Suppose You and I Are the Only Two Individuals in the World

Essay

Suppose you and I are the only two individuals in the world and we both face individual risk in the following way: I get more consumption in state 1 than in state 2 while you get more consumption in state 2 than in state 1.
a.Suppose we are both risk averse and our tastes are state-independent.Will we fully insure one another in a competitive equilibrium?
b.How does your answer change if there is aggregate risk in the sense that overall consumption is higher in state 2 than in state 1?
c.Is it possible that we insure each other if our tastes are risk neutral and state-independent? If so, are the terms actuarily fair?
d.Suppose that there is no aggregate risk but our tastes are state-dependent.How might we fully insure each other if our beliefs about the probability of each state differ?