1. Barbara is a college student seeking to optimize her consumption over two periods, with period 1 being her college years and period 2 her after college life. Her income for her college years (period 1) is $40,000 while her income for her post college years (period 2) is $1,000,000.
a. Barbara can borrow or lend at a 20% interest rate. Graph her budget constraint for income spent on consumption in periods 1 and 2, and be sure to indicate the x-axis and y-axis intercepts for this budget line.
b. Barbara’s utility function for income in periods 1 and 2 is c11/4*c23/4, where c1 is income spent on consumption in period 1 (school years) and c2 is income spent on consumption in period 2. At the 20% interest rate, will Barbara want to borrow, save, or just spend her income of $40,000 in period 1, given her lifetime budget constraint from part a?
2. Bill has a utility of money or wealth function given by u(x) = x1/2 and faces a coin flip (equal .5 probabilities) to win or lose $1,000. Calculate his certainty equivalent wealth level for this gamble if his initial wealth level is a) $5,000; b) $20,000; c) $100,000. Describe what is happening to Bill’s willingness to pay for insurance against this bet as his wealth goes up.
3. Suppose that on average people have $5,000 a year in medical expenses, and when adding in a margin for administrative costs, insurance fraud, and profit, a health insurance policy could be priced at $7,000.
a. Healthy Heather has initial wealth of $50,000, a utility of money given by u(x) = x1/2, and faces a 10% chance of $20,000 in medical expenses. Will Heather purchase health insurance at the price of $7,000? Show your work.
b. Sickly Sarah also has initial wealth of $50,000 and a utility of wealth function given by u(x) = x1/2, but faces a 40% chance of $20,000 in medical expenses. Will Sarah purchase health insurance at the price of $7,000? Show your work.
c. What will average medical expenses be given who purchases health care if policies are priced at $7,000?
4. Joe cares about his income and the income of his cousin, Marty. Joe’s utility function is given by minimum(5*YJoe, YMarty), where YJoe and YMarty are the amounts of money each has to spend.
A. Initially Joe’s income is $200,000 and Marty’s income is $20,000. Calculate the personal utility-maximizing transfer (if any) Joe would make to Marty in this case.
B. Mr. Scrooge does not care at all about his distant cousin Tiny Tim. Draw out the indifference curves which would reflect Scrooge’s preferences about income distribution between himself and Tim.
5. Show whether the following production functions exhibit increasing, constant, or decreasing returns to scale.
a. Q = 3L + 2K
b. Q = min (L, 2*K)
c. Q = 10*K*L
d. Q = L2 + K2
e. Q = 2*K.5*L.5 + 7
6. Let the production function for thingamajigs be Q = L1/2*K1/2, the price of labor be $10 and the price of capital be $20. In the short run, the amount of capital is fixed at K = 100. Complete the following short run cost table for this firm (on your own paper, not this sheet!).
Quantity Labor Total Fixed Cost Average Fixed Cost Total Variable Cost Average Variable Cost Total Cost Average Total Cost
7. Suppose that Acme Widgets has two production facilities, one in Troy and the second in Luverne. The marginal cost of producing widgets of producing widgets in Troy is given by:
MCTroy = 4*(QTroy/100).
The marginal cost of producing widgets at the Luverne plant is:
MCLuverne = 6 + 2*(QLuverne/100).
If Acme wants to minimize the total cost in each case, how should it divide the following production totals between the two plants?
a. 100 b. 600 c. 1200