grasshopper

# grasshopper - Relative and Absolute Risk Aversion Question...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Relative and Absolute Risk Aversion Question 1. A) Define the Arrow-Pratt measure of absolute risk aversion. Answer : Where u is the von Neumann-Morgenstern utility function, R A ( y ) =- u 00 ( y ) u ( y ) . B) Consider the following von Neumann Morgenstern utility function u ( x ) =- 1 α e- αx . For what values of α is a consumer with this utility function risk-averse? Does this consumer display increasing, decreasing, or constant absolute risk aversion? Explain. Answer : This consumer is risk averse if and only if α > 0. For this function, R A ( y ) = α . Since α does not change with y , this consumer has constant absolute risk aversion. C) Consider the following von Neumann Morgenstern utility function u ( x ) = 1 α x α . For what values of α is a consumer with this utility function risk-averse? Does this consumer display increasing, decreasing, or constant absolute risk aver- sion? Does this consumer display increasing, decreasing, or constant relative risk aversion? Answer : In this case, u 00 ( x ) = ( α- 1) x α- 2 . We see that u 00 ( x ) < 0 so long as α < 1, so he is risk averse if and only if α < 1. Taking derivatives and simplifying, we find that R A ( x ) = 1- α x Differentiating with respect to x , we see that he has decreasing absolute risk aversion if α < 1....
View Full Document

{[ snackBarMessage ]}

### Page1 / 4

grasshopper - Relative and Absolute Risk Aversion Question...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online