2. Capital Income and Savings Taxation Consider a 2 period model of retirement savings in which individuals earn labor income Y from working in period 1 and do not work in period 2 (retirement). Individuals choose how much to consume in each period. Savings in period 1 earn an interest rate r. Let C'; denote consumption in period 1, C's denote consumption in period 2, and S denote savings. Suppose that individuals have a utility function U = InC + fInCy. Where 3 = .99 is the individual's discount factor. The gross interest rate is (1 +7) = 7L (a) Set up the individual's lifetime utility maximization problem and solve for the optimal Ct, C3, and S\" in an economy without taxes. If the interest rate is low, in the sense that (14 7)