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Lecture VII: Expected Utility Maxim
I.
Expected Utility
A. Under Bernoulli’s original formulation we assume that utility is a concave,
increasing function of income.
Thus, the value of a bet is less than the
expected return on the bet.
1. For example, let the preferences be represented as
( 29 ( 29
ln
U
ww
=
Assume that the individual is faced with a bet that pays
Table 1. Expected Value of Bet
w
P[w]
ln(w)
75,000
.10
11.225
100,000
.20
11.513
125,000
.40
11.736
150,000
.15
11.918
175,000
.10
12.073
200,000
.05
12.206
( 29
( 29
[ ]
l
n
11.7248
123,599.28
127,500.00
Ew
e
=
=
=
2. Thus, if economic agents act to maximize expected well being
and if the utility function is concave and increasing, then the
amount that the individual is willing to pay is less than the
expected value of the bet.
The difference is the risk premium.
[ ]
(
29
127,50
0
123,599.2
8
3,900.72
E
we
p
=
=
=
B. An axiomatic approach to expected utility.
1. Bernoulli’s original work was not based on tenants or
assumptions of consumer behavior.
2. Basis of Axiomatic Proofs: “An axiomatized theory first selects
its primitive and represents each one of them by a mathematical
object….
Next assumptions on the objects representing the
primitive concepts are specified, and consequences are
mathematically derived from them.
The economic interpretation
of theorems so obtained is the last step of the analysis.
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This note was uploaded on 07/15/2011 for the course AEB 6145 taught by Professor Moss during the Spring '11 term at University of Florida.
 Spring '11
 Moss

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