191ps5sol - ECON191 Spring 2010 Outline of suggested...

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1 ECON191 Spring 2010 Outline of suggested solutions to Problem Set 5 1) 2) Under scenario 1, the expected monetary payoff 600 ) 1200 ( 2 1 ) 0 ( 2 1 Under scenario 2, the expected monetary payoff 600 ) 400 ( 4 3 ) 1200 ( 4 1 So the 2 scenarios have the same expected monetary payoffs at 600. The expected utility under scenario 1 1 0 1200 2 1 2 1 EU U U The expected utility under scenario 2 2 400 1200 4 3 4 1 EU U U [Note that AB = 1/3 of BC, and OD = DC] Since D lies vertically above B, EU 1 >EU 2 .The criminal is better off under the first scenario. The law enforcement agency would use scenario 2 to deter the criminals, i.e., they would use the scheme of high probability of conviction and less severe punishment if the criminals are risk loving. The above can be proved by the numerical example: U = W 2 MP L 1 W = Average MP L 2 W Adverse selection will occur in economy A. Those with MP L above average MP L will go to economy B when wage = 1 W = Average MP L . After the best half of people have left, average MP L will decline. This forces wage rate to go down. More people will leave. Eventually, only the worst person will remain working in economy A. Adverse selection will still occur. Let W* be the average wage offer, which is equal to the average MP L of those who remain. Let V be the value of the attractive feature. People with MP L > W * + V will leave. There exists a W* such that at W * + V , the average MP L of those who remain = W*. Under this condition, the firms in economy A will not lower wage any more. W* becomes an equilibrium and adverse selection stops. Those whose MP L
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191ps5sol - ECON191 Spring 2010 Outline of suggested...

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