Lecture+21+November+18

# Lecture+21+November+18 - Todays agenda Decision-making...

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Today’s agenda Decision-making under Uncertainty Expected value Expected utility Risk aversion Responses to risk Risk sharing Hedging and diversification

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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

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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! I’ll flip a coin repeatedly until it comes up “heads” the first time.

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## This note was uploaded on 11/10/2011 for the course ECON 220:102 taught by Professor Rubin during the Fall '11 term at Rutgers.

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Lecture+21+November+18 - Todays agenda Decision-making...

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