For an auto insurance company, the average cost of collision claims is $500 per year for careful drivers and $3000 per year for poor drivers. The drivers are risk neutral and know whether they are careful or poor, but the insurance company only knows that 15% of drivers are poor. What is the insurance company's breakeven price for the collision insurance? A. $425 per year B. $450 per year C. $875 per year D. $2,625 per year

option (c) $875 per year

Explanation:

Given;

Average cost of collision claims for careful drivers = $500 per year

Average cost of collision claims for for poor drivers = $3000 per year

Poor drivers known by the company = 15%

thus,

Careful drivers = (100% - 15%) = 85%

Therefore,

Insurance company's breakeven price for the collision insurance

= (Poor drivers known * Average cost of collision for poor drivers) + (Careful drivers * Average cost of collision claims for careful drivers)

= 0.15 * $3000 + 0.85 * $500

= $450 + $425

= $875 per year

Hence, the correct answer is option (c) $875 per year