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Decisions in Economics and Finance

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06.12.2018

Some reflections on past and future of nonlinear dynamics in economics and finance

verfasst von: Mikhail Anufriev, Davide Radi, Fabio Tramontana

Erschienen in: Decisions in Economics and Finance | Ausgabe 2/2018

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Abstract

This paper offers an overview of the literature on the economic and financial applications of theory of nonlinear dynamics, especially bifurcation theory. After a short introductory discussion of the first nonlinear dynamic models in social sciences and the economic relevance of the zoo of bifurcations and complicated dynamics that such models can generate, we present an overview of the literature on nonlinear dynamic models in the areas of underdevelopment, environmental poverty traps, the management of common goods, industrial organization and financial markets. The review of the literature is enriched by reflections and ideas for future research.

Nächster Artikel A piecewise linear model of credit traps and credit cycles: a complete characterization

Firms endowed with static expectations assume that the competitor will next period produce the same quantity as in the current one. Under Cournot adjustment process, they play repetitively the best response given these expectations.

The result that more than three firms imply instability in Theocharis (1960) is obtained under the assumptions of static expectations and linear cost function. It is possible to change at least one of these two assumptions so that the dynamical system remains linear but will become stable, converging to the unique Cournot–Nash equilibrium (see, e.g., Fisher 1961).

A reaction function gives the optimal choice of a firm given any possible choice of the competitor. Let us also point out that saying that a reaction function, as well as the inverse demand function, is linear is an abuse of language. In fact, by linear inverse demand function we mean downward sloping, piecewise-linear function with a unique kink point (or point of non differentiability) that originates due to avoidance of negative prices. This kink point in the inverse demand function is reflected in the kink point of the reaction function, which is linear in all other points.

To microfound a demand function means to obtain it as the aggregation of the optimal choices of identical utility maximizing consumers.

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Titel: Some reflections on past and future of nonlinear dynamics in economics and finance
verfasst von: Mikhail Anufriev
Davide Radi
Fabio Tramontana
Publikationsdatum: 06.12.2018
Verlag: Springer International Publishing
Erschienen in: Decisions in Economics and Finance / Ausgabe 2/2018
Print ISSN: 1593-8883
Elektronische ISSN: 1129-6569
DOI: https://doi.org/10.1007/s10203-018-0229-9

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