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28 May, 13:23

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

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  1. 28 May, 16:04
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    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
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