The demand and supply functions for three interdependent commodities are QD1 = 15 - P1 + 2P2 + P3 QD2 = 9 + P1 - P2 - P3 QD3 = 8 + 2P1 - P2 - 4P3 QS1 = -7 + P1 QS2 = -4 + 4P2 QS3 = -5 + 2P3 where QDi, QSi and Pi denote the quantity demanded, quantity supplied and price of good i, respectively. Determine the equilibrium price and quantity for this three-commodity model.

The demand and supply functions for three interdependent commodities are QD1 = 15 - P1 + 2P2 + P3 QD2 = 9 + P1 - P2 - P3 QD3 = 8 + 2P1 - P2 - 4P3 QS1 = -7 + P1 QS2 = -4 + 4P2 QS3 = -5 + 2P3 where QDi, QSi and Pi denote the quantity demanded, quantity supplied and price of good i, respectively. Determine the equilibrium price and quantity for this three-commodity model.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 23EQ: 23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes...

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23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes 1/2 of the food and 1/3 of the manufactured goods. Manufacturing consumes 1/2 of the food and 2/3 of the manufactured goods. Assuming the economy is closed and in equilibrium, find the relative outputs of the farming and manufacturing industries.
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Determine the equilibrium prices of three interdependent commodities that satisfyP1 + 3P2 + 3P3 = 32P1 + 4P2 + 3P3 = 37P1 + 3P2 + 4P3 = 35
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