Consider a pure exchange economy with two goods, 1 and 2, and two consumers, A and B, who have utilities and u^(x₁, x₂) = min{₁, ₂} u³(x₁, x₂) = x³x₂. Recall that the Marshallian demands corresponding to these utility functions are, respectively, and x^(p, w) = | rB (p, w) = w W P₁+P2¹ P1 + P2, 3w W 4p₁ 4p2 Consumer A has endowment wA = (4,0) and B has endowment B = (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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Chapter6: Consumer Choice And Demand
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Consider a pure exchange economy with two goods, 1 and 2, and two consumers, A and B,
who have utilities
and
uA (₁, ₂) = min{x₁, x₂}
u³(x₁, x2) = x³x₂.
Recall that the Marshallian demands corresponding to these utility functions are, respectively,
and
W
x^(p, w) =
P₁+P2 P1+P2,
2³ (p, w) = (3/p1' 4P²)
3w
Consumer A has endowment wA = (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:Consider a pure exchange economy with two goods, 1 and 2, and two consumers, A and B, who have utilities and uA (₁, ₂) = min{x₁, x₂} u³(x₁, x2) = x³x₂. Recall that the Marshallian demands corresponding to these utility functions are, respectively, and W x^(p, w) = P₁+P2 P1+P2, 2³ (p, w) = (3/p1' 4P²) 3w Consumer A has endowment wA = (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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