Question 2: Suppose that Sonya has initial wealth $20,000 that she plans to inve

Question

Question 2: Suppose that Sonya has initial wealth $20,000 that she plans to invest for a year and then con- sume it. There are two assets in which she can invest. First, there is a risk-free asset that yields a certain return of 3%. Second, there is a risky asset that yields a return of 45% with probability 1/3 and a return of-15% with probability 213. If Sonya is an expected-utility maximizer with utility function u(x) = Inx, how much would she invest in each asset? (Note: She must invest all of her initial wealth in one asset or the other.)

Explanation / Answer

2.

Initial wealth = $20000

With risk free asset,

Expected value of wealth after 1 year = 20000*(1+3%) = $20600

Expected utility with risk free asset = ln(20600) = 9.933

With risky asset,

Expected value of wealth after 1 year = (1/3)*20000*(1+.45) + (2/3)*20000*(1-.15) = 21000

Expected utility with risk free asset = ln(21000) = 9.952

Since, expected utility is maximized, with the investment in risky assets, so Sonya should invest in risky asset to maximize her utility.

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