Question

“Fracking” is the practice of shooting liquid into shale deposits in the ground in order to widen and hold open cracks in the shale so that natural gas trapped in the shale can flow into sunken pipes and be extracted as fuel. There is a lot of fracking going on in Central Pennsylvania because of our large Marcellus Shale shield.

The liquid that is pumped into the shale contains toxic chemicals, notably benzene which is a causal factor in acute myeloid leukemia. Because the population of Central PA is at greater risk of leukemia from gas industry practices, the insurance companies that provide health insurance to this population would like to rate their premiums to cover the increased risk and increased cost.

Before the natural gas companies came to Central Pennsylvania and changed the health status of the people living there, 84% of the 200,000 households in one county had employer-paid health insurance. The fair premium per family was $8300 per year, and every policy required each family to pay 20% of their own expenses while the insurance company covered the other 80%. There were also loading factors that we will ignore although they are included in the premium charged to the employer. We are interested in knowing how the premium must change to account for the increased risk of AML and how the cost to the insured (as a deductible) is likely to change.

The premium that is currently being paid is “sunk cost.” It already includes the average risk of AML for the population throughout the country and should not be included in our calculations. We are interested only in calculating the increased risk and increased cost for this particular population, and determining the rating that must be added to the existing premium to cover this new precondition.

The increase in prevalence rate for AML and the cost of treating each case of AML are given in your question set. They are sufficient to calculate the rating as an Expected Value. This rating would then be added on to the $8300 annual payment that employers are already paying.

Question 1: Expected Value Cost of AML to individuals living in the affected county

Within the population of the county the prevalence rate of AML has increased by 0.002% per year (in decimal form, 0.00002). The average cost of treatment associated with one case of AML from diagnosis to death is $180,000.

Question 1: Find the Expected Value Cost as the product of the actual cost of treatment and the increase in prevalence.

What is the EV Cost?

Question 2: How should family health insurance policies in the county be rated?

There are 200,000 households in the County. Those families that have insurance have premiums paid by their employers. In question 1 above, you found the Expected Value Cost associated with one individual. Now we would like to translate this into an insurance premium that will cover all members of a household for 80% of the EV cost.

Step 1: There are 2.3 statistical persons in a household. To find the Expected Value Cost to a household, multiply your EV cost for an individual by the 2.3 statistical persons in a household.

What is the EV Cost per household? (Multiply the EV Cost in question 1 times the number of statistical persons per household)

Step 2: The insurance company will cover 80% of the EV cost per household, and the remaining 20% will be a deductible at the time of treatment if treatment is needed. Multiply your EV cost per household by 80% to get the portion the insurance company pays.

That is the rating on the premium. How much is it?