Redo the problem in Question 2 under the assumption that the person has utility function u(c) = ln(c) (instead of u(c) = √C). The other parameters are the same as those used in Question 2. How the solution found in Question 2 will change? 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). Determine the contingent consumption plan if she does not buy insurance. 1 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. 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 3 (BC) to solve for their values. What is the optimal amount of insurance K the person will buy?
Redo the problem in Question 2 under the assumption that the person has utility function u(c) = ln(c) (instead of u(c) = √C). The other parameters are the same as those used in Question 2. How the solution found in Question 2 will change? 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). Determine the contingent consumption plan if she does not buy insurance. 1 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. 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 3 (BC) to solve for their values. What is the optimal amount of insurance K the person will buy?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
Transcribed Image Text:**Analysis of Insurance Decisions Under Uncertainty**
**Problem Context:**
A person starts with a wealth of $500,000. In the event of a flood, their wealth decreases to $50,000. The probability of a flood occurring is 1/10. Flood insurance is available, costing $0.10 per $1 of coverage. The person’s satisfaction, or utility, from consumption (c) is described by the utility function \( u(c) = \ln(c) \). Previously, the function was \( u(c) = \sqrt{c} \). The task is to assess how this change affects the solution.
**Utility and Consumption:**
**1. No Insurance Contingency Plan:**
- Determine how the individual allocates their wealth if they choose not to purchase any insurance.
**2. Expected Utility Calculation:**
- Utilize the von Neumann-Morgenstern framework to compute expected utility for different consumption plans (\( c_F, c_{NF} \)), where \( c_F \) is the contingent commodity in the event of a flood and \( c_{NF} \) is in the absence of a flood.
- Derive the Marginal Rate of Substitution (MRS) between these contingencies.
**3. Optimal Insurance Coverage:**
- Use the tangency condition (TC) to establish a relationship between \( c_F \) and \( c_{NF} \).
- Apply the budget constraint (BC) to resolve the values of \( c_F \) and \( c_{NF} \).
- Determine the optimal insurance amount (K) that the individual should purchase.
**Note:** Theoretical frameworks explored in lectures may predict the outcome of this problem, but solving from first principles is beneficial for understanding.
This framework facilitates understanding how alterations in utility functions affect insurance decisions under risk, focusing on detailed derivation and solution steps.
Expert Solution
Step 1
Contingent consumption refers to the consumption of the buyer when there are uncertain conditions. The insurance purchasing in this kind of a situation is done for meeting the uncertainties in the future and also maintaining the equal amount of wealth.
The cost of insurance now is 0.10 for $1. let us assume that K is the number of insurances bought. The cost of insurance for M units is 0.10K.
Step by step
Solved in 2 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.Recommended textbooks for you
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Managerial Economics: A Problem Solving Approach
Economics
ISBN:
9781337106665
Author:
Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:
Cengage Learning
Managerial Economics & Business Strategy (Mcgraw-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education