A decision-maker with initial wealth w faces a probability of incurring a loss. If the loss occurs, with probability p the amount of the loss is ₁ and with probability 1-p the amount of the loss is l2, where ₁ > ₂> 0. The decision-maker can buy insurance against both losses at a price of q dollars per unit. If she purchases z units of insurance, she receives a dollars if either loss occurs, even if x is greater than the amount of the loss. There is no limit to the amount of insurance she can purchase. (a) First suppose that the decision-maker is a risk averse expected utility maximizer with von Neumann-Morgenstern utility u(y) over quantities of wealth y. i. Write down the first-order condition characterizing the optimal choice of a when it is interior. Solution: The first-order condition is

A decision-maker with initial wealth w faces a probability of incurring a loss. If the loss occurs, with probability p the amount of the loss is ₁ and with probability 1-p the amount of the loss is l2, where ₁ > ₂> 0. The decision-maker can buy insurance against both losses at a price of q dollars per unit. If she purchases z units of insurance, she receives a dollars if either loss occurs, even if x is greater than the amount of the loss. There is no limit to the amount of insurance she can purchase. (a) First suppose that the decision-maker is a risk averse expected utility maximizer with von Neumann-Morgenstern utility u(y) over quantities of wealth y. i. Write down the first-order condition characterizing the optimal choice of a when it is interior. Solution: The first-order condition is

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.7P

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