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Discrete Dynamics in Nature and Society
Volume 2014, Article ID 137090, 8 pages
http://dx.doi.org/10.1155/2014/137090
Research Article

Hopf Bifurcation in a Cobweb Model with Discrete Time Delays

1Department of Law, University of Genoa, Via Balbi 30/19, 16126 Genoa, Italy
2Department of Management, Polytechnic University of Marche, Piazza Martelli 8, 60121 Ancona, Italy
3Department of Economics and Management, University of Pisa, Via Cosimo Ridol 10, 56124 Pisa, Italy

Received 28 March 2014; Accepted 14 May 2014; Published 12 June 2014

Academic Editor: Mustafa Kulenović

Copyright © 2014 Luca Gori et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We develop a cobweb model with discrete time delays that characterise the length of production cycle. We assume a market comprised of homogeneous producers that operate as adapters by taking the (expected) profit-maximising quantity as a target to adjust production and consumers with a marginal willingness to pay captured by an isoelastic demand. The dynamics of the economy is characterised by a one-dimensional delay differential equation. In this context, we show that (1) if the elasticity of market demand is sufficiently high, the steady-state equilibrium is locally asymptotically stable and (2) if the elasticity of market demand is sufficiently low, quasiperiodic oscillations emerge when the time lag (that represents the length of production cycle) is high enough.