Question

Consider the country general store example, where there is a 50% chance a tornado destroys your store. If it does, you earn $36. If it doesn't, you earn $100. U = M^.5. Suppose I offer you insurance that pays you $20 if your store is destroyed, but you pay me $24 if it is not. Do you buy insurance? Will I offer this insurance? Be sure to calculate expected value and expected utility.

Answer 1

The expected value without insurance is $68, and the expected utility without insurance is 8.

Since the expected utility without insurance is higher than the utility with insurance, it is not rational to buy insurance.

Step-by-step explanation:

To determine if you should buy insurance, you need to compare the expected value and expected utility of the two options.

Let's calculate the expected value first:

1. If the store is destroyed, you earn $36 with a probability of 0.5.
2. If the store is not destroyed, you earn $100 with a probability of 0.5.

The expected value is calculated as (36 * 0.5) + (100 * 0.5) = $68. Therefore, without insurance, you expect to earn $68.

Next, let's calculate the expected utility:

1. If the store is destroyed, the utility is √36 = 6.
2. If the store is not destroyed, the utility is √100 = 10.

The expected utility is calculated as (6 * 0.5) + (10 * 0.5) = 8. The utility of having insurance is obtained as √(68 - 24) = √44 ≈ 6.63.

Since the expected utility of not having insurance (8) is greater than the utility of having insurance (6.63), it is not rational to buy insurance.

As for the insurance company, they would offer the insurance if the expected value of premiums exceeds the expected value of payouts.