The utility possibility frontier for two individuals is given by UA + 2UB = 200. (a) On the graph paper provided, plot the utility possibility frontier. (b) Based on the function W(UA, UB) =max{UA, UB} on the utility possibility frontier in part (a), in order to maximize a Nietzschean social welfare function, what should be the values of UA and UB? (c) If we use a Rawlsian criterion, W(UA, UB) =min{UA, UB}, in order to maximize the social welfare function, what should be the values of UA and UB?
The utility possibility frontier for two individuals is given by
UA + 2UB = 200.
(a) On the graph paper provided, plot the utility possibility frontier.
(b) Based on the function W(UA, UB) =max{UA, UB} on the utility
possibility frontier in part (a), in order to maximize a Nietzschean social welfare
function, what should be the values of UA and UB?
(c) If we use a Rawlsian criterion, W(UA, UB) =min{UA, UB}, in order
to maximize the social welfare function, what should be the values of UA and UB?
(d) If the social welfare is given by W(UA, UB) = U
1/2
A
, U1/2
B
, in this
case, with the utility possibility frontier in part (a) what should be the values of
UA and UB if social welfare is to be maximize?
On the same graph plotted in part (a), show the three social
maxima by drawing a Nietzschean isowelfare line through the Nietzschean
maximum, a Rawlsian isowelfare line through the Rawlsian maximum and a
Cobb-Douglas isowelfare line through the Cobb-Douglas maximum.
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