Question

Agent A and Agent B have utility possibility frontier that is given by the following equation,

U_A+ U_B²= 132

A. Plot the utility possibility frontier on the graph. What is the highest possible utility Agent A can achieve if we set Agent B's utility to zero? what is the highest possible utility Agent B can achieve if we set Agent A's utility to zero.

B. Both A and B believe that the ideal allocation is given by maximizing and appropriate social welfare function. Agent A thinks that U_A= 83, U_B= 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?

C. Now, suppose that social welfare is given by W(UA, U_B) = min [U_A, U_B]. With the above utility possibility frontier, what is the best distribution of welfare?