Question

Assume there are two groups-of consumers. Both sets of consumers are fisk-ayerse. Consumers know their fisk type throughich this. probiern.

1. Group 1 is fcareless" and has a 53 chance of getting into a $30,000 accident. There are 300 petople in group 1.
2. Group 2 is "careful" and has a 0.5% chance of getting into a $30,000 accident. There are 300 people in group 2 .

Imagine an insurance company is considering selling policies, and the market is competitive. Further, assume information is asymmetre.
In this scenario, even with asymmetric information. assume the insuhance company offered actuarially fair premiums to each group. What she insurance companys expected profit?

Answer 1

In the given scenario, the actuarially fair premium for group 1 would be $15,900 and for group 2 would be $150. If all people in each group purchase insurance, the insurance company's expected profit would be $0. However, if some people choose not to purchase insurance, the expected profit would be higher.

Step-by-step explanation:

Actuarially fair premiums are set based on the expected losses for each risk group. In the given scenario, group 1 has a 53% chance of getting into a $30,000 accident and group 2 has a 0.5% chance. Since the insurance company is offering actuarially fair premiums, the premium for group 1 would be 53% of $30,000, or $15,900, while the premium for group 2 would be 0.5% of $30,000, or $150.

In order to calculate the insurance company's expected profit, we need to know the number of people in each group who purchase insurance. If all 300 people in each group purchase insurance, then the insurance company's expected profit would be the sum of the premiums paid by each group minus the expected claim cost for each group. For group 1, the expected claim cost would be 53% of $30,000, or $15,900, and for group 2, the expected claim cost would be 0.5% of $30,000, or $150. So the expected profit would be ($15,900 - $15,900) + ($150 - $150) = $0.

However, if some people in each group choose not to purchase insurance, then the insurance company's expected profit would be higher, as they would be collecting premiums from those who don't make claims.