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 CobbDouglas 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 meanvariance speci±cation or the expected utility of the
gamble are functions of the mean and the variance of the
distribution.
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 Fall '08
 Weldon
 Normal Distribution, Variance, Probability theory, Professor Charles B. Moss

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