(c)

1. Consider sophisticated Robinson's two-period consumption decision problem. The notations of variables are the same as the slides for Chapter 4. His life time utility is given by U(C, C2) = Inc, + InCs Here we are assuming discount rate 6 = 1. Budget constraints are given by C) + B = Y1,Co = Y2 + (1+,r) B, in period 1 and 2 respectively. (a) Derive the intertemporal budget constraint for Robinson (Hint: Combine two budget constraints to eliminate B.). Provide the interpretation of the intertemporal budget constraint. (b) Solve the utility maximization problem and derive the optimal level of consumption in each period, Cy and Cy, (i.e. Express C; and C2 in terms of Y; and Yo .). (c) Now suppose Robinson cannot borrow. Namely, B 0. What is the optimal level of consumption in each period if ; 2? Provide intuition for your answer. (Hint: With the optimal level of consumption you find in question (b), what is the implied borrowing B? Does it satisfy the borrowing constraint B 0? If not, what is the best for Robinson to do? Is it optimal to set B =O, namely consuming everything you have in period 17)