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Redo the problem in Question 2 under the assumption that the person can buy flood insurance at a cost of $0.15 for each $1 worth of coverage. Maintain the remaining parameters of the problem as in Question 2. Compare your answers with those from Question 2 and comment. Q2: 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. Assume that the person has von Neumann-Morgenstern utility function on the 2 contingent consumption plans. Write down the expected utility U(CF, CNF) and derive the MRS. 3 Solve for optimal (CF, CNF). To this end, first use the tangency condition (TC) to find 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 the person will buy? (Note: the general theory developed in lectures allows to know the outcome of the exercise. But it is a good idea to work out the problem from first principles.)

Redo the problem in Question 2 under the assumption that the person can buy flood insurance at a cost of $0.15 for each $1 worth of coverage. Maintain the remaining parameters of the problem as in Question 2. Compare your answers with those from Question 2 and comment. Q2: 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. Assume that the person has von Neumann-Morgenstern utility function on the 2 contingent consumption plans. Write down the expected utility U(CF, CNF) and derive the MRS. 3 Solve for optimal (CF, CNF). To this end, first use the tangency condition (TC) to find 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 the person will buy? (Note: the general theory developed in lectures allows to know the outcome of the exercise. But it is a good idea to work out the problem from first principles.)

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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### Problem Analysis and Application of Economic Theory #### Problem Context: Consider a scenario where an individual with a wealth of $500,000 faces the risk of a flood. In the event of a flood, the wealth diminishes to $50,000. The probability of experiencing a flood is 1/10. The individual has the option to purchase flood insurance at a cost of $0.10 for every $1 of coverage. Assume the satisfaction derived from consuming wealth \( c \) is \( u(c) = \sqrt{c} \). ### Parameters and Variables: - Total wealth: $500,000 - Wealth if flood occurs: $50,000 - Probability of flood: 1/10 - Insurance cost: $0.10 per $1 of coverage - Utility function: \( u(c) = \sqrt{c} \) #### Definitions: - \( c_F \): Contingent commodity in dollars if a flood occurs (horizontal axis) - \( c_{NF} \): Contingent commodity in dollars if no flood occurs (vertical axis) ### Tasks: 1. **Determine the Contingent Consumption Plan without Insurance:** - Analyze the consumption allocation in absence of any insurance policy. 2. **Utility Function and Marginal Rate of Substitution (MRS):** - With the von Neumann-Morgenstern utility function framework, compute the expected utility \( U(c_F, c_{NF}) \) and derive the MRS. 3. **Optimization of Contingent Consumption:** - Using the tangency condition (TC), establish the relation between \( c_F \) and \( c_{NF} \). - Apply the budget constraint (BC) to resolve optimal values for the contingent commodities. - Determine the optimal insurance amount \( K \) that should be purchased. #### Note: The exploration of this problem is essential to comprehend decision making under uncertainty using foundational economic theories. Despite potential prior knowledge of the outcomes, it's worthwhile to analytically work through the problem to solidify understanding. This exercise aims to demonstrate how theoretical insights from lectures apply to practical economic decision-making scenarios involving risk and insurance.
Transcribed Image Text:### Problem Analysis and Application of Economic Theory #### Problem Context: Consider a scenario where an individual with a wealth of $500,000 faces the risk of a flood. In the event of a flood, the wealth diminishes to $50,000. The probability of experiencing a flood is 1/10. The individual has the option to purchase flood insurance at a cost of $0.10 for every $1 of coverage. Assume the satisfaction derived from consuming wealth \( c \) is \( u(c) = \sqrt{c} \). ### Parameters and Variables: - Total wealth: $500,000 - Wealth if flood occurs: $50,000 - Probability of flood: 1/10 - Insurance cost: $0.10 per $1 of coverage - Utility function: \( u(c) = \sqrt{c} \) #### Definitions: - \( c_F \): Contingent commodity in dollars if a flood occurs (horizontal axis) - \( c_{NF} \): Contingent commodity in dollars if no flood occurs (vertical axis) ### Tasks: 1. **Determine the Contingent Consumption Plan without Insurance:** - Analyze the consumption allocation in absence of any insurance policy. 2. **Utility Function and Marginal Rate of Substitution (MRS):** - With the von Neumann-Morgenstern utility function framework, compute the expected utility \( U(c_F, c_{NF}) \) and derive the MRS. 3. **Optimization of Contingent Consumption:** - Using the tangency condition (TC), establish the relation between \( c_F \) and \( c_{NF} \). - Apply the budget constraint (BC) to resolve optimal values for the contingent commodities. - Determine the optimal insurance amount \( K \) that should be purchased. #### Note: The exploration of this problem is essential to comprehend decision making under uncertainty using foundational economic theories. Despite potential prior knowledge of the outcomes, it's worthwhile to analytically work through the problem to solidify understanding. This exercise aims to demonstrate how theoretical insights from lectures apply to practical economic decision-making scenarios involving risk and insurance.
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