A Computational Model of Economies of Scale and Market Share Instability

Replicator dynamics and computer simulation techniques are used to construct a reduced form model which explores negative and positive feedback processes between firm costs and market shares embodied in the dynamics of (dis)economies of scale. After reproducing the standard equilibrium results for decreasing returns to scale (unique equilibrium) and increasing returns to scale (multiple equilibrium), a more dynamic formulation of returns to scale is introduced where scale affects not the direction of costs but the rate of cost reduction. Here we find that negative feedback does not produce self-correcting stabilizing forces in market share but rather instability and turbulence. Life-cycle phenomena are explored by combining positive and negative feedback in a firm's cost function. The alternating periods of market share stability and instability which emerge from the simulations are compared to empirical regularities in market share patterns.