1) 0.04 To find the reduction in terms of number of beverages consumed, simply multiply this by the total number currently consumed (1,000,000). Thus, we find that consumption of alcoholic beverages falls by 40,000. b) Government revenue will increase. Demand is inelastic. Thus, the decrease in quantity demanded will be small relative to the increase in price resulting from the tax. c) One reason that alcoholic beverages have an inelastic demand is because they are addictive. Those who are addicted will purchase alcohol at nearly any price. However, higher prices may discourage new users from consuming alcohol and becoming addicted. Thus, in the long run, demand is likely to be more elastic. The fall in quantity consumed should be greater. The increase in revenue will be smaller, and revenue may decrease if demand becomes elastic.

7 7 5. Reggie consumes only two goods, chocolate and sausage. Suppose that the price of both chocolate and sausage doubles. At the same time, Reggie is given a raise at work, so that his income also doubles. What affect do all of these changes have on Reggie s budget constraint? What does this problem tell you about the effect of inflation that doubles all prices, but in which income also doubles? The key to this question is thinking about the interpretation of the x and y intercepts of the budget constraint. In each case, the intercept is the amount of that good that you could consume if you only bought that good. It is found by dividing total income, I, by the price of the good, P. If both the price and income are doubled, you can still purchase the same amount of the good that you did before. Thus, the budget constraint does not change at all. The intercepts are the same because you can purchase the same amount of the good as before, and the slopes have not changed because relative prices (P S /P C ) have not changed. This problem tells us that if prices increase because of inflation, but income rises at the same rate, the inflation has no real effect, since purchasing power remains the same. Chocolate I/PC = 2I/2PC Slope = PS/PC = 2PS/2PC I/PS = 2I/2P Sausage

8 8 6. Prior to 1979, the food stamp program required families to pay a certain amount for food stamps. Suppose a family can receive, for example, $150 in food stamps for a payment of $50 (that is, the government pays 2/3 of the cost of food). How would this policy affect the budget line? Compared with an outright gift of $100 in food stamps, which is the way the program works now, would this policy lead to more, less, or the same food consumption? The situation prior to 1979 provides a subsidy for food. By spending $50 to purchase food stamps, families can purchase $150 worth of food. Thus, the price of food is one-third the price before food stamps. In this case, the budget constraint simply rotates out. If the family spends all their money on food, they can purchase three times as much food as before An outright gift of $100 shifts the budget constraint out. Other consumption $100 food stamp Pre-1979 program 100 Food Which plan leads to greater food consumption depends on where the typical family s indifference curve is. Families that desire a lot of food consumption will consume more food with the subsidy. The final indifference curve for these families is to the right of where the budget constraints intersect. Families that prefer more of other goods will get more food with the food stamps, since they cannot consume less than $100 worth of food. These families have indifference curves to the left of the intersection.

9 9 7. Concerned about the environmental effects of driving, Transport of Tomorrow (TOT), an environmental advocacy group, proposes increasing the tax on gasoline. a) Draw a budget constraint for a typical family before the proposed tax increase. Assume that gas currently sells for $3 per gallon, and that the typical family has $3,000 per month to spend. Other Consumption Gallons of Gasoline To draw the budget constraint, note that consumers can buy up to 1000 gallons of gasoline (= $3,000/$3), or $3,000 worth of other goods. Note that these endpoints are what we need for the budget constraint we want to show what is possible, not just what the consumers actually do.

10 10 b) Reproduce your graph from part (a). Suppose that TOT s proposed tax would increase the price of gas by $1 per gallon. Add a second budget constraint below representing this new price. Add a set of indifference curves showing how gasoline consumption would change if the tax were approved. Other Consumption 3000 O0 O1 G1 G Gallons of Gasoline Because the tax raises prices, we rotate the budget constraint. If the family only consumes other goods, they can still buy $3,000 worth of these goods. However, if they only buy gasoline, they can only get 750 gallons (= $3,000/4). Since the problem does not specify the amount of gasoline consumed, all that is important for drawing the graphs is that one indifference curve be tangent to each budget constraint, and that the two curves fit inside of each other, so that they do not cross. To show the change in consumption, I have labeled the pre-tax consumption with a 0 subscript, and post-tax consumption with a 1 subscript.

11 11 c) To counter claims that the tax is unfair, as well as general opposition to taxes, TOT proposes that the revenues raised from the gasoline tax be used to lower income taxes. Thus, the tax will raise no new revenue for the government. Reproduce your diagram from part (b). Add a third budget constraint showing the choices available to consumers with higher gasoline prices after the rebate. (Hint: Consider how much money for other consumption the family would have if they purchased the amount of gas in part (b) but did not have to pay the tax. The difference between that amount and the amount they have left after the tax is the tax revenue.) Other Consumption 3000 O 1 O0 O1 G1 G Gallons of Gasoline The key to this problem is the hint. The difference between the two budget constraints is due to the tax. Thus, for any quantity, the difference between the two constraints is the amount of money paid to the government. In this case, the family consumes G 1 after the tax. They have O 1 left to spend. If they had purchased G 1 before the tax, they would have had O 1 to spend. The difference (O 1 - O 1 ) is the tax revenue. For example, if they would have $2,500 left purchasing this amount before the tax, and $2,000 left purchasing the same amount after the tax, the other $500 must go to the government as tax revenue. Thus, the new budget constraint has a steep slope, parallel to the one drawn in part (b), and goes through the original budget constraint at the quantity G 1. I have made this new line blue to highlight its position.

12 12 d) Compared to their pre-tax welfare, would consumers be better off, worse off, or equally happy if the tax and rebate plan is put into effect? Explain As I ve drawn the curves above, consumers are worse off with the tax and rebate plan. Although the rebate helps compensate them, it is not enough to get them back to their original indifference curve. Note that the original indifference curve is infeasible with the blue budget constraint. The reason is that the compensation is only equal to the amount of revenue raised by the tax. As gasoline prices rise, consumers substitute away from gasoline and purchase more of other goods. Because of this substitution effect, the revenue that is raised is not sufficient to get consumers back to their original indifference curve. The key here is that the new indifference curve goes through the original budget constraint. The old indifference curve only touches that constraint in one place. Thus, it is unlikely for the new line to go through the old budget constraint. However, it is possible. If you drew the curves so that there was little change in gasoline consumption, the revenue raised may be sufficient to compensate consumers for their lost welfare. As long as your answer to this question was consistent with your drawing in part (c), either answer is acceptable. The intuition here is that there is a substitution effect people consume less gasoline after the tax, which reduces government revenue and an income effect using the revenue to lower income taxes allows consumers to increase their welfare. One makes consumers better off, and the other makes consumers worse off. For consumers to be better off, the income effect has to dominate the substitution effect. 8. You manage one department in a large corporation. Two years ago, you had 20 workers and produced 40,000 units. The company allocated 10 more workers to your department last year, and output increased to 45,000. You just received a memo from your boss indicating that he is very concerned about the 500-unit fall in the average productivity of your workers. How can you defend yourself? Defend yourself by noting that you were only given additional labor. Because of diminishing returns to inputs, the marginal productivity of the additional labor was less than before. Since marginal product was falling, average product must fall. The problem is likely one of capacity constraints. If you were also given more capital to work with, the productivity of the labor could be maintained.

13 13 9. You are in charge of cost control in a large metropolitan transit district. A consultant you have hired comes to you with the following report: Our research has shown that the cost of running a bus for each trip down its line is $30, regardless of the number of passengers riding the bus. Each bus can carry 50 people. At rush hour, when the buses are full, the average cost per passenger is 60 cents. However, during off-peak hours, average ridership falls to 18 people, and average costs soar to $1.67 per passenger. As a result, we should encourage more rush hour business when costs are cheaper, and discourage off-peak business when costs are higher. Should you follow the consultant s advice? Why or why not? You should not follow the consultant s advice. The problem with the advice is that he or she is ignoring why the costs vary. Because the cost of running a bus is fixed, the average cost falls as the number of riders increases. Lowering ridership during off-peak hours will increase average costs. Similarly, the buses are currently full at rush hour. The only way to increase ridership during rush hour is to run more buses (assuming more buses are available), since the current buses are filled to capacity. Thus, adding more riders at rush hour leads to greater fixed costs. Rather than lowering ridership during off-peak hours, it would make more sense to encourage more ridership then. For example, charging a lower fare during off-peak hours, and a higher fare during rush hour, would encourage those with flexible schedules to take the bus during off-peak hours.

14 Tom s Terrific Turkeys is getting ready for the Thanksgiving rush. Turkeys sell for $30 each, and the market is perfectly competitive. Tom has prepared the following data for his firm: Q TC MC ATC AVC 0 $ $20 $10 $20 $10 2 $35 $15 $17.5 $ $55 $20 $18.33 $15 4 $80 $25 $20 $ $110 $30 $22 $20 6 $145 $35 $24.17 $22.5 a) What are the fixed costs for Tom s firm? How do you know this? Tom s fixed costs are $10. We know this because he has to pay $10 even if he does not produce any turkeys. b) Given the current market price of $30, at what quantity would Tom maximize profits? Explain the economic intuition behind your answer. Since the turkey market is perfect competition, Tom is a price taker, and can sell as many turkeys as he can at $30. Thus, Tom s marginal revenue is $30. To maximize profit, Tom should equate marginal revenue to marginal cost. This occurs when Tom sells 5 turkeys. At this quantity, the amount of extra money he makes by selling a turkey is the same as the additional cost of producing another turkey. c) Is a price of $30 a long-run equilibrium for the turkey industry? Why or why not? No. Tom makes a profit of $40 when he sells 5 turkeys at $30 each. (Total revenue = 5 x $30 = $150, and total cost = $110). In long-run equilibrium, firms must make 0 profits. Because there are profits available, firms will enter the turkey industry until the price falls enough so that no more profits are available. d) Suppose the price fell to $15? How many turkeys would Tom sell now? Would he make a profit? Should Tom continue to operate in the short run? Why or why not? Tom would sell 2 turkeys. He would lose $5. He should continue to operate, however, since he is at least covering his variable costs, and has some money left to pay some of his fixed costs. If he decided to shut down, he would lose $10 (his fixed costs). Obviously, this is worse than losing $5.

15 This question asks you to consider the market for cab rides in Metropolis. The city is currently served by several cab companies, each who own multiple cabs and hire drivers to operate them. The number of cab companies is sufficiently high to consider the market perfectly competitive. a) The industry is currently in long-run equilibrium. Using two diagrams, one to represent the market for cab rides, and a second to represent the costs of a typical cab company, illustrate the current price, quantity and profits of a typical cab company. Explain why you have drawn the curves as you did. b) To reduce traffic in Metropolis, city managers have reduced the number of parking spaces in the city. This has reduced the number of people who bring their own cars into the city, and increased demand for cab rides. Show how this affects the market equilibrium, price, and profits immediately after the policy takes affect. Using one diagram for the cab ride market and a second for a typical cab company, illustrate below. c) Will the scenario you have described in part (b) be a stable long-run equilibrium? Why or why not? Once again using separate diagrams for both the industry and a typical cab company, illustrate the long run equilibrium for cab rides in Metropolis. d) To avoid the possibility you discuss in (c), cab companies lobby for licensing rules that prohibit new entry. They argue that, to avoid new congestion problems, only drivers approved by the city should be allowed to operate cabs. Moreover, they argue that the number of approved drivers should equal to the number of drivers operating before the number of parking spaces was reduced. How would that change your answer to part (c)? Why? e) Economists often call such lobbying efforts rent seeking behavior. Why do you think this is? What is the most that the industry would be willing to spend on such lobbying? a) In long-run equilibrium, firms are making zero economic profits. The price must be equal to the marginal cost at the point where MC intersects the AC curve. Market P S $ Typical company MC AC P0 P0 = MR = AR D Q0 Q q0 q b) The new policy increases demand for cab rides, so demand shifts to the right. In the short run, increased demand leads to a higher equilibrium price and quantity. Each cab company provides more rides than it did before, and earns positive economic profits. Market P $ S P1 P0 Typical company Profits MC AC P1 = MR = AR D1 D0 Q0 Q1 Q q0 q1 q

16 16 c) No, it will not be a stable long-run equilibrium. Since cab companies are making positive economic profits, more companies will enter the market, shifting supply out. As a result, the price of cab rides will fall. This will occur until the price returns to its original level, with cab companies making zero economic profit. Market P $ S0 S1 Typical company MC AC P0 P0 = MR = AR D1 D0 Q0 Q2 Q1 Q q0 = q2 q1 q d) By restricting the number of drivers, supply would not be able to shift out. The result of part (b) would remain in place, and current cab companies would earn positive economic profits. e) The positive profits earned in part (d) are an example of economic rent. Intuitively, the extra value from the restriction is now capitalized into the price of a cab company. If the owner of a cab company making long-run economic profits decided to sell the company, she would be able to sell for a higher price than for a cab company making zero economic profits. Since the policies that result from this lobbying result in economic rent, economists often refer to such behavior as rent seeking. The most an industry would be willing to spend on rent seeking is the total value of the profits to the industry.

17 a) Explain how perfectly competitive markets result in output efficiency. b) Explain why monopolies are a type of market failure. In particular, what part of your answer to part (a) is violated when a product is produced by a monopoly? a) Perfectly competitive markets result in output efficiency through each individual actor maximizing their own self interest. Consumers maximize utility, so that MU X P MRS X XY MUY PY At the same time, producers maximize profits, so that PX MC X PY MCY Putting these together, we see that MRS MU P MC X X X XY. MUY PY MCY Intuitively, resources are allocated so consumers have the maximum possible utility and producers have the maximum possible profit. b) Monopolies are a market failure because the price of the good sold is greater than marginal cost. This occurs because P > MR for a monopolist. As a result, the second equation in part (a) is violated. There is too little of the good produced by the monopolist.

18 Doug's Dogs has the exclusive rights to hot dog vending at SU football games. Assume that the marginal cost of producing hot dogs is constant at $1. Daily demand for hot dogs is P=5-(Q/20). Assume that fixed costs equal zero. a) Find Doug's profit-maximizing quantity of hot dogs and the price at which hot dogs are sold. b) What are Doug's profits? What is the consumer surplus? c) Suppose competition is allowed among hot dog vendors at the games. What will the new price and quantity be? Explain how this problem differs from the monopoly problem above. d) Find the new consumer surplus and profits. How does the sum of consumer surplus and profits in the monopoly case (part b) compare to consumer surplus with perfect competition? Explain any differences between the two. a) Profits are maximized where MR=MC. Since Doug is a monopolist, we know that his marginal revenue curve bisects the demand curve faced by Doug. Thus, MR = 5 - (Q/10). MR = 5 - (Q/10) = 1 = MC Q/10 = 4 Q = 40 To get the price, we need to look at the demand curve, to see how much consumers are willing to pay for 40 hot dogs. We get: P = 5 - (40/20) P = 3 b) Doug s profits are total revenue minus total cost. P 5 Total revenue = PxQ = $120. Because marginal costs are constant and there are no fixed costs, we can get total costs by multiplying MCxQ. Thus, total costs are $40. His profits are $80. A B On the graph to the right, consumer surplus is equal to areas A and B. This area is a triangle with base 40, and a height of 2 (=5-3). Thus, consumer surplus = 0.5(40)(2) = $40. D Q MR c) If competition is allowed, each vendor will now be a price taker, so that MR= P. In equilibrium, MR is equated with MC, which is 1. Thus, the new equilibrium price is P = 1. To get Q, we plug into the demand equation to get: 1 = 5 - (Q/20) Q/20 = 4 Q=80. d) Now, the consumer surplus is areas ABCDE. This is a triangle of base 80, and height 4. Its area is 0.5(80)(4) = 160. Thus, consumer surplus = $160. To calculate profits, note that total revenue = PQ = 80, and total cost = MCxQ = 80. Thus, there are no profits. The sum of consumer surplus and profits is $40 greater than the sum from before. The difference was the deadweight loss from the monopoly (area E). 1 3 C D E MC

19 A computer programmer lobbies against copyrighting software. He argues that everyone should benefit from innovative programs written for personal computers, and that exposure to a wide variety of computer programs will inspire young programmers to create even more innovative programs. Considering the benefits possibly gained by his proposal, do you agree with the programmer s position? There is no one correct answer to this question. I would argue that the programmer is wrong, although other answers are acceptable. The programmer is right on one point. More innovative programs would benefit more people. This is because the knowledge contained in these programs is a public good. It is non-rival -- one person taking advantage of a program does not prevent others from doing so. It is also non-excludable -- there is no way to prevent others from using this knowledge. However, it is the non-excludable nature of knowledge that led to copyrights being used. Copyrights give the programmer the property rights to their ideas, so that they can charge money for them. Without these copyrights, programs would be underprovided. There would be no incentive to create new programs, since, due to the non-excludable nature of knowledge, there would be no way for programmers to be compensated for their work. It is likely that removing copyrights would lead to less, not more, innovative programs. In the past, many people answered this question by discussing externalities, rather than public goods. This is O.K., but you need to be careful when you do this. An externality is created when a person s actions affect someone else, and that person is not charged or compensated for the activity. In this case, there is a positive externality to the programs. Thus, the private marginal benefits of programming are less than the social marginal benefits. An efficient level of production occurs where SMB = MC. Copyrights help to bring this about. Recall that private production occurs where PMB = MC. Without copyrights, the private marginal benefits would be very low, because of non-excludability. Since copyrights allow individuals to be compensated for their work, it shifts out the private marginal benefit curve. Thus, copyrights help to internalize the external benefit. In a sense, the higher prices that result from copyrights act as a subsidy from consumers to programmers. Without copyrights, the level of programming provided by the private market would decrease. Note, however, that this does not imply that copyrights lead to an efficient amount of software being produced. It simply means that more will be produced.

20 Suppose that Elmo, Big Bird, and Oscar are about to vote on whether the government of Sesame Street should undertake a town beautification project. Let the net benefits of a particular project be $150, $140, and $50 respectively for Elmo, Big Bird, and Oscar. a) If the project costs $300 and the costs are to be shared equally, would a majority vote to undertake the project? What would be the net benefit to each person under such a scheme? Would total net benefits be positive? b) Suppose that the project costs $375 and again costs are to be shared equally. Now would a majority vote for the project, and would total net benefits be positive? c) Suppose votes can be bought and sold in a free market. Describe what kind of trades you might expect in parts (a) and (b). a) If costs are shared equally, each must pay $100. Begin by considering the benefits minus cost for each individual: Elmo = = $50 Big Bird = = $40 Oscar = = -$50. Since two of the three voters have positive net benefits, the beautification project will pass. Total net benefits are $40, so this is an efficient outcome. b) In this case, the cost per person is $125. Recalculate net benefits to get: Elmo = = $25 Big Bird = = $15 Oscar = = -$75. Again, the project will pass. However, this time the result is inefficient, since total net benefits are negative (-$35). c) If votes could be bought and sold, Oscar would simply need to make an offer that would convince either Elmo or Big Bird to change his vote. Since Big Bird has lower net benefits in each case, it would be cheaper to buy Big Bird s vote. For (a), suppose Oscar offered Big Bird $45 to vote no. Big Bird would be better off (he would get $45 cash, rather than $40 of benefits from the project). Similarly, Oscar only loses $45, rather than $50. Similarly, Oscar could offer Big Bird some amount greater than $15 to get him to vote no in part (b). Note that trades are possible in both (a) and (b). However, the trades have the opposite implications for efficiency. In part (a), the trade turns an efficient outcome into an inefficient one. In part (b), the trades turn an inefficient outcome into an efficient one.

21 Slimy Steel operates a steel mill along the Kansas River. Slimy s uses water from the river during production. The marginal cost of steel production is: MC = Q where Q is the quantity of steel produced (in tons). Slimy Steel sells its output at a market price of $70/ton. Because the industry is perfectly competitive, the firm s action does not affect the market price. Downstream from the plant, the Boy Scouts run a camp site which uses the river for swimming and fishing. Pollution from steel production reduces the quantity of fish available and makes swimming very unpleasant. Each ton steel produced emits a pound of pollutants that causes a loss of recreation opportunities worth $12. a) How much steel will be produced? b) What is the efficient level of steel production? If the government used a Pigouvian tax to achieve this goal, what would the tax be? a) Without government intervention, Slimy Steel will produce steel until the marginal cost equals the marginal benefit. Because the steel market is competitive, Slimy must take the price of steel as given at $70/ton. Thus, $70 is the marginal benefit from one ton of steel production. The optimal quantity for Slimy Steel is: MC = Q = 70 = MB 6Q = 60 Q = 10 b) To find the efficient level of production, we equate the social marginal cost and marginal benefit. Social marginal cost is the sum of private marginal costs (10 + 6Q) and marginal damages (12). (Note that the marginal damage is 12, not 12Q. 12Q is the total marginal damage for any level of output the damage done by each unit times total output. To find the optimal point, we must work with marginal values.) The algebra needed to find the solution is given on the left below. On the right is a diagram that illustrates the optimal level of steel production, as well as the private market solution. SMC = MPC + MD = Q SMC = Q SMC = Q = 70 = MB 6Q=48 Q = 8 A Pigouvian tax should be set equal to the marginal damage at the efficient level of output. For this problem, marginal damage is constant at $12. Thus, the tax should equal $12. MSC = MPC + MD P 70 MPC MB MD Q

22 In a certain region, two firms emit 600 units of emissions into the air. In order to comply with the Clean Air Act, the two firms combined must abate pollution emissions by 300 units. The marginal abatement cost (MAC) fo the first firm is given by: MAC 1 = 0.5Q 1. MAC for firm 2 is given by MAC 2 = Q 2, where Q 1 and Q 2 represent the quantity of emissions controlled by each firm. a) Suppose the EPA requires each firm to abate by 150 units. What are the MAC s of the two firms under this regulation? Is this an efficient way to reduce pollution? Why or why not? b) What is the efficient level of abatement for the two firms? (Hint: Using what is true about MAC when abatement is efficient, first find the relative amounts of abatement that should be done by each firm. Then, use that result to find out how much each firm must do to reduce pollution by 300 units total.) c) Suppose the EPA auctions off 300 pollution permits at a competitive auction. Each permit allows a firm to emit one unit of pollution. What is the market price of these permits? a) If each firm has to abate 150 units of pollution, the MAC of firm 1 = (0.5)(150) = $75, and the MAC of firm 2 = $150. This is not an efficient way to reduce pollution. Efficiency is achieved when the total reduction is done for the least possible cost. This occurs when the marginal abatement costs are equal. Since they are not, it would be more efficient for firm 1 to abate more, and for firm 2 to abate less. b) As stated above, the efficient level of abatement occurs when MAC s are equal. Simply equate MC 1 and MC 2 and solve for q: MC 1 = 0.5q 1 = q 2 = MC 2 This tells us that firm 1 should control twice as much pollution as firm 2. Now, use the constraint that total reduction must equal 300 units to find the optimal levels for each firm: 300 = q 1 + q 2 = q q 1 = 1.5q 1 q 1 = 200 q 2 = 0.5q 1 = 100 c) Recall that permits bring about an efficient solution, because each firm will be willing to trade permits until the MAC s are equal. Furthermore, a firm will buy a permit when the price is lower than MAC, and will prefer to abate if MAC is lower than the permit price. Thus, the price of a permit will be equal to the MAC at the efficient level of abatement. By plugging our solution to part (b) into the MAC functions, we see that the MAC is equal to $100. Thus, the permits will sell for $100 each.

23 Suppose that the city of Lawrence is debating whether to begin a two-year project designed to fix up the streets of Lawrence. They will spend $500,000 on labor now, and an additional $500,000 next year. In addition, the city must also pay out an additional $100,000 this year to purchase materials for the project. The present value of the benefits generated by better-quality roads is estimated to be $1 million. The city uses a 5% discount rate to evaluate all public projects. a) What is the present value of costs associated with the project? b) Is the project admissible? Why or why not? a) The formula for the present value of the costs is: PV C1 (1 r) C0. In this case, the project involves a $600,000 cost in year 0, and a $500,000 cost in year 1. The present value is: 500,000 PV 600,000 $1,076, (1 0.05) b) The project is worth doing if the present value of all costs is less than the present value of the benefits, which is given as $1 million. Since that is not the case here, the project is not admissible. 19. Suppose that a proposed dam would provide irrigation water to be distributed free to farmers, who would use it to grow an additional 20,000 bushels of sugar beets per year. The price of sugar beets is $1 per bushel. In addition to the water, the production of the sugar beets would require $8,000 worth of other inputs per year. No alternative source of irrigation water is available. a) Assume that the price of sugar beets is determined in a perfectly competitive market, in which millions of bushels of beets are sold every year. What is the annual value of the irrigation water? Explain. b) Currently, the risk-free nominal interest rate is 6.25%, and inflation is 3.5%. Show how you would find the present value of the net benefits found in part (a), assuming that the project has a lifespan of 30 years. (Note: You do not need to carry out the calculation. Simply show how you would set it up.) c) Now, suppose that all the facts from part (a) remain unchanged, except that the government sets a price floor for sugar beets above the market equilibrium price and that it supports this price by buying the excess supply of sugar beets and letting them rot. (Assume this policy is in place even before the irrigation project is being considered.) Now what is the value of the irrigation water produced by the project? a) The annual value of the irrigation water is the value of the additional sugar beets produced, minus the cost of other inputs used to produce the additional beets. Since beets are sold in a competitive market, we may use the market price to represent the value of beets. Thus, $20,000 additional beets are produced, with an additional $8,000 inputs used. The net value is $20,000 - $8,000, or $12,000.

24 24 b) To calculate the net present value, we need to calculate the present value of costs and benefits for each of the next 30 years. It is easiest to use the real rate of interest, so that we do not need to adjust the prices of beets and inputs for inflation each year. The real rate of interest is the risk-free nominal rate minus the rate of inflation. In this problem, it equals 2.75%. The general setup of the net present value calculation is as follows: For this example, we have: NPV B1 C1 B2 C2 BT C NPV B0 C0 2 1 r (1 r) (1 r) $20,000 $8,000 1 r $20,000 $8,000 (1 r) 1 $20,000 $8,000 2 T T $20,000 $8, (1 r) Note that I started with year 0 (that is, I did not discount the benefits and costs in the first year. Since the project lasts for 30 years, and the first year is 0, rather than 1, the last year is 29. For those that are interested, the NPV in this case comes out to $249,674. c) In this case, the market price does not represent the value of the beets. The additional beets simply rot. Consumers do not purchase them, and thus do not receive any value from them. Rather, the new beets simply add to the excess supply of beets that already exists as a result of the price floor. The additional revenue earned by farmers from selling the beets to the government is simply a transfer of resources from taxpayers to the farmers. 20. The National Park Service is considering removing two dams in Olympic National Park. These dams provide nearly 40% of the electricity used by the Daishowa pulp and paper mill in Port Angeles, Washington. The mill gets the rest of its power from the Bonneville Power Administration (BPA). If the dams are torn down, all of the mill s electricity will have to be purchased from the BPA. To evaluate the economic cost of the power lost if these dams are torn down, is the commercial rate for electricity charged by the BPA a good measure of the shadow price of electricity? Why or why not? The appropriate shadow price here would represent the marginal cost of using additional resources to produce power at BPA. Since electricity is sold through regulated monopolies, it is unlikely that the regulated price represents this marginal cost. For example, recall from the lecture on monopolies that average cost pricing is often used to regulate natural monopolies, since marginal cost regulation could result in utilities not earning enough to cover large fixed costs.