两大部类扩大再生产的充分必要条件与求解

On the Sufficient and Necessary Condition for the Two-Sector Expanded Reproduction and Its Solution

两大部类扩大再生产的充分必要条件也就是马克思扩大再生产公式有解的充分必要条件.直到目前,由于还没有严谨地提出对于扩大再生产公式的一般求解方法,因而也没有严格地确定扩大再生产的充分必要条件.本文基于已经有研究获得的扩大再生产的一个必要条件,建立一种求解扩大再生产问题的一般方法,从而证明这个必要条件能够成为充分条件,由此确定它是充分必要条件.进而使用变量替换法,给出了通过直接求解两个部类的剩余价值积累率而求解扩大再生产问题的另一种方法.最后引用《资本论》中的两个实例,对所给出的两种求解扩大再生产问题的一般方法做了计算验证.

The sufficient and necessary condition for the two-sector expanded reproduction is also the condition for the existence of solution of Marx’s expanded reproduction scheme.By now the condition has not been defined strictly because a general method of solution to Marx’s expanded reproduction scheme has not been presented scrupulously.This paper set a gen-eral method of solution to the problem of the two-sector expanded reproduction with a necessary condition which has been ob-tained in some research.Therefore,this necessary condition was proved to be the sufficient and necessary condition for the re-production.Then,by use of a method of variable substitution,the paper gave another method of solution to the expanded re-production by taking direct solutions to the rates of surplus valuable accumulation of two sectors.Finally,two examples from Marx’s “Das kapital”were drawn upon to verify two methods of solution to the problem of the expanded reproduction in a cal-culative way.