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1. Consider a pure exchange economy with two goods, 1 and 2, and two consumers, A and B, who have utilities and u¹(x₁, x₂) = min{1, 2} u³(x₁, x2) = x³x2. Recall that the Marshallian demands corresponding to these utility functions are, respectively, x^(p, w): W W

1. Consider a pure exchange economy with two goods, 1 and 2, and two consumers, A and B, who have utilities and u¹(x₁, x₂) = min{1, 2} u³(x₁, x2) = x³x2. Recall that the Marshallian demands corresponding to these utility functions are, respectively, x^(p, w): W W

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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1. Consider a pure exchange economy with two goods, 1 and 2, and two consumers, A and B, who have utilities and u²(x₁, x₂) = min{x1, x2} u²(x1, x2) = x³x2. Recall that the Marshallian demands corresponding to these utility functions are, respectively, and x^(p, w) = x³ (p, w) = W W P1 P2 P1 P2 3w W 4p1' 4p2 Consumer A has endowment w = (4,0) and B has endowment wB = (0, 2). (a) Find all Walrasian equilibria. (b) Find all Pareto efficient allocations. (c) Does the conclusion of the Second Welfare Theorem hold for this economy? Explain.
Transcribed Image Text:1. Consider a pure exchange economy with two goods, 1 and 2, and two consumers, A and B, who have utilities and u²(x₁, x₂) = min{x1, x2} u²(x1, x2) = x³x2. Recall that the Marshallian demands corresponding to these utility functions are, respectively, and x^(p, w) = x³ (p, w) = W W P1 P2 P1 P2 3w W 4p1' 4p2 Consumer A has endowment w = (4,0) and B has endowment wB = (0, 2). (a) Find all Walrasian equilibria. (b) Find all Pareto efficient allocations. (c) Does the conclusion of the Second Welfare Theorem hold for this economy? Explain.
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