Question

Both Nadia and Samantha are applying to insure their car against theft. Nadia lives in a secure neighborhood, where the probability of theft is 10%. Samantha lives in a lesser secure neighborhood where the probability of theft is 25%. Both Nadia and Samantha own cars worth $10,000, and are willing to pay $100 over expected loss for insurance.

How much would Nadia be willing to pay for the insurance?

How much would Samantha be willing to pay for the insurance?

Suppose the insurance company cannot tell them apart but expects them to be different values and charges them an average premium of $1850. Who is more likely to buy this insurance?

Suppose the insurance company cannot tell them apart but expects them to be different values and charges them an average premium of $1850. How much profit would it make?

If the insurance company can correctly anticipate the adverse selection, what premiums should it charge??

If the insurance company can correctly anticipate the adverse selection, who would be insured?

Answer 1

Here, the worth of both the cars is $10,000.

But, the probability of theft in case of Nadia's neighborhood is 10%.

So, expected loss to Nadia will be 10% of $10,000 = (10/100) * 10000 = $1000

She is willing to pay $100 over her expected loss that is = $( 1000 + 100 ) = $1100

That is, Nadia will be willing to pay $1100

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While, the probability of loss in case of Samantha's neighborhood is 25%.

So, expected loss to her will be = 25/100 * 10000 = $2500

She is willing to pay $100 over her expected loss = $( 2500 + 100 ) = $2600

That is, Samantha will be willing to pay $2600

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If the insurance company charges both of them $1850 it will be profitable for Samantha as she has to pay less than her expected loss. While on the other hand Nadia has to pay more than her expected loss and what she is willing to pay. So, in this case Samantha will be more willing to buy the insurance.

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If the insurance company is charging $1850 to both, the premium from both of them will be = $( 1850 + 1850 ) = $3700

If we sum up the amount both of them are willing to pay we get = $( 2600 + 1100 ) = $3700

The profit to the company can be obtained by deducting the sum of the amount both Nadia and Samantha are willing to pay from the aggregate premium charges, that is = $3700 - $3700 = 0

So, here we see it's a break even point where there is no profit or loss to the insurance company.

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If the insurance company is able to anticipate the adverse selection it will charge premiums equal to individual's willingness to pay. So for both the individuals different premiums will be charged. In case of Nadia premium will be $1100. While on the other hand in case of Samantha it will be $2600. Different premium is charged from both individuals because of difference in their risk probability. If the company is able to anticipate the adverse selection correctly and charge according to the individual's willingness to pay both the individuals will be insured as their risk will be covered without excessively high premium charges.