Question:

Barbara lives for two periods and has preferences represented by the following utility function: _ 1 U(60,Cl_) = 63-5 + 1 + 5 53-5, where the subscripts represent this period (:0) and the next period (I) and Ct is in millions of dollars. Barbara's wealth is 0.5 million dollars, and she has no labor income. Her rate of time preference 5 is 2%. Set up and solve Barbara's intertemporal utilit}r maximization problem (Le... find the optimal amount of consumption in each period} assuming the real interest rate is 2%. How much does she save in period 0'? [1i]I points] Now suppose that the interest rate falls to 1%. What happens to the optimal value of Cg? How does the amount Barbara save in period 0 compare to part (a)? [10 points] Explain what has happened to Barbara's savings between parts {a} and (b) in terms of income and substitution effects. [5 points] CI Suppose I consume C0 today. I save what I don't consume: m - Co. I invest this at interest rate r. (Note: a" investments are someone's savings!) What do I have available to consume tomorrow? C1 = (m C0)(1 +r) Consumption tomorrow = Savings today invested at rate r C1 1+r lie-arranging gives the budget constraint: C0 + = m