application of linear algebra
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 )-1.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.