Ms. Rich has just bought a new $30,000 car. As a reasonably safe driver, she believes that there is only a 5% chance of being in an accident in the forthcoming year. If she is involved in an accident, the damage to her new car depends on the severity of the accident. The probability distribution for the range of possible accidents and the corresponding damage amounts (in dollars) are shown in the table below. Ms. Rich is trying to decide whether she is willing to pay $170 each year for collision insurance with a $300 deductible. Note that with this type of insurance, she pays the first $300 in damages if she causes an accident, and the insurance company pays the remainder.

Question

Distribution of Accident Types and Corresponding Damage Amounts
Type of AccidentConditional ProbabilityDamage to Car
Minor0.60
$200
Moderate0.20
$1,000
Serious0.10
$4,000
Catastrophic0.10
$30,000
Why is there a kink in the line for the "Buy Insurance" line in the above strategy region chart?

What will be an ideal response?

Answer 1

Recall that the minor accident damage amount is $200. Therefore, if she is in a minor accident and the deductible is above that amount, it will be cheaper for her to pay the damages out-of-pocket rather than paying the deductible. If the deductible is below $200, the opposite is true. Accordingly, we see differing sensitivity (different line slope) to the deductible amount above and below a deductible cost of $200 in the chart.