| Наименование статьи | Mathematical formulation and proof of Marx's value transformation conjecture |
|---|
| Страницы | 5-17 |
|---|
| Аннотация | Marx proposed a bold conjecture in volume III of Das Kapital: in the process of total social production, the total value of all commodities equals the total price, and the average rate of profit of all capital equals the average rate of surplus value. For over a century, the academic community was debating the mutual compatibility of these "two equalities", and a rigorous mathematical proof remained elusive. By analyzing the inherent causes underlying the formation of constant and variable capital, distinguishing the dual attributes of capital in the forms of mechanical force and living labor, introducing the interest factor and labor productivity factor, and incorporating the dual relationship between productive capital and monetary capital, this paper constructs a complete mathematical framework for Marx's theory of production prices. Under this framework, the paper rigorously formulates and proves Marx's conjecture: equations in homogeneous sectors admit analytical solutions; equations in heterogeneous sectors can be solved via the "structural elimination-numerical approximation" method; and equations in different static and dynamic scenarios can be addressed using the corresponding fixed-point theorems. This lays a mathematical foundation for the theory of value transformation that integrates theoretical rigor with computational feasibility. |
|---|
| Ключевые слова | MARX'S THEORY OF VALUE, VALUE TRANSFORMATION, TWO EQUALITIES, HOMOGENEOUS TRANSFORMATION, HETEROGENEOUS TRANSFORMATION, STATIC TRANSFORMATION, STATIC-DYNAMIC COMPATIBLE TRANSFORMATION |
|---|
| Журнал | Экономика и математические методы |
|---|
| Номер выпуска | 2 |
|---|
| Автор(ы) | Wu J., Bakhtizin A. R., Makarov V. L., Wu Z. |
|---|