Suppose there exists only one type of auto- insurance policy, and that all the individuals are
Risk- averse. Seventy- five percent of the population consists of low- risk individuals, each of whom has a 10% chance of being in a car accident that causes $5,000 worth of damage. The remainder of the population has a 60% chance of being in such an accident. Given a competitive insurance market consisting of risk- neutral firms that incur no operating expenses, what will be the equilibrium price for full coverage?
A)$525
B)$1,125
C)Either $3,000, or $1,125
D)$3,000

Question

Quizplus · Accepted Answer

In a competitive insurance market, the premium charged by the insurance company must be equal to the expected value of the claim that will be paid out, otherwise consumers will switch to another company with a lower premium.

For the low-risk individuals, the expected value of the claim is:

0.1 x $5,000 = $500

For the high-risk individuals, the expected value of the claim is:

0.6 x $5,000 = $3,000

The proportion of low-risk individuals is 75%, and the proportion of high-risk individuals is 25%.

So the overall expected value of the claim is:

(0.75 x $500) + (0.25 x $3,000) = $937.50

Therefore, in order to make zero economic profit, the insurance companies must charge a premium of $937.50 for full coverage insurance.

However, the question asks for the equilibrium price, which is the price at which supply equals demand. It is possible that consumers are not willing to pay $937.50 for insurance. If this is the case, the price will be lower.

The only answer choice that is close to $937.50 is C, Either $3,000, or $1,125. $1,125 is considerably below the expected value of the claim, so it is unlikely that the insurance companies would charge that price. $3,000 is considerably above the expected value of the claim, but it is possible that consumers would still be willing to pay that price in order to have insurance. Therefore, the equilibrium price is likely to be $3,000.

Suppose There Exists Only One Type of Auto- Insurance Policy