微观经济学（平狄克）课后习题答案平狄克《微观经济学》课后答案 9

CHAPTER 9 THE ANALYSIS OF COMPETITIVE MARKETS TEACHING NOTES With the exception of Chapter 1, Chapter 9 is the most straightforward and easily understood chapter in the text. The chapter begins with a review of consumer and producer surplus. If you have postponed these topics, you should carefully explain the definition of each (refer to teaching suggestions in Chapters 4 and 8). While Section 2 discusses efficiency in competitive markets by comparing competitive outcomes with those under market failure, more analytic discussion of efficiency is left for Chapter 16. The presentation in each section of this chapter follows the same format: there is a general discussion of why market intervention leads to deadweight loss, followed by the presentation of an important policy example. Each section is discussed in one review question and applied in at least one exercise. Exercise (1) focuses on minimum wages presented in Section 9.3. Exercises (4) and (5) reinforce discussion of price supports and production quotas from Section 9.4. The use of tariffs and quotas, presented in Section 9.5, can be found in Exercises (3), (6), (7), (10), and (12). Taxes and subsidies (Section 9.6) are discussed in Exercises (2), (8), and (14). Exercise (9) reviews natural gas price controls in Example 9.1, a continuation of Example 2.7. Exercise (4) may be compared to Example 9.4 and discussed as an extension of Example 2.2. REVIEW QUESTIONS 1. Deadweight loss refers to the benefits lost to either consumers or producers when markets do not operate efficiently. The term deadweight denotes that these are benefits unavailable to any party. For example, an effective price ceiling reduces the price below the market equilibrium price. This policy causes a loss of both consumer and producer surpluses. Consumer surplus decreases because less is purchased and producers do not capture all of this decrease. Producer surplus decreases because less is produced and consumers do not capture all of this decrease. Surplus not captured by market participants is deadweight loss. 2. When the supply curve is completely inelastic, the imposition of an effective price ceiling transfers all loss in producer surplus to consumers. Consumer surplus increases by the difference between the market-clearing price and the price ceiling times the market-clearing quantity. Consumers capture all decreases in total revenue. Therefore, no deadweight loss occurs. 3. If the supply curve was perfectly inelastic and demand increases, a price ceiling will increase consumer surplus. If the demand curve is inelastic, price controls may result in a net loss of consumer surplus because consumers willing to pay a higher price are unable to purchase the price-controlled good or service. The loss of consumer surplus is greater than the transfer of producer surplus to consumers. However, if demand is elastic (and supply is relatively inelastic) consumers in the aggregate will enjoy an increase in consumer surplus. 4. Because a higher price increases revenue and decreases demand, some consumer surplus is transferred to producers but some producer revenue is lost because consumers purchase less. The problem with a price floor or minimum price is that it sends the wrong signal to producers. Thinking that more should be produced as the price goes up, producers incur extra cost to produce more than what consumers are willing to purchase at these higher prices. These extra costs can overwhelm gains captured in increased revenues. Thus, unless all producers decrease production, a minimum price can make producers as a whole worse off. 5. Municipal authorities usually regulate the number of taxis through the issuance of licenses. When the number of taxis is below that which it would be without regulation, those taxis in the market may charge a higher-than-competitive price. State authorities usually regulate the number of liquor licenses. By requiring that any bar or restaurant that serves alcohol have a liquor license and then limiting the number of licenses available, the State limits entry by new bars and restaurants. This limitation allows those establishments that have licenses to charge a higher price for alcoholic beverages. Federal authorities usually regulate the number of acres of wheat or corn in production by creating acreage limitation programs that give farmers financial incentives to leave some of their acreage idle. This reduces supply, driving up the price of wheat or corn. 6. Price supports and acreage limitations cost society more than the dollar cost of these programs because less output is produced, driving prices above competitive levels. This smaller output decreases consumer surplus and leads to deadweight loss. (Note: This loss does not include payments to farmers, because these payments only redistribute the surplus from non-farmers to farmers. Thus, there is no loss to society as a whole from the transfer of surplus.) 7. Changes in domestic consumer and producer surpluses are the same under import quotas and tariffs. There will be a loss in (domestic) total surplus in either case. However, with a tariff, the government can collect revenue equal to the tariff times the quantity of imports and these revenues can be redistributed in the domestic economy to offset the domestic deadweight loss by, for example, reducing taxes. Thus, there is less of a loss to the domestic society as a whole. With the import quota, foreign producers can capture the difference between the domestic and world price times the quantity of imports. Therefore, with an import quota, there is a loss to the domestic society as a whole. If the national government is trying to increase welfare, it should use a tariff. 8. The burden of a tax and the benefits of a subsidy depend on the elasticities of demand and supply. If the ratio of the elasticity of demand to the elasticity of supply is small, the burden of the tax falls mainly on consumers. On the other hand, if the ratio of the elasticity of demand to the elasticity of supply is large, the burden of the tax falls mainly on producers. Similarly, the benefit of a subsidy accrues mostly to consumers (producers) if the ratio of the elasticity of demand to the elasticity of supply is small (large). 9. A tax creates deadweight loss by artificially increasing price above the free market level, thus reducing the equilibrium quantity. This reduction in demand reduces consumer as well as producer surpluses. The size of the deadweight loss depends on the elasticities of supply and demand. As the elasticity of demand increases and the elasticity of supply decreases, i.e., as supply becomes more inelastic, the deadweight loss becomes larger. EXERCISES 1. a.In a free-market equilibrium, LS = LD. Solving yields w = $4 and LS = LD = 40. If the minimum wage is $5, then LS = 50 and LD = 30. The number of people employed will be given by the labor demand, so employers will hire 30 million workers. Figure 9.1.a b. Let w denote the wage received by the employee. Then the employer receiving the $1 subsidy per worker hour only pays w-1 for each worker hour. As shown in Figure 9.1.b, the labor demand curve shifts to: LD = 80 - 10 (w-1) = 90 - 10w, where w represents the wage received by the employee. The new equilibrium will be given by the intersection of the old supply curve with the new demand curve: Therefore, 90-10W** = 10W**, or W** = $4.5 per hour L** = 10(4.5) = 45 million persons employed. Figure 9.1.b 2. a. To find the equilibrium price and quantity, equate supply and demand and solve for QEQ: 10 - Q = Q - 4, or QEQ = 7. Substitute QEQ into either the demand equation or the supply equation to obtain PEQ. PEQ = 10 - 7 = 3, or PEQ = 7 - 4 = 3. b.With the imposition of a $1.00 tax per unit, the demand curve for widgets shifts inward. At each price, the consumer wishes to buy less. Algebraically, the new demand function is: P = 9 - Q. The new equilibrium quantity is found in the same way as in (2a): 9 - Q = Q - 4, or Q* = 6.5. To determine the price the buyer pays, , substitute Q* into the demand equation: = 10 - 6.5 = $3.50. To determine the price the seller receives, , substitute Q* into the supply equation: = 6.5 - 4 = $2.50. c.The original supply curve for widgets was P = Q - 4. With a subsidy of $1.00 to widget producers, the supply curve for widgets shifts outward. Remember that the supply curve for a firm is its marginal cost curve. With a subsidy, the marginal cost curve shifts down by the amount of the subsidy. The new supply function is: P = Q - 5. To obtain the new equilibrium quantity, set the new supply curve equal to the demand curve: Q - 5 = 10 - Q, or Q = 7.5. The buyer pays P = $2.50, and the seller receives that price plus the subsidy, i.e., $3.50. With quantity of 7,500 and a subsidy of $1.00, the total cost of the subsidy to the government will be $7,500. 3. Figure 9.3.a shows the gains and losses from a per-pound subsidy with domestic supply, S, and domestic demand, D. PS is the subsidized price, PB is the price paid by the buyers, and PEQ is the equilibrium price without the subsidy, assuming no imports. With the subsidy, buyers demand Q1. Farmers gain amounts equivalent to areas A and B. This is the increase in producer surplus. Consumers gain areas C and F. This is the increase in consumer surplus. Deadweight loss is equal to the area E. The government pays a subsidy equal to areas A + B + C + F + E. Figure 9.3.a Figure 9.3.b shows the gains and losses from a per-pound tariff. PW is the world price, and PEQ is the equilibrium price. With the tariff, assumed to be equal to PEQ - PW, buyers demand QT, farmers supply QD, and QT - QD is imported. Farmers gain a surplus equivalent to area A. Consumers lose areas A, B, C; this is the decrease in consumer surplus. Deadweight loss is equal to the areas B and C. Figure 9.3.b Without more information regarding government policy, it seems sensible to assume that the Japanese government would avoid paying subsidies by choosing a tariff, but the rice farmers would prefer the subsidy. 4. a. Equating demand and supply, QD = QS, 28 - 2P = 4 + 4P, or P = 4. To determine the equilibrium quantity, substitute P = 4 into either the supply equation or the demand equation: QS = 4 + 4(4) = 20 and QD = 28 - 2(4) = 20. b.Because the free market supply by farmers is 20 billion bushels, the 25 percent reduction required by the new Payment-In-Kind (PIK) Program would imply that the farmers now produce 15 billion bushels. To encourage farmers to withdraw their land from cultivation, the government must give them 5 billion bushels, which they sell on the market. Because the total supply to the market is still 20 billion bushels, the market price does not change; it remains at $4 per bushel. The farmers gain $20 billion, equal to ($4)(5 billion bushels), from the PIK Program, because they incur no costs in supplying the wheat (which they received from the government) to the market. The PIK program does not affect consumers in the wheat market, because they purchase the same amount at the same price as they did in the free market case. c.Taxpayers gain because the government is not required to store the wheat. Although everyone seems to gain from the PIK program, it can only last while there are government wheat reserves. The PIK program assumes that the land removed from production may be restored to production when stockpiles are exhausted. If this cannot be done, consumers may eventually pay more for wheat-based products. Finally, farmers are taxpayers too. Since producing the wheat must have cost something, the program offers them a windfall profit. 5. a.If the quantities demanded and supplied are very responsive to price changes, then a government program that doubles the price of jelly beans could easily cost more than $50 million. In Figure 9.5.a.i, the shaded rectangle is the cost of the program. Figure 9.5.a.i On the other hand, if the demand and supply curves are inelastic, then it is conceivable that the program could cost less than $50 million. See Figure 9.5.a.ii. Figure 9.5.a.ii b.When the demand curve is perfectly inelastic, the loss in consumer surplus is $50 million, equal to ($0.5)(100 million pounds). This represents the highest possible loss in consumer surplus. Therefore, if the demand curve has any elasticity at all, the loss in consumer surplus would be less then $50 million. See Figure 9.5.b. Figure 9.5.b 6. a. To find the equation for demand, we need to find a linear function, e.g., P = a + bQD, such that the line it represents passes through two of the points in the table, e.g. (15,10) and (12,16). First, the slope, b, is equal to the “rise” divided by the “run,” Second, we substitute for b and one point, e.g., (15, 10), into our linear function to solve for the constant, a: , or a = 20. Therefore, . Inverting to obtain the demand curve in its usual form: QD = 40 - 2P. Similarly, we may solve for the supply equation: P = c + dQS, passing through two points, e.g., (6,4) and (3,2). The slope, d, is . Solving for c: or c = 0. Therefore, . Inverting to obtain the supply curve in its usual form: . b.The price elasticity of demand, ED , is equal to Here, is equal to the slope of the demand equation, i.e., -2. From the table or the demand equation derived in part a, at P = 9, QD = 22. Substituting into the equation for elasticity of demand: To determine the elasticity of demand at P = 12, QD = 16, follow the same procedure: c.The price elasticity of supply, ES, is equal to Here, is equal to the slope of the supply equation, i.e., . At P = 9, QS = 6. Substituting into the equation for the elasticity of supply: At a price of 12, the quantity supplied is equal to 8. Substituting into the formula for the elasticity of supply: d.If there are no trade restrictions, the world price of $9.00 will prevail in the U.S. From the table, we see that at $9.00 domestic supply will be 6 million pounds. Similarly, domestic demand will be 22 million pounds. Imports will provide the difference between domestic demand and domestic supply: 22 - 6 = 16 million pounds. e.With a $9.00 tariff, the U.S. price will be $15 (the domestic equilibrium price), and there will be no imports. Because there are no imports, there is no revenue. The deadweight loss is equal to (0.5)(16 million pounds)($6.00) = $48 million, where 16 is the difference at a price of $9 between 22 demanded and 6 supplied, and $6 is the difference between $15 and $9. f.With an import quota of 8 million pounds, the domestic price will be $12. At $12, the difference between domestic demand and domestic supply is 8 million pounds, i.e., 16 million pounds minus 8 million pounds. The cost of the quota to consumers is equal to the area of the trapezoid ABCE in Figure 9.6.f. (12 - 9)(16) + (0.5)(12 - 9)(22 - 16) = $57 million. Figure 9.6.f The gain to domestic producers is equal to the area of the trapezoid AGFE. Therefore, total domestic producer gain is (12 - 9)(6) + (0.5)(9 - 6)(12 - 9) = $22.5 million. 7. a. With a $9 tariff, the price of the imported metal on U.S. markets would be $18, the tariff plus the world price of $9. To determine the domestic equilibrium price, equate domestic supply and domestic demand: P = 40 - 2P, or P = $15. The equilibrium quantity is found by substituting a price of $15 into either the demand or supply equations: and . The equilibrium quantity is 10 million ounces. Because the domestic price of $15 is less than the world price plus the tariff, $18, there will be no imports. b.With the Voluntary Restraint Agreement, the difference between domestic supply and domestic demand would be limited to 8 million ounces, i.e. QD - QS = 8. To determine the domestic price of the metal, set QD - QS = 8 and solve for P: , or P = $12. At a price of $12, QD = 16 and QS = 8; the difference of 8 million ounces will be supplied by imports. 8. a.Section 9.6 in the text provides a formula for the “pass-through” fraction, i.e., the fraction of the tax borne by the consumer. This fraction is , where ES is the own-price elasticity of supply and ED is the own-price elasticity of demand. Substituting for ES and ED, the pass-through fraction is Therefore, 95 percent of the tax is passed through to the consumers because supply is relatively elastic and demand is relatively inelastic. b.With an increase in the price of liquor (from the large pass-through of the liquor tax), consumers will substitute away from liquor to beer, shifting the demand curve for beer outward. With an infinitely elastic supply for beer (a perfectly flat supply curve), there will be no change in the equilibrium price of beer. 9. From Example 9.1, we know that the supply and demand curves for natural gas in the 1970s can be approximated as follows: QS = 14 + 2PG + 0.25PO and QD = -5PG + 3.75PO, where PG is the price of gas and PO is the price of oil. With the price of oil at $12 per barrel, these curves become, QS = 17 + 2PG and QD = 45 - 5PG. Setting quantity demanded equal to quantity supplied, 17 + 2PG = 45 - 5PG, or PG = $4. At this price, the equilibrium quantity is 25 thousand cubic feet (Tcf). If a ceiling of $1 is imposed, producers would supply 19 Tcf and consumers would demand 40 Tcf. Consumers gain area A - B = 57 - 3.6 = $53.4 billion in the figure below. Producers lose the area -A - C = -57 - 9 = $66.0 billion. Deadweight loss is equal to the area C + B, 53.4 - 66 = $12.6 billion. Figure 9.9 10. a. We are given the equations for the total market demand for sugar in the U.S. and the supply of U.S. producers: QD = 23.86 - .25P QS = -8.19 + 1.07P. The difference between the quantity demanded and supplied, QD - QS, is the amount of sugar imported which is restricted by the quota. If the quota is increased from 3 billion pounds to 4 billion pounds, then we will have QD - QS = 4 and we can solve for QS and P from: QS + 4 = 23.86 - .25 P QS = -8.19 + 1.07 P So 23.86 - .25P - 4 = -8.19 + 1.07P or P = 28.05/1.32 = 21.25 cents per pound and QS = -8.19 + (1.07)(21.25) = 14.5 billion pounds QD = QS + 4 = 18.5 billion pounds. b. Figure 9.10.b The gain in consumer surplus is the sum of the areas A through D in Figure 9.10.b. On the other hand, domestic producers suffer a loss of producer surplus equal to area A. Numerically: A = (.75)(14.5) + (.75)(15.35-14.5)/2 = 10.88 + .32 = 11.20 B = (.75)(15.35-14.5)/2 = .32 C = (.75)(18.5-18.35)/2 = .06 D = (.75)3 = 2.25 These numbers are in billions of cents or tens of millions of dollars. Thus, consumer surplus increases by A+B+C+D = 13.83 = $138.3 million, while domestic producer surplus decreases by A = 11.2 = $112 million. c.When the quota is 3 billion pounds, the profit earned by foreign producers are represented by the areas D and G (the world price for sugar is assumed to be 12 cents per pound). When the quota increases to $4 billion, these profits are then represented by the areas E, F, and in Figure 9.10.b. The change in profits to foreign producers is thus (E+F+G) - (D+G) or E+F-D. Numerically: E +F = (21.25-12) [(15.35-14.5) + (18.5-18.35)] = 9.25 (in tens of millions of dollars). Thus, the profits earned by foreign producers increase by 9.25-2.25 = 7 or $70 million. The deadweight loss of the quota decreases by an amount equal to the areas B+E and C+F. Deadweight loss thus decreases by .32 + .06 + 9.25 = 9.63 or $96.3 million. 11. a. At a price P=22 cents per pound, the quantity demanded QD would be 23.86 - (.25)(22) or 18.36 billion pounds. The quantity supplied by the domestic producers QS would be -5.19 + (1.07)(22) or 18.35 billion pounds which almost matches the quantity demanded. (Note: The true equilibrium price with no imports is 22.007 cents per pound.) Use P = 22 and Q = 18.35 in the rest of the answer. Figure 9.11.a b.At the price P=22, domestic demand for sugar will be 18.4 billion pounds. If the government wants to allow 2.5 billion pounds of sugar imports, it must constrain the domestic producers to supply no more than 18.4 - 2.5 = 15.9 billion pounds. This amounts to a quota on domestic producers of 15.9 billion pounds. The domestic supply curve will thus become vertical at this quantity (see Figure 9.11.b). Figure 9.11.b We now compare the current case with the free market equilibrium where the price of sugar in the U.S. is equal to the world price of 12 cents per pound. The extra cost to consumers is the loss in consumer surplus which is represented by the areas A through D. The benefit to domestic producers is the increase in producer surplus which is represented by area A. The profits of the foreign producers increase by an amount represented by area D. Finally, the deadweight loss associated with the current outcome is represented by areas B and C. Numerically: B = (15.9-7.7)*(19.7-12)/2 = 31.57 C = (20.9-18.4)*(22-12)/2 = 12.5 D = 2.5(22-12) = 25 A = [15.9(22-12)] - B = 159-31.57 = 127.43. These numbers are in billions of cents or tens of millions of dollars The loss in consumer surplus is 127.43 + 31.57 + 12.5 + 25 = 196.5 or $1.97 billion. The gain in domestic producer surplus is 127.43 or $1.27 billion. The increase in foreign producer surplus is 25 or $250 million. The deadweight loss is 12.5 + 31.57 = 44.07 or $441 million. 12.To analyze the influence of a tariff on the domestic hula bean market, start by solving for domestic equilibrium price and quantity. First, equate supply and demand to determine equilibrium quantity: 50 + Q = 200 - 2Q, or QEQ = 50. Thus, the equilibrium quantity is 50 million pounds. Substituting QEQ equals 50 into either the supply or demand equation to determine price, we find: PS = 50 + 50 = 100, and PD = 200 - (2)(50) = 100. The equilibrium price P is $1 (100 cents). However, the world market price is 60 cents. At this price, the domestic quantity supplied is 60 = 50 - QS, or QS = 10. Similarly, domestic demand at the world price is 60 = 200 - 2QD, or QD = 70. Imports are equal to the difference between domestic demand and supply, or 60 million pounds. If Congress imposes a tariff of 40 cents, the effective price of imports increases to $1. At $1, domestic producers satisfy domestic demand and imports fall to zero. As shown in Figure 9.11, consumer surplus before the imposition of the tariff is equal to the area bounded by the demand curve and a price of 60 cents. (0.5)(200 - 60)(70) = 4,900 million cents or $49 million. After the tariff, the price rises to $1.00 and consumer surplus falls to (0.5)(200 - 100)(50) = $25 million, a loss of $24 million. Domestic profit is equal to total revenue minus total cost. Before the tariff, TR = $6 million. TC is equal to the area under the supply curve up to a quantity of 10 million pounds, i.e., $5.5 million. Therefore, profit is $500,000 before the tariff. Using the same method to calculate profit after the tariff, profit is equal to the triangle above the supply curve and below the price of $1 up to the quantity of 50. (0.5)(50)(50) = $12.5 million. Therefore, domestic profit increases by $12 million (12.5 - 0.5 = 12). Finally, because domestic production is equal to domestic demand at $1, no hula beans are imported and the government receives no revenue. What happens to the difference between the loss of consumer surplus and the increase in producer profit? Part of the difference is lost through increased cost, i.e., the area under the supply curve equal to (0.5)(50 - 10)(100 - 60) = $8 million, and the rest is deadweight loss: (0.5)(70 - 50)(100 - 60) = $4 million. See Figure 9.12. Figure 9.12 13. If the labor market is competitive, that is, both employers and employees take the wage as given, then shifting an equal tax amount from the employee to the employer will have no effect on the amount of labor employed and on the wage kept by the employee after taxes. The equilibrium amount of labor employed is determined by the total amount of tax paid by both employees and employers. This is represented by the difference between the wage paid by the employer and the wage received by the employee. As long as the total tax doesn’t change, the same amount of labor is employed and the wages paid by the employer and received by the employee (after tax) will not change. Hence, employees would be no better or worse off if the employers paid the full amount of the social security tax. 14. For products with demand characterized by a stock adjustment process, the short-run demand curve is more elastic than the long-run demand curve because consumers can delay their purchases of these goods in the short run. For example, when price rises, consumers may continue using the older version of the product, which they currently own. However, in the long run, a new product will be purchased. Thus, the long-run demand curve is more inelastic than the short-run one. Consider the effect of imposing a 20 percent sales tax on automobiles in the short and long run. To analyze the influence of the tax, we can shift the demand curves because consumers are forced to pay a higher price. Notice that this tax is an ad valorem tax. The demand curve does not shift parallel to the old ones, but pivots to reflect the higher tax paid per unit at higher prices. The burden of the tax shifts from producers to consumers as we move from the short run (Figure 9.14.a) to the long run (Figure 9.12.b). In these figures, PC is the consumer’s price, PS is the producer’s price, and PC - PS is the value of the tax. Intuitively, we may assume consumers have a more inelastic demand curve in the long run. They are less able to adjust their demand to price changes and must carry a larger burden of the tax. In both figures, the supply curve is the same in the long and short run. If the supply curve is more elastic in the long run, then even more of the tax burden is shifted to consumers. Short Run Figure 9.14.a Long Run Figure 9.14.b Unlike the automobile market, the gasoline demand curve is not characterized by a stock adjustment effect. The long-run demand curve will be more elastic than the short-run one, because in the long run substitutes (e.g., gasohol or propane) will become available for gasoline. We may analyze the effect of the tax on gasoline in the same manner as the tax on automobiles. However, the gasoline tax is a per unit or specific tax, so the demand curves exhibit a parallel shift. In Figures 9.14.c and 9.14.d, the tax burden shifts from consumers to producers as we move from the short to the long run. Now the elasticity of demand increases from the short run to the long run (the usual case), resulting in less gasoline consumption. Also, if the supply curve is more elastic in the long run, some of the burden would again be shifted back to consumers. Note that we have drawn demand curve shifts in both cases, assuming the consumers pay the tax. The same results may be obtained by shifting the supply curve, assuming the firms pay the tax. Short Run Figure 9.14.c Long Run Figure 9.14.d PAGE 16 _921260566. _927733558.ppt _927899456.ppt _925886378.ppt _921433104.ppt _921433101.ppt _921259963.ppt