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1
Von NeumannMorgenstern and
Lecture II
I.
Utility and different views of risk
A. Knightian – Frank Knight
1.
Risk – known probabilities of events
2.
Uncertainty – unknown or unknowable probabilities
B. Von Neumann – Morgenstern
1. Axiomatic treatment
2.
Consumers maximize expected utility
C. Savage
1.
Consumers maximize subjective utility
D. Arrow – Debreu
1.
State – preference securities
II.
Numerical Stuff
A. In the preceding lecture, we found the expected utility of a gamble that paid
$150,000 with probability of .6 and $50,000 with probability .4.
Assuming a
0.5
r
=
, the power utility function yields a certainty equivalent of $103,569.
B. Let’s work on a slightly different problem; again assume that we have a risky
gamble that pays $150,000 with some probability
p
and $50,000 with
probability
()
1
p
−
.
1.
I assert that we can find a
p
that makes the decision maker indifferent
between the risky gamble and a certain payoff of $108,000.
Naturally, we
assume that
p
is higher than .6 (why?).
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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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