Dynamical Models for Prices with Distributed Delays

Gabriela Mircea, Mihaela Neamţu and Laura Mariana Cismaş
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Gabriela Mircea: Faculty of Economics and Business Administration, West University of Timisoara, Romania
Mihaela Neamţu: Faculty of Economics and Business Administration, West University of Timisoara, Romania
Laura Mariana Cismaş: Faculty of Economics and Business Administration, West University of Timisoara, Romania
Authors registered in the RePEc Author Service: Laura-Mariana Cismaș

Timisoara Journal of Economics and Business, 2015, vol. 8, issue 1, 91-102

Abstract: In the present paper we study some models for the price dynamics of a single commodity market. The quantities of supplied and demanded are regarded as a function of time. Nonlinearities in both supply and demand functions are considered. The inventory and the level of inventory are taken into consideration. Due to the fact that the consumer behavior affects commodity demand, and the behavior is influenced not only by the instantaneous price, but also by the weighted past prices, the distributed time delay is introduced. The following kernels are taken into consideration: demand price weak kernel and demand price Dirac kernel. Only one positive equilibrium point is found and its stability analysis is presented. When the demand price kernel is weak, under some conditions of the parameters, the equilibrium point is locally asymptotically stable. When the demand price kernel is Dirac, the existence of the local oscillations is investigated. A change in local stability of the equilibrium point, from stable to unstable, implies a Hopf bifurcation. A family of periodic orbits bifurcates from the positive equilibrium point when the time delay passes through a critical value. The last part contains some numerical simulations to illustrate the effectiveness of our results and conclusions.

Keywords: delayed economic models; local stability; price dynamics; Hopf bifurcation. (search for similar items in EconPapers)
JEL-codes: C61 C62 O41 (search for similar items in EconPapers)
Date: 2015
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