Suppose a household solves the following two-period consumption-savings problem with taxes: max u(c) + Bu(c2) 1,a,c2 Subject to a+c1 = ao+y1 - T1 = C22T2+(1+r)a with u(c), where: c is consumption at time 1, c is consumption at time 2, y is income at time 1, y2 is income at time 2, T are taxes at time 1, T2 are taxes at time 2, and ao is initial wealth. 1. Solve for the household's choice of C1, C2 and a in closed form 2. How does c/y depend on y2? What would happen if households suddenly become opti- mistic about the future? 3. How does c/y depend on ao? Please give economic intuition. 4. How does c/y depend on ? Please give economic intuition. Problem 4 A household solve a special case of the previous problem with T =T =a0 = 0. Suppose that, by coincidence, the values of ; r; y and y2 are such that it is optimal for the household to consume: c = y and c = y2. 1. What will happen to c if interest rates increase? [A graph will be helpful. Make sure you draw it carefully, it's probably useful to make it large] 2. Does the overall utility achieved by the household increase, decrease or stay the same?