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