There are two types of drivers, safe types who have an annual probability of getting in an accident of 10% and risky types who get in a car crash with probability 20%. Each type represents half of the population. When a car crash occurs, it costs the insurance company $10,000. This problem is about asymmetric information, specifically in insurance markets. To answer this question, it helps to understand insurance. Insurance contracts work in the following way. The amount that the insurer pays in the event of an accident is Payout = (Accident cost - Deductible) *Coinsurance rate. The rest is paid by the individual. The expected value of a firm's expenses are E[Payout] = (probability of an accident)*Payout. The insurance premium is the price the consumer pays for insurance. It is paid regardless of whether there is an accident. Therefore, the insurer's expected profit = Premium - E[Payout]. a. Suppose the insurer offered only one type of contract: deductible=0 and coinsurance rate = 100%. What's the expected value of the insurer's payout for safe types? What about the risky types? b. What insurance premium would cause the company to break even? Would both types buy car insurance? d. Describe how mandating insurance purchase would affect the market. e. Suppose the insurance company began offering a menu of plans. One plan had no deductible and a premium of $2000. Another plan had a $3000 deductible, but only had a premium of $700. Which menu option would each type select?
There are two types of drivers, safe types who have an annual probability of getting in an accident of 10% and risky types who get in a car crash with probability 20%. Each type represents half of the population. When a car crash occurs, it costs the insurance company $10,000. This problem is about asymmetric information, specifically in insurance markets. To answer this question, it helps to understand insurance. Insurance contracts work in the following way. The amount that the insurer pays in the event of an accident is Payout = (Accident cost - Deductible) *Coinsurance rate. The rest is paid by the individual. The expected value of a firm's expenses are E[Payout] = (probability of an accident)*Payout. The insurance premium is the price the consumer pays for insurance. It is paid regardless of whether there is an accident. Therefore, the insurer's expected profit = Premium - E[Payout]. a. Suppose the insurer offered only one type of contract: deductible=0 and coinsurance rate = 100%. What's the expected value of the insurer's payout for safe types? What about the risky types? b. What insurance premium would cause the company to break even? Would both types buy car insurance? d. Describe how mandating insurance purchase would affect the market. e. Suppose the insurance company began offering a menu of plans. One plan had no deductible and a premium of $2000. Another plan had a $3000 deductible, but only had a premium of $700. Which menu option would each type select?
Chapter18: Asymmetric Information
Section: Chapter Questions
Problem 18.5P
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![There are two types of drivers, safe types who have an annual probability of getting in an accident of 10%
and risky types who get in a car crash with probability 20%. Each type represents half of the population.
When a car crash occurs, it costs the insurance company $10,000.
This problem is about asymmetric information, specifically in insurance markets. To answer this question,
it helps to understand insurance. Insurance contracts work in the following way. The amount that the
insurer pays in the event of an accident is
Payout = (Accident cost - Deductible) *Coinsurance rate.
The rest is paid by the individual. The expected value of a firm's expenses are E[Payout] = (probability of
an accident)*Payout. The insurance premium is the price the consumer pays for insurance. It is paid
regardless of whether there is an accident. Therefore, the insurer's expected profit = Premium - E[Payout].
a. Suppose the insurer offered only one type of contract: deductible=0 and coinsurance rate= 100%.
What's the expected value of the insurer's payout for safe types? What about the risky types?
b. What insurance premium would cause the company to break even? Would both types buy car insurance?
d. Describe how mandating insurance purchase would affect the market.
e. Suppose the insurance company began offering a menu of plans. One plan had no deductible and a
premium of $2000. Another plan had a $3000 deductible, but only had a premium of $700. Which menu
option would each type select?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb28d0932-8da7-46d3-82d0-3997d746def2%2Ff63c9d9e-4cbc-4f6f-8944-cb0c4feb7e69%2F03nua3f_processed.png&w=3840&q=75)
Transcribed Image Text:There are two types of drivers, safe types who have an annual probability of getting in an accident of 10%
and risky types who get in a car crash with probability 20%. Each type represents half of the population.
When a car crash occurs, it costs the insurance company $10,000.
This problem is about asymmetric information, specifically in insurance markets. To answer this question,
it helps to understand insurance. Insurance contracts work in the following way. The amount that the
insurer pays in the event of an accident is
Payout = (Accident cost - Deductible) *Coinsurance rate.
The rest is paid by the individual. The expected value of a firm's expenses are E[Payout] = (probability of
an accident)*Payout. The insurance premium is the price the consumer pays for insurance. It is paid
regardless of whether there is an accident. Therefore, the insurer's expected profit = Premium - E[Payout].
a. Suppose the insurer offered only one type of contract: deductible=0 and coinsurance rate= 100%.
What's the expected value of the insurer's payout for safe types? What about the risky types?
b. What insurance premium would cause the company to break even? Would both types buy car insurance?
d. Describe how mandating insurance purchase would affect the market.
e. Suppose the insurance company began offering a menu of plans. One plan had no deductible and a
premium of $2000. Another plan had a $3000 deductible, but only had a premium of $700. Which menu
option would each type select?
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