# exo2f - Econ 333 Financial Economics Spring 08 Homework#2...

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Econ 333 - Financial Economics Spring 08 Homework #2 Exercise 1: Risk aversion. Consider the following functions (defined over wealth Y): U ( Y ) = Y γ γ U ( Y ) = αY - βY 2 . a - Check that they are well behaved ( U > 0 , U < 0) or state restrictions on the param- eters so that they are. For the second function, take positive α and β , and give the range of wealth over which the utility function is well behaved. b - Compute the absolute and relative risk-aversion coefficients c - What is the effect of parameter γ ? d - Classify the function as increasing/decreasing risk-aversion utility functions (both abso- lute and relative). Exercise 2: Certainty equivalent. Consider the lottery L1 = (50,000; 10,000; 0.50). Determine the lottery L2 = (x;0;1) that makes an agent indifferent with utility function U = ln Y. Exercise 3: An individual (operating in perfect capital markets) with a zero initial wealth, and the utility function U ( Y ) = Y 1 / 2 is confronted with the gamble (16;4;1/2). a - What is the certainty equivalent for this gamble? b - if there is an insurance policy that, together with the original gamble, would guarantee

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Unformatted text preview: him the expected payoﬀ of the gamble, what is the maximum premium he would be willing to pay for it? c -What is the minimum required increase (the probability premium) in the probability of the high-payoﬀ state so that he will not be willing to pay any premium for such an insurance policy? (Note that the insurance policy still pays the expected payoﬀ of the unmodiﬁed gamble) d -Now assume that he is confronted with the gamble (36;16;1/2). Calculate the certainty equivalent, the insurance premium, and the probability premium for this case as well. Explain what is going on, and why? Exercise 4: Consider two investments with the following characteristics. States State 1 State2 State 3 π 1/3 1/3 1/3 Returns e z 10 10 e y 10 20 a -Is there state-by-state dominance between these two investments? b -Is there FSD between these two investments?...
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