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Uncertainty and Cost Benefit Analysis
Fall 2011
Page 1
Incorporating Uncertainty into Cost Benefit Analysis
All good decisionmaking involves costbenefit analysis  weighing the costs of taking an action against the
benefits of taking that action.
Most decisions involve uncertainty about future costs and benefits, so we
need a way to incorporate that uncertainty.
Expected value is one method of incorporating uncertainty into
the costbenefit analysis.
Expected value is a weightedaverage that weighs the value of possible future outcomes by their
probabilities.
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For example, suppose you are one of a thousand people that received a lottery ticket for a prize worth $400.
If you hold the winning ticket, you will win the prize.
Otherwise, you will receive nothing.
In other words,
you have a 1/1,000 chance of winning the prize and a 999/1,000 chance of receiving nothing.
So, the
expected value of your raffle ticket is
1/1,000 * $400 + 999/1,000*$0 = $0.40
Uncertain outcomes are sometimes pictured as a “tree.”
For instance, an action that has three possible
outcomes, $10,000, $4,000, $0, with probabilities .25, .55, .20 could be shown as:
The expected value of the action depicted above is
.25 * $10,000 + .55*$4,000 + .20*$0 = $4,700
Note that the outcome probabilities sum to 1.0.
That’s because exactly one of the possible outcomes will
happen, even though you don’t know which on it will be.
Note also that the meaning of the word “expected” in expected value is a bit different than the ordinary
English usage of the word.
It does not mean what is most likely to happen or what you think will actually
happen.
The term “expected value” means “probabilityweighted possible future values.”
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If you have taken economics classes, you may have seen a similar concept :
expected utility.
Expected utility is a
weighted average that weighs future utilities by their probabilities.
$10,000
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 Spring '11
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