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Chapter 8

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Hannah Holmes

APPLICATION: THE COSTS OF TAXATION 8 Problems and Applications 1. a. Figure 3 illustrates the market for pizza. The equilibr1um price is P , the equilibrium quantity is1Q , 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 bB buyers, P , is now higher than the price received by sellSrs, P ,BwheSe P = P + $1. The quantity d2clines to Q , 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 Q , as in the case without the 1 tax, and the equilibrium price wou1d be P . 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 149 150 ✦ Chapter 8 /Application: The Costs of Taxation B+D to the government, then all three parties, including the government, would be better off. This illustrates the inefficiency of taxation. Chapter 8 /Application: The Costs of Taxation ✦ 151 2. a. The increase in demand increases the market price, as Figure 4 shows. Since the supply of land is assumed inelastic, the revenue to landlords increases. Price of Land Supply D 2 D 1 Quantity of Land Figure 4 b. A tax on land reduces the demand. Since the supply of land is inelastic, the landlords have to decrease the price exactly by the amount of the tax in order to maintain the quantity demanded at the same level as the fixed amount of land supplied. The entire burden of the tax is, thus, born by the landlords. . c. The deadweight loss is zero, because the equilibrium quantity does not change. d. George’s land tax may not apply to real estate because the supply of real estate is not perfectly inelastic: more houses can be built when demand increases. Another difference is that real estate requires maintainance and upgrading, as opposed to unimproved land. 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. 152 ✦ Chapter 8 /Application: The Costs of Taxation 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 5 shows, consumer surplus declines considerably, by area A+B, but producer surplus doesn't fall much at all, just by area C+D. Figure 5 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 6 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 6 Chapter 8 /Application: The Costs of Taxation ✦ 153 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 7 illustrates the market for socks and the effects of the tax. Without a tax, the
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