Question 1)An expected utility maximiser owns a car worth £60000 and has a bank account with £20000. The money in the bank is safe, but there is a 50%50% probability that the car will be stolen. The utility of wealth for the agent is ?(?)=ln(?)u(y)=ln⁡(y) and they have no other assets.How much the individual would be willing to pay for full car insurance, i.e., where the indemnity is equal to the value of the car?Question 2)Consider the setup from Question 1. A risk-neutral insurance company is willing to insure the car at the premium of π=£2/3 for every one pound of coverage.How much insurance coverage will the individual choose to buy?Question 3)Consider the setup from Questions 1 and 2. How much profits, in expectation, does the insurance company earn on insuring the individual?QUESTION 4) ONLY ANSWER THIS QUESTION Consider the setup from Questions 1-3. Suppose that the firm is not charging the agent per unit of indemnity. Instead, it canpropose to give the agent the total wealth x1 in the 'good state' and the total wealth x2 in the 'bad state' in return for theagents entire wealth W = 60 000 + 20000 = 80 000 and W – L = 80000 – 60 000 = 20 000, respectively. Below, weshall refer to the pair (x1, x2) as a contract.Given the coverage chosen by the individual in Question 2, which of the following statements is correct?a. There is a contract that is preferable to the outcome selected in Question 2 for both by the consumer and the firm.O b. There is NO contract that is preferable to the outcome selected in Question 2 for both the consumer and the firm.O c. Any contract that the agent would be willing to accept must be equal to the outcome selected in Question 2.O d. Any contract that the agent would be willing to accept must be Pareto efficient.

Note:- “Since you have asked multiple question, we will solve the first question for you. If you…

Answered: Question 1) An expected utility…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question 1)

An expected utility maximiser owns a car worth £60000 and has a bank account with £20000. The money in the bank is safe, but there is a 50%50% probability that the car will be stolen. The utility of wealth for the agent is ?(?)=ln(?)u(y)=ln⁡(y) and they have no other assets.

How much the individual would be willing to pay for full car insurance, i.e., where the indemnity is equal to the value of the car?

Question 2)

Consider the setup from Question 1. A risk-neutral insurance company is willing to insure the car at the premium of π=£2/3 for every one pound of coverage.

How much insurance coverage will the individual choose to buy?

Question 3)Consider the setup from Questions 1 and 2. How much profits, in expectation, does the insurance company earn on insuring the individual?

QUESTION 4) ONLY ANSWER THIS QUESTION

Consider the setup from Questions 1-3. Suppose that the firm is not charging the agent per unit of indemnity. Instead, it can
propose to give the agent the total wealth x1 in the 'good state' and the total wealth x2 in the 'bad state' in return for the
agents entire wealth W = 60 000 + 20000 = 80 000 and W – L = 80000 – 60 000 = 20 000, respectively. Below, we
shall refer to the pair (x1, x2) as a contract.
Given the coverage chosen by the individual in Question 2, which of the following statements is correct?
a. There is a contract that is preferable to the outcome selected in Question 2 for both by the consumer and the firm.
O b. There is NO contract that is preferable to the outcome selected in Question 2 for both the consumer and the firm.
O c. Any contract that the agent would be willing to accept must be equal to the outcome selected in Question 2.
O d. Any contract that the agent would be willing to accept must be Pareto efficient.

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