4. Assume the following utility functions: U1 = x3\" and u2 = x114 a. What is the marginal utility of both utility functions? b. Draw a graph showing the marginal utility of both-functions in terms of number of contacts. Assuming that the marginal cost of a disease remains constant at 0.5, how many contacts would the two persons with utility functions U; and U; choose to have? Explain your answer 5. Set up the matrix of a symmetric vaccination game for two players (player 1 and player 2) where the 2 strategies are to Vaccinate or Not Vaccinate. If the cost of the vaccine is $10 and the cost of not vaccinating is given by the probability that one of the players is infected, times the transmission rate, times the cost of infection if the other players gets the disease: :1. Explain the pure strategy equilibrium ifthe cost of not being vaccinated is less than S] 0. b. What would the equilibrium be in mixed strategies if we assume that player 2 chooses to vaccinate with a probability of p; and not vaccinate with a probability of ( l -p2)