Utility functions

2, (30 points) There are two groups, each with a utility function given by U(W) = VW , where W = 400 is the initial wealth level for every individual. Each reamber of Group 1 faces a loss of 300 with probability 0.2. Each member of Group 2 faces the same lotss, but with a probability of only 0.1. a. What is the most that a member of each group would be willing to pay to insure against this loss? Show your work. Insurance companies cannot discern which individuals belong to which group. Insurance companies are regulated and charge exactly enough in premiums to cover their expected payouts to policy holders. b. Find the largest portion x of Group 1 in the population (the portion of Group 2 being 1 - x) such that . insurance companies will be able to offer insurance that will be purchased by members of both groups. c. If the actual portion of Group 1 in the population exceeds x, what will the insurance premium be? Relative to a situation in which the portion of Group 1 in the population is less than x, will Group I win or lose? Group 2? Explain