Two men agree to insure each other against heart attack, which would incapacitate but not kill them. For simplicity, treat this as a one- period problem. The probability that the ?rst man will have a heart attack is 1/10, as is the probability that the second will have one. For simplicity again, assume that it is impossible for them to have a heart attack simultaneously. Only one, or neither, will have one. Each man earns 100 if healthy and nothing after a heart attack. Each has a von Neumann-Morgenstern utility function, with the utility for money or income, x, being ln(x).
(a) Compute the Arrow-Debreu equilibrium and the expected utility of the men after trading in insurance but before the state is revealed, that is, before it is known whether either has a heart attack and if so who does. What is the expected utility of each man in this equilibrium?
(b) Suppose that a new medical technology makes it possible to know in advance who will and who will not have a heart attack. This knowledge is available at the time trading in contingent claims occurs. Describe an Arrow-Debreu equilibrium in the new situation. What are the expected utilities of the two men in this situation, where the expectation is calculated from the point of view of a moment just before the new technology provides the information about who is going to have a heart attack? Does the new medical technology increase their expected utility? Give an intuitive explanation of why or why not.