Lecture14-2010

# Lecture14-2010 - Closed Form Solutions to Expected Utility:...

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Closed Form Solutions to Expected Utility: Lecture XIV Charles B. Moss September 21, 2010 I. Closed Form Solutions A. By the von Neumann and Morgenstern proof we conclude that decision makers choose those decisions in a way that maximizes their expected utility. 1. We conclude that decision makers prefer more expected utility to less. 2. We use a variety of algebraic structures for utility that are positively monotonic and concave. 3. The Cobb-Douglas speci±cation of utility yields an indirect utility function which is close to the power utility function. U ( Y )= Y 1 - r 1 - r (1) 4. To complete our problem we add information about the dis- tribution function. a) Following our discussion not expectations are closed form (i.e., have analytical solutions). b) This is compounded by the form of the utility function. 5. Many of the closed form solutions we obtain are variants of the mean-variance speci±cation or the expected utility of the gamble are functions of the mean and the variance of the distribution.

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## This note was uploaded on 02/01/2012 for the course AEB 6182 taught by Professor Weldon during the Fall '08 term at University of Florida.

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Lecture14-2010 - Closed Form Solutions to Expected Utility:...

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