3. (25 points) (Expected Utility) Consider the following situation: There are two levels of monetary gains, Z1 and 22 that occur with probabilities p1 = 0.5 and p2 = 0.5 respectively. We also know that Z1 = 64 and 22 = 36. The expected utility function is (a) (b) EU = pix/Zl +P2x/Z2 Find the expected utility of the lottery. Suppose as we discussed in class there are two agents. Each faces the same lottery as above, but as discussed in class the outcomes are independent. Hence with probability 0.25 each receives, $36, with probability 0.25 each receives $64, and with probablity 0.5, one receives 36 and the other 64. The two agents agree , that if one receives 36 and the other 64, the fortunate agent will transfer $14, to the less fortunate one. Such an arrangement is the essence of insurance policy pe0ple facing uncorrelated risks can use the fact that they are unlikely to both experience losses, to eliminate some of the risks they face. Calculate their expected utility under this arrangement. Suppose again, that the same two agents are facing the exactly same lottery, but this time the lotteries are perfectly correlated. Hence, either both receive 36, or both receive 64. Compute the expected utility. Suppose again, the agents make an arrangement like (b.), i.e., that if one receives 36 and the other 64, the fortunate agent will transfer $14, to the less fortunate one. Compute the expected utilities and compare your answer with (b)