15 - Uncertainty

# 15 - Uncertainty - Von Neumann-Morgenstern Utility Special...

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1 Von Neumann-Morgenstern Utility ± Special Functional Form of Preferences U = Π 1 V(X 1 ) + Π 2 V(X 2 ) ± V(X) is called the “Scaling function.” ± Π 1 and Π 2 are probabilities of the states ( Π 1 + Π 2 = 1) X 1 X 2 Indifference Curves 45º ± MRS = Π 1 V (X 1 ) 2 V (X 2 ) MRS = Π 1 2 whenever X 1 = X 2 smaller expected values Fair Insurance Premium ± Definition: The expected value of a lottery is the probability-weighted average of its prizes: Π 1 X 1 + Π 2 X 2 X 1 X 2 ω larger expected values |slope| = isoexpected value locus through endowment ± Definition: “Fair” premium permits purchase of lotteries with the same expected value as endowment γ / (1- γ ) = Π 1 / Π 2 Fair Insurance Premium ± Risk averse consumer chooses riskless point on certainty line if premium is fair ( γ = Π 1 ) X 1 X 2 ω γ / (1- γ ) = Π 1 / Π 2 45º MRS = Π 1 / Π 2 ± Definition: The expected value of a lottery is the probability-weighted average of its prizes: Π 1 X 1 + Π 2 X 2 ± Definition: “Fair” premium permits purchase of

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15 - Uncertainty - Von Neumann-Morgenstern Utility Special...

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