From 1990 to 2013,1 in approximately every 277 cars produced...

From 1990 to 2013,1 in approximately every 277 cars produced 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. a. What should the premium for a fair insurance policy have been in 2013 for a policy that replaces Beth's car if it is stolen? 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.

From 1990 to 2013,1 in approximately every 277 cars produced 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.
a. What should the premium for a fair insurance policy have been in 2013 for a policy that replaces Beth's car if it is stolen?
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.

Key Concepts

Moral Hazard

Moral hazard describes the tendency for individuals to take on greater risks when they do not bear the full consequences of those risks, often because they are insured. This concept is important for insurance companies as it can lead to behavior that increases the likelihood or severity of claims, thereby impacting the overall risk and cost structure of providing insurance.

Risk Neutrality

Risk neutrality is an economic assumption where a decision-maker is indifferent to risk, focusing solely on maximizing expected monetary gains rather than accounting for the variability of outcomes. A risk-neutral individual would compare the cost of an insurance policy directly with the expected loss without requiring additional compensation for risk.

Expected Value

Expected value is a statistical concept that sums the products of the outcomes and their probabilities, providing a measure of the average outcome over many trials. In the context of insurance, it is used to set a fair premium by multiplying the probability of an adverse event (such as theft) by the financial loss associated with that event.

Insurance Premium Calculation

This concept involves determining the cost of an insurance policy by basing it on the expected loss from an insured event. A fair premium is calculated such that its expected value equals the cost of the loss, serving as an equilibrium where neither the insurer nor the insured gains an immediate benefit from the arrangement.

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