Lecture VIII: Expected Utility Hypothesis
Basis for Applied Work
I.
From the Theory
A. The von NuemannMorgenstern proof that consumers maximize expected
income is based on basic tenants of consumer behavior.
The proof was
once harolded as a solid axiomatic proof near and dear to the hearts of
mathematical economists.
B. The expected utility maxim simply states that the consumer’s utility of a
risky investment is equal to the expected utility of the possible outcomes:
(
29
(
29
[
]
1
(
)
(
)
N
i
i
i
U
E U w
U w f w dw
or
U w P w
∞
∞
=
=
=
=
∫
∑
This maxim thus replaces an early belief that consumer’s maximize the
expected value of the payoff:
[
]
(
29
[
]
1
N
i
i
i
E w
w f w dw
or
w P w
∞
∞
=
=
=
∫
∑
Notice that the older framework is a special case of the von Nuemann
Morgenstern framework {Risk Neutrality, or a linear utility function}
C. Three attitudes toward risk:
Notice that when we proved the linkage
between lottery space and utility space we only required that the
transformation
U
(.) be positive monotonic.
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 Spring '11
 Moss
 WI, relative risk aversion, Agricultural Finance, expected utility, Professor Charles B. Moss

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