Question

There are two kinds of consumers who are looking to buy auto insurance from an insurance firm – Reckless drivers (R) and Safe Drivers (S). 50 percent of the consumer population is R and 50 percent is S.The insurance company’s cost of servicing a consumer is $80 if she is a safe driver and $120 if she is a reckless driver. The value of the insurance is $100 to S and $150 to R.

What is the total surplus?

Suppose the firm cannot distinguish between reckless and safe drivers.

What is the total surplus at this market equilibrium?

Answer 1

We know that 50% of drivers are safe, and the other 50% are reckless. Now, given the cost of servicing both is $80 and $120 respectively, we can calculate the cost per customer to the isurance company by the below formula -

0.5 * (cost of servicing safe customer) + 0.5 * (cost of servicing reckless driver)

= 0.5*$80 + 0.5*$120

= $40 + $60

= $100

The cost of servicing per customer comes out to be $100.

Now, given the value of insurance, the amount of premium per customer that the insurance company will receive is given by -

0.5 * (value of insurance for safe customer) + 0.5 * (value of insurance for reckless driver)

= 0.5*$100 + 0.5*$150

= $50 + $75

= $125

The company will receive an average of $125 per customer, but will only spend $100. Its surplus therefore

= Value of insurance - cost per customer

= $125 - $100

= $25

Now, suppose that the firm cannot distinguish between safe and reckless customer. The cost of servicing would remain the same at $100. The frim however, won't be able to price discriminate between safe and reckless drivers. Say it charges the average of the two ($100 and $150) from all customers.

Insurance premium value per customer = (100+150)/2

= $125

Therefore, surplus in this case as well will remain the same at ($125-$100) = $25