Answers to Text Questions and Problems in Chapter 7

Transcription

1 Answers to Text Questions and Problems in Chapter 7 Answers to Review Questions 1. If a policy is not efficient, then it can, by definition, be altered in a way that benefits at least some people without harming others. Economists favor efficient policies, because such policies make additional resources available for the pursuit of other goals. 2. The proposed policy will make retirees better off by $10 million per year but will make workers worse off by $1 million per year. To assure that everyone is better off, this policy could be combined with a measure that makes workers better off by at least $1 million per year and makes retirees worse off by less than $10 million per year. 3. More inelastic demand or supply increases the size of the economic surplus in a perfectly competitive market. 4. The less elastic is supply, the smaller is the loss of economic surplus caused by a price ceiling, due to the much smaller response to a reduction in price. 5. The less elastic is supply, the larger is the distributive impact of a price ceiling.. The loss experienced by participants in the market for a taxed good will be offset in part by the benefit citizens receive from the public goods purchased with the resulting tax revenue. 7. supports encourage producers to expand production beyond the point at which the marginal cost of production is equal to its marginal benefit (i.e., the point at which supply and demand intersect). All output beyond that point costs more to produce than what buyers are willing to pay for it. Answers to Problems 1. The equilibrium price is $14 per unit, so consumer surplus is (2 14) + (24 14) + (22 14) + (20 14) + (18 14) + (1 14) = $42. Producer surplus is (14 2) + (14 4) + (14 ) + (14 8) + (14 10) + (14 12) = $42. Total economic surplus is $ Supply Demand Quantity

2 a. Consumer surplus is the triangular area between the demand curve and the price line. Its area is equal to ½ b h, where b is the base of the triangle and h is the height. The base is units and the height is 1.5 units, measured in dollars. Therefore, consumer surplus is (0.5)($1.5)(), or $4.50 per week. b. Producer surplus is the triangular area between the supply curve and the price line. Using the baseheight formula, it is (0.5)($4.50)(), or $13.50 per week. c. The maximum weekly amount that consumers and producers together would be willing to pay to trade in wristwatches is the sum of gains from trading in wristwatches namely, the total economic surplus generated per week, which is $18 per week. 3a. At a price of $7.50, the quantity supplied per week = 2. The quantity demanded at this price is 18 per week, which implies a weekly shortage of 1 wristwatches. b. The weekly economic surplus lost as a result of the price ceiling is the area of the dark-shaded triangle in the diagram, or the sum of the areas of the two triangles ABC and ACD. Using the information given in the graph, this amount is calculated as (0.5)(4)(1) + (0.5)(4)(3) = $8 per week. B 12 P=+0.75Q 1 C 4 3 D A P= Q 2 48 Quantity c. At a price of $7.50, only 2 wristwatches are supplied. At that quantity, buyers will value a third wristwatch at $11.50, and sellers will provide an additional wristwatch at a cost of only $7.50. Thus, if a third wristwatch were traded at a price of, say, $10, the buyer would be better off by $1.50, and the seller better off by $ a. When there is no charge for the tour, the surplus enjoyed by someone who takes it equals his or her reservation price for the tour. If the warden operates the tour on a first-come first-served basis, Penny, Fran, and Faith will be turned away. The combined consumer surplus when the four who arrive first take the tour is $20 + $14 + $30 + $15 = $79. b. An offer of $15 compensation generates 3 volunteers to return another day: Fran, Jon, and Jack. The four who go on the tour receive a total consumer surplus of $40 + $30 + $20 + $17 = $107. The warden pays $45 in compensation payments to the three volunteers, which causes him a loss in economic surplus of $45 that is exactly offset by the gain in economic surplus to the three volunteers. Total economic surplus from the tour operation is now $107 $28 higher than before. c. The compensation policy is more efficient than the first-come first-served policy because it establishes a market for a scarce resource that would otherwise be allocated by non-market means. People who choose not to miss the tour that day are paying an opportunity cost of $15 not to miss it. Therefore, only those people to whom the tour is worth more than $15 will actually take it. d. Suppose the warden auctions off the right to take the tour by steadily increasing the tour price by $1 increments until only 4 people are willing to pay. The auction will stop when the price reaches $1, and Faith, Herman, Kate, and Penny will be the four remaining. The warden will collect $4 from the auction. He can then give refunds to Herman and Kate, who would have gotten to go for free under the first-come first-served scheme, so they will be just as well off as before. He can give $1 to Jack, which is $1 more

3 than enough to compensate him for not getting to go. And he can give $15 to Jon, which is also $1 more than enough to compensate him. That leaves the warden with $1, so he too is better off than before. Faith is $1 better off than before, and Penny is $24 better off than before. All others are exactly as well off as before. 5a. The equilibrium price is $5 and the equilibrium quantity is 3000 units per week. The consumer surplus is the area below the demand curve and above the equilibrium price, which is (0.5)($3)(3000) = $4500 per week. The producer surplus is the area above the supply curve and below the equilibrium price, which is (0.5)($3)(3000) = $4500 per week. Therefore, the total economic surplus is $9000 per week. b. The tax shifts the vertical intercept of the supply curve up by $2 to $4. The new equilibrium price and quantity are $ and 2000 respectively. The tax revenue is $2(2000), or $4000 per week. Consumer surplus is now (0.5)($2)(2000) = $2000 per week. Net of the $2 tax, sellers receive a price of $4 per unit. Their surplus is (0.5)($2)(2000) = $2000 per week. c. The tax revenue collected is ($2 per unit)(2000 units per week) = $4000 per week. Counting the revenue from the tax as part of total economic surplus, the new total economic surplus is thus $2000 per week + $2000 per week + $4000 per week = $8000 per week, or $1000 per week less than without the tax. a. 8 P = 4 + Q P = 2 + Q 4 2 P = 8 Q b. 2 3 Quantity 8 P = 5/3 Q 5 P = 8 Q 3 Quantity

4 c. P = 5, Q = 3. This is the same equilibrium price and quantity as in problem 5(a). d. Consumer surplus = (0.5)($3)(3000) = $4500, and producer surplus = (0.5)($5)(3000) = $7500, so total economic surplus = $ $7500 = $12,000. Consumer surplus is the same as in problem 5(a), but producer surplus is greater since the supply curve is less elastic, so total economic surplus is also greater. 7. When the price ceiling is removed, suppliers are able to sell more milk at a higher price, so they are better off; producer surplus rises by ($1)(1000) + (0.5)($1)(2000) = $2000. Buyers who were previously unable to obtain milk are better off now that they can obtain milk at the going price; their consumer surplus rises by (0.5)($1)(2000) = $1000. But buyers who were previously able to buy milk at the low price are worse off now that the price has risen; their consumer surplus falls by ($1)(1000) = $1000. Overall, total surplus rises by $ (d) All of the answers are consequences of the price support. 9. At a price of $1 per litre, Islandians will consume 5 million litres of oil per year. The true marginal cost of oil for the nation is the international price, which is $2 per litre. If Islandians had been charged this price, they would have consumed only 4 million litres per year. The lost surplus from consuming the larger amount of oil is the cumulative difference between the cost of the oil and the most they would have been willing to pay for it. This difference is the area of the shaded triangle in the diagram, or $500,000 per year. P ($/litre) Lost surplus Q (millions of litres/yr) 10a. As there are one million households, the individual household s demand for oil would be P = Q, where Q is in litres, rather than millions of litres. The demand curve is as shown in the diagram. P ($/litre) A Lost B 2 1 D 4 C E 5 Q (litres/yr) b. With the subsidy, each family receives consumer surplus equal to the area of triangle ADE. Without the subsidy, consumer surplus equals the area of triangle ABC. The difference is the area BCED, which equals $4.50 per year. c. The government s oil subsidy per family is ($1/litre)(5 litres/yr) = $5 per year. So the government could cut each family s taxes by $5 per year by not subsidizing oil.

5 d. The family s net gain would be the $5 it saves in taxes minus the $4.50 it loses in consumer surplus from its heating oil purchases, or $0.50 per year. e. The aggregate gain from the tax cut and removal of the subsidy is $500,000 per year, the same as the loss in total consumer surplus that resulted from the subsidy. 11. Profit is the difference between the company s total revenue and its total cost. Producer surplus is the difference between total revenue and the firm s reservation price for the quantity it sells. So the question boils down to whether the firm s total cost of producing a given quantity is the same as its reservation price for selling that quantity. Its reservation price is, by definition, the lowest total dollar amount for which it could sell that quantity and still be no worse off than before. That dollar amount is the sum of the respective marginal costs of producing each unit. So producer surplus is the difference between total revenue and the sum of all marginal costs incurred. That is not the same as profit, which is total revenue minus the sum of not only all marginal costs incurred, but also fixed costs. Sample Homework Assignment 1. Assume the market for fruit from a local fruit stand has the supply and demand curves given below. P = Q P = Q Where P is in dollars and Q is in hundreds of pounds. Use the information given to: a. find equilibrium price and quantity in the market. b. calculate consumer surplus at equilibrium. c. calculate producer surplus at equilibrium. d. determine total economic surplus. 2. Using the market information provided in question 1 above, calculate the loss in total economic surplus if a price ceiling is imposed on the market at a price of $ Assume the supply and demand curves for cars given below. Calculate the deadweight loss that results from a tax of $100 per car collected from sellers. Hint: graph the curves. P = 15, Q P = 10,000 Where P is in dollars and Q is in millions of cars per month. Multiple Choice Quiz 1. A situation is efficient if a. no change can help some people without hurting others. b. the gain for some people offsets the loss for others. c. the gain for some people more than offsets the loss to others. d. consumer surplus is maximized. e. producer surplus is maximized. 2. Assume I bring 30 cookies into a class with 30 students. Which of the following situations is efficient? a. I give one cookie to each student. b. I give all 30 cookies to one student.

6 c. I divide all of the cookies equally among the dark-haired students. d. I let the best 15 students have 2 cookies each. e. All of the above.

7 3. If a market is not in equilibrium, which of the following is always true? a. The quantity exchanged is below the equilibrium quantity. b. The quantity exchanged is above the equilibrium quantity. c. The price is above the equilibrium price. d. The price is below the equilibrium price. e. No transaction can be made that will benefit both a buyer and seller. 4. Total economic surplus is a. the sum of all the individual economic surpluses gained by buyers and sellers in a market. b. the sum of producer and consumer surplus in a market. c. maximized at market equilibrium. d. a measure that can be used to determine efficiency. e. all of the above. 5. A price ceiling a. prevents sellers from charging less than a certain amount. b. leads to efficiency in the market. c. must be above equilibrium price to have an effect on the market. d. results in a loss in total economic surplus. e. all of the above.. A policy that reduces total economic surplus a. always changes who gets the largest slice of the pie. b. gives everyone a larger slice of the pie. c. decreases the size of the pie. d. redistributes a pie of equal size. e. makes society better off (improves the taste of the pie). 7. Rent control will a. increase consumer surplus, but not producer surplus. b. increase producer surplus, but not consumer surplus. c. increase both consumer and producer surplus. d. decrease both consumer and producer surplus. e. decrease producer surplus, but vary in their effect on consumer surplus. 8. A price floor a. guarantees that suppliers will receive at least a specified amount for their product. b. guarantees that consumers will pay at least a specified amount for a product. c. increases total economic surplus. d. leads to economic efficiency. e. creates a shortage in the market. 9. Which policy is most efficient when dealing with overbooked airline flights? a. First-come first-served policy. b. A compensation policy. c. A price ceiling. d. A price floor. e. Random selection.

8 10. If the government places a tax on sellers in a market, who will pay the tax? a. Only sellers. b. More sellers than buyers. c. Buyers and sellers equally. d. Only buyers. e. It depends on the situation in the market. Problems/Short Answer 1. Assume a tax of $10 per unit is placed on sellers in the market for bicycles. Use the supply and demand functions below to find each of the following: P = 150 P = Q where P is in dollars and Q is in millions of bicycles. a. consumer surplus before the tax. b. consumer surplus after the tax. c. the loss in consumer surplus from the tax. d. How does deadweight loss from the tax compare to the loss in consumer surplus in this particular situation? Explain. 2. Use a graph to show the effect of a price ceiling on total economic surplus. Be sure to identify consumer and producer surplus before and after the price ceiling using your graph. Answer Key to Extra Questions in Instructor s Manual Sample Homework Assignment 1a. P = $0.2, Q = 8. b. Consumer surplus = 1/2 (8) ( ) = 1/2 (8) (0.4) = 2.5. c. Producer surplus = 1/2 (8) ( ) = 1/2 (8) (0.1) = 0.4. d. Total economic surplus = C.S. + P. S. = = The loss in economic surplus is area A + area B on the graph below = [1/2 (3) (0.24)] + [1/2 (3) (0.0)] = 1/2 (0.72) + 1/2 (0.18) = = Supply A 0.2 B 0.20 Demand 5 8 Quantity

9 3. In the graph below, the deadweight loss is equal to area A, the loss in consumer surplus, which is 1/2 (100) (0.04) = 1/2 (4) = 2 million cars. 15,000 10,100 Supply + $100 A 10,000 Supply Demand Multiple Choice 1. a 2. e 3. a 4. e 5. d. c 7. e 8. a 9. b 10. e Problems/Short Answer Quantity 1a. C.S. before the tax = 1/2 (20) (150) = 1/2 (3000) = b. C.S. after the tax = 1/2 (18.7) (140) = 1/2 (213.8) = c. The loss in consumer surplus = = d. Since the supply curve is horizontal (the price elasticity of supply is infinite), there is no producer surplus in this case. Consumer surplus decreases by , but (10)(18.7) = is collected in tax revenue. The deadweight loss is equal to the loss in consumer surplus less the tax revenue, which is =.4. The deadweight loss triangle, calculated directly, equals 1/2 (1.33) 10 = 1/ =.5 (which equals the above when rounding error is considered).

10 2. a Supply b c d e f h g Demand ceiling Quantity Consumer surplus before the ceiling = area ace Consumer surplus after the ceiling = area abgf Producer surplus before the ceiling = area ceh Producer surplus after the ceiling = area fgh Loss of economic surplus is shown on the graph as the shaded area.