Consider an exchange economy with two agents, A and B, and two commodities, X and Y. Assume their endowments are (w,w) = (3,8) and (w) = (2,2). Also assume their utility functions are U(A₁YA) = FAYA and U(TB₁YB) = £B + YB. (a) Draw an Edgeworth box and show their endowments. (b) Find Pareto Efficient Allocations and show them on your Edgeworth box. Show the core of this exchange economy. (c) Is there a competitive equilibrium? If there is, find competitive equilibrium price ratio and allocation. If there exists no competitive equilibrium, tell which condition(s) of the first theorem of welfare economics is violated and show what goes wrong when price ratio is 1.

Consider an exchange economy with two agents, A and B, and two commodities, X and Y. Assume their endowments are (w,w) = (3,8) and (w) = (2,2). Also assume their utility functions are U(A₁YA) = FAYA and U(TB₁YB) = £B + YB. (a) Draw an Edgeworth box and show their endowments. (b) Find Pareto Efficient Allocations and show them on your Edgeworth box. Show the core of this exchange economy. (c) Is there a competitive equilibrium? If there is, find competitive equilibrium price ratio and allocation. If there exists no competitive equilibrium, tell which condition(s) of the first theorem of welfare economics is violated and show what goes wrong when price ratio is 1.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Consider an exchange economy with two agents, A and B, and two commodities, X and Y. Assume
their endowments are (w,w%) = (3,8) and (w,w%)
U (xA, YA) = XAYA and U(xB, YB) = xB + YB•
(2, 2). Also assume their utility functions are
(a) Draw an Edgeworth box and show their endowments.
(b) Find Pareto Efficient Allocations and show them on your Edgeworth box. Show the core of this
exchange economy.
(c) Is there a competitive equilibrium? If there is, find competitive equilibrium price ratio and allocation.
If there exists no competitive equilibrium, tell which condition(s) of the first theorem of welfare
economics is violated and show what goes wrong when price ratio is 1.

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Step 1: Define Edgeworth Box.

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Step 2: Draw Edgeworth box showing endowments

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Step 3: Find pareto effecient allocation

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Step 4: Determine if there is competitive eqilibrium.

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Step 5: Find competetive equilibrium allocation

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