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Question # 2: Consider an open economy with three indust operation, electricity-generating plant and an auto-manufa produce $1 of coal, the mining operation must purchase S production, $0.30 of electricity and $0.1 worth of automo To produce $1 of electricity, it takes $0.25 of coal, $0.4 o automobile. Finally, to produce $1 worth of automobile, t plant must purchase $0.2 of coal, S0.5 of electricity and c automobile. Assume also that during a period of one weel exterior demand of $50,000 worth of coal, S75,000 wortl $125,000 worth of autos. Lets suppose that equation for production (output) is give P = (1 - A)d.

Question # 2: Consider an open economy with three indust operation, electricity-generating plant and an auto-manufa produce $1 of coal, the mining operation must purchase S production, $0.30 of electricity and $0.1 worth of automo To produce $1 of electricity, it takes $0.25 of coal, $0.4 o automobile. Finally, to produce $1 worth of automobile, t plant must purchase $0.2 of coal, S0.5 of electricity and c automobile. Assume also that during a period of one weel exterior demand of $50,000 worth of coal, S75,000 wortl $125,000 worth of autos. Lets suppose that equation for production (output) is give P = (1 - A)d.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 6EQ: Redo Exercise 5, assuming that the house blend contains 300 grams of Colombian beans, 50 grams of...
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Applications of linear algebra.

Economy: The input-output model Question # 2: Consider an open economy with three industries: coal-mining operation, electricity-generating plant and an auto-manufacturing plant. To produce $1 of coal, the mining operation must purchase $0.1 of its own production, $0.30 of electricity and $0.1 worth of automobile for its transportation. To produce $1 of electricity, it takes $0.25 of coal, $0.4 of electricity and $0.15 of automobile. Finally, to produce $1 worth of automobile, the auto-manufacturing plant must purchase $0.2 of coal, $0.5 of electricity and consume $0.1 of automobile. Assume also that during a period of one week, the economy has an exterior demand of $50,000 worth of coal, $75,000 worth of electricity, and $125,000 worth of autos. Lets suppose that equation for production (output) is given by P= (I - A)d. Where A is the coefficient matrix having each sector's purchase as column entries and d is the demand vector. I is corresponding n*n square matrix Find the production level of each of the three industries in that period of one week in order to exactly satisfy both the internal and the external demands.
Transcribed Image Text:Economy: The input-output model Question # 2: Consider an open economy with three industries: coal-mining operation, electricity-generating plant and an auto-manufacturing plant. To produce $1 of coal, the mining operation must purchase $0.1 of its own production, $0.30 of electricity and $0.1 worth of automobile for its transportation. To produce $1 of electricity, it takes $0.25 of coal, $0.4 of electricity and $0.15 of automobile. Finally, to produce $1 worth of automobile, the auto-manufacturing plant must purchase $0.2 of coal, $0.5 of electricity and consume $0.1 of automobile. Assume also that during a period of one week, the economy has an exterior demand of $50,000 worth of coal, $75,000 worth of electricity, and $125,000 worth of autos. Lets suppose that equation for production (output) is given by P= (I - A)d. Where A is the coefficient matrix having each sector's purchase as column entries and d is the demand vector. I is corresponding n*n square matrix Find the production level of each of the three industries in that period of one week in order to exactly satisfy both the internal and the external demands.
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