Hi, can I have some help with this question?

Hi, can I have some help with this question? It's dealing with Pareto Efficiency in an Exchange Economy.

Problem 2

Consider an exchange economy, with two goods, x and y, and three individuals, A, B and C.

There are Na individuals of type A, Nb individuals of type B and Nv individuals of type C. Let Ua = .3l(xA) + .2 ln(yA), Ub = .7 ln(xB) + .1 ln(yB) & UC = .5 ln(xC) + .5 ln(yC) where xA, xB, xC , yA,yB, yC denote the consumptions of goods x and good y by individuals of type A, B andC. Suppose that ωA = (5, 5), that is, each individual A has an endowment of 5 units of good x and 5 units of good y, ωB = (20, 20) and ωC = (5, 25) .

1. Characterize ALL of the Pareto efficient allocations for this economy.

2. Show that the general equilibrium of this economy is a Pareto efficient allocation.

3. Select a Pareto efficient allocation from amongst those characterized in answering the first part of this question that is NOT the competitive equilibrium. Find a set of lump-sum taxes and transfers, and an equilibrium price vector, such that the allocation you selected is supported as a competitive equilibrium allocation, given the lump-sum taxes and transfers, and the new price vector.