L11 Uncertainty.

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Presentation transcript:

L11 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: wealth Endowment: wealth in two states New: No markets for but insurance Consumption bundle = lottery

Insurance contract Insurance contract Premium insurers choice Coverage consumer’s choice Timing:

Uncertainty and Lotteries

Budget Constraint

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)

3 Risk attitudes (aversion) Example Lottery D:Risk aversion: Risk neutrality. Risk loving

Risk attitudes Example 1: Example 2: Example 3:

Indifference curves

Marginal Rate of Substitution

Choice of Insurance

Magic formulas

Fair vs. not fair Insurance Fair premium Not fair premium Why? Expected profit of insurer Free Entry drives profit to zero

Fair premium = full insurance

Partial Insurance First secret of happiness