8. The degree of risk aversion for an individual can be captured by the curvature of the utility function over wealth. Suppose two people with $200 of wealth face the same independent risk of a $100 loss. With probability of 10%, each may have wealth of 100 instead of $200. Person A has a utility function over wealth of u(w) = w0.5. Is it possible to find a contract that benefits both parties? If so, write a contingent contract that can given that person B has the following utility functions. (Contingent means a 2 contract that depends on an outcome.) Show, for your proposed contract, that both parties have higher expected utility. You will need to calculate the expected utility for each individual and each contract separately. As a hint, it is useful to recognize that, if the risks are independent, there is a 1% chance of both losses occurring; an 18% chance of one loss; and an 81% chance of no loss at all. a. UB = w b. UB = WB ,0.5 C. UB = WB d. Suppose that the risks are not independent. Is it still possible to write a contract that benefits both parties? Explain.

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