Nelly's preferences between consumption this year, , and consumption next year, , are given by the utility function . She is endowed with income of $4,000 in period 0 and $11,000 in period 1.
a. If she can borrow and lend at an interest rate of 10 percent, how much will she consume in period 0 and in period 1?
b. Suppose she can lend at the interest rate of 8 percent, but due to a bad credit history Nelly can only borrow from a loan shark, who charges her an interest rate of 40 percent. How much will she consume in each period? [Hint: draw a diagram of her inter-temporal budget constraint and sketch her indifference curves.]