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 U¹(x¹, y¹; x²) := (x¹y¹)¹/² + 7x² and U²(x², y²; y¹) := (x²y²)¹/2 + 7y¹. 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? А

Exploring Economics
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ISBN:9781544336329
Author:Robert L. Sexton
Publisher:Robert L. Sexton
Chapter10: Consumer Choice Theory
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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?
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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