5. (b) Consider the two-person, two goods economy given by: W₁ = (1/2, 1/2) U₁ = 2X11 + X12, U2=X21 + 2X22, W₂ = (1/2, 1/2) (i) Solve for a competitive equilibrium (ii) Show that the MRS of person 1 = MRS of person 2 does not hold at competitive equilibrium. (iii) Is competitive equilibrium Pareto Optimal? Why?

5. (b) Consider the two-person, two goods economy given by: W₁ = (1/2, 1/2) U₁ = 2X11 + X12, U2=X21 + 2X22, W₂ = (1/2, 1/2) (i) Solve for a competitive equilibrium (ii) Show that the MRS of person 1 = MRS of person 2 does not hold at competitive equilibrium. (iii) Is competitive equilibrium Pareto Optimal? Why?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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2(a) Suppose x is a Pareto efficient allocation in which each agent holds a positive amount of each good. Also suppose that preferences are convex, continuous and monotonic. Then show that x' is a Walrasian equilibrium for the initial endowments that are redistributed such that w, = x' for i =1,.n.
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