Leontief逆矩阵和Ghosh逆矩阵性质应用的再研究

Further Research on Applications of Properties of Leontief Inverse Matrix and Ghosh Inverse Matrix

本文首先总结了价值型Leontief逆矩阵、Ghosh逆矩阵和实物型Leontief逆矩阵的性质,回顾了这些性质在产出调整分析和价格调整分析中的一些应用,然后研究了这些性质在产出调整分析中关于投入乘数方面,以及在价格调整分析中关于产出乘数方面进一步的应用,结论是如果只有部门i的实物型最终产出增加(减少)而其余部门的不变,那么部门i的投入乘数一定不增加(不减少),而且至少存在一个部门i_0(i_0≠i)的投入乘数一定不减少(不增加);对偶地,如果只有部门j的增加值上升(下降)而其余部门的不变,那么部门j的产出乘数一定不增加(不减少),而且至少存在一个部门j_0(j_0≠j)的产出乘数一定不减少(不增加)。

We summarize the properties of the monetary Leontief inverse matrix,the Ghosh inverse matrix and the physical Leontief inverse matrix,review some applications of these properties to output adjustment analysis and to price adjustment analysis,and further research the new applications of these properties to input multiplier in output adjustment analysis and to output multiplier in price adjustment analysis. The conclusions are that if the physical final output of sector is increased(decreased） and all others are not,then the input multiplier of sector cannot be increased(decreased）,and there exists at least one sector such that its input multiplier cannot be decreased(increased）; dually,if the value-added of sector is risen(fallen） and all others are not,then the output multiplier of sector cannot be increased(decreased）,and there exists at least one sector such that its output multiplier cannot be decreased(increased）.