Question

4.) Suppose that that there are only two people in society, Mark and Judy, who must split a fixed amount of income of $300. Mark’s Utility function is U_M and income is I_M. Judy’s Utility function is U_J and income is I_J. Suppose that

t that there are only two people in society, Mark and Judy, wh me of $300. Mark's Utility function is UM and income is IM. Ju nd income is I. Suppose that Un = 100(1) and UJ-200(1) ) .5 .5 Welfare function be on of the total income between Mark and Judy maximizes social

Let the Social Welfare function be

W = U_M + U_J

What distribution of the total income between Mark and Judy maximizes social welfare?

Answer 1

We have Im + Ij = 100

To maximize welfare we equate the marginal utility of Mark and Judy from Income.

MUm = dUm/dI = 50Im^-0.5

MUj = dUj/dI = 100Ij^-0.5

Now, MUm = MUj

50Im^-0.5 = 100Ij^-0.5

Im^-0.5 = 2Ij^-0.5

2Im^0.5 = Ij^0.5

4Im = Ij

We have Im+Ij =100, Ij = 100-Im

4Im = 100-Im

Im = 20

Hence Ij = 80