Assignment
Problem 1
Consider a consumer who contemplates his optimal consumption plan for two period. Assume that the interest rate at which all consumers can borrow and lend is 10%. This consumer has income 6O in period fi and income 39 in period £.
(i) If the consumer would like to consume equal amounts in the two periods, how much does he need to save in period 1? How much will he end up consuming in both periods?
Suppose now that economy is populated by many copies of such consumers (whose income and optimal choices are all as described above).
The government decides to offer a deficit- financed transfer of fiO in period fi to all consumers. Assume that the government can borrow and lend at the same rate (10%) as consumers, and that the deficit is repaid by lump-sum taxes in period £.
(ii) How do optimal savings respond to this government policy?
(iii) What is the optimal consumption sequence for consumers faced with this policy?
Assume now that the government offers the mirror image of this policy, raising lump-sum taxes of fiO for all consumers in the first period, and giving transfers of fifi in the second.
(iv) How do optimal savings respond to this government policy?
(vi) What is the optimal consumption sequence for consumers faced with this policy?
Problem 2
As in problem 1, consider an economy where there are 10 identical consumers who contemplate their optimal consumption plan for two period. Assume now that the interest rate at which all consumers (and the government) can borrow and lend is xero. These consumers have income 6O in period fi and income 4O in period 2.
(i) If the consumer would like to consume equal amounts in the two periods, how much does he need to save in period fi? How much will he end up consuming in both periods?
Assume that the government must spend a total of 200 in the first period to repair a damaged bridge, and that spending is financed by a distortionary tax on all 10 consumers: every x dollars (per capita) raised cost consumers x + 1/10x2 dollars.
(ii) Should the government run a deficit? Why?
(iii) If the answer to (ii) is yes, how large exactly should the deficit be?
(iv) Assume now that the spending must take place in period £ instead of period fi. How do your answers to parts (ii) and (iii) change?
Problem 3
A number of Web sites, such as www.quickquote.com, offer instant quotes for term life insurance. Use one such web site to compare the prices of $1 million 10 -year term life policies for 50-year-old men and women.
Explain the difference in quotes for men and women. Suppose the U.S. government were to pass a law requiring insurers to offer the same prices for men and women. What effect would you expect the law to have on prices and insurance coverage?
Problem 4
Suppose that you have a job paying $50,000 per year. With a 5% probability, next year your wage will be reduced to $20,000 for the year.
a. What is your expected income next year?
b. Suppose that you could insure yourself against the risk of reduced consumption next year. What would the actuarially fair insurance premium be?
Problem 5
The country of Gheapland currently has a national health insurance system that reim- burses citixens for 90% of all heath care costs incurred. Gheapland‘s government is considering a policy change that would provide medical care providers with a fixed reimbursement level for each diagnosed illness so that citixens would no longer bear any out-of-pocket expenses for medical care. In what ways will this policy change reduce moral haxard? In what ways will it increase it?