考虑到时滞与结构演化的动态投入产出模型

A Dynamic Input-Output Model with Time Delay and Evolutionary Structure

自Leontief关于投入产出的静态平衡系统x(k)=Ax(k)+y(k)提出以来,一方面它相当成功地用以描写生产、消费系统,另一方面它又被改造成为考虑到投资、再生产的动态系统 x(k)=Ax(k)+B[x(x+1)-x(k)]+y(k) (1.1) 由于投资系统矩阵B通常是奇异的,所以有些研究工作者曾设法解决此问题。再则,由投资开始到投产往往有时间上的延迟(时滞),所以如何表达时滞于模型中并设法求解也是研究中的一个方面。

So far ,most of the existing dynamic input-output models have been time-invariant, hence incapable of depicting technical progress because of constant system plant matris; and a few time-variant models are not practical because of their awkwardness in treating time delay incorporated in the investment matrix.Here presented is an improved model in which investment is expressed as an input function instead of the usual investment matrix and a versatile method for expressing the complicated temporal behaviour in investment during different phases of capital construction and production is obtained. The new model consists of a dynamic subsystem de-scribing an evolutionary structure and a static one in the form of Leontief input-output equilibrium.