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ECON 7266

Spring 2022

SECOND TAKE-HOME EXAM

1. All first-world governments face the problem of an increasing cost to fund their old age pension programs. The US is no exception. A number of solutions to the looming bankruptcy of its Social Security trust fund have been proposed. Critically discuss each the following proposed reforms of the US social security system in terms of long-term program viability, and in terms of who gains and who loses.

a. Eliminate the maximum payroll tax cutoff (currently at $147,000) and extend this tax to all earnings from work.

b. Raise the minimum retirement age from 62 to 64 while keeping the benefits from early and full retirement ages actuarially neutral.

c. Phase out social security benefits to those earning more than $80,000 a year from other sources.

d. To adjust benefits to inflation, replace the consumer price index for workers with a price index for purchases by elderly Americans.

2. In class we examined the excess burden of a tax on a good. This question explores some extensions to this analysis.

a. In working examples of finding the excess burden of an excise tax we assumed for simplicity that supply was horizontal. Suppose we wish to find the excess burden of a tax in a market characterized by a downward-sloping demand curve and an upward-sloping supply curve. Specifically, suppose that a 5 percent tax on wine served by the glass reduces its consumption of by 1,000 units. The price elasticity of demand is -0.5 and the price elasticity of supply is 2.0. If the before-tax price of wine was $2.00, what is the deadweight loss?

b. Now suppose that a different good is taxed, and the before-tax and after-tax quantities bought are identical. Is there an excess burden? Explain, using a diagram to support your analysis.

c. Last, suppose that as head of the state revenue department you are asked to raise $1 million in extra tax revenue during the current recession.  You work in a politically correct state, and you are limited to levying per unit taxes of any amount on cigarettes and beer. Assume that the supply of both is perfectly elastic. The price of a pack of cigarettes is $4.00, and the demand for a pack of cigarettes is

Q_C = 500,000 – 50,000P_c  

The price of a six-pack of beer is $3.00, and its demand is 

Q_B = 500,000 – 20,000P_B

What per unit taxes should you levy on cigarettes and beer to (1) raise the required revenue, and (2) do so with the least deadweight loss?

3. The objective of optimal tax theory is to design an efficient system of taxation consistent with society’s distributional objectives. Changes in tax law may contribute to or detract from this objective. Discuss the likely effects on optimal taxation of the following hypothetical changes.

a. substituting a consumption tax for most or all of the current personal income tax.

b. eliminating the tax-deductibility of employer-provided health insurance.

c. eliminating the earned income tax credit.

d. charging a marginal tax rate of 0 to the highest skilled citizen.

e. changing social security from a tax-transfer system to a private savings account, similar to a 401k plan.

4. Assume that a government is changing from a proportional personal income tax to one with a progressive rate structure. Both generate the same yield. Using economic theory, describe comprehensively how increasing the progressivity of the personal income tax would likely affect

a. labor supply.

b. saving and borrowing.  

In your answer, please note what both theory and empirical analysis have to say about these issues. Also, in your answer discuss whether and how you think that the effect of increased income tax progressivity would separately affect the labor supply of men and women.

5. Suppose that women require more medical care than men. Assume that women have an 80 percent chance of illness leading to a $1,000 loss in a given year, but men only have a 20 percent chance of an identical loss. There are an equal number of men and women. Both have an initial wealth of $10,000 and have utility of wealth functions of U = ln (W).

First, assume that there is a single insurance company.

a. What are the optimal rates for this insurer to charge?

b. Suppose the insurer decides to insure women only. What rate would it charge?

Now assume that insurance is offered by competitive insurance companies.

c. Suppose that men and women in equal numbers purchase full insurance at whatever is the rate offered by the companies. If these companies cannot distinguish between men and women and offer only one full-insurance contract, what will be the actuarially fair premium? 

d. Who will buy insurance at the premium you calculated in (c)?

e. Given your response in (d), did the companies correctly calculate the premium?

6.  The US government has elected to have a single-payer health care system, yes is striving to increase health insurance coverage and limit growth in medical spending. Please answer the following questions on its government’s interventions in the health care market.

a. Who qualifies for Medicaid? Who qualifies for Medicare?

b. How is Medicaid funded? How is Medicare funded?

c. How has the Affordable Care Act (aka Obamacare) affected health insurance coverage and medical care costs?