The Core Insight: Two Types of Goods, Two Ways of Trading
At the heart of our research lies a deceptively simple but profound observation about modern economies: not all goods are traded the same way. When you buy coffee at a café, you participate in a competitive market—the price reflects supply and demand from countless anonymous buyers and sellers. But consider how that café acquired its espresso machine, or how the machine manufacturer sourced specialised components. These transactions happen through bilateral relationships: specific buyers negotiating with specific sellers, often based on technical specifications, quality requirements, and long-term partnerships.
This paper formalises this fundamental distinction by separating economic goods into two categories: consumption goods (like the coffee you drink) that trade in competitive markets, and intermediate goods (like the espresso machine components) that are exchanged through bilateral relationships within production chains. While economists have long recognised that different goods trade differently, traditional frameworks—from Arrow-Debreu general equilibrium theory to Leontief’s input-output analysis—treat all goods uniformly, applying the same pricing mechanism throughout. This uniformity obscures critical features of how modern production actually works.
Why does this matter? Consider a smartphone supply chain. The final phone sells in competitive retail markets with prices determined by supply and demand. But the specialized chips inside don’t trade on open markets—they’re negotiated between chip manufacturers and phone producers in relationships characterised by technical specifications, volume commitments, and relationship-specific investments. A production network encompassing semiconductor fabrication, component assembly, and final manufacturing requires us to understand both competitive pricing (for the phone) and negotiated pricing (for intermediate inputs). The framework developed here provides the mathematical architecture to analyse such systems rigorously.
This distinction has profound implications for understanding economic sustainability. When intermediate goods flow through bilateral relationships rather than anonymous markets, the question of whether all producers can earn positive incomes—what we call viability—depends fundamentally on the architecture of the production network itself, not just on market-clearing prices.
The Structured Production System Framework
The paper models production as a network of fully specialised producers, each embodying a “profession” defined by a fixed production plan: specific inputs required to generate a specific output. Some professions produce consumption goods (brought to market), while others produce intermediate goods (traded bilaterally with other producers). This captures the reality of modern supply chains where highly specialised firms occupy specific positions in production networks.
A structured production system consists of:
- A set of producers, each assigned a profession
- A professional production system specifying how each good is produced (inputs required, outputs generated)
- The requirement that all intermediate goods are fully absorbed in production—only consumption goods emerge as final output
Production networks (think: automotive supply chains, semiconductor manufacturing) and supply chain networks are concrete incarnations of these structured production systems. The mathematical framework captures their essential properties: who produces what, who supplies whom, and how goods flow through the network.
This representation is more general than that of production networks. It is quite similar to Leontief’s representation of a sectoral economy (1936) in his seminal work that created input-output analysis.
The Concept of Viability
The paper introduces viability as a foundational requirement: at given prices, every producer must earn positive income. Without viability, producers would exit the system, disrupting production chains and preventing any stable economic configuration. This is weaker than full equilibrium (which requires market clearing) but essential as a prerequisite—you cannot have equilibrium if producers are losing money and exiting.
Viability depends critically on the price system: consumption good prices (competitive) and intermediate good prices (negotiated). A structured production system is viable if there exists at least one price configuration where all producers earn positive incomes. It is completely viable if for every possible set of consumption good prices, there exist intermediate good prices that make all producers profitable.
Key Theoretical Results
Acyclic Production Systems Are Always Viable
The paper’s most elegant result (Theorem 3.5b) establishes that acyclic production systems—those without circular conversion processes among goods—are always viable.
What does “acyclic” mean? A production system is acyclic if you never have situations like: good A is used to produce good B, which is used to produce good C, which is used to produce good A. All production flows purposefully toward consumption goods without circular detours. Think of a tree structure: raw materials at the roots, intermediate processing in the trunk and branches, consumption goods at the leaves—with flows moving only upward.
This result provides powerful guidance: if you design production networks to avoid circular dependencies, you guarantee that viable price systems exist. The proof uses sophisticated matrix theory (the Hawkins-Simon condition) but the intuition is clear: without circular dependencies, you can always find prices that allow each producer to cover costs.
Complete Viability and Input Restrictions
A deeper result (Theorem 3.10) characterizes complete viability through input restrictions. The paper shows that complete viability is intimately connected to whether consumption goods serve as inputs for other consumption goods.
Consider two production architectures:
- Consumption goods never serve as inputs for any goods (Restricted Input Property): Complete viability is guaranteed
- Consumption goods don’t serve as inputs for other consumption goods (Weak Restricted Input Property): Necessary for complete viability
The sweet spot is prohibiting consumption goods from feeding back into the production of other consumption goods. This architectural choice—consumption goods as terminal outputs only—ensures robust viability across all possible competitive price configurations.
This has practical implications: production systems structured to minimize consumption goods serving as intermediate inputs exhibit greater structural stability. When final outputs don’t circle back as inputs for other final outputs, the system is more resilient to price fluctuations.
Coherence and Viability
The paper also establishes (Theorem 3.5a,c) that viability requires coherence: the production system cannot contain meaningless conversion cycles where intermediate goods are converted into other intermediate goods without ultimately producing consumption goods. Any production that doesn’t contribute to final outputs represents wasted economic activity that undermines viability.
Relevance to the Contemporary Global Economy
Modern global production embodies exactly the two-tier structure this paper analyses. Smartphones, automobiles, pharmaceuticals—all emerge from complex production networks mixing competitive markets (for final products) with bilateral relationships (for specialised components).
The viability framework addresses fundamental questions:
- Which production network structures are inherently sustainable?
- How does network architecture affect income distribution across producers?
- What design principles promote economic resilience?
The finding that acyclic structures guarantee viability suggests that production networks organised as hierarchies (raw materials → intermediate processing → final assembly) are more stable than those with circular dependencies. The input restriction results suggest that keeping consumption goods from serving as inputs enhances robustness.
These insights matter for supply chain design, industrial policy, and understanding economic development. Countries integrating into global production networks need to understand which positions in the network can sustain positive incomes and how network structure affects this sustainability.
What’s New Here
Traditional frameworks treat all goods uniformly. Arrow-Debreu general equilibrium theory applies competitive pricing throughout; Leontief input-output analysis emphasises technical coefficients without explicit price formation mechanisms. Neither adequately captures the dual nature of modern production: competitive markets coexisting with bilateral relationships.
This paper’s innovation lies in formally accommodating both pricing mechanisms within a unified framework. By allowing consumption goods to have competitive prices while intermediate goods have negotiated prices, it captures essential features of real production systems that existing models obscure.
The viability concept itself is novel—a minimal sustainability requirement weaker than equilibrium but essential for any stable configuration. By separating viability from market clearing, the framework enables modular analysis: first establish when price systems can sustain all producers, then layer on market clearing and bargaining mechanisms.
The structural results—linking viability to network architecture through acyclicity and input restrictions—are new contributions. They provide tractable conditions for determining when production systems admit sustainable price configurations.
Connection to the Leontief-Sraffa Framework
Leontief’s input-output analysis models production through technical coefficients: fixed ratios of inputs to outputs across industrial sectors. Sraffa’s production theory emphasises how income distribution emerges from production requirements and prices. Both frameworks analyse production structure systematically.
This paper builds on this foundation while making crucial extensions:
- Individual producers replace industrial sectors: Rather than aggregating into sectors, the framework models fully specialised individual producers, capturing finer-grained network structure
- Explicit distinction between good types: Leontief and Sraffa don’t formally distinguish consumption goods from intermediate goods in terms of trading mechanisms
- Modern network perspective: The framework naturally accommodates insights from contemporary network economics about how network topology affects economic outcomes
- Separation of viability from equilibrium: Traditional input-output frameworks move directly to equilibrium conditions; this paper establishes viability as a prior requirement
The structured production system can be seen as a specific implementation of Leontief’s framework, but modified to enable equilibrium pricing analysis and enriched with the consumption/intermediate goods distinction. The Z-matrix representation of the professional production system directly parallels Leontief’s input-output matrices, but the viability analysis extends beyond traditional input-output theory by asking when price systems can sustain all productive activities—a question Leontief didn’t centrally address.
Looking Forward
This paper provides the foundation for a three-stage research programme. Stage two will introduce general equilibrium combining viability with market clearing. Stage three will endogenise intermediate good prices through explicit bargaining mechanisms. Together, these papers will develop a comprehensive theory of how competitive markets and bilateral relationships jointly determine prices, quantities, and income distributions in modern production networks.
By establishing when price systems can sustain all productive activities, this research enables rigorous analysis of economic phenomena that existing frameworks cannot adequately capture: how production network structure affects sustainability, how bilateral relationships shape income distribution, and how the architecture of supply chains influences economic resilience. In an era of complex global production networks, these insights are increasingly vital.
This exposition summarizes: Gilles, R. P. and M. Pesce (2025). “Structured Production Systems: Viability.” Available here on the page concerning research on the social division of labour.
The paper is also available on the arXiv web deposit of research:
https://doi.org/10.48550/arXiv.2512.24777