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Part I

Economics

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Part I. True/False/Uncertain (5 points each). Please make sure you justify the answer to every question!

1. Suppose the sale of drugs is illegal. The police catch a fraction of the dealers, and they are punished with a fine. An increase in the fine would increase the expected punishments, but it would also increase the inequality in net income between those who are caught and those who avoid being caught. The increase in inequality in outcomes could attract more dealers into this industry if all dealers are risk-preferrers.
2. Given that people are naturally impatient (β < 1) and storage is costly (δ < 1), no rational individual would choose to store.
3. An increase is the price of housing will make homeowners better off.
4. If a man has an income of 100 dollars and he is offered the option to pay 5 dollars for a lottery ticket that gives equal probability to winning 10 dollars and losing 0 dollars and he accepts it, then his marginal utility of income must be increasing.
5. If the rich spend a higher proportion of their income on frozen meals relative to the poor, then frozen meals must be normal goods.
6. Suppose that a consumer’s demand function for eggs is given by:

x = 24 − 24p_x.

If he purchases a dozen eggs, then he must be willing to pay at most 50 cents for the marginal egg and, consequently, would refuse an “all-ornothing” offer to pay 8 dollars for a dozen.

Question 1: Trading Oil. (35 points)

Suppose that the world consists of two countries: the US and Saudi-Arabia, each represented by one consumer. The US consumer enjoys consumer goods, c, and oil, o. The utility function for the US consumer is given by:

UUS (c,o) = cαo1−α

The Saudi consumer, on the other hand, only enjoys the consumer good. The utility function for the Saudi consumer is given by:

U^SA (c,o) = c^γ,

where α,γ ∈ (0,1). Let p denote the relative price of oil measured in terms of consumer goods foregone. The US has an endowment of consumer goods, ω¯_c, but no endowment of oil. Saudi-Arabia has an endowment of oil, ω¯_o but no endowment of consumer goods.

1. (5 points) Solve for the Marshallian demand and indirect utility functions for the US and Saudi Arabia.
2. (5 points) Compute a CE for the two country economy.
3. (5 points) Consider, for this question only, the case where the endowments are switched, so that the US holds all the oil, and Saudi-Arabia holds all the consumer goods. Would this endowment point be a Pareto Optimal allocation? Explain whether your solution is consistent with the welfare theorems and, if not, explain why not.

Suppose, now, that the US and Saudi-Arabia realize that there is a third country in the world, Norway. Like Saudi-Arabia, Norway’s endowment is purely oil,

 and the Norwegian consumer gains no utility from consuming oil.

 

4. (5 points) Compute a CE for the three country economy (please use the original endowments for the US and Saudi Arabia).
5. (5 points) If the world initially consisted of only the US and Saudi-Arabia, is Saudi Arabia better off now that Norway has joined the world market? Is the US? Provide a measure of welfare that substantiates your answer and state whether it corresponds to the CV or to the EV.
6. (10 points) If the world initially consisted of the US, Saudi-Arabia and Norway and Norway decided to drop out of the world market for oil, how does this impact Saudi Arabia? The US? Provide a measure of welfare that substantiates your answer, state whether it corresponds to the CV or to the EV, and relate it to your answer to the previous part.

Question 2: Government Assistance and Labor Force Participation. (35 points)

Peter derives utility from consumption (c) and leisure (R). He has 60 hours per week to enjoy leisure or to work (l). He can work as many hours as he wants to up to 60 per week and his hourly wage is w. Peter receives government assistance, denoted A, to help him cover his minimum consumption level, denoted c¯. Peter’s utility function is given by:

 

U (c,R) = ^p(c − c¯)R,

You may assume that the price of consumption satisfies p_c = 1.

1. (3 points) Set-up and solve Peter’s utility maximization problem under the assumption that he receives assistance A and has minimum consumption equal to c¯. You may assume an interior solution.
2. (6 points) Using your solution from part 1, please determine Peter’s consumption and hours worked if A = c¯= 0? How much would Peter consume and work if A > 0 and c¯ = 0? Is Peter better off with the government’s assistance? Explain why or why not.
3. (5 points) Suppose that A > 0 and c¯> 0. Derive Peter’s reservation wage, w^R.
4. (5 points) Suppose, now, that A > 0 and c¯ > 0. Are there conditions under which Peter will not work or conditions under which he will take no leisure? How does the existence of subsistence consumption, c¯ > 0, affect your answer? Explain the intuition behind your conditions.
5. (6 points) What is the wage elasticity of Peter’s labor supply function? If A < c¯, how does Peter supply of labor change in response to a change in the wage? How does your answer change if A > c¯? If labor supply moves opposite the change in the wage, can you conclude that leisure is a Giffen good? Why or why not?
6. (10 points) Currently the subsidy provided by the government is such that A > c¯, but the government is evaluating to reduce A exactly to c¯. Use your previous results to discuss the consequences of this policy change in terms of Peter’s labor force participation and welfare.