Abstract
The Arrow-Debreu general equilibrium model stands as one of the most mathematically sophisticated frameworks in modern economic theory. This article argues that the very mathematical formalism that lends the model its apparent rigor can also serve to obscure fundamental conceptual errors at its core. By examining the model's assumptions and logical structure, the analysis reveals how mathematical elegance may mask theoretical weaknesses that deserve closer scrutiny.
Introduction
Since its formal articulation in the 1950s, the Arrow-Debreu model has occupied a central place in neoclassical economics. Its mathematical architecture — built on fixed-point theorems, convexity assumptions, and sophisticated topology — has been widely celebrated. Yet the model's conceptual foundations have received comparatively less critical attention. This paper contends that the mathematical apparatus, far from guaranteeing soundness, can divert attention from problematic premises embedded in the model's construction.
Mathematical Formalism and Conceptual Oversight
A recurring theme in heterodox economic methodology is the risk that formal techniques outpace conceptual clarity. In the Arrow-Debreu framework, the use of advanced mathematics creates an impression of completeness and precision. However, several of the model's foundational assumptions — including perfect competition, complete markets, and the treatment of time and uncertainty — embed conceptual commitments that the mathematics itself does not justify but rather presupposes.
The Role of Fixed-Point Arguments
The existence proof at the heart of the model relies on fixed-point theorems whose applicability depends on conditions that may not hold in real economies. The mathematical demonstration of equilibrium existence can lend an unwarranted sense of empirical relevance to a construct that remains, in important respects, detached from observable economic behavior.
Implications for Economic Methodology
This critique carries broader implications for how economists evaluate theoretical models. When mathematical sophistication becomes a proxy for theoretical soundness, the discipline risks privileging formal elegance over substantive economic reasoning. The article calls for a methodological approach in which mathematical tools serve economic analysis rather than define its boundaries.
Conclusion
The Arrow-Debreu model remains a landmark achievement in mathematical economics. Yet its legacy should include not only admiration for its formal structure but also a clear-eyed recognition of the conceptual errors that its mathematics can conceal. A pluralistic economic methodology — one that treats mathematics as a tool rather than an arbiter of truth — is essential for advancing the discipline.