Please show calculations and explanations for all parts, along with the final answers derived for parts a-d.

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 (' denote consumption in period 1, 'y denote consumption in period 2, and S denote savings. Suppose that individuals have a utility function 7 = In y + 3 In Cs. Where 3 = 99 is the individual's discount factor, {a) Set up the individual's lifetime utility maximization problem and solve for the optimal 7, C3, and S in an economy without taxes. If the interest rate is low, in the sense that (1+r)