Q1) An expected utility maximiser owns a car worth £60000£60000 and has a bank account with £20000£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 u(y)=ln(y)u(y)=ln⁡(y) and they have no other assets. Q2) Consider the setup from Question 1. A risk-neutral insurance company is willing to insure the car at the premium of π=£2/3π=£2/3 for every one pound of coverage.Q3) Consider the setup from Questions 1 and 2. How much profits, in expectation, does the insurance company earn on insuring the individual? 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 theagent the total wealth r1 in the 'good state' and the total wealth x2 in the 'bad state' in return for the agents entire wealthW = 60 000 + 20 000 = 80 000 and W – L= 80 000 – 60 000 = 20000, respectively. Below, we shall refer to the pair (a1, x2) as acontract.Given the coverage chosen by the individual in Question 2, which of the following statements is correct?O a.There is a contract that is preferable to the outcome selected in Question 2 for both by the consumer and the firm.Ob.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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Answered: Q1) An expected utility maximiser owns…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Q1) An expected utility maximiser owns a car worth £60000£60000 and has a bank account with £20000£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 u(y)=ln(y)u(y)=ln⁡(y) and they have no other assets.

Q2) Consider the setup from Question 1. A risk-neutral insurance company is willing to insure the car at the premium of π=£2/3π=£2/3 for every one pound of coverage.

Q3) Consider the setup from Questions 1 and 2. How much profits, in expectation, does the insurance company earn on insuring the individual?

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 r1 in the 'good state' and the total wealth x2 in the 'bad state' in return for the agents entire wealth
W = 60 000 + 20 000 = 80 000 and W – L= 80 000 – 60 000 = 20000, respectively. Below, we shall refer to the pair (a1, x2) as a
contract.
Given the coverage chosen by the individual in Question 2, which of the following statements is correct?
O a.
There is a contract that is preferable to the outcome selected in Question 2 for both by the consumer and the firm.
Ob.
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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