1. Assuming that all other commodities (except for cable and satellite television) were untaxed, then optimal tax policy suggests the commodities should be taxed according to the inverse elasticity rule. Goolsbee and Petrin (2001) find that the elasticity of demand for basic cable service is -0.51, and the demand for direct broadcast satellites is -7.40.
Applying the inverse elasticity rule would imply that (tBASIC/tSATELLITE)=(ηSATELLITE/ηBASIC)=(7.40/0.51)=14.5. Thus, tax rates on basic cable should be 14.5 times higher than tax rates on satellite television because basic cable is inelastically demanded, while demand for satellite television is highly elastic. Among the assumptions that go into the inverse elasticity rule are that goods are neither complements nor substitutes, and that the elasticities are the Hicksian compensated elasticities rather than the Marshallian uncompensated elasticities. In this case, it is likely that the first of these assumptions is false – basic cable and satellite television are likely substitutes for each other. The Hicksian and Marshallian demand elasticities are likely to be close to each other because the income effects are likely to be small for this commodity.
2. Although the tax schedule is progressive, the incidence is not clear at all. This is determined by the relative demand and supply elasticities for expensive cars. One may argue that behavior will be distorted only at the margin, and hence demanders largely bear the burden. However, administration of this tax would not be straightforward: One could imagine methods of evasion such as misrepresenting invoices or selling the car in parts!
Q0
D0 S
P
Q FIGURE 13.8 – Excess burden of a unit tax imposed on demanders
P0
D1 Q1
Pn Pg
unit tax
excess burden tax revenue
www.elsolucionario.net
3. The beard tax was progressive because it was a function of social position. It’s hard to know about the efficiency consequences unless one knows more about the price elasticity of demand for the privilege of having a beard. If the elasticity was small, then it would be an efficient tax. However, conventional notions of horizontal equity suggest that the tax was unfair.
4. If the nut fee is truly collected whether or not the farmer collects nuts, then it is independent of the farmer's behavior. Hence, it is a lump-sum tax, and perfectly efficient (unless it drives some individuals out of farming). However, optimal tax theory tells us that we must consider equity as well as efficiency considerations. If the fee is the same for all households, regardless of their incomes, then it is regressive. With a conventional utilitarian welfare function, this is unlikely to be optimal. Because farmers who are not alike in relevant aspects (e.g., income) pay the same tax, the nut tax would seem to violate horizontal equity. Things become even worse when we bring city-dwellers, who don't have to pay the nut tax at all, into the picture.
Moral: An efficient tax need not be optimal or horizontally equitable.
5. One could use Figure 14.5 on page 351, on tax evasion, to understand this phenomenon.
The horizontal axis now represents the amount of underreporting of the value of commodities, and the vertical axis represents the cost in dollars. Fisman and Wei (2001) find that in the case of China, a 1 percent increase in the tax rate results in a 3 percent increase in evasion (by “reclassifying” a commodity as a lower-taxed commodity). The 1 percent increase shifts up the MB curve, which leads to a new intersection between MB and MC, and a higher R*, which was found to be 3 percent higher.
www.elsolucionario.net
6. Figure 14.5 equates the marginal benefit of underreporting $1’s worth of income to the marginal cost. The marginal benefit is equal to the taxes saved, which is simply the person’s marginal tax rate, or MB=t. The expected marginal cost of underreporting $1 of income is equal to the product of the probability of getting caught and the fine per dollar of underreporting, or MC=ρ*Marginal Penalty. As shown in Figures 14.5 and 14.6, the optimal amount of underreporting, R* equals zero if MC≥MB. Thus, if ρ*Marginal Penalty≥t, then there will be no underreporting. With ρ=0.02 and t=0.36, the inequality becomes 0.02*Marginal Penalty≥0.36, or Marginal Penalty≥$18. With a fine of $18 (or more), Sharlene would not cheat on her taxes. The figure below illustrates this case.
R*
MC
MB0=t
$ savings
Amount of underreporting FIGURE 14.5 – Underreporting of
commodities in China due to tariffs
MB1=t+.01
1.03R*
www.elsolucionario.net
7. The one-time tax of 14.25 percent on net wealth over $10 million is similar to a lump sum tax and would, on the surface, be efficient. In principle, such a one-time policy should not affect current incentives to save for the future. As discussed on page 344, however, such a policy would run into the problem of “time inconsistency of optimal policy.” The government would have an incentive to renege on its promise that the tax would only be levied once, because it could conceivably raise more money without excess burden. Thus, the government’s incentives are inconsistent with the stated policy, and capitalists realize this and adjust accordingly.
8. a. It is true that a proportional tax on all commodities (including leisure) is equivalent to a lump sum tax. To illustrate, consider the simplest example where there are only two goods: consumption goods and leisure. The budget constraint is equal to: pCC+wL=I, where pC and w are the prices of consumption goods and leisure, C and L are the quantities of consumption and leisure, and I is income.
Then a proportional tax on all goods changes the budget constraint to: (1- τ)pCC+(1-τ)wL=I, or rearranging, pCC+wL=I’, where I’=I/(1-τ)<I. Thus, a proportional tax on all goods does not change relative prices and is equivalent to taking away income. So it is equivalent to a lump sum tax.
b. It is (usually) false that efficiency is maximized when all commodities are taxed at the same rate; this will not be true if leisure is untaxed. Imagine a more complicated budget constraint: pCC+pFF+wL=I. If leisure cannot be taxed, then
R*=0
MC=ρ*MP=0.02*$18
MB=t=0.36
$ savings
Amount of underreporting FIGURE 14.6 – Fine that induces no
underreporting
www.elsolucionario.net
a tax on commodities leads to a budget constraint of (1-τ)pCC+(1-τ)pFF+wL=I, which does change the relative price of leisure compared with food or consumption goods. Thus, it is not a lump sum tax. Instead, the inverse elasticity rule given in equation (14.9) on page 333 of the textbook would suggest that the ratio of the tax rates are inversely related to the ratio of the compensated demand elasticities for all commodities that can be taxed. That is, (tC/tF)=(ηF/ηC).
c. It is true that average cost pricing for a natural monopoly allows the enterprise to break even, but the outcome is inefficient. Figure 14.3 in the textbook on page 338 shows the typical natural monopoly problem, with an initial fixed cost, and an ever-declining marginal cost curve. In this case, the average cost curve is always declining, but above the marginal cost curve. Setting P=AC results in an output level of ZA and zero economic profits. The figure illustrates, however, that the marginal benefit of more output exceeds the marginal cost, so the efficient level of production occurs at P=MC, or an output level Z*>ZA. The deadweight loss is the area between the demand curve DZ and marginal cost curve, going from ZA to Z*. If output were at the efficient level, however, there would be economic losses rather than zero profits.
d. One notion of horizontal equity is that people in equal positions should be treated equally by the tax system. Under this traditional notion of horizontal equity, the fact that Tom’s workplace provides free access to a fitness room suggests this kind of compensation should be taxed; Jerry pays “full taxes” on his compensation while Tom does not. Another notion of horizontal equity relies on the utility definition of horizontal equity. This concept says that if two individuals have the same utility without taxes, they should have the same utility with taxes, and the taxes should not affect the utility ordering. One implication of the utility definition is that any existing tax structure does not violate the notion of horizontal equity if individuals are free to choose their activities and expenditures.
If Tom and Jerry have free choice between the two different jobs (and identical preferences), then the net after-tax rewards (including amenities) must be the same at both jobs; otherwise there would be migration. In this case, the before- tax wage on Tom’s job adjusts for the fact that there is a fringe benefit.