Intermediate Microeconomics
Professor Yongmin Chen
Topic 11
.
Risk and Information
Expected Values
When a person is uncertain about the outcomes of an action or a choice but he can
assign probabilities to these outcomes, we say the person faces a decision (choice)
problem involving risk.
Suppose your company offers you the following incentive plan: if the company’s
profit goes up by at least 10% this year,
you will receive a bonus of $10,000; and
otherwise you receive zero bonus.
Suppose also that you believe that, with a good effort
of yours, there is 50% chances that the company’s profits will grow at least 10% this
year.
What is your expected value of participating in your company’s incentive plan?
$10,000x0.5 + $0x0.5 = $5,000.
In general,
suppose there are n possible outcomes, and the payoffs associated
with these outcomes are x
1
, x
2
, .
.., x
n
.
Suppose you assign probabilities p
1
, p
2
, .
.., p
n
to these outcomes.
Then the expected value is V = x
1
p
1
+ x
2
p
2
+ .
.. + x
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 Spring '07
 LOH,JOYCE
 Microeconomics, Game Theory, Utility, monetary values

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