Dante and Naia get utility from having money. Dante’s utility function is UD = 10M^1/3; Naia’s utility function is UN = 10 M^1/2 Dante currently has $1,000; Naia has $400.

a. The Rawlsian social welfare function values egalitarianism. Compute the value of the Rawlsian social welfare function for Dante and Naia.

b. A transfer program will take $100 from Dante and transfer it to Naia. Does this transfer program improve welfare under a Rawlsian social welfare function?

c. Suppose, instead, the program described in (c) will take $100 from Naia and transfer it to Dante. Evaluate the effect of this program on social welfare for both of the social welfare functions.

d. If a transfer from Dante to Naia results in a decrease in Rawlsian social welfare, then why does a transfer from Naia to Dante not increase social welfare?

e. Here’s another social welfare function that places some value on egalitarianism: W = U_D + U_N – 0.3(|U_D - U_N|). Dante’s and Naia’s utilities are added together, but as the difference between their utilities increases, social welfare declines. Compute the value of this social welfare function for Dante and Naia, and then evaluate the transfer described in (b). Would a society that values egalitarianism in this way make the same recommendation regarding this transfer as a Rawlsian society? Explain.