Nathan’s income in a typical year is $75,000. There is a 10 percent chance that Nathan will be seriously ill next year, incurring $15,000 in medical expenses. Samantha also earns $75,000 in a typical year. Her chance of becoming seriously ill next year and incurring $15,000 in medical expenses is 20 percent.
a. Calculate the actuarially fair premium for full insurance for (i) Nathan and (ii) Samantha.
b. Suppose that a private insurance firm cannot distinguish between Nathan and Samanthain terms of their risk and assumes the risk of being seriously ill in the general population is 10%. In this context, discuss the adverse selection problem the firm might face.
c. Can a compulsory, government-run health insurance program avoid the problem of adverse selection? Explain why or why not.