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Final Exam, Econ 210A
Answer as many questions as you can. Enjoy.
1.
A poor fellow is an expected utility maximizer with a von Neumann Mor
genstern utility function
v
(
x
) =
x
1
/
2
. He has a wealth of $99
,
000. His shady
brotherinlaw has given him inside information on the outcome of an upcoming
sports event. On the basis of this information, the poor fellow believes that the
probability that Team A will defeat Team B is 2/3, despite the fact that Team
B is twotoone favorite to win among the betting community. It is possible for
the poor fellow to bet as much money as he wishes on Team A to win at the
prevailing odds. That is, for every dollar that he bets, he will get back $2 if
Team A wins and will get back nothing if Team A does not win.
a.
Let
x
A
be the contingent commodity “wealth if Team A wins” and let
x
B
be
“wealth if Team B wins.” Write a budget equation expressing the combinations
of
x
A
and
x
B
that the poor fellow can aﬀord by betting some amount of money
on Team A.
Draw a graph to show all of these combinations.
b.
If this poor fellow bets so as to maximize his expected utility, what will be
his wealth if Team A wins?
What will be his wealth if Team B wins?
c.
Another poor fellow has a von Neumann Morgenstern utility function
v
(
x
) =

x

1
and he also has a wealth of $99
,
000. He has the same shady brother
inlaw and the same inside information on the outcome of an upcoming sports
event. This poor fellow also believes that the probability that Team A will
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This note was uploaded on 02/01/2011 for the course ECONOMY 6 taught by Professor Fallahi during the Spring '10 term at Cambridge.
 Spring '10
 fallahi
 Utility

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