Question

Question 2 (based on 15.13) Suppose you are a risk-averse decision maker with a utility function given by U(1)=1-101-2, where I denotes your monetary payoff from an investment in thousands. You are considering an investment that will give you a payoff of $10,000 (thus I 10) with probability 0.7 and a payoff of $5,000 ( 5) with probability 0.3. It will cost you $8,500 to make the investment. Should you make the investment? Why or why not거

Answer 1

The given information utility function u(I) = 1 - 10I^-2 investment payoff = 10,000 (thus I = 10) Probability = 0.7 payoff = 5,000(I = 5) probability = 0.3 cost = $ 8,500 In order to determine whether he should make the investment of not we first have to find expected utility he will get if he makes the investment. If expected utility of investment is greater than utility if he keeps 8500(i.e U(8500)) with himself utility of investment is lesser than U(8500) then he should not invest. \r\n Expected Utility(EU) = p_1^* U( Vertical-bar _1) + P_2^* U( Vertical-bar _2) Here P_1 = (0.7) and P_2 (= 0.3) are probabilities of getting payoff Vertical-bar _1(= 10) & Vertical-bar _2(= 5) EU = 0.7 U(10) + 0.3 U(5) EU = 0.7(1 - 10/10^2) + 0.3(1 - 10/5^2) = 0.7(0.9) + 0.3(0.6) = 0.63 + 0.18 = 0.81 cost of investment = 8500 & hence 1 = 8.5 Hence U(8.5) = 1 - 10/(8.5)^2 = 0.86