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Dynamic Input-Output Analysis

Let X be the vector of outputs by industry and K be the vector of capital goods by type. The required capitals
goods for outputs X is given by

K = BX

The capital goods industries and their productions are included as part of X. The demand for additional
capital goods depends upon the growth of output from one period to the next ΔX. Thus

ΔK = BΔX

The demand for industrial output is made up of final demands F, interindustry demand AX,
Where A is the matrix of technical coefficients, and investment demand for capital goods, B*ΔX,
where B* is the matrix B augmented with blocks of zeroes to make it compatible with X.