Midterm 2 Solution
ECN131: Public Finance
Practice
Prof. Farshid Mojaver
Name: ANSWER
Tax Burden
1- Suppose that the demand for apples is perfectly elastic and the government levies a tax
on the producers of apples. Assume that the supply of apples is neither perfectly elastic
nor perfectly inelastic.
a. How will the price paid by consumers change? Is this change bigger or smaller
than the price change that would result if the demand for apples were not perfectly
elastic?
b. How will the quantity of apples consumed change due to the tax? Is this change
in quantity larger or smaller than the change that would result if the demand for
apples were not perfectly elastic?
c. Explain the significance of your answers in both part a and part b in terms of how
the tax affects the welfare of consumers in the apple market
Ans)
a. The price paid by consumers will not change at all. If the demand for apples is
perfectly elastic, it means that consumers have perfect substitutes for apples and
will buy another product (and be no worse off) if the price goes up at all.
Consequently, apple producers bear the entire burden of the tax. In contrast, if the
demand for apples were not perfectly elastic, the price paid by consumers would
rise and consequently the consumers would bear some of the tax burden.
b. The quantity of apples will fall dramatically. If the demand for apples were
neither perfectly elastic nor perfectly inelastic (and if supply were neither
perfectly elastic or perfectly inelastic), then the quantity would fall but by less
than it falls when the demand for apples is perfectly elastic.
c. Only price changes caused by the tax affects the welfare of the consumers in the
market. Since in this case the price paid by consumers does not change,
consumers are made no better or worse off because of the tax, even though they
consume fewer apples. The reason for this is that the perfectly elastic demand
curve for apples implies that consumers are indifferent between consuming apples
at that price and consuming other goods at that price. Consequently, although
people shift consumption to another good, they are no better or worse off for it.
2- What does the Congressional Budget Office (CBO) assume about the tax incidence of
the following items:
a) Income taxes
b) Payroll taxes
c) Excise taxes
d) Corporate taxes
Just state the assumption. You do not need to rationalize the assumptions.
Optimal Taxation
1- When supply is infinitely elastic the relationship between commodity taxes and DWL
can be written as the following: DWL = -0.5dQ 2 where d is the Hicksian price
elasticity of demand and  is a specific tax.
a. With the help of a graph explain what the formula says about the relationship
betwax rate and DWL
b. What does the formula say about the relationship between inefficiency of taxes of
certain characteristics of the commodity being taxed?
c. What does the formula imply about the efficiency of progressive taxation?
d. What does the formula imply about the broadness of commodity taxation?
e. Is this recipe for optimal taxation consistent with the equity consideration of the society?
2. Ramsy Rule: MDWLi/MRi = ,
a. What does this rule say?
b. Show how this formula is derived
c. Use DWL = -0.5dQ 2 to solve for optimal taxation ,/d
d. Discuss the meaning of Ramsy optimal taxation:
i. Given this formula how do we know how to tax different commodities?
ii. Suppose we have two goods F (food from grocery) and R (food from
restaurant), suppose price elasticity of demand for F is 0.5 and that of R is 2.
What is the optimal tax ratio of R to F?
3. Optimal Income Tax: MUi/MRi = 
a. What is the goal of optimal income tax analysis
b. How that goal is met using the above formula for OIT? Use a graph to make you
point.
c. Write the income tax analyst’s problem and derive the above OIT formula.
4. What is the optimal tax rate for those with above average income when the SWF is
Utilitarian and the total income is fixed?
5. Simulation exercise of Gruber and Saez (2000)
a. What is the question in the exercise?
b. Roughly what are the answers?
c. How is the exercise caries on?
i. Set up the problem that Gruber and Saez (2000) want to solve.
ii. Describe SWF employed the reason for its format
iii. What are the choice variables in the problem?
d. What do you conclude from the study about the optimal mix of tax/subsidy
consistent with equity and efficiency considerations both?
e. Why are these results so different from those that we get from problem (4) above?
f. If the social planner cared less for the top 20 percent rich individuals would we
get a more favorable tax scheme for the poor?
g. Could the result be different if the exercise was carried out for a different country
say Europe, Japan or Canada? Explain.
h. Are these results consistent with the Optimal Income Tax rule above? Explain.
6. Discuss the equity implications of the Ramsey rule for optimal commodity taxation.
How can these equity issues be addressed, if at all?
The Ramsey rule states that commodities with low elasticities of demand should be taxed at
higher rates than commodities with high elasticities of demand. However, low-income people
might spend a higher proportion of their incomes on commodities with low elasticities of demand
(food, clothing, and so on) than might high-income people. Consequently, following the Ramsey
rule may result in a regressive taxation scheme society may view as inequitable.
The equity issue could be addressed by reducing commodity taxes on goods consumed
disproportionately by low-income groups below that implied by the inverse elasticity rule.
However, while doing so would increase equity, it would reduce efficiency. Consequently, the
extent to which society would want to reweight the optimal commodity taxes depends on how
much society wants to trade off efficiency to gain equity
Taxes and labor Supply
1- Suppose that Chifeng and Kristine are married and have two children. Chifeng is the
primary earner in the household. Kristine is considering joining the labor force, at which
point she would earn $25 per hour for 40 hours per week. The cost of child care would be
$10 per hour for 40 hours per week. Kristine is indifferent between working and staying
at home except for the financial impact. Assume that the marginal tax rate is 50%.
a. Assume that child care is NOT tax deductible and that child care at home is NOT
imputed and taxed. Will Kristine work or stay home, and how much better off is she
by doing one instead of the other? Explain your answer.
b. Now assume that child care at home is imputed and taxed based on the market cost of
providing that service. Does this affect your answer to part a? Explain.
c. Again, assume that child care is NOT tax deductible and that child care at home is
NOT imputed and taxed. However, suppose that Kristine values staying at home with
her children at some value $x, where x is either positive (implying that she prefers
staying home) or negative (implying that she prefers to work). What must x be such
that Kristine is indifferent between staying home and joining the labor force?
Ans)
a. If Kristine works, she makes $1,000 per week, of which $500 is taxed. Child care
costs $400 per week. Consequently, Kristine will choose to work since the value
of working ($500) exceeds the value of providing the child-care-at-home $400.
b. Now Kristine will owe $200 in taxes if she stays home and provides the child care
herself ($200 = 0.50*$400). Consequently, the value of staying home is now $200
while the value of working does not change from $500, so the answer to part a
will not change.
c. From part a, it is clear that if Kristine values child care for an additional $100 per
week, the value of providing the child care herself increases to $500 and is equal
to the value from working of $500. Consequently, x = 100.
2- Suppose that as a policy maker, you have three options for expanding the Earned
Income Tax Credit (EITC) using a given increase in your budget:
Option 1: Increase the compensation rate in the phase-in portion of the EITC schedule.
Option 2: Increase the maximum tax credit a person can receive.
Option 3: Lower the rate of reduction in the phase-out portion of the EITC schedule.
a. Suppose that the goal of your agency is to increase the size of the labor force.
Which option would meet this goal in the most cost-effective manner? Explain.
b. Suppose that you chose Option 2. Explain in terms of income and substitution
effects how your choice would affect someone who is on the phase-out portion of
the EITC schedule.
Ans)
a. Option 1 would be the best bet. By increasing the initial wage subsidy, there is a
substitution effect that raises the price of an hour of leisure for someone who wasn't
working before, thus inducing the person to join the labor force. Just as significantly,
since the target group is people who aren't in the labor force, Option 1 does not have
an income effect that would induce people to work less.
b. One effect of Option 2 on this person is the income effect. By increasing the transfer
to this person, the person is now better off and can purchase more of all goods,
including leisure. Consequently, the income effect will induce the person to work
fewer hours. In addition, since the person loses a bit of the tax credit for each
additional hour he or she works, the substitution effect continues to induce the person
to work less. Consequently, the overall effect of Option 2 on this person is to
unambiguously lower his or her labor supply.