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Consider a pure exchange economy with two goods, x and y, and two consumers, A and B. Consumer A cares not only about her own consumption, but also benefits from B consuming good r. (For example, you can think of good x as art that, when consumed by B, A sometimes has the opportunity to see.) The consumers' utility functions are and u₁(x, y) = XAYA+XB up(x, y) = xBYB, respectively, where (A, YA) is the bundle consumed by A and (TB, YB) is the bundle consumed by B. The endowments are (2, 1) for consumer 1, and (1,1) for consumer 2. You may use without proof the fact that a consumer with utility u(x, y) = xªy has Marshallian demand x(p,w) = ((a+b)p₁¹ (a+b)p²) · aw (a) Find a Walrasian equilibrium. Assume as usual that each consumer chooses only her own bundle. (Note that the value of TB does not affect A's optimal choice.) (b) Is the allocation in the Walrasian equilibrium you found in part (a) Pareto optimal? Explain carefully.

Consider a pure exchange economy with two goods, x and y, and two consumers, A and B. Consumer A cares not only about her own consumption, but also benefits from B consuming good r. (For example, you can think of good x as art that, when consumed by B, A sometimes has the opportunity to see.) The consumers' utility functions are and u₁(x, y) = XAYA+XB up(x, y) = xBYB, respectively, where (A, YA) is the bundle consumed by A and (TB, YB) is the bundle consumed by B. The endowments are (2, 1) for consumer 1, and (1,1) for consumer 2. You may use without proof the fact that a consumer with utility u(x, y) = xªy has Marshallian demand x(p,w) = ((a+b)p₁¹ (a+b)p²) · aw (a) Find a Walrasian equilibrium. Assume as usual that each consumer chooses only her own bundle. (Note that the value of TB does not affect A's optimal choice.) (b) Is the allocation in the Walrasian equilibrium you found in part (a) Pareto optimal? Explain carefully.

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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Consider a pure exchange economy with two goods, x and y, and two consumers, A and B. Consumer A cares not only about her own consumption, but also benefits from B consuming good r. (For example, you can think of good x as art that, when consumed by B, A sometimes has the opportunity to see.) The consumers' utility functions are and u₁(x, y) = TAYA+IB 3 uв(x, y): = I BYB, respectively, where (XA, YA) is the bundle consumed by A and (TB, YB) is the bundle consumed by B. The endowments are (2, 1) for consumer 1, and (1,1) for consumer 2. You may use without proof the fact that a consumer with utility u(x, y) = xªy has Marshallian demand x(p,w) = ((a+b)p₁' (a+b)p²). (a) Find a Walrasian equilibrium. Assume as usual that each consumer chooses only her own bundle. (Note that the value of в does not affect A's optimal choice.) (b) Is the allocation in the Walrasian equilibrium you found in part (a) Pareto optimal? Explain carefully.
Transcribed Image Text:Consider a pure exchange economy with two goods, x and y, and two consumers, A and B. Consumer A cares not only about her own consumption, but also benefits from B consuming good r. (For example, you can think of good x as art that, when consumed by B, A sometimes has the opportunity to see.) The consumers' utility functions are and u₁(x, y) = TAYA+IB 3 uв(x, y): = I BYB, respectively, where (XA, YA) is the bundle consumed by A and (TB, YB) is the bundle consumed by B. The endowments are (2, 1) for consumer 1, and (1,1) for consumer 2. You may use without proof the fact that a consumer with utility u(x, y) = xªy has Marshallian demand x(p,w) = ((a+b)p₁' (a+b)p²). (a) Find a Walrasian equilibrium. Assume as usual that each consumer chooses only her own bundle. (Note that the value of в does not affect A's optimal choice.) (b) Is the allocation in the Walrasian equilibrium you found in part (a) Pareto optimal? Explain carefully.
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