The economy consists of Will and Grace. They have identical utility functions U = 100(y_i)^0.5 where the marginal utility of income function is MU = 50(y_i)^-0.5. The total income available in the economy is fixed and equal to $20,000.
a. Use an Excel spreadsheet to graph the utilities possibility curve for the economy.
b. What is the welfare maximizing distribution of income if the social welfare function is W = U^W + U^G? What do the social indifference curves look like in this case?
c. What is the welfare maximizing distribution of income if the social welfare function is W = min[UW, U^G]. What do the social indifference curves look like in this case?
d. Suppose that Will and Grace do not have identical utility functions. Instead, assume that Will’s utility function is U^W = 200(y_W)0.5 where marginal utility is given by MU^W = 100(y_W)-0.5. Grace’s utility is as above. Draw the new utility possibilities curve. What distribution of income maximizes social welfare when the social welfare function is W = U^W + U^G? Does the answer change if the social welfare function is given as W = min[U^W, U^G]?