For the empirical research on the labor theory of value using input-output tables, this paper conducts a relatively systematic and comprehensive study, aiming to basically form a logicalclosed loop so as to deepen and enrich the empirical research on the theory. The value magnitude defined in Marx’s labor theory of value—the socially necessary labor time is a unity of the “first meaning” and the “second meaning”. The socially necessary labor time of the “second meaning” can only be established through the realization of social reproduction. Therefore, the empirical research on the labor theory of value must be integrated with the realization of social reproduction to be complete. Such empirical research cannot bypass Marx’s social reproduction theory on the composition of the product value of the means of production and the means of consumption in the context of realizing the social reproduction with two major categories. Such empirical research by use of the input-output table is necessary and possible to expand the scope of the two major categories of goods, namely means of production and means of consumption, to include service goods, and it should be in the context of social reproduction with fixed capital occupation and depreciation in reality. Under the value system and the price system, the realization of social reproduction will make social reproduction “productive”. Therefore, if the assumption that “the total amount of surplus value is equal to the total amount of profit” is followed, a theoretical relationship between the value and price of two commodities of means of production and means of consumption is obtained, which is namely “the price of a unit commodity of means of production and means of consumption is equal to its value”. The paper introduces the concept of joint production and uses the value-based input-output tables to calculate the price composition of products of means of production and means of consumption, so as to map the input-occupation-output of each industrial sector to produce the two “pure products” of means of production and means of consumption. This approach can be regarded as corresponding to the preparation of input-output tables using the indirect derivation method—UV table method. By respectively applying the sector technology assumption and the product technology assumption, a certain linear transformation is carried out on the broad input, that is, the price composition of the output of each industrial sector, converting it into the price composition of the two “pure products” of means of production and means of consumption. Given that the conclusion can be reached that “the price of a unit commodity of means of production and means of consumption is equal to its value”, the different calculation results of the product price composition of the two “pure products” obtained under the two technical assumptions using input-output tables can all be regarded as the empirical research results of the labor theory of value.

von Neumann Output Ratio is a widely influential concept and term in mathematical economics. von Neumann Output Ratio of Marx's reproduction with two major categories is the ratio between the total output of the means of production category and the total output of the consumption category while the two major categories obtain the maximum equilibrium growth rate. It can most centrally formalize the social structure in the state of the highest equilibrium growth. It is of theoretical significance to establish the relationship between the quantity relation of Marx's theory of social capital reproduction and von Neumann Output Ratio, and to identify and clarify von Neumann Output Ratio of Marx's reproduction with two major categories.

Based on Marx's theory of social reproduction, following the stand, viewpoint, basic model and analysis method of this scientific theory, this paper focuses on the unity of opposites between von Neumann Output Ratio of Marx's reproduction with two major categories and personal consumption of capitalists, and connects Marx's social reproduction formula and the equation system of output growth of the two major categories. By finding and determining the equilibrium growth transfer matrix of output column vector of the two major categories from this term to next term, the paper proved just the development rate of the output of the two major categories which maintains original output structure is the eigenvalue of the transfer matrix. Then, by using the constant capital growth rate of the whole society of social reproduction as an intermediary, it is determined that the equilibrium growth rate of output of the two major categories is a monotone increasing function of the ratio of output of category Ⅰ to output of category Ⅱ, so as to determine that "preferential growth of means of production" is the path to obtain von Neumann Output Ratio of Marx's reproduction.

By use of the research result that the ratio between the two major categories in Marx's social reproduction can be convergent through the preferential growth of the means of production, von Neumann Output Ratio of Marx's reproduction is obtained, and then the maximum equilibrium growth rate of the output of the two major categories and the minimum personal consumption of capitalists are also determined. von Neumann Output Ratio of Marx's reproduction is formalized in terms of several basic concepts and terms in Marx's theory of social reproduction. It was also verified that von Neumann Output Ratio of Marx's reproduction, the maximum equilibrium growth rate and the minimum personal consumption of capitalists satisfy the equation system of output growth of the two major categories.

This paper refuted the theory of labor income share and capital income share in western economics, and used Marx's formula of social reproduction to conduct normative research on labor income share and capital income share. Three factors that affect the labor income share and capital income share in the social reproduction were clarified. They are the capital organic composition of the two major categories, the ratio between the two, and the surplus value accumulation rate of the whole society. The relationship of economic growth rate with labor income share and capital income share was obtained, by taking capital accumulation as the link between labor income share/capital income share and economic growth.On this basis, it was analyzed and tested that the consistency of raising labor income share and raising economic growth rate, and that priority growth of means of production is the common path to raise the both. With the help of an example in Marx's “Das Kapital”, the author verified the consistency of raising the both.

Marx's social reproduction has the characteristic of automatic balanced growth, which is obviously contrary to the reality. The automatic balanced growth of the social reproduction reveals that the structure of total capital has no after-effect. According to Marx's theory of total social capital movement, fixed capital is a component of constant capital whose physical form is the means of production. After deducting the depreciation of the fixed capital actually consumed in the current year, the remaining part still exists and remains in the social reproduction of the following year.This has a significant effect on the distribution of total capital in the two major categories. Therefore, the total social capital has a certain "structural inheritance", and the total capital structure of the social reproduction has a post-effect.

In the classic Marx social reproduction formula, the fixed capital turnover is simplified as intermediate consumption, and its value is transferred to this category of products at one time, in fact, forming a social reproduction formula without fixed capital occupation and depreciation. This is contrary to the characteristics of fixed capital in the theory of turnover discussed by Marx, and just is the reason that the total capital structure of the social reproduction has no after-effect. Following Marx's theory of fixed capital turnover, we introduce fixed capital occupation and depreciation into the social reproduction formula, and establish the social reproduction formula with fixed capital occupation and depreciation, which can remove the structure of total capital no after-effect.

This paper analyzed and compared two representative models that have been used to study fixed capital: Sraffa co-production model and Yamada and Yamada's dynamic iteration model focusing on the reinvestment effect of depreciation funds and its general generalization. The paper stated that both of these approaches change the basic structure of the classical Marx two categories social reproduction formula. Therefore they are all not convenient or impossible to analyze the problem of automatic equilibrium growth of the two categories, and to clearly reveal the after-effect of the total social capital structure.

This paper constructed a social reproduction formula with fixed capital occupation and depreciation according to Marx's fixed capital turnover theory, so as to maintain the basic framework of the classic Marx two-part social reproduction formula. It facilitates the analysis of whether the automatic equilibrium growth of the two categories can be changed, and to clearly show whether the total capital structure has after-effect after the introduction of fixed capital depreciation. Also it is conducive to maintaining the scientific unity of Marx's social reproduction theory and its formula.

At last the paper expounded that the total capital structure of the social reproduction with fixed capital occupation and depreciation has after-effect, and proved such reproduction does not automatically balance growth. Therefore, we can solve the riddle of the auto-balanced growth of Marx's social reproduction and maintain the self-consistency of Marx's social reproduction theory and its formula.