Please answer the first question. EXERCISE 4. An expected utility maximizer who

Question

Please answer the first question.

EXERCISE 4. An expected utility maximizer who derives utility from future consumption, with cardinal utility index (x) ln(x), allocates her wealth, w 0, between two uses: she can leave money under her mattress, where it incurs no risk, and she can invest in a project whose payoff is 1+T+R, er unit of investment, for a random variable R that can be either -1 or 2, with equal probability. (Premium is a constant between -1/2 and 1 1. write her optimal portfolio problem. 15 pointsj 2. How would you expect variations in to affect the amount the individual invests in the risky project is increasing in premium T. 15 pointsl

Explanation / Answer

1. Let her wealth be distributed as k under the mattress and w-k invested

Future value of under the mattress amount is k and that of invested amount is (w-k)* (1+R + pi)

So, expected utility = ln(k) + ln((w-k)*(1+R+pi)

u(k) = ln(k*(w-k)*(1+R+pi))

To maximize u(k) we maximize k*(w-k)*(1+R+pi)

R is deterministic and if pi is a constant, then du(k)/dk = 0

So, (1+R+pi)*(w-2k) =0, k=w/2 is her optimal portfolio investment

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---