1. a. The supply of land is fixed, or perfectly inelastic, so there is no excess burden because the lower price that sellers receive does not cause quantity supplied to fall.
b. If consumers purchase cell phones in other states in order to avoid the tax, then the excess burden will be quite large.
c. It is possible that companies could identify themselves as high-tech in order to receive the subsidy. Thus, the supply is quite elastic, and there will be substantial excess burden.
d. Consumers and sellers will likely agree to avoid cups and glasses in order to avoid the tax. A tax that is easily avoided does not have much of an impact, except to create some inconvenience, and does not raise revenue.
e. A tax on all computer software will have a smaller excess burden (relative to revenues collected) than a tax on one particular type of software like the Excel spreadsheet. This is because it is easier to substitute away from one type of software than software in general.
f. There are many good substitutes for blueberries. Therefore, their demand is quite elastic, and a tax on them will have a substantial excess burden, relative to the size of revenues collected.
2. Equation 15.3 relates excess burden to elasticity, price, quantity, and the tax rate.
Replacing a general sales tax with a tax on a few products would require a higher tax rate, which increases excess burden, other things equal. The equation indicates that it is better to tax many commodities at a lower rate than to tax a few commodities at a higher rate.
3. The quote is misleading. The way in which the presence of the t-squared makes the tax more ―important‖ is that when the tax increases, the excess burden increases with its square. Thus, when the tax doubles, the excess burden quadruples.
4. Figure 15.9 shows how a tax on market activity leads to "too much" nonmarket activity.
More generally, the model shows that when different sectors are taxed at different rates, the allocation of resources is distorted, and real income falls as a result. The more pervasive distortionary taxes are in an economy, the more severe the misallocation of resources, and the lower is real income. Hence, it is no surprise that economies with a lot of distortionary taxes tend to grow relatively slowly.
5. It is likely that the elasticity of demand for television is quite inelastic. It follows that the excess burden from a $233 per year television tax is small relative to the revenues that are collected.
6. The horizontal distance OO’ measures the total amount of capital available in society.
Any point along OO’ represents some allocation of capital between the manufacturing sector and the non-manufacturing sector. Assume that firms allocate capital between the two sectors to maximize total incomes. It follows that the value of the marginal product of capital is the same in both sectors. In the graph below, equilibrium occurs where OK*
units of capital are devoted to the non-manufacturing sector and O’K* units of capital are devoted to the manufacturing sector.
Now assume that a subsidy is available for the purchase of capital goods in the manufacturing sector, but not in the non-manufacturing sector. The subsidy raises the rate of return on capital in the manufacturing sector to (1+s)VMPMANU and causes an increase in the allocation of capital to the manufacturing sector to O’KS, along with a decrease in the allocation of capital to the non-manufacturing sector to OKS. The excess burden is equal to the shaded triangle in the graph.
$ $
O’
R2
O R1
VMPMANU
VMPNON-MANU
Capital used in the
non-manufacturing sector Capital used in the
manufacturing sector K*
KS (1+s)VMPMANU
(1+s)R2
74
7. a. The value of the marginal product of capital in the corporate sector is given by VMPc=100-Kc, and the value of the marginal product of capital in the noncorporate sector is given by VMPn=80-2Kn. With 50 units of capital altogether in society (Kc+Kn=50), and no taxation, capital should be allocated so that the values of the marginal products in each sector are equalized. Thus, setting VMPc=VMPn gives 100-Kc=80-2Kn and substituting in the constraint of 50 units gives 100-50+Kn=80-2Kn or Kn=10. This implies that Kc=40. This is illustrated below:
b. If a unit tax of $6 is leveled on capital employed in the corporate sector, the after-tax value of the marginal product in the corporate sector falls. It is now given by VMPc’
=100-Kc-6=94-Kc. Now setting VMPc’
=VMPn gives 94-Kc=80-2Kn and substituting in the constraint of 50 units gives 94-50+Kn=80-2Kn or Kn=12. This implies that Kc=38. This is illustrated below:
VMPC=100-KC VMPCORPORATE
QNONCORPORATE
Allocation of capital to the corporate and non-corporate sectors
100
VMPNONCORPORATE
80
VMPN=80-2KN
QCORPORATE KC=40
KN=10
Thus, ΔK=2 and the tax wedge is t=$6, so the excess burden is ½(2)($6)=$6.
VMPC=94-KC VMPCORPORATE
QNONCORPORATE
FIGURE 13.7b – Reallocation after per-unit tax on corporate capital
100
VMPNONCORPORATE
80
VMPN=80-2KN
QCORPORATE KC=38
KN=12 94
Excess burden from
$6 per unit tax
76
8. a. Before-tax equilibrium: P = $10 and Q = 300,000 After-tax equilibrium: P = $10.60 and Q = 288,000 Consumers pay $10.60 and producers receive $9.60.
Excess Burden = ½(12,000)($0.60) + ½(12,000)($0.40) = $6,000.
b. If the negative external cost were equal to $1 per gallon, then a $1 tax would achieve an efficient allocation and would create no excess burden. With a negative external cost of $0.50 per gallon, there is still an excess burden associated with a $1 per gallon tax, but it is smaller since the efficient level of output in this market would be between 288,000 and 300,000.
300,000
D0 S
P
Q
$10
D1
288,000
$9.60
$10.60
unit tax
excess burden tax revenue