Question

Nadia lives in a secure neighborhood, where the probability of theft is 10%. Samantha lives in a less secure neighborhood where the probability of theft is 25%. They are both risk-averse, and so each is willing to pay “$100 over expected loss” for insurance.

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

a. $900

b. $1000

c. $1100

d. $1200

Suppose the insurance company cannot tell Nadia and Samantha apart in terms of how “risky” their neighborhoods are. However, because the company suspects that the risk levels may be different, it decides that it would be willing to sell policies to each of them for $1850. Who is likely to actually buy this insurance?

a. Samantha

b. Nadia

c. Both of them

d. Neither of them

If we assume that: (a) the insurance company charges a premium of $1850, and (b) both Nadia and Samantha decide correctly whether or not to purchase based on their respective values for the insurance, how much profit on average would the insurer expect to make?

a. $1850

b. Zero, the insurer would break even

c. The insurer would incur a loss of $650

d. The insurer would incur a loss of $1100

If the company correctly anticipates the adverse selection problem in this situation, what premium would it charge?

a. $2500

b. $2600

c. $1000

d. $1100

Suppose that not only does the company correctly anticipate the adverse selection problem, it does even better by successfully “screening” both Nadia and Samantha into appropriate insurance policies. If this is true, then on the average we would expect the company to earn...

a. a loss equal to ($200)

b. a profit equal to $200

c. a loss equal to ($3500)

d. a profit equal to $3500

Answer 1

1) Nadia lives in a secure neighborhood, where the probability of theft is 10%. Samantha lives in a less secure neighborhood where the probability of theft is 25%. They are both risk-averse, and so each is willing to pay "$100 over expected loss" for insurance.

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

Solution: $1,100

Nadia's willingness to pay, is simply her expected loss: 0.1 * $10,000) = $1,000

$1,000 + WTP over the loss of $100, = $1,100

?

2) Suppose the insurance company cannot tell Nadia and Samantha apart in terms of how "risky" their neighborhoods are. However, because the company suspects that the risk levels may be different, it decides that it would be willing to sell policies to each of them for $1850. Who is likely to actually buy this insurance?

Solution: Samantha

Explanation: Since Samantha is more likely to benefit from the deal thus is more likely to actually buy this insurance

3) If we assume that: (a) the insurance company charges a premium of $1850, and (b) both Nadia and Samantha decide correctly whether or not to purchase based on their respective values for the insurance, how much profit on average would the insurer expect to make?

Solution: Zero, the insurer would break even

Working: Samantha : 0.25 * 10,000 = 2,500; 2,500 + 100 = 2600

Nadia's : 1,000 + 100 = 1100

1850 * 2 - (1100 + 2600 ) = 3700, thus a break-even

4) If the company correctly anticipates the adverse selection problem in this situation, what premium would it charge?

Solution: $2,500

Working: 0.25 * 10,000 = 2,500