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An economy consists of will and grace they have identical utility of income function U=100 (y)^0.5 where the marginal utility of income function is MU= 50(y)^-0.5. The total income available in the economy is fixed and equal to $20000.
a) What is the welfare maximizing distribution of income if the social welfare function is W=U6W+U^G? What will the social indifference curve look like?
b) What is the welfare maximizing distribution of income if the social welfare function is W=min(U^W.U^G). What do the social indifference curves look like in this case?
c) Suppose that Will and Grace do not have identical utility functions instead assume that Will's utility function is U^W= 200(yw)^0.5 where marginal utility is given by MU^W= 100(yw)^-0.5. Grace's utility is as above. Draw the new utility possibility curve, what distribution of income maximizes social welfare function when W=U^W+U^G. Does the answer change if the social welfare function is given as W= min(U^W.U^G)?
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