In an economic system, each of three industries depends on the others for raw materials. To make $1 worth of processed wood requires 30 ¢ worth of wood, 20 ¢ steel, and 10 ¢ coal. To make $1 worth of steel requires no wood, 30 ¢ steel, and 20 ¢ coal. To make $1 worth of coal requires 10 ¢ wood, 20 ¢ steel, and 5 ¢ coal.
(a) Give the input-output matrix A for this economy.
(b) Determine the matrix (I - A)-1.
(c) What level of output should each sector produce to meet a consumer demand for $1 worth of wood, $4 of steel, and $2 of coal?
(d) How much of the output of each sector is used to meet internal consumption?