application of linear algebra

Question

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.

Answer 1