A risk neutral insurer offers to insure an individual with a wealth of 25 dollars against a loss of 21 dollars (i.e. leaving the individual with 4 dollars after the loss). The individual is equally likely to be either of two types, A or B, which differ only in the probability that the loss occurs. For type A, the loss occurs with probability 1/3, and for type B the loss occurs with probability 2/3. Both types have von Neumann-Morgenstern utility u(x)=√√. The individual's type is not observable to the insurer. (a) Suppose the insurer offers full insurance at a price p. The individual chooses only whether or not to buy this insurance; he cannot choose how much insurance to buy. If the individual buys the insurance, he pays p to the insurer regardless of whether the loss occurs, and the insurer pays him the value of the loss (21 dollars) if the loss occurs. Assuming the insurer wants to maximize expected profit, at what price should she offer to sell the insurance?

A risk neutral insurer offers to insure an individual with a wealth of 25 dollars against a loss of 21 dollars (i.e. leaving the individual with 4 dollars after the loss). The individual is equally likely to be either of two types, A or B, which differ only in the probability that the loss occurs. For type A, the loss occurs with probability 1/3, and for type B the loss occurs with probability 2/3. Both types have von Neumann-Morgenstern utility u(x)=√√. The individual's type is not observable to the insurer. (a) Suppose the insurer offers full insurance at a price p. The individual chooses only whether or not to buy this insurance; he cannot choose how much insurance to buy. If the individual buys the insurance, he pays p to the insurer regardless of whether the loss occurs, and the insurer pays him the value of the loss (21 dollars) if the loss occurs. Assuming the insurer wants to maximize expected profit, at what price should she offer to sell the insurance?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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