Public Economics, Course 01:220:460
Sample Exam, Two Pages
1. Consumer choice. There are two divisible private goods: Good 1 and Good 2. Alice has endowment (5, 2), and she views the goods as perfect complements. The market prices are (p1, p2) = (4, 2).
(a). [5] Write down a utility function that represents Alice’s preferences.
(b). [5] Calculate Alice’s choice from her budget set.
(c). [5] On a graph, show Alice’s budget set, Alice’s choice, and Alice’s indifference curve through her choice.
2. Exchange economies. There are two divisible private goods, Good 1 and Good 2, and two consumers, Alice and Bob. Alice’s indifference curves are all lines with slope −2, and her endowment is ωA = (0, 4). Bob’s indifference curves are all lines with slope − 2/1, and his endowment is ωB = (4, 0).
(a). [5] Draw the Edgeworth box and the allocation where both agents consume their endowments. Is this allocation efficient? Why or why not?
(b). [10] Calculate the competitive equilibrium, giving the allocation and some prices (p1, p2) compatible with the allocation. In an Edgeworth box, illustrate Alice’s budget set, Bob’s budget set, Alice’s choice with its indifference curve, and Bob’s choice with its indifference curve.
(c). [5] Is the competitive equilibrium envy-free? Why or why not?
3. Public goods. Suppose Alice, Bob, and Carol have the following demand functions for rockets: QA(p) = 16 − p, QB(p) = 7 − 2/1p, and QC(p) = 6 − 2/1p. Rockets are a public good, and there is a constant marginal cost for rockets equal to 12.
(a). [5] What is the efficient quantity?
(b). [5] What are the Lindahl prices?
(c). [5] What is the total cost of public provision? How much does each agent pay in total?
4. Externalities. Briefly (but accurately!) answer the following questions on the topic of externalities.
(a). [5] Describe the Coase Theorem.
(b). [5] For reducing emissions, is cap-and-trade cost-effective? Explain.
(c). [5] For reducing emissions, is an emissions fee cost-effective? Explain.
5. Healthcare. A risk-neutral insurance company sells policies to fully insure against healthcare costs for a market with 1000 low-risk customers and 1000 high-risk customers. All customers are risk-neutral, each low-risk customer has an expected healthcare cost of $5, 000, each high-risk customer has an expected healthcare cost of $20, 000, and the company is not able to observe who is high-risk and who is low-risk without experience rating. For the following questions, if there are several possible outcomes, then consider the possible outcome that has the most trade.
(a). [5] If there is no experience rating or government intervention, what is the outcome? Explain.
(b). [5] With experience rating, what is the outcome? Explain.
(c). [5] With community rating backed by mandate, what is the outcome? Explain.
6. Education. Briefly (but accurately!) answer the following questions on the topic of education.
(a). [4] Provide an argument for government intervention in education.
(b). [4] Provide a second argument for government intervention in education.
(b). [2] Provide a third argument for government intervention in education.
7. Retirement. There are three periods: year zero (the present), year one, and year two. The interest rate is r = 0.5. There are three equally likely scenarios:
1. Alice pays 6 in year zero, then does not continue.
2. Alice pays 6 in year zero, then receives 9 in year one, then does not continue.
3. Alice pays 6 in year zero, then receives 9 in year one, then receives 9 in year two.
(a). [5] Calculate Alice’s Social Security Wealth.
(b). [5] Suppose innovations in medicine make the first scenario less likely. Does Alice’s Social Security Wealth increase, decrease, or stay the same? Explain.