Please answer all parts!

Question 7 [7 points) [7 marks] Agent A and Agent B have a utility possibility frontier that is given by the following equation, [155+ng 132 '1. [2 marks] Plot the utility possibility frontier on the graph. What is the highest possible utility Agent A can achieve if we set Agent Es utility to zero? What is the highest possible utility Agent 3 can achieve if we set Agent A's utility to zero. 2. [2 marks] Both A and B believe that the ideal allocation is given by maximizing an appropriate social welfare function. Agent A thinks that HA 2 33, U3 2 7 is the best distribution of welfare. and presents the maximization solution to a weighted-sum-of-the-utilities social welfare function that confirms this observation. What was A's social welfare function? 3. [3 marks] Now, suppose that social welfare is given by WWA, U3) : mn{UA, U3}. With the above utility possibility frontier. what is the best distribution of welfare