Marx and Sraffa to Miyazawa: Income Distribution, Production and Economic Reproduction in an Input-Output Framework

Marxian, Sraffian, and Miyazawa approaches share an important analytical concern: production, income distribution, and economic reproduction cannot always be treated as independent phenomena. Nevertheless, they approach this relationship from fundamentally different theoretical and mathematical perspectives. Marx developed a theory of capitalist reproduction in which the production of commodities and surplus value is inseparable from class relations and the accumulation process. Sraffa constructed a system of production of commodities by means of commodities in which relative prices, the wage-profit distribution, and the surplus are determined from the technical conditions of production together with a distributional variable. Miyazawa, by contrast, extended the Leontief input-output system by endogenizing household consumption and income formation, thereby establishing an explicit feedback between production and income distribution. This paper examines the relationship between these approaches through the structure of the extended Miyazawa multiplier. The resulting structure reveals an income-consumption-production-income feedback mechanism, which the paper argues can be interpreted as an operator of economic propagation and reproduction. The interpretation does not identify Miyazawa with Marx or Sraffa; rather, it shows that the Miyazawa framework provides an empirical input-output representation of a mechanism that is conceptually related to the broader classical and Marxian concern with reproduction and distribution. The paper further discusses how this operator interpretation can be extended to demographic-economic models and interregional input-output systems, offering a possible bridge between input-output analysis, demographic-economic feedback, and classical political economy.