San José State University
Department of Economics
& Tornado Alley
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
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
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.
If production is equal to demand then
Labeling the output by time period gives
The levels of production in period t are given by
Suppose Ft=eλtF0 where λ is possibly a complex number to allow for cycles.
Then assume Xt=ektX0. The condition to be satisfied is that
In order for this to be satisfied for all t, k must be equal to λ. Furthermore division by eλt shows that
(To be continued.)