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, s0.5 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 = (1 - 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.
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, s0.5 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 = (1 - 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.
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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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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