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Unformatted text preview: Today’s agenda • Decisionmaking under Uncertainty • Expected value • Expected utility • Risk aversion • Responses to risk • Risk sharing • Hedging and diversification Expected value of a random variable • Suppose you roll a fair die repeatedly. • On average, how many dots do you see? • Expected value of the number of dots is the weighted average of the possible numbers of dots, where the weights are the probabilities with which you see the various numbers: • Will you ever roll the die and see 3.5 dots? • Expected value is the average number you expect to see in large numbers of repeated rolls. ( ) 2 1 3 6 6 1 5 6 1 4 6 1 3 6 1 2 6 1 1 6 1 = × + × + × + × + × + × = d E You think there is an 75% chance that the final exam in this course will be easy and you’ll get a 90. There is a 25% chance it will be hard and you’ll get a 70. The expected value of your grade is: A. 90 B. 85 C. 80 D. 75 E. 70 Preferences over uncertain outcomes • Suppose a decision maker is choosing between two actions (investments?) with different monetary outcomes. • Need a way to think about preferences over these outcomes. • First idea: compare them by expected payoff . • Suppose you will receive • payoff m 1 with probability q 1 • payoff m 2 with probability q 2 • etc. • Why not evaluate this prospect as q 1 m 1 + q 2 m 2 + … + q n m n ? St. Petersburg paradox • Have I got a deal for you!...
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 Fall '10
 Prusa
 Microeconomics, Utility, Expected utility hypothesis, contingent wealth levels

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