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erive and compute the contract curve and illustrate. State the First Theorem of elfare Economics.

erive and compute the contract curve and illustrate. State the First Theorem of elfare Economics.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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6. Consider an exchange economy with 2 agents and 2 goods. Suppose agent A has the utility function u₁(x, y) = x + y and agent B has the utility function ug (x, y) = xy and the endowment of A is (1,0), one unit of good x and 0 units of good 2, and the endowment of B is (0,1), zero unit of good x and 0 unit of good y. a. In an Edgeworth-Bowley diagram, illustrate the endowment allocation, the competitive (Walrasian) equilibrium prices and the competitive (Walrasian) equilibrium allocations for A and B. Explain. b. In an Edgeworth-Bowley diagram, illustrate the contract curve (the set of Pareto optimal allocations). Is the endowment allocation Pareto optimal? Explain. c. Compute the competitive (Walrasian) equilibrium prices (PxPy), the competitive (Walrasian) equilibrium allocations, and explain how much of good x and of good y is sold or bought by agent A and agent B in this equilibrium. Explain. d. Derive and compute the contract curve and illustrate. State the First Theorem of Welfare Economics.
Transcribed Image Text:6. Consider an exchange economy with 2 agents and 2 goods. Suppose agent A has the utility function u₁(x, y) = x + y and agent B has the utility function ug (x, y) = xy and the endowment of A is (1,0), one unit of good x and 0 units of good 2, and the endowment of B is (0,1), zero unit of good x and 0 unit of good y. a. In an Edgeworth-Bowley diagram, illustrate the endowment allocation, the competitive (Walrasian) equilibrium prices and the competitive (Walrasian) equilibrium allocations for A and B. Explain. b. In an Edgeworth-Bowley diagram, illustrate the contract curve (the set of Pareto optimal allocations). Is the endowment allocation Pareto optimal? Explain. c. Compute the competitive (Walrasian) equilibrium prices (PxPy), the competitive (Walrasian) equilibrium allocations, and explain how much of good x and of good y is sold or bought by agent A and agent B in this equilibrium. Explain. d. Derive and compute the contract curve and illustrate. State the First Theorem of Welfare Economics.
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