Suppose that Jake considers two alternative investment plans of $1,000 for one-year. Investment A is a no-risk plan: deposit into a bank account with interest rates with 5%. That is, it makes $1,050 in a year for sure. Investment B is a risky plan: buying stocks. This plan could make $1,500 in a year if the economy is good, but if the economy is bad in a year, it could make only $600. According to recent forecases by economists, the probability that the economy is good in a year is 1/2.
1. Find the expected income and standard deviation of Investment B. (3 points)
Suppose Jake’s utility function is U = √I, where I is the income. Find the expected utility from each investment. (3 points)
Which investment would Jake choose? Why?(2 points)
Is Jake risk-loving? Explain why shortly. (2 points)
(Bonus Questions) How much of certain income would he give up to avoid risk? (Hint: What is a certain income that yields the same utility as an uncertain income yields?) (4 points)