Expanding Health Insurance Coverage: Some countries are struggling with the problem of expanding the fraction of the population that has good health insurance.
A: Continue with the set-up first introduced in exercise 22.7 including the definition of x as the amount of insurance coverage bought by an individual. Assume throughout that demand for health insurance by the relatively healthy (type 2) is lower than demand for health insurance by the relatively sick (type 1)—i.e. d1 > d2.
(a) Illustrate d1, d2, MC1 and MC2 —and identify the contracts A and B from exercise 22.7.
(b) Suppose that the fraction of relatively sick (type 1) consumers is sufficiently high such that no pooling contract can keep this from being an equilibrium. On the MC1 line, indicate all the contracts that can be offered in this equilibrium (even though only A is chosen). Similarly, indicate on theMC2 line all the contracts that can be offered in this equilibrium (even though only B is chosen).
(c) True or False: Insurance companies in this equilibrium restrict the amount of insurance that can be bought at the price p = MC2 in order to keep type 1 consumers from buying at that price.
(d)Why is the resulting separating equilibrium inefficient? How big is the deadweight loss?
(e) Suppose that the government regulates this health insurance market in the following way: It identifies the zero-profit pooling price p∗ and requires insurance companies to charge p∗ for each unit of x but does not mandate how much x every consumer consumes. Illustrate in your graph how much insurance type 1 and type 2 consumers will consume under this policy? Does overall insurance coverage increase or decrease?
(g) True or False: This policy is efficiency enhancing but does not lead to efficiency.
(h) It may be difficult for the government to implement the above price regulation p∗ because it does not have enough information to do so. Some have suggested that the government instead set the insurance level to some  and then let insurance companies compete on pricing this insurance level. Could you suggest, in a new graph, a level of  that will result in greater efficiency than regulating price? (You need to do this on a new graph for the following reason: If the government sets  between the amounts consumed by type 1 and 2 under the zero-profit price regulation p∗, the resulting competitive price p̅ should be lower than p∗)?
B: Now consider again whether we can find analogous conclusions in the model from Section B as modified in exercise 22.7.
(a) Interpreting the model as in exercise 22.7, illustrate the separating equilibrium in a graph with the insurance benefit b on the horizontal axis and the insurance premium p on the vertical. Include in your graph a zero-profit pooling contract line that makes the separation of types an equilibrium outcome.
(b) How would you interpret the price regulation proposed in A(e) in the context of this model?
(c) Illustrate in your graph how insurance coverage will increase if the government implements this policy.
(d) Now consider the same problem in a graph with y2 —the consumption level when healthy— on the horizontal axis and y1 —the consumption level when sick—on the vertical. Illustrate the “endowment point” E = (1, 2) that both types face in the absence of insurance.
(e) Illustrate the actuarially fair insurance contracts for type 1 and 2 consumers. Then indicate where the separating equilibrium contracts A and B lie assuming state-independent tastes.
(f) Introduce into your graph a zero-profit pooling contract line such that the separating equilibrium is indeed equilibrium. Then illustrate how the proposed government regulation affects the choices of both types of consumers.
(g) Suppose that, instead of regulating price, the government set an insurance benefit level  (as in part A (h)) and then allowed the competitive price to emerge. Where in your graph would the resulting contract lie if it fully insures both types?
(h) Suppose next that tastes were state-dependent—with u1(y) and u2(y) the functions (for evaluating consumption when sick and when healthy) that we need to use in order to arrive at our expected utility function. If u1 and u2 are the same for both consumer types, does our main conclusion that the price regulation will cause an increase in insurance coverage change?