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L12 Uncertainty
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Three Applications Model with real endowments 1. Labor Supply
(Labor-Leisure Choice) 2. Intertemporal Choice (Consumption-Savings Choice) 3. Uncertainty (Insurance) (Consumption across states of the world)
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Uncertainty Two States of the world: no rain and rain Probabilities
Goods: consumption Endowment: wealth in two states Possibility of insurance
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Budget Constraint
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Uncertainty and Lotteries
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Translation: (“as if” markets)
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Preferences and Utility
Uncertainty – special preferences Von Neumann-Morgenstern is a Bernoulli utility function Expected Utility Useful property:
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Risk aversion (uncertainty)
Bundle defines a lottery Expected value: “Average payment” Examples Risk aversion better than
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Risk attitudes Example 1: Example 2: Example 3:
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Utility and Risk Aversion
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Uncertainty (three functions)
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Choice of Insurance
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Magic Formulas Bernouli utility:
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Fair Insurance Fair Insurance, why? Expected profit
Free Entry and Law of Large Numbers
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Insurance
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Not Fair Insurance When Insurance is not fair
In optimum: (First secret of happiness)
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Certainty Equivalent Certainty equivalent of lottery Example
Risk Aversion:
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