Medicare administration costs are approximately $500 per year per person covered by Medicare. This is about 4.5% of the total annual health care expenses covered by Medicare. U.S. private health insurance administration costs are approximately $490 per year per person covered by private health insurance—about 8.5% of the total annual health care expenses covered by private insurers.

a. Explain carefully how it is possible for the Medicare and private insurance administration costs to be about the same per person covered. (Private administration costs are slightly less.) Yet, at the same time, private administration costs are nearly twice as high as Medicare administration costs as percentages of the insurers’ total covered health care expenses. Given the information above, what conclusion can you draw about health care expenses covered by Medicare per person covered by Medicare compared to health care expenses covered by private insurers per person covered by those insurers? Explain. Hint: Give labels to the relevant variables listed above and use algebra.

b. Consider a proposal under which everyone in the U.S. who currently has private health insurance would be offered Medicare insurance in the same way that people over age 65 receive it. What do you expect would be the effect on Medicare administration cost per person covered by Medicare? Would it rise? Fall? Stay about the same? Explain carefully what you base your prediction on. In answering, try to think what insurance administration costs are mostly related to. Are they proportional to the number of people covered? Do they also depend on the number of treatments the people receive? For the purpose of answering this question, what are the most important differences between people currently covered by Medicare and other people who have private health insurance?

c. If you had access to Medicare and private insurers’ administrative records, what kinds of data from these records would be most useful for determining the answer to the question in part b? Explain carefully how you could use such data.