Exploration Of Reverse Adjustment For The Input Coefficient Matrix

Input-output analysis method is one of the important tools in analyzing macro economic and regional economic problems.This theory is designed to explore the quantitative relationship between the various departments in the national economy running. It was established by Prof Wassily Leontief,who is the famous economist in America and published the first essay "The quanti-tative relations of input-output in American economic system" about input-output analysis in1936.This essay proclaimed the birth of the input-output theory. For his outstanding contribution in the field, he was awarded the Nobel Prize in economic in1973.The core of input-output technology is input-output table.In the process of using input-output method in studying economic problem,we usually repre-sent the quantitative interdependent relationship between the economic activ-ities under studying by establishment of mathematical model,which consists of mathematical form like linear equation or nonlinear equation.So the term input-output model is often used.This paper is based on the input-output table,combined with the curren-t research status of input-output technology Domestic and international.Our research centres on the positive eigenvector law,which is put forward in the paper "mathematical theory of a wide range of optimization of planned econ-omy".and get some meaningful results.This paper is divided into five chapters, the first chapter is the intro-duction part of this paper, introducing emergence and development of the input-output technique; the second chapter introduces principles of input-output method and some theory Foundation of this paper; the third chapter and the fourth chapter are the main content of this article.The fifth chapter is empirical analysis.By the " positive eigenvector law ", to make the national economy as a whole system maintain balance, the production vector and the price vector each year should respectively be the right and left positive eigenvectors of the direct consumption coefficient matrix. But according to the final demand, the production and the price we expect may not be consistent with the above positive eigenvector.Then We should seek the method to adjust the direct consumption matrix to make sure that its right and left eigenvectors are the desired production vector and the price vector. The third chapter and the fourth chapter respectively discusses this problem with different methods.The third chapter bases on a series of methods of the reverse adjustment for the input coefficient matrix, using nonlinear programming method to solve the problem. The basic idea is to construct a matrix, whose right and left positive eigenvectors are the given production vector and price vector, and then adjust the matrix to make it has the smallest gap with the original direct consumption coefficient matrix.Based on the idea from simple to complex we first consider only the production, after obtaining the reasonable results, we then consider production and price comprehensively.The fourth chapter uses the wellknown RAS method. The basic idea is to use the RAS method to adjust the original input coefficient matrix,and make its left and right eigenvectors respectively has a gap small enough with given production and price. Of course, as with the third chapter, this chapter is to consider only the production first, and then consider production and price comprehensively. In the fifth chapter empirical analysises for chapter three and four are given.