Norton and Ralph have a utility possibility frontier that is given by the following equation, U_R +U²_N = 100 (where R and N signify Ralph and Norton respectively).

(a) If we set Norton’s utility to zero, what is the highest possible utility Ralph can achieve? ___________ If we set Ralph’s utility to zero, what is the best Norton can do? _________

(b) Plot the utility possibility frontier on the graph below.

(c) Derive an equation for the slope of the above utility possibility curve.

d) Both Ralph and Norton believe that the ideal allocation is given by maximizing an appropriate social welfare function. Ralph thinks that UR = 75, UN = 5 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 Ralph’s social welfare function?

(e) Norton, on the other hand, believes that U_R = 19, U_N = 9 is the best distribution. What is the social welfare function Norton presents?