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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
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