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# Lecture 12 - Uncertainty MercedesMiranda BE530 1...

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Mercedes Miranda BE530 1 Uncertainty

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2 1. Describing Risk 2. Preferences Toward Risk 3. Reducing Risk 4. Behavioral Economics Lecture Outline
3 1. Describing Risk Probability probability: Likelihood that a given outcome will occur. Subjective probability is the perception that an outcome will occur. Expected Value expected value: Probability-weighted average of the payoffs associated with all possible outcomes. payoff: Value associated with a possible outcome. The expected value measures the central tendency —the payoff or value that we would expect on average. Expected value = Pr(success)(\$40/share) + Pr(failure)(\$20/share) = (1/4)(\$40/share) + (3/4)(\$20/share) = \$25/share E(X) = Pr 1 X 1  + Pr 2 X 2 E(X) = Pr 1 X 1  + Pr 2 X 2  + . . . +  Pr n X n More generally:

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4 Describing Risk: Variability variability: Extent to which possible outcomes of an uncertain event differ. deviation: Difference between expected payoff and actual payoff. standard deviation: Square root of the weighted average of the squares of the deviations of the payoffs associated with each outcome from their expected values. OUTCOME 1 OUTCOME 2 Probability    Income (\$) Probability    Income (\$) Expected Income (\$) Job 1: Commission Job 2: Fixed Salary .5 .99 2000 1510 1000 510 .5 .01 1500 1500 TABLE 1 Income from Sales Jobs TABLE 2 Deviations from Expected Income (\$) Outcome 1  Deviation  Outcome 2  Deviation Job 1 Job 2 2000 1510 500 10 1000 510 - 500 - 990 TABLE 1     Income from Sales Job (\$)
5 Ex. 1: Outcome Probabilities for Two Jobs Variability Outcome 1 Deviation Squared Deviation Squared Outcome 2 Deviation Squared Weighted Average Standard Deviation Job 1 Job 2 2000 1510 250,000 100 1000 510 250,000 980,100 250,000 9900 500 99.50 Table 3 Calculating Variance (\$) The distribution of payoffs associated with Job 1 has a greater spread and a greater standard deviation than the distribution of payoffs associated with Job 2. Both distributions are flat because all outcomes are equally likely.

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6 2. Preferences Toward Risk expected utility: Sum of the utilities associated with all possible outcomes, weighted by the probability that each outcome will occur.
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