PLEASE CHECK THIS HOW TO SOLVE . Consider an Edgeworth Box economy with a total endowment of 1 unit of each of the twogoods. Give a precise description of the Pareto set for each of the following preferences.In addition, in each case, sketch the indifference curves and the efficient allocations in anEdgeworth box.(a) u¹(x) = x₁ + x₂ and u²(x) = x1 + 2x2.Solution: The Pareto set consists of all (x1, x2, x³, x²) such that x² + x² = 1 = x² + x²and either x = 1 or x = 0.(b) u¹(x) = x₁ + x₂ and u²(x) = x1 + x2.Solution: The Pareto set consists of all feasible allocations, i.e. all (x1, x², x³, x²) suchthat x + x² = 1 = x² + x².(c) u¹(x) = x₁ + 2x2 and u²(x) = min{x₁, x2}.Solution: The Pareto set consists of all (x1, x2, x1, x²) such that x1 + x² = 1 = x² + x²and x = x₂.(d) u¹(x) = x₁x² and u²(x) = x²x₂.Solution: The Pareto set consists of those feasible allocations where the marginal ratesof substitution for the two agents are equal; that is, all (x1, x1, x1, x²) such that x +x² = 1 = x² + x² and 2²4 = 2 (the superscripts here are agents, not exponents), orequivalently, 4x = x² + 3x1x².

Given utility function U1=X1+X2 U2=X1+2X2 The Pareto efficiency point is the equilibrium point from…

Consider an Edgeworth Box economy with a total endowment of 1 unit of each of the two goods. Give a precise description of the Pareto set for each of the following preferences. In addition, in each case, sketch the indifference curves and the efficient allocations in an Edgeworth box. (a) u¹(x) = x₁ + x₂ and u²(x) = x₁ + 2x2. Solution: The Pareto set consists of all (x1, x1, x², x3) such that x² + x² = 1 = x² + x²

Consider an Edgeworth Box economy with a total endowment of 1 unit of each of the two goods. Give a precise description of the Pareto set for each of the following preferences. In addition, in each case, sketch the indifference curves and the efficient allocations in an Edgeworth box. (a) u¹(x) = x₁ + x₂ and u²(x) = x₁ + 2x2. Solution: The Pareto set consists of all (x1, x1, x², x3) such that x² + x² = 1 = x² + x²

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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