L12 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: wealth in two states Possibility of insurance

Budget Constraint

Uncertainty and Lotteries

Translation: (“as if” markets)

Expected value Lottery (random variable) Expected value: average payment Examples

Preferences and Utility Uncertainty – special preferences Bernoulli utility function Von Neumann-Morgenstern utility (Expected utility)

Risk attitudes Example 1: Example 2: Example 3:

Indifference curves

Marginal Rate of Substitution

Choice of Insurance

Fair vs. not fair Insurance Why? Free Entry and Law of Large Numbers

Fair Insurance

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