Consider an economy where investors have constant relative risk aversion with RR
ID: 2784793 • Letter: C
Question
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.Explanation / Answer
U(C) = C1-Q
1-Q
a) Q = 2, U(C) = -1/C
Ideal Investement Level =
Risk relative aversion =
c) There is over investment in long term assets because as it helps to represent the companies financial position and their investments like stocks, and long term assets can be hold for more than 1 yr as compared to short term assets.
It is very easy to sold short term assets but long term assets are very difficult to sold.