The master equation approach to nonlinear economics

Abstract

A concept for modelling nonlinear economic dynamics is presented and exemplified by a concrete model. Generally, a configuration of macro-economic variables is considered whose probabilistic evolution is coupled to the decision making of agents and is described by a master equation. The transition rates in the master equation are modelled in terms of utility measures of the agents. Nonlinear dynamic meanvalue equations can be derived from the master equation. The concrete model describes firms producing substitutable durable commodities. They compete with respect to the quality of their products and a positive feedback between quality enhancement and customer’s reaction to quality is assumed. The case of two competing firms is treated explicitely. It is shown that beyond a critical value of a “competitivity parameter” a homogenous market will develop into an inhomogenous one with a winner and a loser firm.

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