Kindly solve the following
(3) Consider an exchange economy with two consumers. Consumer A has utility function U-(21, 12) = 1 + 12 and endowment w = (60, 10). Consumer B has utility function UB(I1, 12) = 1142 and endowment w = (20, 30). (a) Draw wn Edgeworth box with the initial endowment and the correspond indifference curves through the endowment for consumer A and consumer B. (b) Note that at any Pareto efficient allocation where both consumers get strictly positive amounts of each good, their MRS must be the same. Use this observation to construct the contract curve. Are there Pareto effcient point where consumer A does not get a strictly positive allocation of both goods.? Draw the contract curve in the Edgeworth box. (c) Find the competitive equilibrium prices and competitive allocation. (d) Now consider an economy with 1000 consumers identical to consumer A and 1000 con- sumers identical to consumer B. That is each consumer A has the same initial endowment and utility functon, and similarly, each consumer B has the same endowment and utility function. Find a competitive equilibrium of the economy with 2000 consumers.Problem 2 Consider a pure exchange economy with two consumers and two goods. Consumer 1 has endowment 1= (8,2) and utility function U(x) = 12 Consumer 2 has endowment w = (4,4) and utility function As we discussed in class, in the Edgeworth Box, the collection of all Pareto efficient allocations is a curve that goes from the lower left corner to the upper right corner of the box. At a Pareto efficient allocation where both consumers consume strictly positive amounts of good 1 and good 2 corresponds to a point strictly inside the Edgeworth Box (a feasible allocation) where the indifference curves of the two consumers are tangent. But, for Pareto efficient points on the edge of the box, this tangency condition need not be satisfied. (a) Find all Pareto efficient allocations where both consumers consume strictly positive amounts of good 1 and good 2. (b) Find a Walrasian equilibrium.Consider an economy with two consumers and two goods. Consumer I has endowment wl = (11,8) and utility function UI(x) = r +2 2 Consumer 2 has endowment w? = (4,8) and utility function Us(r) = ntly As we discussed in class, in the Edgeworth Box, the collection of all Pareto efficient allocations is a curve that goes from the lower left corner to the upper right corner of the box. This curve is called the contract curve. At a Parcto efficient allocation where both consumers consume strictly positive amounts of good 1 and good 2 (at a point strictly inside the Edgeworth Box), the indifference curves of the two consumers must be tangent. But, for Pareto efficient points on the edge of the box, this tangency condition need not be satisfied. a) Find all Pareto efficient allocations where both consumers consume strictly positive amounts of good 1 and good 2. b) Argue that any feasible allocation a = (a'r'), where r) = 16 and 12
