MI PS09 - Problem Set 9 Decision Making Under Uncertainty 1...

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Problem Set 9: Decision Making Under Uncertainty 1) An individual has a Expected utility function u( ) and initial wealth w. Let lottery L o ff er a payo ff of G with probability p and a payo ff B with probability 1 − p. (a) If the individual owns the lottery, what is the minimum price he would sell it for? (b) If he does not own, what is the minimum price he would be willing to pay for it? (c) Are buying and selling prices equal? Give an economic interpretation of your answer. Find conditions on the parameters of the problem under which buying and selling prices are equal. (d) Let G = 10, B = 5, w = 10 and u(x) = x 0.5 . Compute the buying and selling prices for this lottery and this utility function. 2) Suppose that an individual has an expected utility function u (x) = x 0.5 . (a) Calculate the Arrow-Pratt coe cients of absolute and relative risk aversion the level of wealth w = 5. (b) Calculate the certainty equivalent and the risk premium for a gamble (16, 4; 1/2, 1/2). (c) Calculate the certainty equivalent and the risk premium for a gamble (36, 16; 1/2, 1/2). Compare this result with the one in b) and interpret. 3) A wage earner, Mister T, with initial wealth w = 1000, has an expected utility function u(x) = x 0.5 . His monthly wage amounts to 3000 RMB. He can be fired with probability 0.05. An insurance company designs an insurance contract against unemployment. Mister T would pay an insurance premium of 200 Yuan to receive 22000 Yuan if he were fired. There are only two periods: a first one at which decisions are taken and a second one at which all uncertainty is resolved.

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