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uncertainty_sol

uncertainty_sol - COMM/FRE295 SolutiontoQuestions#3...

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COMM/FRE 295 Solution to Questions #3 Uncertainty and Consumer Behavior 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: C ompare 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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