答案ch08

156 ( Chapter 8 /Application: The Costs of Taxation Chapter 8 /Application: The Costs of Taxation ( 171 Chapter 8 Application: The Costs of Taxation WHAT’S NEW IN THE THIRD EDITION: There have been no substantial changes to this chapter. LEARNING OBJECTIVES: By the end of this chapter, students should understand: · how taxes reduce consumer and producer surplus. · the meaning and causes of the deadweight loss from a tax. · why some taxes have larger deadweight losses than others. · how tax revenue and deadweight loss vary with the size of a tax. CONTEXT AND PURPOSE: Chapter 8 is the second chapter in a three-chapter sequence dealing with welfare economics. In the previous section on supply and demand, Chapter 6 introduced taxes and demonstrated how a tax affects the price and quantity sold in a market. Chapter 6 also described the factors that determine how the burden of the tax is divided between the buyers and sellers in a market. Chapter 7 developed welfare economics—the study of how the allocation of resources affects economic well-being. Chapter 8 combines the lessons learned in Chapters 6 and 7 and addresses the effects of taxation on welfare. Chapter 9 will address the effects of trade restrictions on welfare. The purpose of Chapter 8 is to apply the lessons learned about welfare economics in Chapter 7 to the issue of taxation that was addressed in Chapter 6. Students will learn that the cost of a tax to buyers and sellers in a market exceeds the revenue collected by the government. Students will also learn about the factors that determine the degree by which the cost of a tax exceeds the revenue collected by the government. KEY POINTS: 1. A tax on a good reduces the welfare of buyers and sellers of the good, and the reduction in consumer and producer surplus usually exceeds the revenue raised by the government. The fall in total surplus—the sum of consumer surplus, producer surplus, and tax revenue—is called the deadweight loss of the tax. 2. Taxes have deadweight losses because they cause buyers to consume less and sellers to produce less, and this change in behavior shrinks the size of the market below the level that maximizes total surplus. Because the elasticities of supply and demand measure how much market participants respond to market conditions, larger elasticities imply larger deadweight losses. 3. As a tax grows larger, it distorts incentives more, and its deadweight loss grows larger. Tax revenue first rises with the size of a tax. Eventually, however, a larger tax reduces tax revenue because it reduces the size of the market. CHAPTER OUTLINE: I. The Deadweight Loss of Taxation A. Remember that it does not matter who a tax is levied on; buyers and sellers will likely share in the burden of the tax. B. If there is a tax on a product, the price that a buyer pays will be greater than the price the seller receives. Thus, there is a tax wedge between the two prices and the quantity sold will be smaller if there was no tax. C. How a Tax Affects Market Participants 1. We can measure the effects of a tax on consumers by examining the change in consumer surplus. Similarly, we can measure the effects of the tax on producers by looking at the change in producer surplus. 2. However, there is a third party that is affected by the tax—the government, which gets total tax revenue of T × Q. If the tax revenue is used to provide goods and services to the public, then the benefit from the tax revenue must not be ignored. 3. Welfare Before a Tax a. Consumer surplus is equal to: A + B + C. b. Producer surplus is equal to: D + E + F. c. Total surplus is equal to: A + B + C + D + E + F. 4. Welfare with Tax a. Consumer surplus is equal to: A. b. Producer surplus is equal to: F. c. Tax revenue is equal to: B + D. d. Total surplus is equal to: A + B + D + F. 5. Changes in Welfare a. Consumer surplus changes by: –(B + C) b. Producer surplus changes by: –(D + E) c. Tax revenue changes by: +(B + D) d. Total surplus changes by: –(C + E) 6. Definition of deadweight loss: the fall in total surplus that results from a market distortion, such as a tax. D. Deadweight Losses and the Gains from Trade 1. Taxes cause deadweight losses because they prevent buyers and sellers from benefiting from trade. 2. This occurs because the quantity of output declines; trades that would be beneficial to both the buyer and seller will not take place because of the tax. 3. The deadweight loss is equal to areas C and E (the drop in total surplus). 4. Note that output levels between the equilibrium quantity without the tax and the quantity with the tax will not be produced, yet the value of these units to consumers (represented by the demand curve) is larger than the cost of these units to producers (represented by the supply curve). II. The Determinants of the Deadweight Loss A. The price elasticities of supply and demand will determine the size of the deadweight loss that occurs from a tax. 1. Given a stable demand curve, the deadweight loss is larger when supply is relatively elastic. 2. Given a stable supply curve, the deadweight loss is larger when demand is relatively elastic. B. Case Study: The Deadweight Loss Debate 1. Social Security tax and federal income tax are taxes on labor earnings. A labor tax places a tax wedge between the wage the firm pays and the wage that workers receive. 2. There is considerable debate among economists concerning the size of the deadweight loss from this wage tax. 3. This is because the size of the deadweight loss depends on the elasticity of labor supply and demand, and there is disagreement about the magnitude of the elasticity of supply. a. Economists who argue that labor taxes are not very distorting believe that labor supply is fairly inelastic. b. Economists who argue that labor taxes lead to large deadweight losses believe that labor supply is more elastic. C. FYI: Henry George and the Tax on Land 1. Henry George was a 19th century economist who suggested that the government use only a single tax on land to raise revenue. 2. Note that the burden of a tax falls more heavily on the side of the market that is less elastic. Since the supply of land is fixed, the supply of land is a vertical line and the elasticity is equal to zero. Thus, landowners bear the entire burden of the tax. 3. There would also be no tax wedge in this case because the supply curve is vertical and this implies that there is no deadweight loss (because the government’s tax revenue is exactly equal to the landowners’ losses). 4. However, the tax would occur without a deadweight loss only if it was a tax on raw land rather than improvements on the land. III. Deadweight Loss and Tax Revenue as Taxes Vary A. As taxes increase, the deadweight loss from the tax increases. B. In fact, as taxes increase, the deadweight loss rises more quickly than the size of the tax. 1. The deadweight loss is the area of a triangle and the area of a triangle depends on the square of its size. 2. If we double the size of a tax, the base and height of the triangle both double so the area of the triangle (the deadweight loss) rises by a factor of four. C. As the tax increases, the level of tax revenue will eventually fall. D. Case Study: The Laffer Curve and Supply-Side Economics 1. The relationship between the size of a tax and the level of tax revenues is called a Laffer Curve. 2. Supply-side economists in the 1980s used the Laffer curve to support their belief that a drop in tax rates could lead to an increase in tax revenue for the government. 3. When taxes rates were lowered after Reagan took office, revenue from personal income taxes fell while personal incomes rose. 4. However, tax revenues collected from the richest Americans did rise when their tax rates were cut. 5. The important lesson that must be learned is that we cannot predict how much tax revenues will change in response to a change in tax rates just by looking at the tax rates themselves. The government must understand how a change in tax rates will affect individuals’ behavior. SOLUTIONS TO TEXT PROBLEMS: Quick Quizzes 1. Figure 1 shows the supply and demand curves for cookies, with equilibrium quantity Q1 and equilibrium price P1. When the government imposes a tax on cookies, the price to buyers rises to PB, the price received by sellers declines to PS, and the equilibrium quantity falls to Q2. The deadweight loss is the triangular area below the demand curve and above the supply curve between quantities Q1 and Q2. The deadweight loss shows the fall in total surplus that results from the tax. Figure 1 2. A tax on beer would have a larger deadweight loss than a tax on milk, since the demand for beer is more elastic than the demand for milk and the deadweight loss of a tax is larger the greater is the elasticity of demand. 3. If the government doubles the tax on gasoline, the revenue from the gasoline tax could rise or fall, depending on where the tax falls on the Laffer curve. However, if the government doubles the tax on gasoline, you can be sure that the deadweight loss of the tax rises, since deadweight loss always rises as the tax rate rises. Questions for Review 1. When the sale of a good is taxed, both consumer surplus and producer surplus decline. The decline in consumer surplus and producer surplus exceeds the amount of government revenue that is raised, so society's total surplus declines. The tax distorts the incentives of both buyers and sellers, so resources are allocated inefficiently. 2. Figure 2 illustrates the deadweight loss and tax revenue from a tax on the sale of a good. Without a tax, the equilibrium quantity would be Q1, the equilibrium price would be P1, consumer surplus would be A+B+C, and producer surplus would be D+E+F. The imposition of a tax places a wedge between the price buyers pay, PB, and the price sellers receive, PS, where PB = PS + tax. The quantity sold declines to Q2. Now consumer surplus is A, producer surplus is F, and government revenue is B+D. The deadweight loss of the tax is C+E, since that area is lost because of the decline in quantity from Q1 to Q2. Figure 2 3. The greater the elasticities of demand and supply, the greater the deadweight loss of a tax. Since elasticity measures the response of quantity to a change in price, higher elasticity means the tax induces a greater reduction in quantity, hence a greater distortion to the market. 4. Experts disagree about whether labor taxes have small or large deadweight losses because they have different views about the elasticity of labor supply. Some believe that labor supply is inelastic, so a tax on labor has a small deadweight loss. But others think that workers can adjust their hours worked in various ways, so labor supply is elastic, and thus a tax on labor has a large deadweight loss. 5. The deadweight loss of a tax rises more than proportionally as the tax rises. Tax revenue, however, may increase initially as the tax rises, but as the tax rises further, revenue eventually declines. Problems and Applications 1. a. Figure 3 illustrates the market for pizza. The equilibrium price is P1, the equilibrium quantity is Q1, consumer surplus is area A+B+C, and producer surplus is area D+E+F. There is no deadweight loss, as all the potential gains from trade are realized; total surplus is the entire area between the demand and supply curves(A+B+C+D+E+F. Figure 3 b. With a $1 tax on each pizza sold, the price paid by buyers, PB, is now higher than the price received by sellers, PS, where PB = PS + $1. The quantity declines to Q2, consumer surplus is area A, producer surplus is area F, government revenue is area B+D, and deadweight loss is area C+E. Consumer surplus declines by B+C, producer surplus declines by D+E, government revenue increases by B+D, and deadweight loss increases by C+E. c. If the tax were removed and consumers and producers voluntarily transferred B+D to the government to make up for the lost tax revenue, then everyone would be better off than without the tax. The equilibrium quantity would be Q1, as in the case without the tax, and the equilibrium price would be P1. Consumer surplus would be A+C, because consumers get surplus of A+B+C, then voluntarily transfer B to the government. Producer surplus would be E+F, since producers get surplus of D+E+F, then voluntarily transfer D to the government. Both consumers and producers are better off than the case when the tax was imposed. If consumers and producers gave a little bit more than B+D to the government, then all three parties, including the government, would be better off. This illustrates the inefficiency of taxation. 2. a. The statement, "If the government taxes land, wealthy landowners will pass the tax on to their poorer renters," is incorrect. With a tax on land, landowners can not pass the tax on. Since the supply curve of land is perfectly inelastic, landowners bear the entire burden of the tax. Renters will not be affected at all. b. The statement, "If the government taxes apartment buildings, wealthy landowners will pass the tax on to their poorer renters," is partially correct. With a tax on apartment buildings, landowners can pass the tax on more easily, though the extent to which they do this depends on the elasticities of supply and demand. In this case, the tax is a direct addition to the cost of rental units, so the supply curve will shift up by the amount of the tax. The tax will be shared by renters and landowners, depending on the elasticities of demand and supply. 3. a. The statement, "A tax that has no deadweight loss cannot raise any revenue for the government," is incorrect. An example is the case of a tax when either supply or demand is perfectly inelastic. The tax has neither an effect on quantity nor any deadweight loss, but it does raise revenue. b. The statement, "A tax that raises no revenue for the government cannot have any deadweight loss," is incorrect. An example is the case of a 100 percent tax imposed on sellers. With a 100 percent tax on their sales of the good, sellers won't supply any of the good, so the tax will raise no revenue. Yet the tax has a large deadweight loss, since it reduces the quantity sold to zero. 4. a. With very elastic supply and very inelastic demand, the burden of the tax on rubber bands will be borne largely by buyers. As Figure 4 shows, consumer surplus declines considerably, by area A+B, but producer surplus doesn't fall much at all, just by area C+D. Figure 4 b. With very inelastic supply and very elastic demand, the burden of the tax on rubber bands will be borne largely by sellers. As Figure 5 shows, consumer surplus does not decline much, just by area A+B, while producer surplus falls substantially, by area C+D. Compared to part (a), producers bear much more of the burden of the tax, and consumers bear much less. Figure 5 5. a. The deadweight loss from a tax on heating oil is likely to be greater in the fifth year after it is imposed rather than the first year. In the first year, the elasticity of demand is fairly low, as people who own oil heaters are not likely to get rid of them right away. But over time they may switch to other energy sources and people buying new heaters for their homes will more likely choose gas or electric, so the tax will have a greater impact on quantity. b. The tax revenue is likely to be higher in the first year after it is imposed than in the fifth year. In the first year, demand is more inelastic, so the quantity does not decline as much and tax revenue is relatively high. As time passes and more people substitute away from oil, the equilibrium quantity declines, as does tax revenue. 6. Since the demand for food is inelastic, a tax on food is a good way to raise revenue because it does not lead to much of a deadweight loss; thus taxing food is less inefficient than taxing other things. But it is not a good way to raise revenue from an equity point of view, since poorer people spend a higher proportion of their income on food, so the tax would hit them harder than it would hit wealthier people. 7. a. This tax has such a high rate that it is not likely to raise much revenue. Because of the high tax rate, the equilibrium quantity in the market is likely to be at or near zero. b. Senator Moynihan's goal was probably to ban the use of hollow-tipped bullets. In this case, a tax is as effective as an outright ban. 8. a. Figure 6 illustrates the market for socks and the effects of the tax. Without a tax, the equilibrium quantity would be Q1, the equilibrium price would be P1, total spending by consumers equals total revenue for producers, which is P1 x Q1, which equals area B+C+D+E+F, and government revenue is zero. The imposition of a tax places a wedge between the price buyers pay, PB, and the price sellers receive, PS, where PB = PS + tax. The quantity sold declines to Q2. Now total spending by consumers is PB x Q2, which equals area A+B+C+D, total revenue for producers is PS x Q2, which is area C+D, and government tax revenue is Q2 x tax, which is area A+B. b. Unless supply is perfectly elastic, the price received by producers falls because of the tax. Total receipts for producers fall, since producers lose revenue equal to area B+E+F. Figure 6 c. The price paid by consumers rises, unless demand is perfectly elastic. Whether total spending by consumers rises or falls depends on the price elasticity of demand. If demand is elastic, the percentage decline in quantity exceeds the percentage increase in price, so total spending declines. If demand is inelastic, the percentage decline in quantity is less than the percentage increase in price, so total spending rises. Whether total consumer spending falls or rises, consumer surplus declines because of the increase in price and reduction in quantity. 9. Since the tax on gadgets was eliminated, all tax revenue must come from the tax on widgets. The tax revenue from the tax on widgets equals the tax per unit times the quantity produced. Assuming that neither the supply nor the demand curves for widgets are perfectly elastic or inelastic and since the increased tax causes a smaller quantity of widgets to be produced, then it is impossible for tax revenue to double--multiplying the tax per unit (which doubles) times the quantity (which declines) gives a number that is less than double the original tax revenue from widgets. So the government's tax change will yield less money than before. 10. a. Figure 7 illustrates the effects of the tax increase on the new car market in New Jersey. The quantity of cars sold declines from Q1 to Q2, the price paid by consumers rises from PB1 to PB2, and the price received by producers declines from PS1 to PS2, where PB1 = PS1 + $100 and PB2 = PS2 + $150. Figure 7 b. The following table shows the welfare impact of the change in the tax. OLD NEW CHANGE Consumer Surplus A+B+C A –(B+C) Producer Surplus F+G+H H –(F+G) Government Revenue D+E B+D+F +(B+F)–E Total Surplus A+B+C+D+E+F+G+H A+B+D+F+H –(C+E+G) c. The change in government revenue is B + F – E, which could be positive or negative. d. The change in deadweight loss is positive, as it increases by C+E+G, meaning that the economy as a whole is worse off. e. The demand for cars in New Jersey is probably fairly elastic, since people could travel to nearby states to buy cars. With elastic demand, area B in the figure will be very small, so the additional tax is less likely to increase government revenue. New Jersey could try to reduce the elasticity of demand by requiring people to pay sales tax to New Jersey when they buy a car outside the state. 11. From the standpoint of economic efficiency, the British poll tax is wonderful, because it does not distort any economic incentives, so it has no deadweight loss. But such a tax is inequitable, because it is more burdensome on the poor than on the rich. As a result, the tax was quite unpopular. 12. Figure 8 illustrates the effects of the $2 subsidy on a good. Without the subsidy, the equilibrium price is P1 and the equilibrium quantity is Q1. With the subsidy, buyers pay price PB, producers receive price PS (where PS = PB + $2), and the quantity sold is Q2. The following table illustrates the effect of the subsidy on consumer surplus, producer surplus, government revenue, and total surplus. Since total surplus declines by area D+H, the subsidy leads to a deadweight loss in that amount. OLD NEW CHANGE Consumer Surplus A+B A+B+E+F+G +(E+F+G) Producer Surplus E+I B+C+E+I +(B+C) Government Revenue 0 –(B+C+D+E+F+G+H) –(B+C+D+E+F+G+H) Total Surplus A+B+E+I A+B–D+E–H+I -(D+H) Figure 8 13. a. Setting quantity supplied equal to quantity demanded gives 2P = 300 – P. Adding P to both sides of the equation gives 3P = 300. Dividing both sides by 3 gives P = 100. Plugging P = 100 back into either equation for quantity demanded or supplied gives Q = 200. b. Now P is the price received by sellers and P+T is the price paid by buyers. Equating quantity demanded to quantity supplied gives 2P = 300 - (P+T). Adding P to both sides of the equation gives 3P = 300 – T. Dividing both sides by 3 gives P = 100 - T/3. This is the price received by sellers. The buyers pay a price equal to the price received by sellers plus the tax (P+T = 100 + 2T/3). The quantity sold is now Q = 2P = 200 – 2T/3. c. Since tax revenue is equal to T x Q and Q = 200 - 2T/3, tax revenue equals 200T - 2T2/3. Figure 9 shows a graph of this relationship. Tax revenue is zero at T = 0 and at T = 300. Figure 9 d. As Figure 10 shows, the area of the triangle (laid on its side) that represents the deadweight loss is 1/2 x base x height, where the base is the change in the price, which is the size of the tax (T) and the height is the amount of the decline in quantity (2T/3). So the deadweight loss equals 1/2 x T x 2T/3 = T2/3. This rises exponentially from 0 (when T = 0) to 45,000 when T = 300, as shown in Figure 11. Figure 10 Figure 11 e. A tax of $200 per unit is a bad idea, because it's in a region in which tax revenue is declining. The government could reduce the tax to $150 per unit, get more tax revenue ($15,000 when the tax is $150 versus $13,333 when the tax is $200), and reduce the deadweight loss (7,500 when the tax is $150 compared to 13,333 when the tax is $200). 8 APPLICATION: THE COSTS OF TAXATION Figure 1 Figure 2 If you spent enough time covering consumer and producer surplus in Chapter 7, students should have an easy time with this. � EMBED MS_ClipArt_Gallery ��� Figure 3 Figure 4 Show the students that the nature of this deadweight loss stems from the reduction in the quantity of the output exchanged. Stress the idea that goods that are not produced, consumed, or taxed do not generate benefits for anyone. � EMBED MS_ClipArt_Gallery ��� Figure 5 Activity 1 – Labor Taxes Type : In-class discussion Topics: Deadweight loss, taxation Materials needed: None Time: 10 minutes Class limitations: Works in any size class Purpose Most students have not spent a great deal of time considering the effects of taxation on labor supply. This in-class exercise gives them the opportunity to consider the effects of proposed tax rates on their own willingness to supply labor. Instructions Ask students to assume that they are full-time workers earning $10 per hour, $80 per day, $400 per week, $20,000 per year. Ask them if they would quit their jobs or keep working if the tax rate was 10%, 20%, 30%, … (up to 100%). Keep a tally as they show hands indicating that they are leaving the labor force. Ask students what they think the “best” tax rate is. Points for Discussion Many students have no idea that current marginal tax rates are greater than 30% for many taxpayers. Students will likely say that a tax rate of zero would be best, but remind them that there would be no roads, libraries, parks, or national defense without at least some revenue raised by the government. Figure 6 Figure 7 ALTERNATIVE CLASSROOM EXAMPLE: Draw a graph showing the demand and supply of paper clips. (Draw each curve as a 45º line so that buyers and sellers will share any tax equally.) Mark the equilibrium price as $0.50 (per box) and the equilibrium quantity as 1000 boxes. Show students the areas of producer and consumer surplus. Impose a $0.20 tax on each box. Assume that sellers are required to “pay” the tax to the government. Show students that: the price buyers pay will rise to $0.60. the price sellers receive will fall to $0.40. the quantity of toilet paper purchased will fall (assume to 800 units). tax revenue would be equal to $160 ($0.20 ( 800). Have students calculate the area of deadweight loss. (You may have to remind students how to calculate the area of a triangle.) Show students that as the tax increases (to $0.40, $0.60, and $0.80), tax revenue rises and then falls, and the deadweight loss increases. Activity 2 – Tax Alternatives Type : In-class assignment Topics: Taxes and deadweight loss Materials needed: None Time: 20 minutes Class limitations: Works in any size class Purpose The market impact of taxes can be a new concept to many students. This exercise helps them think about the different effects of taxes on different goods. Taxes that may be appealing for equity reasons can be distortionary from a market perspective Instructions Tell the class, “The state has decided to increase funding for public education. They are considering four alternative taxes to finance these expenditures. All four taxes would raise the same amount of revenue.” List these options on the board: 1. A sales tax on food. 2. A tax on families with school-age children. 3. A property tax on vacation homes. 4. A sales tax on jewelry. Ask the students to answer the following questions. Give them time to write an answer, then discuss their answers before moving to the next question: A. Taxes change incentives. How might individuals change their behavior because of each of these taxes? B. Rank these taxes from least deadweight loss to most deadweight loss. Explain. C. Is deadweight loss the only thing to consider when designing a tax system? Common Answers and Points for Discussion A. Taxes change incentives. How might individuals change their behavior because of each of these taxes? 1. A sales tax on food. At the margin, some consumers will purchase less food. Overall food purchases won’t decrease substantially because the tax will be spread over a large number of consumers and demand is relatively inelastic. 2. A tax on families with school-age children. Very few families would put their children up for adoption to avoid taxes. A large tax could have implications for family planning; couples may choose not to have children, or to have fewer children, over time. A more realistic concern would be relocation to other states by mobile families. 3. A property tax on vacation homes. This tax would be concentrated on fewer households. A large tax would discourage people from buying homes. Developers would build fewer vacation homes in the long run. In many areas, people could choose an out-of-state vacation home. 4. A sales tax on jewelry This tax would also be relatively concentrated. People would buy less jewelry, or they would buy jewelry in other states with lower taxes. B. Rank these taxes from least deadweight loss to most deadweight loss. Lowest deadweight loss—tax on children, very inelastic. Then—tax on food. Demand is inelastic; supply is elastic Third—tax on vacation homes. Demand is elastic; short-run supply is inelastic. Most deadweight loss—tax on jewelry. Demand is elastic; supply is elastic C. Is deadweight loss the only thing to consider when designing a tax system? No. This can generate a lively discussion. There are a variety of equity or fairness concerns. The taxes on children and on food would be regressive. Each of the taxes would tax certain households at much higher rates than other households with similar incomes. 155 _1020516231.doc