Midterm 2
ECN131: Public Finance
20 Nov 06
Prof. Farshid Mojaver
Name:_________
(pts 15) 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.
(pts 6) 2- Empirical findings on labor supply
a.
What are the empirical findings on the elasticity of labor supply for primary income
earners?
b.
What about the secondary income earners?
Ans)
a. The empirical studies show that the primary income earners are not very
responsive to changes in their wages. For every 10% change in their after-tax
wages, primary earners work about 1% fewer hours (the elasticity is 0.1).
b. The studies show that the secondary earners are much more responsive to wages.
The elasticity of labor supply for this group is between 0.5% and 1%.
(pts 20) 3-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 price elasticity of demand and  is a
specific tax.
a.
Using a graph discuss what the formula says about the relationship between 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?
Ans)
a. The formula illustrates that DWL increase exponentially with tax rate.
b. The magnitude of DWL is directly related to the demand elasticity of the
commodity in question. The higher the elasticity the higher the DWL.
c. The formula implies that progressive taxation is not efficiency.
d. Since DWL increases exponentially with tax rate for given revenue target it is
better to have low tax rates on many goods than very high taxes on a few.
e. The formula implies that commodities with low demand elasticities should be
taxed most. But some of these good might be necessity goods consumed by low
income families. This is certainly inconsistent with equity considerations of the
society.
(pts 10) 4. Ramsy optimal taxation:
a.
State the formula and write what it says
b.
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?
Ans)
a. Here is the Ramsy rule for optimal taxation: MDWLi/MRi = , or ,/d
The formula says that the government should set taxes across commodities so that
the ratio of marginal DWL to marginal revenue raised is equal across
commodities. , is the Lagrangian multiplier in the optimization problem. Here it
can be interpreted as the value of additional government revenue, or marginal
benefit of the revenue. MDWLi/MRi can be interpreted as the marginal cost of the
revenue raised in terms of efficiency loss.
b. Ramsy rule implies that  R FF /R = 0.5/2 = 1/4
(pts 8) 5. 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.
Ans)
a. Here the goal is to maximize social well being (measured by a social welfare
function) subject to a revenue target. This goal implicitly reconciles both
efficiency and equity concerns of the society.
b. The OIT rule implies different tax rates for different groups. The groups might
differ in their income and the elasticity of their labor supply. This implies
progressive taxation (for MU/MR to be equal across the rich and the poor tax
rate on the rich must be higher).
MUi MU/MR
MUi Poor
MUi Rich
MUMU/MRpoor =
MU/MRRich
MU P
 R MUiTax Rate
(pts 21) 6- Questions on the EITC program (a & b 6 pts each, c 9 pts)
a.
Describe the EITC program using a graph
b.
Theoretically speaking what kind of effects do we expect to see on the labor supply of the
EITC recipients and why?
c.
What are the empirical findings:
i.
On the effect of the program on the labor supply of single mothers not in the labor
force?
ii.
What about the people that are already in the labor force
iii.
What is the impact of the program on the labor supply of married women
Ans)
a. The Earned Income Tax Credit (EITC) is a federal income tax policy that subsidizes
the wages of low-income earners. The EITC presents a 40% wage-subsidy, by
offering a refundable tax credit, and when earnings are sufficiently high, the credit is
reduced at a tax rate of 21%.
b. The figure shows four distinct groups:
- For those out of the labor force, located at point A, the EITC unambiguously
increases labor force participation through the substitution effect.
- For those at points like B, the subsidy creates ambiguous effects on hours of
work. The substitution effect increase work, while the income effect
decreases it.
- For those at points like C, the subsidy decreases hours of work because of
the income effect. There is no substitution effect.
- For those at points like D, the phase-out region, the income and substitution
effects both decrease labor supply.
c. The conclusions from a number of quasi-experimental studies about the EITC
show that:
- Labor force participation increased for single mothers.
- Conditional on work, the EITC does not seem to much affect hours of work.
- Since the EITC is computed based on family income, married couples are
likely to fall into the phaseout range. Eissa and Hoynes (1998) find a
modest reduction in labor supply among married women in response to the
EITC.
(pts 8) 7- Inflation, Taxation and Savings
a.
What is the effect of inflation on the amount of tax collected by the government in the
current U.S. tax system?
b.
What is the effect of inflation of individual savings?
Ans)
a. In the current U.S. tax system inflation leads to higher tax collected by the
government.
b. The effect on individual saving is negative
(pts 12) 8- Tax-preferred retirement savings
c.
What are three ingredients of all tax-preferred retirement saving programs?
d.
What are their effects on personal savings? National savings?
e.
What is the effect of such programs on national welfare?
Ans)
a. All Tax-preferred retirement savings (1) avoid paying income tax on their
contribution, (2) Earnings accumulate at the before-tax rate of return. (3)
withdrawals are taxed as ordinary income (not capital) tax rate, (4) they all have
the potential to withdraw the money when a person is in a lower tax bracket
b. Empirically it is not clear what the effects of these programs on personal
savings are but they certainly reduce public savings because of the subsidies.
c. The programs increase national savings because it provides saving options to
people with various saving incentives (retirement, self control and
precautionary).