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)
Preferences and Utility Uncertainty – special preferences Von Neumann-Morgenstern is a Bernoulli utility function Expected Utility Useful property:
Risk aversion (uncertainty) Bundle defines a lottery Expected value: “Average payment” Examples Risk aversion better than
Risk attitudes Example 1: Example 2: Example 3:
Utility and Risk Aversion
Uncertainty (three functions)
Choice of Insurance
Magic Formulas Bernouli utility:
Fair Insurance Fair Insurance, why? Expected profit Free Entry and Law of Large Numbers
Insurance
Not Fair Insurance When Insurance is not fair In optimum: (First secret of happiness)
Certainty Equivalent Certainty equivalent of lottery Example Risk Aversion: