45. Consider an exchange economy with two agents, 1 and 2, and two goods, X and Y. There are 6 units of X and 4 units of Y available. An allocation is denoted by (x1,y1), (x2, y2), where (x1,y1) is agent 1's consumption bundle, (x2, y2) is agent 2's consumption bundle, x1 + x2 = 6 and y₁ + ¥2 = 4. Agent 1 has the utility function u₁ = min{x1,y1} and agent 2 has the utility function u2(x2, y2) = min{x2,y2}. Which of the following allocations is not Pareto efficient? A. (2,2), (4,2) B. (3,2), (3,2) C. (3,1), (3,3) D. (1,2), (5,2)
45. Consider an exchange economy with two agents, 1 and 2, and two goods, X and Y. There are 6 units of X and 4 units of Y available. An allocation is denoted by (x1,y1), (x2, y2), where (x1,y1) is agent 1's consumption bundle, (x2, y2) is agent 2's consumption bundle, x1 + x2 = 6 and y₁ + ¥2 = 4. Agent 1 has the utility function u₁ = min{x1,y1} and agent 2 has the utility function u2(x2, y2) = min{x2,y2}. Which of the following allocations is not Pareto efficient? A. (2,2), (4,2) B. (3,2), (3,2) C. (3,1), (3,3) D. (1,2), (5,2)
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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The question is based on pure exchange economy.
1. For 45 provide the set of all outcomes that are pareto efficient.
2. For 46, provide an algebric solution if possible. Prove the result mathematically (answer for 46 is C since X is abundant)
3. For 47, provide a set of points (if exists) that will take us to the given equilibrium.
Thank you.
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