Intermediate Microeconomics question

3. (10 marks) Nelly's preferences between consumption this year, co, and consumption next year, C , are given by the utility function u(co,c, ) = Co c,". She is endowed with income of $4,000 in period 0 and $11,000 in period 1. MUo=1/3co-2/3 c12/3 and MU1=2/3col/3 c1-1/3. 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.]