An economy is based on three sectors: Agriculture, Manufacturing, and Energy. Production of a cedi’s worth of agriculture requires inputs of GH¢0.2 from agriculture, GH¢0.15 from manufacturing, and GH¢0.2 from energy. Production of a Ghana cedi’s worth of manufacturing2requires inputs of GH¢0.40 from agriculture, GH¢0.10 from manufacturing, and GH¢0.10 from energy. Production of a Ghana cedi’s worth of energy requires inputs of GH¢0.3 from agriculture, GH¢0.10 from manufacturing, and GH¢0.10 from energy.There is a final demand of GH¢10 billion for agriculture, GH¢15 billion for manufacturing, and GH¢20 billion for energy.(a) Formulate the system of linear equations which must be solved to give the combination of output for the three sectors that will satisfy the final demand.(b) Write the equations in matrix form(c) Determine the output for each sector using theinverse matrix method.

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Description: An economy is based on three sectors: Agriculture, Manufacturing, and Energy. Production of a cedi’s worth of agriculture requires inputs of GH¢0.2 from agriculture, GH¢0.15 from manufacturing, and GH¢0.2 from energy. Production of a Ghana cedi’s wor

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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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An economy is based on three sectors: Agriculture, Manufacturing, and Energy. Production of a cedi’s worth of agriculture requires inputs of GH¢0.2 from agriculture, GH¢0.15 from manufacturing, and GH¢0.2 from energy. Production of a Ghana cedi’s worth of manufacturing
2

requires inputs of GH¢0.40 from agriculture, GH¢0.10 from manufacturing, and GH¢0.10 from energy. Production of a Ghana cedi’s worth of energy requires inputs of GH¢0.3 from agriculture, GH¢0.10 from manufacturing, and GH¢0.10 from energy.
There is a final demand of GH¢10 billion for agriculture, GH¢15 billion for manufacturing, and GH¢20 billion for energy.
(a) Formulate the system of linear equations which must be solved to give the combination of output for the three sectors that will satisfy the final demand.
(b) Write the equations in matrix form
(c) Determine the output for each sector using the
inverse matrix method.

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An economy is based on three sectors: Agriculture, Manufacturing, and Energy. Production of a cedi’s worth of agriculture requires inputs of GH¢0.2 from agriculture, GH¢0.15 from manufacturing, and GH¢0.2 from energy. Production of a Ghana cedi’s worth of manufacturing 2