Questions on microeconomics, provide solutions for the same

(p 500) 212 (HMO, p; healthy) (p 1000)2 u2(full insurance, p; healthy) (p 1000)2 (HMO , p; not healthy) (p 2000)2 u2(full insurance, p; not healthy) (a) Does the model have a separating PBE where only the unhealthy workers buy full (b) For what values of q does this model have a pooling PBE where all types of player I buy full imsurance? (c) Suppose that rather than there being just two types of player I there are a continuum of ptsible types. In particular, assume that player I observes his expected health care expenditures for the year before making his health plan choice and that player 2's prior is that these are uniformly distributed on [O, 20001. What kinds of equilibria seem like they might be possible in this model? Show that there is no PBE in which player I buys full insurance with positix-e probability. (d) What does this model suggest about the dangers of a free market in health insurance? What modifications to the model would be if you wanted to think about the inefficiency of health insurance more seriously?