480PS4.pdf - Problem Set 4 — Risk Aversion Oleg Muratov Penn State University Fall 2019 Due Tuesday November 5th at the beginning of class Show your

480PS4.pdf - Problem Set 4 — Risk Aversion Oleg Muratov...

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Problem Set 4 — Risk Aversion Oleg Muratov Penn State University Fall 2019 Due: Tuesday, November 5th at the beginning of class. Show your work. 1. For a utility function u ( x ) the measure of Absolute Risk Aversion is defined as A ( x ) = - u ( x ) 00 u ( x ) 0 . Consider the utility function u ( x ) = 1 - e - α × x , where α is some positive parameter. Show that this utility function is for risk-averse consumer (concave utility/negative second derivative). Show that this utility function exhibits Constant Absolute Risk Aversion. Find the value of this constant.
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Unformatted text preview: 2. For a utility function u ( x ) the measure of Relative Risk Aversion is defined as R ( x ) =-x × u ( x ) 00 u ( x ) . Consider the utility function u ( x ) = x 1-r-1 1-r , where r is some parameter, r ∈ (0 , 1). Show that this utility function is for risk-averse consumer (concave utility/negative second derivative). Show that this utility function exhibits Constant Relative Risk Aversion. Find the value of this constant. 1...
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