Suppose there are two types of drivers on the road. Speed Racers have a 7% chanc

Question

Suppose there are two types of drivers on the road. Speed Racers have a 7% chance of causing an accident per year, while Low Riders have a 2% chance of causing an accident per year. There are the same number of Speed Racers as there are Low Riders. The cost of an accident is $20,000.

a. Suppose the insurance companies know with certainty each driver’s type. What would be the actuarially fair premium that the company would charge each type of driver?

b. Now suppose there is asymmetric information so that the insurance company does not know with certainty each driver’s type. What will happen if the insurance company asks drivers to self-report their type?

c. What will happen if the insurance company admits that it has no idea which drivers are Speed Racers and offers one insurance plan at a price that is based on the average risk across all drivers? Explain the problem of adverse selection in this context.

Explanation / Answer

if company knows with certanity each driver's type then they will charge seperately for both category

So company will not go for issuing any insurance in case b) and c)

The problem of adverse selection is when insured knows about his risk level more than the insurer, which may lead insurance company sugger loss. This was seen in option b) and c), riders knew about their risk level but the insurer dit not and at the end it was suffering loss.

Assuming there are 100 riders of each type Cost per loss % loss for speed % loss for Low premium for speed premium for Low Numbers of riders for speed racer Numbers of low riders Premium earned by insurance company Total loss beared by company Revenue for insurance company a) 20000 7% 2% 1400 400 100 180000 180000 0 As company is asking the riders so all riderss will claim that they are low riders to save premium Cost per loss % loss for speed % loss for Low premium for speed premium for Low Numbers of speed racers as told by riders themselves Numbers of low riders as told by riders themselves Premium earned by insurance company Total loss beared by company Revenue for insurance company b) 20000 7% 2% 1400 400 0 200 80000 180000 -100000 Company will take average of the premium for both type of riders trying to divide risk equaly in both segment, but low riders will consider this a loss so they will not go for insurance. Cost per loss % loss for speed % loss for Low premium for speed premium for Low Total number of riders ready to take insurance Premium earned by insurance company Total loss beared by company Revenue for insurance company c) 20000 7% 2% 900 900 100 90000 140000 -50000

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