The master equation approach to nonlinear economics
- 239 Downloads
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 maret will develop into an inhomogenous one with a winner and a loser firm.
Key wordsEconomic modelling concepts Master equation Nonlinear dynamics Quality competition
Unable to display preview. Download preview PDF.
- Arthur WB (1986) Self-reinforcing mechanisms in economics. In Anderson PW, Arrow KJ, Pines D (eds.) The economy as an evolving complex system. Addison-Wesley Publishing Co.Google Scholar
- Arthur WB (1990) Positive feedbacks in the economy. Scientific American 80Google Scholar
- Braun M (1992) Modellierung und Analyse dynamischer, nichtlinearer, ökonomischer Prozesse. PhD thesis, Universität StuttgartGoogle Scholar
- Haag G (1990) A master equation formulation of aggregate and disaggregate economic decisionmaking. Sistemi Urbani 1:65–81Google Scholar
- Haken H (1978) Synergetics—An Introduction. Springer, Berlin Heidelberg New YorkGoogle Scholar
- Lancaster KJ (1966) A new approach to consumer theory. JPE 74:132Google Scholar
- Nelson RR, Winter SG (1982) An Evolutionary Theory of Economic Change. Harvard University Press, CambridgeGoogle Scholar
- Schumpeter JA (1934) Theory of Economic Development. Oxford University Press, New YorkGoogle Scholar
- Weidlich W, Haag G (1988) Interregional Migration-Dynamic Theory and Comparative Analysis. Springer, Berlin Heidelberg New YorkGoogle Scholar
- Weidlich W, Haag G (1983) Concepts and Models of a Quantitative Sociology. Springer, Berlin Heidelberg New YorkGoogle Scholar