借助拉格朗日乘数法优化社会扩大再生产

摘要

The paper presented a method of optimization of the two-sector social expanded reproduction with the help of Lagrange Multiplier method. By use of Lagrange Multiplier method, a problem of getting optimal solution to the expanded reproduction was converted to a problem of comparing and deciding several values of an objective function only at several frontier points of its definition, so that the problem becomes very simple and explicit. And then both of the frontier points where are just the optimal solution to the expanded reproduction and the optimal solutions themselves were determined. An example from Marx's "Das kapital" was drawn upon to verify the method in a calculative way.%文章提出一种借助拉格朗日乘数法优化两大部类社会扩大再生产的方法。运用拉格朗日函数法，将获得扩大再生产的最优解析解问题，转化成目标函数在定义域边界点上的若干取值比较和判定问题，使问题变得很简单、明确。进而容易地确定扩大再生产的最优解所处的边界点，获得最优解。借助马克思《资本论》中的一个举例，对此方法做了计算验证。