Consider the following competitive market for insurance. There are two states of the world: good and bad . Consumers have wealth 500. If the bad state occurs their wealth is reduced by 200. Consumers are expected utility maximisers, with common utility function () = . There are two types of consumers: high risk types and low risk types . Consumers know their own types, but firms cannot distinguish between different types of consumers. The probabilities that and types find themselves in the bad state are p_H = 0.5 and p_L = 0.4. It is estimated that 70% of the population are low risk. Firms are expected profit maximisers that offer consumers state-contingent contracts = (c_G,c_B) in exchange for their endowment = (e_G,e_B).

QUESTION: In steps, determine the equilibrium set of contracts.