Deductive Expansion: The Inner Logic of Marx’s Production Function Thought and Economic Growth Models

This paper shows that the idea of the production function originated with classical political economists. The formula W=c+v+m, which appears for the first time in Volume 3 of Capital, is a typical expression of a linear production function. Although some attempts to exponentiate the Marxian production function (e.g., the study of Onishi Hiroshi) are not yet satisfactory, the progress of the study of the production function from the particular to the general reveals that both the linear production function and the exponential production function (especially the C-D production function) belong to the special case of the CES-type production function, and the two are united in this sense. When the production function is further generalized to the VES type, the intrinsic connection between Marx's production function and other related production functions becomes clear. Marx's model of reproduction is also a kind of production function, which is a production function in the form of a set of equations constructed by Marx by using the means of economic analysis to derive the equilibrium conditions of simple reproduction and expanded reproduction, which contains the self-regulating mechanism, through the exchange relationship between the two categories. In conclusion, the production function is a new field of political economy research, originated from the new understanding of Marxist economics triggered by the progress of the fusion of mathematics and economics, and it is a promising new subject in the combination of the inheritance and the development of Marxist economics. It can not only expand the theory of Marxist economics in a new dimension but also further improve the application system of Marxist economics, especially providing new tools or means for the formulation or analysis of economic policies, so that economic theories can better serve the solution of real economic problems.