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?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![### Understanding Asymmetric Information in Insurance Markets
In this scenario, we explore the dynamics within insurance markets, focusing on asymmetric information which is a critical component in understanding how these markets operate.
#### Types of Drivers and Accident Probability
There are two types of drivers:
- **Safe drivers:** Annual accident probability of 10%
- **Risky drivers:** Annual accident probability of 20%
Each group represents 50% of the driver population. In the event of a car crash, the financial cost to the insurance company is $10,000.
#### Insurance Payout Structure
Insurance contracts specify the following payout formula:
\[ \text{Payout} = (\text{Accident cost} - \text{Deductible}) \times \text{Coinsurance rate} \]
The remaining cost is covered by the insured individual.
#### Expected Value of Firm’s Expenses
The expected value of the insurer's expenses (E[Payout]) is calculated as follows:
\[ \text{E[Payout]} = (\text{Probability of an accident}) \times \text{Payout} \]
The insurance premium is a predetermined amount paid by the consumer, contributing to the insurer's profit:
\[ \text{Expected profit} = \text{Premium} - \text{E[Payout]} \]
### Problem Set Analysis
#### (a) Effect on Insurer’s Payout with a Single Contract
Assuming the insurer only offers one contract where:
- Deductible = $0
- Coinsurance rate = 100%
**Expected Payout Values:**
- **Safe types:** \( E[Payout] = 10\% \times 10,000 = 1,000 \)
- **Risky types:** \( E[Payout] = 20\% \times 10,000 = 2,000 \)
#### (b) Premium Calculation for Break-Even
To determine a break-even insurance premium, set the premium equal to the expected payout.
\[ \text{Premium} = E[Payout] \]
- If both types are insured, calculate a weighted average premium:
\[ \text{Average premium} = \frac{1,000 \times 0.5 + 2,000 \times 0.5}{1} = 1,500 \]
**Would both types buy insurance?**
If the premium is $1,500, both safe and risky drivers may weigh the cost versus their respective probabilities of needing](/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:### Understanding Asymmetric Information in Insurance Markets
In this scenario, we explore the dynamics within insurance markets, focusing on asymmetric information which is a critical component in understanding how these markets operate.
#### Types of Drivers and Accident Probability
There are two types of drivers:
- **Safe drivers:** Annual accident probability of 10%
- **Risky drivers:** Annual accident probability of 20%
Each group represents 50% of the driver population. In the event of a car crash, the financial cost to the insurance company is $10,000.
#### Insurance Payout Structure
Insurance contracts specify the following payout formula:
\[ \text{Payout} = (\text{Accident cost} - \text{Deductible}) \times \text{Coinsurance rate} \]
The remaining cost is covered by the insured individual.
#### Expected Value of Firm’s Expenses
The expected value of the insurer's expenses (E[Payout]) is calculated as follows:
\[ \text{E[Payout]} = (\text{Probability of an accident}) \times \text{Payout} \]
The insurance premium is a predetermined amount paid by the consumer, contributing to the insurer's profit:
\[ \text{Expected profit} = \text{Premium} - \text{E[Payout]} \]
### Problem Set Analysis
#### (a) Effect on Insurer’s Payout with a Single Contract
Assuming the insurer only offers one contract where:
- Deductible = $0
- Coinsurance rate = 100%
**Expected Payout Values:**
- **Safe types:** \( E[Payout] = 10\% \times 10,000 = 1,000 \)
- **Risky types:** \( E[Payout] = 20\% \times 10,000 = 2,000 \)
#### (b) Premium Calculation for Break-Even
To determine a break-even insurance premium, set the premium equal to the expected payout.
\[ \text{Premium} = E[Payout] \]
- If both types are insured, calculate a weighted average premium:
\[ \text{Average premium} = \frac{1,000 \times 0.5 + 2,000 \times 0.5}{1} = 1,500 \]
**Would both types buy insurance?**
If the premium is $1,500, both safe and risky drivers may weigh the cost versus their respective probabilities of needing
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