The Circular Flow Revisited: A Comparative Exposition of Leontief's Input-Output Analysis and Sraffa's Production of Commodities

TL;DR

This paper compares Leontief's input-output analysis with Sraffa's production model, highlighting their differences and similarities, and proposes a unified mathematical framework to deepen understanding of economic systems as circular production processes.

Contribution

It offers a comprehensive comparison of Leontief's and Sraffa's models and introduces a unified algebraic structure linking their frameworks.

Findings

Both models can be represented within a single algebraic framework

The analysis clarifies the roles of prices, quantities, and technology in both models

A mathematical unification enhances understanding of economic inter-industry relationships

Abstract

This paper delves into the foundational contributions of Wassily Leontief and Piero Sraffa to the understanding of economic systems as circular processes of production. It provides a comprehensive analysis of Leontief's Input-Output (I-O) framework and Sraffa's model of "Production of Commodities by Means of Commodities," highlighting their distinct yet complementary perspectives on the structure of modern economies. By meticulously examining the mathematical underpinnings and economic assumptions of both models, this paper elucidates their respective treatments of prices, quantities, surplus, and the role of technology. The analysis extends to a comparative exploration of their approaches to value, distribution, and the representation of economic systems, drawing upon detailed examples and the theoretical frameworks presented in the foundational texts. The paper argues that a synergistic understanding of Leontief's empirical framework and Sraffa's theoretical critique offers profound insights into the intricate web of inter-industry relationships that characterise contemporary economies. The appendix part of this paper proposes a rigorous mathematical unification of the classical price theory of Piero Sraffa and the empirical input-output analysis of Wassily Leontief. While both frameworks model the economy as a circular process of production, their theoretical foundations and applications have often been treated separately. We demonstrate that they are two facets of a single, underlying algebraic structure.