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<p>This paper revisits J. S. Metcalfe’s evolutionary theory of firm-population competition by extending his notion of the normal prices into a stochastic dynamic setting. While Metcalfe’s original formulation translates Fisher’s Fundamental Theorem of Natural Selection into a market context, its reliance on a fixed technological configuration space and on the equalization of demand and supply growth rates renders the normal prices too static to account for empirical regularities such as entry, exit, cumulative advantage, and the Pareto type of firm-size distribution. To overcome these limitations, I integrate H. A. Simon’s cumulative advantage model with Metcalfe’s replicator dynamics, constructing a stochastic feedback system in which firm size, unit cost, markup, price, growth rate, and market share coevolve endogenously. Within this framework, the configuration space becomes a stochastic cost variable, and the resulting “second normal price” emerges as a dynamic structural benchmark shaped jointly by the Pareto index, cost dispersion, and the demand–supply gap. Simulation analysis reveals several key findings. First, the second normal price is not a static equilibrium but a nonlinear outcome of the full feedback loop linking structure, costs, prices, and selection. Second, the joint dynamics of the variables <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\left\{\rho , \lambda , \overline{h }, {sd}_{h}, {p}_{2}, HHI\right\}\)</EquationSource> </InlineEquation> exhibit robust correlation patterns that reflect the regeneration of market structure. Third, measures of diversity and inequality—Shannon entropy, the effective number of firms, and correlation–matrix entropy—identify “islands” of persistent competition characterized by long memory and multidimensional correlation structure. These results suggest that the persistence of competition depends critically on the stochastic regeneration of firm size and the endogenous evolution of price. The integration model thus advances Metcalfe’s framework toward a dynamic account of market structure consistent with the empirical features of restless capitalism.</p>

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Revisiting the notion of normal prices in J. S. Metcalfe's theory: toward a stochastic integration via H. A. Simon's cumulative advantage model

  • 期刊论文

  • 发表日期：

    2026年4月30日

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  • Tomonori Koyama

摘要

This paper revisits J. S. Metcalfe’s evolutionary theory of firm-population competition by extending his notion of the normal prices into a stochastic dynamic setting. While Metcalfe’s original formulation translates Fisher’s Fundamental Theorem of Natural Selection into a market context, its reliance on a fixed technological configuration space and on the equalization of demand and supply growth rates renders the normal prices too static to account for empirical regularities such as entry, exit, cumulative advantage, and the Pareto type of firm-size distribution. To overcome these limitations, I integrate H. A. Simon’s cumulative advantage model with Metcalfe’s replicator dynamics, constructing a stochastic feedback system in which firm size, unit cost, markup, price, growth rate, and market share coevolve endogenously. Within this framework, the configuration space becomes a stochastic cost variable, and the resulting “second normal price” emerges as a dynamic structural benchmark shaped jointly by the Pareto index, cost dispersion, and the demand–supply gap. Simulation analysis reveals several key findings. First, the second normal price is not a static equilibrium but a nonlinear outcome of the full feedback loop linking structure, costs, prices, and selection. Second, the joint dynamics of the variables \(\left\{\rho , \lambda , \overline{h }, {sd}_{h}, {p}_{2}, HHI\right\}\) exhibit robust correlation patterns that reflect the regeneration of market structure. Third, measures of diversity and inequality—Shannon entropy, the effective number of firms, and correlation–matrix entropy—identify “islands” of persistent competition characterized by long memory and multidimensional correlation structure. These results suggest that the persistence of competition depends critically on the stochastic regeneration of firm size and the endogenous evolution of price. The integration model thus advances Metcalfe’s framework toward a dynamic account of market structure consistent with the empirical features of restless capitalism.