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 lottery: “Average payment” Examples Risk aversion better than

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

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)