uncertainty_sol

uncertainty_sol - COMM/FRE 295 Solutions Choice Under...

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COMM/FRE 295 Solutions Choice Under Uncertainty Question #1 Suppose Smith’s utility function is given by U(m) = m. If Smith has an initial wealth of $10, 000, which of the following gambles has the highest expected utility? Gamble 1: If the coin comes heads, Smith wins $100; if tails he loses $0.50. Gamble 2: If heads, he wins $200; if tails he loses $100. Gamble 3: If heads he wins, $20, 000; if tails he loses $10, 000. Hint: Gamble #1 E(u) = 0.5 U(10,000+100) +0.5 U(10,000 – 0.5) = 0.5 (10,100) 0.5 + 0.5 (9999.5) 0.5 = ? ( Follow the same process for Gambles 2 and 3 and compare E(U) ) Question #2 Suppose you have been accepted by two universities A and B. A is a much more demanding and also much more prestigious institution than B. B is a safe option in the sense that you know you will do reasonably good there and will land an “adequate” job that pays you m = $690, 000 for your lifetime. If you manage to survive academically at A, you will land a great job that pays you $1000, 000. If you do poorly you will end up with a bad job that pays you $250,000 (all the payments are in present values terms). The probability of surviving at A = 0.6. If your utility function U(m) = m, which university will you attend? (Hint: compare the E(U) of the two alternatives and pick the one with higher E(U)) Question # 3 Suppose your utility function is given by w w U 10 ) ( , where w = your income in thousand dollars. You are currently earning an income of $ 40 and can also earn that income next year with certainty if you continue with the same job.
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uncertainty_sol - COMM/FRE 295 Solutions Choice Under...

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