A person has wealth of $500,000. In case of a flood her wealth will be reduced to$50,000. The probability of flooding is 1/10. The person can buy flood insurance at acost of $0.10 for each $1 worth of coverage. Suppose that the satisfaction she derivesfrom c dollars of wealth (or consumption) is given by u(c) = √c. Let C denote thecontingent commodity dollars if there is a flood (horizontal axis) and CNF denote thecontingent commodity dollars if there is no flood (vertical axis).1 Determine the contingent consumption plan if she does not buy insurance.2Assume that the person has von Neumann-Morgenstern utility function on thecontingent consumption plans. Write down the expected utility U(CF, CNF) andderive the MRS.3Solve for optimal (CF, CNF). To this end, first use the tangency condition (TC) tofind the relation between the two contingent commodities (CF, CNF). Next, use(BC) to solve for their values. What is the optimal amount of insurance K theperson will buy?(Note: the general theory developed in lectures allows to know the outcome ofthe exercise. But it is a good idea to work out the problem from first principles.)

Given information: Wealth (W) = $500,000 Incase of flood W goes down by $50,000 (L) Probability of…

A person has wealth of $500,000. In case of a flood her wealth will be reduced to $50,000. The probability of flooding is 1/10. The person can buy flood insurance at a cost of $0.10 for each $1 worth of coverage. Suppose that the satisfaction she derives from c dollars of wealth (or consumption) is given by u(c) = √c. Let CF denote the contingent commodity dollars if there is a flood (horizontal axis) and CNF denote the contingent commodity dollars if there is no flood (vertical axis). 1 Determine the contingent consumption plan if she does not buy insurance.

A person has wealth of $500,000. In case of a flood her wealth will be reduced to $50,000. The probability of flooding is 1/10. The person can buy flood insurance at a cost of $0.10 for each $1 worth of coverage. Suppose that the satisfaction she derives from c dollars of wealth (or consumption) is given by u(c) = √c. Let CF denote the contingent commodity dollars if there is a flood (horizontal axis) and CNF denote the contingent commodity dollars if there is no flood (vertical axis). 1 Determine the contingent consumption plan if she does not buy insurance.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.7P

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