Reducing Costs in Health Care: Putting the Consumer Back in the Game.

The Affordable Care Act, passed in 2010, aimed to provide comprehensive health insurance for all Americans.  While the public health benefits from expanded insurance coverage are undeniable (e.g., lower need for hospitals to write off bad debts, more treatment of diseases earlier when care is less expensive, and a strong insurance market thereby stabilizing prices)[1], there has been much legislative debate about the costs of the program.

One candidate for the House of Representatives believes a significant  cause in the rising cost of healthcare is the third party payment system.  She proposes a plan for how costs may be managed differently by incorporating what she calls Health Insurance Supplement Accounts (HISA).

In her plan, at the end of each calendar year, an insurance company computes the difference between an individual’s annual  insurance premiums (i.e., how much the individual paid the insurance company, adjusted to cover administrative costs) and the claims against the policy (i.e., money the insurance company paid for the individual’s medical care throughout the year).  If the insurance company collected more than it paid out, then a certain percentage, x, of that difference is deposited into the individual’s HISA.  If the claims exceed the adjusted premiums, the HISA would be tapped to pay the overage until the balance is used up.

As the balance in an individual’s HISA rises, his premiums are reduced, providing an  incentive for him to frugal when making health care choices. In addition, the balance of his HISA may be willed to a beneficiary’s (or collection of beneficiaries’) HISA upon his death.  Thus, he might choose to forgo very expensive end-of-life treatments to make life easier on his heirs.

Your team has been asked to do some research and modeling to help the candidate develop her plan.

  1. Create a model for a reasonable “adjustment” for insurance premiums. Should this be a flat rate for every individual, or should it be a percentage of premiums or claims?
  2. Use a mathematical model to determine the ideal value for the percentage x.  Should it be the same for all or vary depending on the type of insurance, the deductible, and/or the HISA balance?
  3. Use modeling to determine how the reduction in premiums associated with a positive HISA balance should be computed.  Estimate how much money an insurance company might save per insured individual.

Some sites that may be of assistance are:




Problem submitted by Kathleen Shannon, a professor in the department of mathematics and computer science at Salisbury University, Maryland..