Exploring Economics
Exploring Economics
8th Edition
ISBN: 9781544336329
Author: Robert L. Sexton
Publisher: SAGE Publications, Inc
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Question
III. First Welfare Theorem: Suppose we have an endowment economy with two consumers i = 1,2. Let e' = (1,1) be the endowment for both consumers. Let preferences be given by U'(x', y'; x²) := (x'y')'/² + 7x² and U²(x², y²; y') := (x²y²)/2 + 7y'. When maximimizing utilty each consumer takes the others choices as given. Show that p* = (1, 1) is a competitive equilibrium where each consumer demands her own endowment. Find a feasible allocation that is a Pareto improvement. Why does the first welfare theorem not apply?
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Transcribed Image Text:III. First Welfare Theorem: Suppose we have an endowment economy with two consumers i = 1,2. Let e' = (1,1) be the endowment for both consumers. Let preferences be given by U'(x', y'; x²) := (x'y')'/² + 7x² and U²(x², y²; y') := (x²y²)/2 + 7y'. When maximimizing utilty each consumer takes the others choices as given. Show that p* = (1, 1) is a competitive equilibrium where each consumer demands her own endowment. Find a feasible allocation that is a Pareto improvement. Why does the first welfare theorem not apply?
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Step 1: Define the relevance of microeconomic equilibrium
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Step 2: Show that each consumer demands their own endowment.
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Step 3: Find a feasible allocation that is a Pareto improvement
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Step 4: Explain why does the first welfare theorem not apply
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