1. (30 points) Consider a two-period consumption-savings decision problem. The agent takes income y1 and y2 as well as the interest rate r as given. The agent chooses c and c2 to maximize log(c) + Blog(c2) where B E (0, 1) is the discount factor. For simplicity assume that y2 = 0, hence the agent only has income in the first period. Her constraints are C + s = y1 and 02 = s[1 + r(1 - 7)] here s is savings/borrowing between periods 1 and 2, and ~ is a tax on interest income. 2 (a) Derive the lifetime budget constraint of the agent. (b) Compute the first order condition, and derive the Euler equation. (c) What is the optimal consumption decision of this agent? Find c; and c; as functions of all the parameters of the economy