Question

Suppose an insurance company wants to charge a very healthy individual a premium of $1,200 a year for health coverage. It also wants to charge a less healthy individual a premium of $3,600 a year for health coverage. It is seeking to ascertain from any given customer information regarding his/her health by asking for several pieces of health-related information, such as doctor assessments of the person's health, history of health-related problems, etc. The opportunity cost of a very healthy person securing a health report is $250 and the opportunity cost of a less healthy person securing a health report is $650. Of the choices below, how many reports should the company request to best ensure its paying the right premium to the right person? Reconsider the previous health insurance question. Of the choices below, which one is closest to the spread between the minimum possible number of reports and the maximum possible reports to achieve the company's desired outcome? 0 6. 10. 3.

Answer 1

To determine the number of reports the insurance company should request to ensure it pays the right premium to the right person, we need to consider the opportunity costs and find the optimal balance.

Let's analyze the situation for both very healthy and less healthy individuals:

For a very healthy individual:

Premium: $1,200 per year

Opportunity cost: $250 per health report

For a less healthy individual:

Premium: $3,600 per year

Opportunity cost: $650 per health report

To minimize the overall cost and ensure the right premiums, the insurance company should request health reports until the opportunity cost of obtaining an additional report is equal to the difference in premiums between the two individuals.

Calculating the difference in premiums:

Premium difference = $3,600 - $1,200 = $2,400

Calculating the difference in opportunity costs:

Opportunity cost difference = $650 - $250 = $400

To find the number of reports, we divide the premium difference by the opportunity cost difference:

Number of reports = Premium difference / Opportunity cost difference

Number of reports = $2,400 / $400

Number of reports = 6

Therefore, the insurance company should request 6 health reports to best ensure it pays the right premium to the right person.

As for the second part of the question, none of the provided choices (0, 6, 10, 3) represents the spread between the minimum possible number of reports and the maximum possible reports to achieve the company's desired outcome.