Suppose there are two consumers, A and B, in an endowment economy. Each has preferences u=xy. The initial endowment for A is (4,16) and the initial endowment for B is (20,20). Each consumer is a price taker (Perfect competition). Let P(y)=1.

Suppose that the government wants to impose the 'egalitarian' outcome where each person ends up with (12,18). Assume that lump-sum taxes are possible, find an income tax/transfer scheme starting from the initial endowment that generates this outcome, and show the new equilibrium in an edge worth box.

Hint: find an income tax on person B that shifts the budget constraints of each person to what whey would be to produce the egalitarian outcome. Then show that with these incomes, we can reach the desired allocation with competitive markets.