1. Roys utility function over consumption in periods 1 and 2 is given by U (c1, c2 ) = c1 c2, with MRS = c2 /c1. His endowments of income are m1 = 60, 600 in period 1 and m2 = 42, 900 in period 2, and he can borrow or save at an interest rate of r = 0.3.

(a) What is the present value of his endowments, and what is the future value of his endowments?

(b) Write out his present value budget constraint and tangency condition for utility maximisation. Hence solve to find how much will he consume in period 1, and how much in period 2.

(c) Will he be a borrower or a saver in period 1? How much will he borrow or save? If he is a borrower, how much will he have to repay in period 2? If he is a saver, how much will he be repaid for his savings?

(d) Now suppose that the interest rate falls to r = 0.1. What is the new present value of Roys endowments? At his new utility maximum, how much will he consume in period 1, and how much in period 2?

(e) When the interest rate is r = 0.1, what is the present value of his original consump- tion bundle from part (b)? (Report your answer to the nearest integer.) Does that bundle lie within, on, or outside his budget at an interest rate of r = 0.1?

(f) At an interest rate of r = 0.1, suppose that Roys endowments were hypothetically adjusted to have the same present value that you found in part (e). In that case, how much would he consume in period 1, and how much in period 2? (Report answers to the nearest integer.)

(g) Does the substitution effect increase or decrease his demand for c1? What about the income effect? What about the substitution and income effects for c2?