Question

In 2008, 1 in approximately every 200 cars in the United States was stolen. Beth owns a car worth $20,000 and is considering purchasing an insurance policy to protect herself from car theft. For the following questions, assume that the chance of car theft is the same in all regions and across all car models.

Requried:
a. What should the premium for a fair insurance policy have been in 2014 for a policy that replaces Beth’s car if it is stolen? (Round up to three decimal places.)
b. Suppose an insurance company charges 0.6% of the car’s value for a policy that pays for replacing a stolen car. How much will the policy cost Beth?
c. Will Beth purchase the insurance in part b if she is risk-neutral?
d. Discuss a possible moral hazard problem facing Beth’s insurance company if she purchases the insurance.

Answer 1

A) The amount of the premium in fair insurance policy that replaces Beths car, must be equal to the probability or expectation of claim of car theft.

Therefore, the Premium amount = 20000 x (1/200)

= 20000 (0.005)

= $100

B) If an Insurance company charges 0.6% for replacing a stolen car, then the policy will cost beth:

20000* 0.6%

= 12,000/100

= $ 120

C) To be risk-neutral means to be indifferent to the risk. This means that Beth would be indifferent. She most likely will be focused on maximizing value for money. In other words, she will NOT pay for the insurance policy in part b because part A provides her with the exact (or fair) premium for her insurance.

D) The moral hazard problem is this, people tend to become more careless with an insurance policy in place. This moral hazard arises form the knowledge that there is an insurance policy that caters to their risks.

As a matter of practice, therefore, insurance companies factor this increased risk into their premiums. Where the premium was supposed to be $100, they may charge $120.

In summary, it means that Beth most likely will move from becoming risk neutral to becoming (to a certain degree) more risk loving.

Cheers!