Use the following setup for 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.
-If the company can correctly anticipate the adverse selection,what premiums would it charge?
A)$2500
B)$2600
C)$1000
D)$1100

Question

​Use the following setup for 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.
-If the company can correctly anticipate the adverse selection,what premiums would it charge?​
A)​$2500
B)$2600
C)$1000
D)​$1100

Quizplus · Accepted Answer

The expected loss for Nadia would be 10% of $10,000 = $1000. She is willing to pay an additional $100, so the premium charged would be $1100.

For Samantha, the expected loss would be 25% of $10,000 = $2500. She is also willing to pay an additional $100, so the premium charged would be $2600.

Since the company can correctly anticipate the adverse selection and charge different premiums based on the risk of theft, it would charge Nadia a lower premium of $1100 and Samantha a higher premium of $2600. The average premium would be ($1100 + $2600) / 2 = $1850, which is lower than the maximum possible premium of $2500. So, option B is the correct choice.

​Use the Following Setup for Question

Use the Following Setup for Question