1
Problem Set 5
ECN 131
Public Finance
Prof. Farshid Mojaver
Part A: Ch19
1. The Congressional Budget Office (CBO) has examined the incidence of taxation in the U.S. The CBO
assumes:
(a) Income taxes are fully borne by the households that pay them.
(b) Payroll taxes are fully borne by workers, regardless of the statutory incidence.
(c) Excise taxes are fully shifted forward to prices.
(d) Corporate taxes are fully shifted forward to the owners of capital.
These assumptions are generally consistent with empirical evidence.
For each of these item discuss what the assumption means. Why are some taxes (income and payroll taxes
for example) fully born by one party (households and workers in (a) and (b)) and some others are fully
shifted forward. Draw a supply and demand graph to make your point when appropriate.
Ans) Income taxes are fully borne by the households that pay then means that the households will take the
whole burden of the taxes. Similarly, Payroll taxes are fully borne by workers means that the workers will
take the whole burden of the taxes. Excise taxes are fully borne shifted forward to prices means that the
effect of the taxes on decreasing the producer price will be almost zero and all the burden of the taxes will
be took by the consumers in proportion to their consumption of the taxed item. Similarly, corporate taxes
are fully shifted forward to the owners of capital means that the corporate taxes are fully borne in
proportion to each individual’s capital income.
The reason why these taxes are fully borne by a certain party is can be explained with relative elasticity of
each party. For example, for the payroll taxes, as we have seen the question 1, labor supply is inelastic, so
workers will take the whole burden of the taxes. Similarly income is inelastic. Demand for the goods where
excise tax is imposed (such as cigarettes) is inelastic. That is why the tax burden is fully born by consumers.
Corporate taxes are taxes on undistributed profits held inside the corporation that is why it cannot be shifted
to workers or stock holders.
price
wage
D
S
S
t
t
D
L
Q
2. Discuss what would be happened (it can be happened immediately even before the tax is collected) on
the land price if a new tax is imposed on the land ownership (Hint; think about the present value of all
future tax payments)
Ans) First note that land is in fixed supply, immobile and durable.
Assume annual rental rate is $Rt at time t.
If market for land is competitive, its value is simply equal to the present discounted value of rental
payments:
PR  $ R0 
$ R1
$ R2
$ RT

...
2
1  r  1  r 
1  r T
2
Assume a tax of $ut is then imposed in each period t. The returns on owning land therefore fall, and
purchasers take this into account. Thus, the price falls to:
PR  $ R0  u0  
$ R1  u1   $ R2  u2  ... $ RT  uT 
1  r 
1  r 2
1  r T
The difference in these prices is simply the present discounted value of tax payments:
PR  PR  $u0 

•
•
u1
u2
uT

...
2
1  r  1  r 
1  r T
At the time the tax is imposed (not collected), the price of the land falls by the present value of all
future tax payments, a process known as capitalization.
The person who bears the full burden of the tax forever is the landlord at the time the tax is levied.
Future landlords pay the tax, but do not actually bear the “burden” because they paid a lower price
for the land from the current landlord.
Part B: Ch20
1. Specify whether the following statements are true, false, or uncertain and explain your answer in 1-2
paragraphs.
(a) A cut in the capital gains tax rate will promote new entrepreneurial activity and provide good
“bang for the buck.”
(b) Excluding food from a state sales tax is a good idea because food is a necessity.
(c) A government law that requires firms to provide life insurance for their employees will impose a
burden on the companies’ shareholders.
(d) Eliminating the top tax bracket of 39.6% in the US will decrease the revenue collected by the
personal income tax.
Ans)
a) False. The first statement is true: a cut in the capital gains tax rate should promote new
entrepreneurial activity by increasing the return to risk taking. However, this would not provide good
“bang for the buck.” The tax cut would benefit all capital, including capital already in place, where the
risks have already been taken, so it would be a windfall for owners of old capital. A better idea would
be to give the tax cut only to new investments. It is also worth noting that a cut in the capital gains tax
rate would mostly benefit the rich.
b) Uncertain. We know from optimal commodity taxation that the tax rate on each good should be
proportional to one over the elasticity of demand, so we should tax inelastic goods more. Food is a
fairly inelastic good, so it is a good candidate for taxation from an efficiency perspective. On the other
hand, a tax on food will hurt the poor more because food is a larger percentage of their consumption,
so it should be exempted from an equity perspective.
c) Uncertain. It depends on whether employees value the insurance. If they do, their wages may fall to
fully offset the cost (or even fall by more than the cost, if there was
previously an insurance market failure and employees value the insurance at more than its cost). If they
value the insurance at less than its cost, there will be deadweight loss and the firm and its shareholders
will probably bear some of the cost.
d) Uncertain. The Laffer curve says that a decrease in tax rates can increase or decrease tax revenues,
depending on the initial tax rate, t. A tax rate of 0% or of 100% raises no revenue. There is a rate t*
between 0 and 100% that raises the most revenue. If t is above t*, lowering t raises the revenue
collected; if t is below t*, lowering t lowers revenue. So it depends whether t* is above or below
39.6%.
Another key point: if we lower t, people may shift their compensation from non-taxed forms (like
company cars) to regular taxable income. This would lead to an increase in tax revenue.
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2. How is it possible for marginal tax rates to decline as income increases while average
tax rates rise with income? How does the optimal tax system simulated by Gruber and
Saez (2000) represent an optimal trade-off between equity and efficiency concerns?
A taxpayer’s marginal tax rate is the rate paid on the last dollar of income; the average
rate is calculated based on the taxpayer’s entire income. As long as marginal rates are above
average rates, average rates will be increasing. The higher marginal, or last, rate will bring the
average up. This is analogous to the behavior of cost functions, grade point averages, and all
other phenomena for which both marginal and average functions are calculated.
When the marginal unit is below the average, it brings the average down. When the
marginal unit exceeds the average, it brings the average up. In the example given by Gruber and
Saez (2000), it is true that marginal rates decline with income, but those rates are still greater than
the average tax rate, and so must bring the average tax rate up. In the case of taxes, the marginal
rate has the greatest effect on decision making: a rational worker will choose to change labor time
on the basis of his marginal net wage, not his average wage. Thus, the marginal tax rate has
important efficiency implications. If it is too high, it will discourage work. The work deterrence
of an income tax is highest for high-income workers, as their marginal utility from additional
income is low (by the concept of diminishing marginal utility of income). Thus, falling marginal
tax rates for high-income earners reduces the efficiency loss of work deterrence. On the other
hand, the fairness, or equity, concerns of a tax system would indicate lower average tax rates for
poorer taxpayers. The system simulated by Gruber and Saez (2000) accomplishes that. Higherincome taxpayers face higher average tax rates than do lower-income taxpayers.
3. Suppose that a state mandates that both women and men be provided family leave by
their employers following the birth of a child.
a. How would you empirically test how this policy change affected the relative wages of
men and women in the state?
Because this is a state mandate, you could compare data from states that did not have the
new provision with data from states that mandated family leave. The data set for states that
mandated family leave would have to include data on wages and employment of men and women
both before and after the mandate took effect. You would also want to include data for other
possible explanations, including the educational attainment and marital and family status of each
worker, age, employment history, and characteristics of the state that might affect wages, such as
industrial mix and urbanization.
The same data would be needed from states that did not adopt the mandate. With this
data, you could look at the change in wages and employment for men in states that adopted the
policy, the change in wages and employment for women in states that adopted the policy, and the
changes in wages and employment for the two groups in states that did not adopt a family leave
policy. If changes in employment levels were approximately the same in the states regardless of
the mandate, but wages fell by more in the states with the policy than they did in comparable
states without the policy, you could conclude that the evidence was consistent with the tax-benefit
linkage literature—namely, this mandate causes firms to offer lower wages in order to pay for the
benefit and causes workers to accept lower wages in exchange for the benefit.
b. Based on the empirical evidence on group-specific employer mandates described in the
text, what do you expect to happen to the relative wages of men and women in the state?
This mandate is similar to the maternity leave benefit discussed in the text. The results of
that group-specific mandate were to lower wages by the full amount of the cost, while having
almost no effect on employment levels. These results suggest that a family leave mandate like the
one discussed in b would result in little deadweight loss, because there would be little change in
employment levels, but that the workers would bear the full incidence of the costs of the mandate.
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Part C: Ch21
1. Suppose that you can earn $16 per hour before taxes and can work up to 80 hours per week. Consider
two income tax rates, 10% and 20%.
(a) On the same diagram, draw the two weekly consumption-leisure budget constraints reflecting the
two different tax rates.
(b) Draw a set of representative indifference curves such that the income effect of the tax increase
outweighs the substitution effect.
(c) Draw a set of representative indifference curves such that the substitution effect of the tax
increase outweighs the income effect.
(a) The maximum weekly consumption, in dollars, without a tax is 80 x $16 = $1,280.
A 10% tax reduces that amount to 0.9*
0.8*
$1,024. These give the y-intercepts of the budget constraints. The x-intercept, measuring leisure, is always
80 hours.
(b) When the income effect outweighs the substitution effect, a lower tax leads to more leisure because a
higher income allows a person to acquire more of a normal good, in this case leisure:
(c) When the substitution effect outweighs the income effect, a lower tax leads to less leisure because
leisure now has a higher opportunity cost (the higher after-tax wage):
2. Suppose that you estimate the following female labor supply relationship:
Labor supply Li = –320 + 85∙Wi + 320∙Gi –120∙Mi
where labor supply is measured in annual hours worked and wages are expressed in hourly wages.
Wi : after-tax wage
Gi : dummy variable (college graduate)
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Mi : dummy variable (married)
(a) Interpret the coefficient on after-tax wages. What does this coefficient imply about the effect of
increasing wages from $6 to $10 per hour on labor supply?
(b) What can we learn from this estimate about the income and substitution effects of wages on labor
supply?
(c) How might this coefficient estimate be biased? Explain.
(a) The coefficient on after-tax wages is positive, indicating that a higher after-tax wage increases labor
supply. The magnitude of the effect is 85: for each dollar increase in aftertax wage, all else equal, a female
will work 85 more hours per year. For a $4 increase (from $6 to $10), that translates to 4 *85 = 340 hours.
(b) This particular estimate does not explicitly include a measure of nonlabor income.
The approach described in the text subtracted the nonwage income effect from the wage effect to isolate the
substitution effect of wages on labor supply. That cannot be done here. The most we could confidently state
is that the total of income and substitution effects is positive, and so any negative effect on labor supply
arising from the income effect is more than offset by the substitution effect. The substitution effect, which
induces more work as leisure becomes more expensive, must be greater than the income effect, which
induces less work as income increases.
There is a hint in the estimation that the income effect matters, though. Being married enters as a negative
number, indicating that having another possible income in the household reduces labor supply.
(c) This estimate holds marital status and having a college degree constant. Given those controls, the
coefficient of interest is +85, indicating that women who earn a higher wage work more hours. A number
of other explanatory variables would have to be included to avoid bias. There is no control for family size
or presence of children, and it may be the case that mothers are more likely to work part-time and to accept
a lower hourly wage in exchange for work hour flexibility. It is also possible that the women who are
earning the highest wages and working the longest hours are somehow different from other women, not just
in presence of children but in chosen careers, in attitudes about working, or in ambition. Thus, there are a
number of competing explanations for the observed correlation between wages and hours that this crosssectional estimate cannot distinguish.
3. You graduate from UC Davis and take a job as a research assistant with a wage of $25 per hour. Your
job is extremely flexible: you can choose any number of hours from 0 to 2000 per year.
Suppose there is a income tax of the following form:
Income up to $10,000: no tax
Income from $10,000 - $30,000: 20% tax rate
Income from $30,000 up: 30% tax rate
(a) Draw a graph in [hours, consumption] space showing your opportunity set with and without the
tax system.
(b) Say you choose to work 1500 hours per year. What is your marginal tax rate? What is your
average tax rate? Do these rates differ? Why or why not?
(c) Suppose that the tax rates in the second and third brackets are increased to 25% and 50%. What
is the likely effect on the labor supply of men? What is the likely effect on the labor supply of
married women? Explain how the responses might differ between these groups, both in terms of
underlying economic effects, and in terms of the empirical evidence on labor supply responses.
(d) Suppose that the government replaces the current tax system with a lump-sum tax: each person
pays $10,000 per year in taxes regardless of what they earn. Discuss this tax change on equity
and efficiency grounds. Draw a new graph in [hours, consumption] space as part of your answer.
(e) Instead, suppose that the government replaces the current tax system with a negative income tax:
you receive $5,000 from the government and pay a tax of 25% on all income you earn. Discuss
this tax change on equity and efficiency grounds. Explain the likely effects in terms of the
empirical evidence on labor supply responses. Draw a new graph in [hours, consumption] space
as part of your answer.
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a) Draw non-linear BC with slope of –25 from 0 to 400 hours, slope of -.8*25 from 400 to
1200 hours, and slope of -.7*25 from 1200 to 2000 hours (intercept at income = $40,000).
Non-taxed BC is line with slope of –25 and intercept at income of $50,000.
C
50,000
40,000
26,000
10,000
800
1,600
2,000
Leisure
b) Marginal tax rate = 30%. Average tax rate = (0%*10,000) + (20%*(30,000-10,000)) +
(30%*(37,500-30,000) / 37,500 = 16.67%. Average is less than marginal because most of
your income is taxed at a lower rate than your marginal rate.
c) Two theoretical effects, net effect is ambiguous.
Substitution effect: higher taxes mean leisure is relatively cheaper, choose more leisure.
Income effect: higher taxes mean you are poorer, choose less leisure.
For men, the empirical research shows that taxes have little net effect; the two effects offset.
Empirical research shows that women are much more likely to decrease labor supply because
there’s a large substitution effect (presumably, women have more outside options). Key is
that non-market labor, which women are more likely to engage in, is not taxed, so women are
more likely choose to work at home.
C
50,000
35,000
25,000
10,000
800
1,600
2,000
Leisure
d) The new BC has a slope of –25; the income at 2000 hours is $40,000 and the income at 0
hours is -$10,000. This tax is good on efficiency grounds, because there is no DWL; you have
to pay the tax regardless of how much you work, so it can’t distort your decision to work. On
the other hand, this system is regressive; now the poor pay a much larger percentage of their
income in taxes than the rich.
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C
50,000
40,000
0
1,600
2,000
Leisure
-1000
e) The new BC has a slope of -.75*25; the income at 2000 hours is $42,500 ($5,000 plus
2000 * .75 * 25) and the income at 0 hours is $5,000. This tax may distort labor supply and
generate DWL relative to the lump-sum tax, since workers keep only 75 cents of every dollar
they earn and because of the income effect of the $5,000 guarantee. However, this system is
preferable on equity grounds to the lump-sum tax; the tax rate is flat, so it’s neither a
progressive or regressive system, while the lump-sum tax was regressive. The first tax was
more progressive than this tax, but this tax provides a safety net for the very needy, so
relative to the first tax the equity effects are ambiguous. Relative to the first tax, this tax has a
broader base, but it’s not clear how many people have lower rates and how many have higher
rates, so the efficiency effects are also ambiguous.
C
50,000
42500
5000
2,000
Leisure