Let Consider the following insurance market. There are two states of the world, B and G, and two types of consumers, H and L, who have probabilities pH =0.5 and pL =0.25 (high and low risk) simultenaoulsy of being in state B. They have common endowment e=(eG,eB) = (£900, £100). The individuals have expected utility preferences over state-contingent consumptions c=(cG,cB), with common utility function u(ci)=ln(ci), where i=B,G. Insurance firms are risk-neutral profit maximisers and offer contracts in exchange for the individuals' endowments.
Assume the market is competitive.
a) Outline the definition of a competitive equilibrium of this market and describe why every contract, offered by every firm, must earn zero profit in equilibrium.
b) Assume the information concerning individuals' types is symmetric, but void. It is commonly known, though, that the proportion of low risk consumers is 0.4. Derive the equilibrium set of contracts.