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1. (26 pts) Consider a two-period consumption model similar to the one we discussed in lecture, but in which total lifetime utility is given by (c2) 1001 + 1+r? where ci and C2 are period 1 and period 2 consumption levels, respectively, of a consumption good with price normalized to one, and r is the individual's impatience level. (Notice that this lifetime utility function implies that the individual has a Bernoulli utility function of u1(x) 10x in the first period and a different Bernoulli utility function of u2(x) = x2 in the second period.) Let I, and I2 be the person's income levels in the two respective periods and suppose she can lend or borrow any amount at interest rate i as long as ci and ca are both non-negative. Throughout this question, assume that i=s=0.2. (a) (8 pts) Suppose I1 = I2 = 5. Find optimal consumption quantities ct and c for the individual. Is the individual "consumption smoothing" across the two periods? Briefly explain. (b) (8 pts) Suppose I1 = 12 = 10. Find optimal consumption quantities ci and c for the individual. Is the individual "consumption smoothing" across the two periods? (Is anything different than in part a?) Briefly explain. (c) (10 pts) Explain how your conceptual results (in which period is the individual consuming more in each of parts a and b) differ from the standard model in which the individual has a concave Bernoulli utility function in both periods. (Hint: It may help to think about the two graph explanation of consumption smoothing we discussed in lecture, in which we graphed the two periods' utility functions separately and compared their slopes for different consumption levels in each period.)