Cost-Based Competition and Market Share Determination: A CES Analytical Framework

This study examines the micro-level mechanisms through which increasing market concentration and the entrenchment of competitive advantage arise. We develop a theoretical framework based on a constant elasticity of substitution (CES) production function and a CES demand structure, integrating—within a unified analytical chain—firms’ inter-firm cost competition, cost-plus pricing, demand allocation, and market-share decision-making. Methodologically, we first derive the relationship between firm prices and productivity from cost minimization and optimal pricing rules and then obtain explicit expressions for market shares and sales under CES demand. We subsequently introduce endogenous learning effects, in which firms’ market shares feed into future productivity growth via a learning curve mechanism, thereby characterizing the conversion of static advantage into dynamic competitive advantage. We further incorporate technology-factor substitutions, such as robotics, into firms’ production and cost structures to analyze how cost savings and efficiency gains accelerate the evolution of concentration and to show how learning disadvantages induced by insufficient market shares deter potential entry. The results indicate that firms’ market shares are primarily determined by their relative productivity, while profits respond asymmetrically to productivity differentials. Learning and technological substitution support the accumulation of advantages for incumbent firms and endogenously generate barriers to entry. Overall, this paper explains how the entrenchment of competitive advantage is reinforced through dynamic feedback, driving industries toward higher levels of concentration.