Buying and Selling: Uncertainty

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)

Uncertainty Two States of the world: no rain and rain Probabilities Goods: consumption Endowment: income in two states and states Possibility of insurance

Uncertainty and Lotteries

Uncertainty Bundle defines a lottery Expected value: “Average payment” Examples Risk aversion better than

Utility Uncertainty – special preferences Von Neumann-Morgenstern is a Bernoulli utility function Expected Utility Useful property:

Examples (Risk attitudes)

Utility and Risk Aversion

Utility and Risk Aversion

Utility and Risk Aversion

Uncertainty (three functions)

Certainty Equivalent Certainty equivalent of lottery Example Risk Aversion:

Choice of Insurance

Fair Insurance Fair Insurance, why? Expected profit Free Entry and Law of Large Numbers

Insurance Bernoulli utility, In optimum: (First secret of happiness)

Insurance

Not Fair Insurance When Insurance is not fair In optimum: (First secret of happiness)