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Economics for Management Studies
Mc Kinon

Chapter 9: The Analysis of Competitive Markets 8. The burden of a tax is shared by producers and consumers. Under what conditions will consumers pay most of the tax? Under what conditions will producers pay most of it? What determines the share of a subsidy that benefits consumers? The burden of a tax and the benefits of a subsidy depend on the elasticities of demand and supply. If the absolute value of the ratio of the elasticity of demand to the elasticity of supply is small, the burden of the tax falls mainly on consumers. If the ratio is large, the burden of the tax falls mainly on producers. Similarly, the benefit of a subsidy accrues mostly to consumers (produ cers) if the ratio of the elasticity of demand to the elasticity of supply is small (large) in absolute value. 9. Why does a tax create a deadweight lo ss? What determines the size of this loss? A tax creates deadweight loss by artificia lly increasing price above the free market level, thus reducing the equilibrium quanti ty. This reduction in quantity reduces consumer as well as producer surplus. Thesize of the deadweight loss depends on the elasticities of supply and demand and on the size of the tax. The more elastic supply and demand are, the larger will be the dead weight loss, and the larger the tax, the greater the deadweight loss. EXERCISES 1. In 1996, Congress raised the minimum wage from $4.25 per hour to $5.15 per hour, and then raised it again in 2007. (See Example 1.3 [page 13].) Some people suggested that a government subsidy could help employers fi nance the higher wage. This exercise examines the economics of a minimum wage an d wage subsidies. Suppose the supply of low-skilled labor is given by L = 10 w, where L is the quantity of low-skilled labor (in millions of persons employed each year), and w is the wage rate (in dollars per hour). The demand for labor is given by L D = 80 – 10w. a. What will be the free-market wage rate and employment level? Suppose the government sets a minimum wage of $5 per hour. How many people would then be employed? In a free-market equilibrium, L = L . Solving yields w = $4 and L = L = 40. If the minimum wage is $5, then L = 50 and L = 30. The number of people employed will be given by the labor demand, so employers will hire only 30 million workers. w L S 8 5 4 LD L 30 40 50 80 140 Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 9: The Analysis of Competitive Markets b. Suppose that instead of a minimum wage, the government pays a subsidy of $1 per hour for each employee. What will the total level of employment be now? What will the equilibrium wage rate be? Let w senote the wage received by the sellers (i.e., the employees), and w the wbge paid by the buyers (the firms). The new equilibrium occurs where the vertical difference between the supply and demand curves is $1 (the amount of the subsidy). This point can be found where D S L (w b = L (w s, and ws– w b 1. Write the second equation as w b = w s 1. This reflects the fact that firms pay $1 less than the wage received by workers because of the subsidy. Substitute for w bn the demand equation: L D(w b = 80 – 10(w s 1), so L (w )b= 90 – 10w .s Note that this is equivalent to an upward shift in demand by the amount of the $1 subsidy. Now set the new demand equal to supply: 90 – 10w = 10w . Therefore, w = s s s $4.50, and L = 90 – 10(4.50) = 45. Employment increases to 45 (compared to 30 with the minimum wage), but wage drops to $4.50 (compared to $5.00 with the minimum wage). The net wage the firm paysfalls to $3.50 due to the subsidy. w S 8 L w s 4.50 4.00 $1 Subsidy w b 3.50 LD L 40 45 80 2. Suppose the market for widgets can be described by the following equations: Demand: P = 10 – Q Supply: P = Q – 4 where P is the price in dollars per unit andQ is the quantity in thousands of units. Then: 141 Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 9: The Analysis of Competitive Markets a. What is the equilibrium price and quantity? Equate supply and demand and solve forQ: 10 – Q = Q – 4. Therefore Q = 7 thousand widgets. SubstituteQ into either the demand or the supply equation to obtainP. P = 10 – 7 = $3.00, or P = 7 – 4 = $3.00. b. Suppose the government imposes a tax of $1 per unit to reduce widget consumption and raise government revenues. What will the new equilibrium quantity be? What price will the buyer pay? What amount per unit will the seller receive? With the imposition of a $1.00 tax per unit, the price buyers pay is $1 more than the price suppliers receive. Also, at the new equilibrium, the quantity bought must equal the quantity supplied. We canwrite these two conditions as P b P s 1 Q b Q .s Let Q with no subscript stand for the common value ofQ band Q .sThen substitute the demand and supply equations for the two values ofP: (10 – Q) – (Q – 4) = 1 Therefore,Q = 6.5 thousand widgets. Plug this value into the demand equation, which is the equation for P ,bto find P b 10 – 6.5 = $3.50. Also substitute Q = 6.5 into the supply equation to getP s= 6.5 – 4 = $2.50. The tax raises the price in the market from $30 . 0 (as found in part a) to $3.50. Sellers, however, receive only $2.50 after the tax is imposed. Therefore, the tax is shared equally between buyers and sellers, each paying $0.50. c. Suppose the government has a change of heart about the importance of widgets to the happiness of the American public. Th e tax is removed and a subsidy of $1 per unit granted to widget producers. What will the equilibrium quantity be? What price will the buyer pay? What amount per unit (including the subsidy) will the seller receive? What will be the total cost to the government? Now the two conditions that must be satisfied are P – P = 1 s b Q b Q .s As in part (b), letQ stand for the common value of quantity. Substitute the supply and demand curves into the first condition, which yields (Q – 4) – (10 –Q) = 1. Therefore, Q = 7.5 thousand widgets. Using this quantity in the supply and demand equations, suppliers will receiveP s= 7.5 – 4 = $3.50, and buyers will pay P = b0 – 7.5 = $2.50. The total cost to the government is the subsidy per unit multiplied by the number of units. Thus, the cost is ($1)(7.5) = $7.5 thousand, or $7500. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 9: The Analysis of Competitive Markets 3. Japanese rice producers have extremely high production costs, due in part to the high opportunity cost of land and to their inability to take advantage of economies of large-scale production. Analyze two policies intended tomaintain Japanese rice production: (1) a per- pound subsidy to farmers for each pound of rice produced, or (2) a per-pound tariff on imported rice. Illustrate with supply-and- demand diagrams the equilibrium price and quantity, domestic rice production, government revenue or deficit, and deadweight loss from each policy. Which policy is the Japanese government likely to prefer? Which policy are Japanese farmers likely to prefer? We have to make some assump tions to answer this question. If you make different assumptions, you may get a different answer. Assume that initially the Japanese rice market is open, meaning that foreign prod ucers and domestic (Japanese) producers both sell rice to Japanese consumers. The world price of ricW isP . This price is below P 0 which is the equilibrium price that would occur in the Japanese market if no imports were allowed. In the diagram below, S is the domestic supply, D is the domestic demand, and Q 0 is the equilibrium quantity that would prevail if no imports were allowed. The horizontal line atWis the world supply of rice, which is assumed to be perfectly elastic. Initially Japanese consumers purchasDQ rice at the world price. Japanese farmers supply Q at that price, and Q – Q is imported from foreign S D S producers. Now suppose the Japanese government pays a subsidy to Japanese farmers equal to the difference between 0 and PW. Then Japanese farmers would sell rice on the open market for P Wplus receive the subsidy of 0 – PW. Adding these together, the total amount Japanese farmers would receive is P 0erpoundofrice. Atthispricethey would supply Q 0pounds of rice. Consumers would still pay PWand buy Q D Foreign suppliers would importQ D Q p0unds of rice. This policy would cost the government (P0– P WQ 0 which is the subsidy per pound ti mes the number of pounds supplied by Japanese farmers. It is represented on thediagram as areas B + E. Producer surplus increases from area C to C + B, soΔPS = B. Consumer surplus is not affected and remains as area A + B + E + F. Deadweight loss is area E, which is the cost of the subsidy minus the gain in producer surplus. P S A P0 Subsidy = Tariff =0P –WP B E F PW C D Q Q S Q0 Q D 143 Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 9: The Analysis of Competitive Markets Instead, suppose the government imposes a ta riff rather than paying a subsidy. Let the tariff be the same size as the subsidy, 0 –PW. Now foreign firms importing rice into Japan will have to sell at the world price plus the tarifW: P(P0–P W = P 0 But at this price, Japanese farmers will supply Q0, which is exactly the amount Japanese consumers wish to purchase. Therefore, there will be no imports, and the government will not collect any revenue from the tariff. The increase in producer surplus equals area B, as it is in the case of the subsidy. Consumer surplus is area A, which is less than it is under the subsidy because consumers pay more ( P 0) and consume less (Q0). Consumer surplus decreases by B + E + F. Deadweight loss is E + F, which is the difference between the decrease in consumer surplus and the increase in producer surplus. Under the assumptions made here, it seem s likely that producers would not have a strong preference for either the subsidy or the tariff, because the increase in producer surplus is the same under both policies. The government might prefer the tariff because it does not require any governmentexpenditure. On the other hand, the tariff causes a decrease in consumer surplus, an d government officials who are elected by consumers might want to avoid that. Notethat if the subsidy and tariff amounts were smaller than assumed above, some tariffs would be collected, but we would still get the same basic results. 4. In 1983, the Reagan Administration intr oduced a new agricultural program called the Payment-in-Kind Program. To see how the program worked, let’s consider the wheat market. D S a. Suppose the demand function is Q = 28 – 2P and the supply function is Q = 4 + 4P, where P is the price of wheat in dollars per bushel, and Q is the quantity in billions of bushels. Find the free-market equilibrium price and quantity. Equating demand and supply,Q = Q , S 28 – 2P = 4 + 4P, or P = $4.00 per bushel. To determine the equilibrium quantity, substituteP = 4 into either the supply equation or the demand equation: Q = 4 + 4(4) = 20 billion bushels, or Q D = 28 – 2(4)= 20 billion bushels. b. Now suppose the government wants to lowerthe supply of wheat by 25 percent from the free-market equilibrium by paying farmers to withdraw land from production. However, the payment is made in wheat rather than in dollars – hence the name of the program. The wheat comes from vast government reserves accumulated from previous price support programs. The amountof wheat paid is equal to the amount that could have been harvested on the la nd withdrawn from production. Farmers are free to sell this wheat on the market. How much is now produced by farmers? How much is indirectly supplied to the market by the government? What is the new market price? How much do farmers gain? Do consumers gain or lose? ► Note: The answer at the end of the book (first printing) calculates the farmers’ gain incorrectly. The correct cost ving and gain is given below. Because the free-market supply by farmers is 20 billion bushels, the 25-percent reduction required by the new Payment-In-Kind (PIK) Program means that the farmers now produce 15 billion bushels. To encourage farmers to withdraw their land from cultivation, the government must givethem 5 billion bushels of wheat, which they sell on the market. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 9: The Analysis of Competitive Markets Because the total quantity supplied to the mrket is still 20 billion bushels, the market price does not change; it remains at $4 per bushel. Farmers gain because they incur no costs for the 5 billion bushels received from the government. We can calculate these cost savings by taking the area under the supply curve between 15 and 20 billion bushels. These are the variable costs of prucing the last 5 billion bushels that are no longer grown under the PIK Program. To fi nd this area, first determine the prices when Q = 15 and when Q = 20. These values are P = $2.75 and P = $4.00. The total cost of producing the last 5 billion bushels is therefore the area of a trapezoid with a base of 20 – 15 = 5 billion and an average height of (2.75 + 4.00)/2 = 3.375. The area is 5(3.375) = $16.875 billion. The PIK program does not affect consum ers in the wheat market, because they purchase the same amount at the same price as they did in the free-market case. c. Had the government not given the wheat back to the farmers, it would have stored or destroyed it. Do taxpayers gain from th e program? What potential problems does the program create? Taxpayers gain because the government does not incur costs to store or destroy 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 of wheat are exhausted. If this cannot be done, cons umers may eventually pay more for wheat- based products. 5. About 100 million pounds of jelly beans are consumed in the United States each year, and the price has been about 50 cents per pound. However, jelly bean producers feel that their incomes are too low and have convinced the government that price supports are in order. The government will therefore buy up asmany jelly beans as necessary to keep the price at $1 per pound. However, government economists are worried about the impact of this program because they have no estimates of the elasticities of jelly bean demand or supply. a. Could this program cost the government more than $50 million per year? Under what conditions? Could it cost less than $50 million per year? Under what conditions? Illustrate with a diagram. 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 this case, the change in pr ice will cause a large change in quantity supplied, and a large change in quantity demanded. In Figure 9.5.a.i, the cost of the program is ($1)(QS–Q D. If Q SQ iD larger than 50 million, then the government will pay more than $50 million. If instead su pply and demand were relatively price inelastic, then the change in price would result in small changes in quantity supplied and quantity demanded, and (Q –S ) Dould be less than $50 million as illustrated in Figure 9.5.a.ii. 145 Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 9: The Analysis of Competitive Markets P S 1.00 .50 D Q Q D 100 Q S Figure 9.5.a.i We can determine the combinations of supplyand demand elasticities that yield either result. The elasticity of supply is ES = (% ΔQ S/(%ΔP), so the percentage change in quantity supplied is %ΔQ S E (%SP). Since the price incre ase is 100 percent (from $0.50 to $1.00), %ΔQS = 100ES. Likewise, the percentage change in quantity demanded is %ΔQ D = 100E D The gap between Q aDd Q in Sercentage terms is %ΔQ – %ΔQS= D 100E S100E = D00(E – E S. IfDthis gap is exactly 50 percent of the current 100 million pounds of jelly beans, the gap will be 50 million pounds, and the cost of the price support program will be exactly $50 million. So the program will cost $50 million if 100(E – E ) = 50, or (E – E ) = 0.5. If the difference between the elasticities is S D S D greater than one half, the program will cost more than $50 million, and if the difference is less than one half, the program will cost less than $50 million. So the supply and demand can each be fairly inelastic (for example, 0.3 and –0.4) and still trigger a cost greater than $50 million. 146 Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 9: The Analysis of Competitive Markets P S 1.00 .50 D Q QD 100 QS Figure 9.5.a.ii b. Could this program cost consumers (in terms of lost consumer surplus) more than $50 million per year? Under what conditions? Could it cost consumersless than $50 million per year? Under what conditions? Again, use a diagram to illustrate. When the demand curve is perfectly inelas tic, the loss in consumer surplus is $50 million, equal to ($0.50)(100 million pounds). This represents the highest possible loss in consumer surplus, so the loss cannot more than $50 million per year. If the demand curve has any elasticity at all, the loss in consumer surplus will be less then $50 million. In Figure 9.5.b, the loss in consumer surplus is area A plus area B if the demand curve is the completely inelastic Dand only area A if the demand c′.ve is D P D S 1.00 B A .50 D′ Q 100 Figure 9.5.b 147 Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 9: The Analysis of Competitive Markets 6. In Exercise 4 in Chapter 2 (page 62), we examined a vegetable fiber traded in a competitive world market and imported into th e United States at a world price of $9 per pound. U.S. domestic supply and demand for various price levels are shown in the following table. PriSeupp.y. U.S. Demand (million pounds) (million pounds) 3 2 34 6 4 28 9 6 22 8 1612 15 10 10 18 12 Answer the following questions about the U.S. market: a. Confirm that the demand curve is given by Q D 40− 2P , and that the supply curve 2 is given byQ S P . 3 To find the equation for demand, we need to find a linear funDtion Q = a + bP so that the line it represents passes through two of the points in the table such as (15, 10) and (12, 16). First, the slope,b, is equal to the “rise” divided by the “run,” ΔQ = 10−16 = −2 =b. ΔP 15−12 Second, substitute forb and one point, e.g., (15, 10), into the linear function to solve for the constant,a: 10 = a − 21) , or a = 40. Therefore,QD= 40 − 2P. Similarly, solve for the supply equationQ = c + dP passing through two points such as S (6, 4) and (3, 2). The slope,d, is ΔQ 4 − 2 2 = = . . ΔP 6 − 3 3 Solving forc: ⎛ ⎞ 4 = c +⎜ ⎟(6), or c = 0. ⎝ ⎠ ⎛ ⎞ Therefore,QS= ⎝ ⎠ P. 3 b. Confirm that if there were no restrictions on trade, the United States would import 16 million pounds. If there were no trade restrictions, the worl d price of $9.00 would prevail in the U.S. From the table, we see that at $9.00 dmestic supply would be 6 million pounds. Similarly, domestic demand would be 22 million pounds. Imports provide the difference between domestic demand and dostic supply, so imports would be 22 – 6 = 16 million pounds. 148 Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 9: The Analysis of Competitive Markets c. If the United States imposes a tariff of $3 per pound, what will be the U.S. price and level of imports? How much revenue will th e government earn from the tariff? How large is the deadweight loss? With a $3.00 tariff, the U.S. price will be $12 (the world price plus the tariff). At this price, demand is 16 million pounds and is 8 million pounds, so imports are 8 million pounds (16–8). The government willcollect $3(8) = $24 million, which is area C in the diagram below. To find deadweig ht loss, we must determine the changes in consumer and producer surpluses. Consumers lose area A + B + C + D because they pay the higher price of $12 a
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