Structured Production Systems: Viability

Robert P. Gilles and Marialaura Pesce

Papers from arXiv.org

Abstract: This paper introduces a novel framework for analysing equilibrium in structured production systems that incorporate a static social division of labour, distinguishing between consumption goods traded in competitive markets and intermediate goods exchanged through bilateral relationships. We develop the concept of viability -- the requirement that all producers earn positive incomes, as a foundational equilibrium prerequisite. Our main theorem establishes that a structured production system is viable if and only if it is coherent, admitting no circular conversion processes that yield no net output, which in turn is equivalent to the non-singularity of its matrix representation. We further investigate completely viable systems, in which viable prices exist for all consumption good price vectors. We show that complete viability stands exactly between two input restrictions: it is guaranteed in coherent systems where no consumption good is used as an input in production, and it requires that no consumption good is used as an input in the production of another consumption good. The analysis thus reveals fundamental relationships between the architectural design of production systems and their economic sustainability. Our framework also contributes to the literature on the existence of positive output price systems and the Hawkins-Simon condition in input-output analysis.

Date: 2025-12, Revised 2026-06
New Economics Papers: this item is included in nep-hme
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