Assume PG Is the fair insurance price for Good drivers and Pb is the fair insura

Question

Assume PG Is the fair insurance price for Good drivers and Pb is the fair insurance price for Bad drivers, where PG = 200, PB = 400 and 30% of the drivers are Good drivers, insurers do not have a mechanism to distinguish good and bad drivers, what price(x) will result in the mandatory insurance market (assume linear risk preference cannot, on average, overcharge customers)? Identify which group of drivers dislike the resulting pricing scheme and comment as to why. Discuss how imperfect information (screening applications) could/would improve the outcome.

Explanation / Answer

(a)

Since insurers cannot distinguish between the "Good" & "Bad" customers, they will price based on an expected value.

Expected value of price = 30% x Pg + (100% - 30%) x Pb

= 30% x $200 + 70% x $400

= $(60 + 280) = $340

(b)

At this expected value of price, good drivers will dislike the pricing scheme since the expected price is higher than Pg ($340 > $200). Therefore they will take up less of the insurance, while more bad drivers will take up the insurance (Since expected price < Pb, $340 < $400).

As a result, more customers will belong to the bad segment than good. This is the typical Adverse Selection problem.

(c)

Application screening will higely help the insurers to identify the riskier customers by reviewing their past driving record, number of accidents, traffic violation tockets etc. Accordingly they can cluster the applications into good and bad, and can effectively charge discriminated pricing.

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