Suppose the utility possibility frontier for two individuals is given by UA + 2UB = 200. On the graph below, plot the utility frontier.
(a) In order to maximize a “Nietzschean social welfare function,” W(UA, UB) = max{UA, UB}, on the utility possibility frontier shown above, one would set UA equal to _________ and UB equal to ______________
(b) If instead we use a Rawlsian criterion, W(UA, UB) = min{UA, UB}, then the social welfare function is maximized on the above utility possibility frontier where UA equals _________ and UB equals ___________
(c) Suppose that social welfare is given by W(UA, UB) = U1/2A U1/2B. In this case, with the above utility possibility frontier, social welfare is maximized where UA equals _________ and UB is _________
(d) Show the three social maxima on the above graph. Use black ink to draw a Nietzschean isowelfare line through the Nietzschean maximum. Use red ink to draw a Rawlsian isowelfare line through the Rawlsian maximum. Use blue ink to draw a Cobb-Douglas isowelfare line through the Cobb-Douglas maximum.