动态投入产出理论的扩充及其方程解

An Extension of Dynamic Theory in Input-Output Economics and Solutions to Its Equations

本文首先给出经典动态投入产出体系的差分方程组矩阵形式的求解公式,然后引入二阶资本结构矩阵及含有二阶投资的动态投入产出体系的差分方程组及其矩阵形式,并求得其求解公式。最后把所得的方程及其求解公式推广到有关矩阵的各元素依赖于时间t的场合。

In the first section of this paper the difference matrix-vector equation of the dynamic theory in input-output economics is formed and the formulae for its solutions are derived. In the second section asecond matrix of capital coefficient is introduced, the matrix-vector equation of the dynamic theory concerning the investment in enlargement to next two years' capacity is formed, and the solution to the equation is obtained. In the final section, all the results obtained in the first two sections are generalized to the cases in which the relevant matrices' elements are time dependent.