22.7 Business Application: Competitive Provision of Health Insurance: Consider the challenge of providing health insurance to a population with different probabilities of getting sick.

A. Suppose that, as in our car insurance example, there are two consumer types: consumers of type 1 that are likely to get sick, and consumers of type 2 that are relatively healthy. Let x represent the level of health insurance, with x 5 0 implying no insurance and higher levels of x indicating increasingly generous health insurance benefits. Assume that each consumer type has linear demand curves (equal to marginal willingness to pay), with d 1

representing the demand curve for a single consumer of type 1 and d 2

representing the demand curve for a single consumer of type 2. Suppose further that the marginal cost of providing additional health coverage to an individual is constant, with MC1 . MC2

.

a. For simplicity, suppose throughout that d 1

and d 2

have the same slope. Suppose further, unless otherwise stated, that d 1

has higher intercept than d 2

. Do you think it is reasonable to assume that type 1 has higher demand for insurance?

b. Begin by drawing a graph with d 1

, d 2

, MC1

, and MC2 assuming that the vertical intercepts of both demand curves lie above MC1

. Indicate the efficient level of insurance x 1

and x 2

for the two types.