1. Suppose that Martha has a utility function over current and future consumption given by U(C1, C2) = 20102 where c denotes the amount consumed in period 1 and c2 indicates the amount consumed in period 2. Let p1 = p2 = 1 and " = 0.2. (As in class, we assume that Martha can borrow and lend money at the interest rate r = 0.2.) In addition, suppose that the income level of Martha in period 1 is m1 = 25 and her income level in period 2 is my = 20. (a) Calculate the Marginal Utility of Martha with respect to c1. (10 points) (b) Calculate the Marginal Rate of Substitution of Martha (in absolute value). (10 points) (c) Suppose Martha saves all her income in period of time 1. What would be her maximum level of consumption in period of time 27 (10 points) (d) Find the optimal consumption levels of and c. (10 points)