UPLOADED AGAIN !!

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ECONOMICS

THEORY OF UNCERTAINITY.

PLEASE DO IT MATHEMATICALLY.

Consider an EU maximizer who has to decide how much to save in the first of the two periods she lives. Her utility over consumption in the two periods, c1 and C2, is given by c1+E[u(C2)], where we assume that c1 is known with certainty while C2 is a random variable. The individual has a fixed income x1 in the first period, while in the second period she faces uncertainty and her income is the random variable X2 with expectation X2 and variance >0. Suppose that u(x)=(Sx)2, for a (very large) positive constant S11 In the first period, she can invest an amount k, in exchange for an interest rate in the future. a. Assuming that the second-period income is fixed at X2, write the equation that defines her optimal level of savings, k. b. Now, allowing for uncertainty on X2, find her optimal level of savings, k. c. Compare k and k. How do you make sense of this result? 1 Suppose that S is large enough that the inequality C20. Suppose that u(x)=(Sx)2, for a (very large) positive constant S11 In the first period, she can invest an amount k, in exchange for an interest rate in the future. a. Assuming that the second-period income is fixed at X2, write the equation that defines her optimal level of savings, k. b. Now, allowing for uncertainty on X2, find her optimal level of savings, k. c. Compare k and k. How do you make sense of this result? 1 Suppose that S is large enough that the inequality C2