exo2fc - Econ 333 Financial Economics Spring 08 Homework#2...

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Econ 333 - Financial Economics Spring 08 Homework #2: Anwer keys 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. Answer : U ( Y ) = Y γ - 1 > 0 U ( Y ) = ( γ - 1) Y γ - 1 < 0 γ > 1 U ( Y ) = α - 2 βY > 0 Y < α 2 β U ( Y ) = - 2 β < 0 b - Compute the absolute and relative risk-aversion coefficients Answer : R A = 1 - γ Y R r = 1 - γ R A = 2 β α - 2 βY > 0 R r = 2 β α - 2 βY Y > 0 c - What is the effect of parameter γ ? Answer : γ controls for the degree of risk aversion. We check it with the derivative of R A and R r w.r.t. γ . d - Classify the function as increasing/decreasing risk-aversion utility functions (both abso- lute and relative). Answer : ∂R A ∂Y = - 1 - γ Y 2 < 0 ∂R 4 β 2
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Exercise 2: Certainty equivalent.
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