Question

Updated: Desperately needs help with question C and question D. This is all the information given for this exercise:

There are two assets, X and Y. Both are risky, and pay out only in the range 1, 0, 1.The agent has 1 unit of income and must exhaust his income on these two assets: he cannot hold cash. The price of both assets is 1. The joint distribution of the payoff of the two assets has the form -1 0 0 Pigo Pogo Ph do A. Assume X and Y are statistically independent, so p 0. Suppose that every investor, when presented with the choice between X and Y, chooses X. Suppose further that the expected return of X does not equal the expected return of Y. What are all the implications of this fact for the relationships between the various probabilities? That is, what are all the statements you can make about pi vs qo, etc B. Assume X and Y are statistically independent, so ρ-0. Assume p,-ph-: p and q,-q," q Assume q > p. What kind of investor chooses X over Y? Make the strongest statement possible C. Drop the assumption of independence, instead now assume p,-q,-0. Let α denote the optimal share of income put into asset X. Assume the price of each asset is 1 and total income is 1. Write out the first order conditions for the case when both assets are purchased. Using utility function u(m)--e". find conditions in which d%ρ ls increasing D. The conditions are the same as in (C), except now we analyze the case when only one asset is consumed. Under which conditions is X, and only X, purchased?

Answer 1