Suppose the utility possibility frontier for two individuals is given by U_A + 2U_B = 200. On the graph below, plot the utility frontier.

(a) In order to maximize a "Nietzschean social welfare function," W(U_A, U_B) = max{U_A, U_B}, on the utility possibility frontier shown above, one would set U_A equal to ___ and UB equal to ____

(b) If instead we use a Rawlsian criterion, W(U_A, U_B) = min{U_A, U_B}, then the social welfare function is maximized on the above utility possibility frontier where U_A equals _____ and U_B equals _____.

(c) Suppose that social welfare is given by W(UA, UB) = U_A^1/2 U_A^1/2 . In this case, with the above utility possibility frontier, social welfare is maximized where U_A equals _____ and U_B is _______. (Hint: You might want to think about the similarities between this maximization problem and the consumer's maximization problem with a Cobb-Douglas utility function.)

(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.

Note:

In the book is the answer, but I want to know the precedent

34.2 (2) Suppose the utility possibility frontier for two individuals is given by UA + 2Up = 200. On the graph below, plot the utility frontier.(a) In order to maximize a "Nietzschean social welfare function," W(UA, UB) = max{VA, UB}, on the utility possibility frontier shown above, one would set UA equal to 200 and Up equal to 0 . (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 possi- bility frontier where UA equals 66. 66 and Up equals 66.66. (c) Suppose that social welfare is given by W(UA, UB) = U)/U.?. In this case, with the above utility possibility frontier, social welfare is max- imized where UA equals 100 and Up is 50. (Hint: You might want to think about the similarities between this maximization problem and the consumer's maximization problem with a Cobb-Douglas utility function.) (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