The topics presented in this paper are all new attempts to some extent, and so far, although there is some kind of attempts to reinterpret Marx's economic theory by using the Cobb-Douglas production function, there are few systematic studies of Marxist economics from the point of view of the production function. This paper reveals clear evidence that Marx had the idea of the production function in Capital and emphasizes that there is no such formulation in Capital as the so-called Marxian value equation c+v+m = w , written in letters, but that the formula W =c+v+m , which appears for the first time in Volume III of Capital, belongs to the typical format of a linear production function. From this it can also be recognized that the vertical Leontief production function actually stems from the decomposition of the variable capital part of Marx's production function. In terms of research methodology, this paper, based on a multi-party series of research results obtained from the study of production functions from the special to the general, after clarifying that the basic characteristic of Marx's production function is a linear production function, it achieves generalization by expanding it into the form. of the CES production function, thus clarifying the intrinsic connection between Marx's linear production function and other forms of production functions. The significance of this paper lies mainly in the fact that by exploring and analyzing Marx's idea of the production thought, we can deepen our understanding of Marx's economic theory, especially by further expanding the model of economic growth derived from the reproduction schema, and be conducive to comparative analyses with the economic theories of other schools of thought.
