TITLE:
Systemic Modeling of Supply and Demand Functions in Light Industry: A Lagrangian Extension via the CS-LR Model
AUTHORS:
Mamadou Salla Gueye
KEYWORDS:
Complex Systems, CS-LR Model, Supply Function, Lagrange Multiplier, Light Industry, Professional Didactics, West Africa
JOURNAL NAME:
Journal of Financial Risk Management,
Vol.15 No.4,
November
11,
2026
ABSTRACT: In this paper, we challenge the boundaries of standard microeconomics to analyze the supply function, demand function, and short-run profit maximization in West African light industries (mechanics, sheet metal, and electrical workshops) (Gueye, 2026a). Classical models assume perfect instrumental rationality and a transparent market, while we introduce managerial and consumer complexity by means of the CS-LR model (Confidence, Satisfaction, Loyalty, Risks) (Gueye, 2023; Gueye et al., 2020a). This paper proposes a theoretical framework where market equilibrium is modeled as an emergent property, structurally dependent on discrepancies between managers’ declarative data and the psychosocial variables observed on the shop floor, by formalizing the producer’s and consumer’s optimization frameworks in a Lagrangian extension. The double-loop feedback mechanism points to the didactic and linguistic mediation based on the semantic plasticity of the national languages as a means of reducing informational uncertainty (in economic terms, the entropy of the system) and organizational risks. This model is characterized by the redefinition of the firm’s shutdown point from a psychosocial perspective and the formalization of the relational resonance proposition. This purely conceptual framework aims at posing formal conjectures on relational resilience, constituting a theoretical basis waiting for subsequent econometric validations.