Consider an economy where investors have constant relative risk aversion with RRA equal to . That is, the investors' utility function can be written as follows. c1-8 In(C) With probability 1/2, an investor will find him/herself impatient and valuing only t = 1 consumption, with complimentary probability, he or she will be patient and valuing only t = 2 consumption. The investor has one unit initial endowment, and makes a portfolio choice between cashand long-term investment. Cash generates zero net returns, and long-term investment generates a gross return R = 1.44. Consider the case where = 2, so that U(C) =-1/C. Calculate what would be ideal (first-best) investment level. I. 2. Now consider the case with a financial market. Recall that the equilibriumm price of one unit long-term asset at t 1 is 1, Show that in equilibrium the investment in the long-term asset is 1/2. 3. Explain why there is over-investment in the long-term asset as compared to the first-best level, and why this is not desirable. Now consider the case = 1, Show that the pair {ci, c) that maximize the investors' expected utility is such that C-1 and C2 = R 4. 5. Discuss why this would be the case, and more generally, why the gap between ci and should be decreased when increases