3. Consider an exchange economy with two consumers N = {A, B} and two goods L = {1, 2}. The utility functions of the two consumers are given by u^(X1, X2) = min{14x2, 5x₁ + 4x2} and u³(X1,X2) = 2x2 + X₁. The endowments of each consumer are w₁ = (12,2) y wB=(3,9) (a) Draw the Edgeworth box that represents this economy. (b) Clearly show on the box the allocations that are efficient in the Pareto sense. (c) Clearly show in the box the allocations that belong to the core of this economy. (d) Find the Marshallian demands of consumer A and B. (e) Find the only competitive equilibrium in this economy (Hint: If you want, you can assume that p2 = 1). Show it clearly on the box, for the full point show how you find it. (f) If we redistribute endowments, is it possible that the following allocations are part of a competitive equilibrium? Explain using the first welfare theorem: = i.x A (15.11) and x^B = (0.0). ii. x A = (0.0) and x B = (15.11)
3. Consider an exchange economy with two consumers N = {A, B} and two goods L = {1, 2}. The utility functions of the two consumers are given by u^(X1, X2) = min{14x2, 5x₁ + 4x2} and u³(X1,X2) = 2x2 + X₁. The endowments of each consumer are w₁ = (12,2) y wB=(3,9) (a) Draw the Edgeworth box that represents this economy. (b) Clearly show on the box the allocations that are efficient in the Pareto sense. (c) Clearly show in the box the allocations that belong to the core of this economy. (d) Find the Marshallian demands of consumer A and B. (e) Find the only competitive equilibrium in this economy (Hint: If you want, you can assume that p2 = 1). Show it clearly on the box, for the full point show how you find it. (f) If we redistribute endowments, is it possible that the following allocations are part of a competitive equilibrium? Explain using the first welfare theorem: = i.x A (15.11) and x^B = (0.0). ii. x A = (0.0) and x B = (15.11)
Chapter1: Making Economics Decisions
Section: Chapter Questions
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Transcribed Image Text:3. Consider an exchange economy with two consumers N = {A, B} and two goods L =
{1, 2}. The utility functions of the two consumers are given by u^(X1, X2) = min{14x2,
5x₁ + 4x2} and u³(X1,X2) = 2x2 + X₁. The endowments of each consumer are w₁ =
(12,2) y wB=(3,9)
(a) Draw the Edgeworth box that represents this economy.
(b) Clearly show on the box the allocations that are efficient in the
Pareto sense.
(c) Clearly show in the box the allocations that belong to the core of this economy.
(d) Find the Marshallian demands of consumer A and B.
(e) Find the only competitive equilibrium in this economy (Hint: If you want, you can
assume that p2 = 1). Show it clearly on the box, for the full point show how you find it.
(f) If we redistribute endowments, is it possible that the following allocations are part
of a competitive equilibrium? Explain using the first welfare theorem:
=
i.x A (15.11) and x^B = (0.0). ii. x A = (0.0) and x B = (15.11)
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