#question.Question: Answer all parts (a, b, c, d, e & f).
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) respectively 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.
Suppose the market is competitive.
a) Outline the definition of a competitive equilibrium of this market and explain why every contract, offered by every firm, must earn zero profit in equilibrium. [7 marks]
b) Suppose the information concerning individuals’ types is symmetric, but void. It is commonly known, however, that the proportion of low risk consumers is 0.4. Derive the equilibrium set of contracts. [5 marks]
c) Find the equilibrium set of contracts when information is symmetric and perfect. [5 marks]
Now suppose that information is asymmetric; individuals know their own type but insurance firms cannot distinguish between types. (Note: there does exist an equilibrium set of contracts for this market. You may make use of this fact without proving it).
d) Explain why it must be that, if {cH,cL} is the equilibrium set of contracts, then
cH ? cL. [4 marks]
e) Explain and derive the equilibrium contract offered to high risk individuals. [3 marks]
f) Explain and derive the equilibrium contract offered to low risk individuals. [9 marks]