Hopf Bifurcation in a Cobweb Model with Discrete Time Delays

Luca Gori (), Luca Guerrini and Mauro Sodini

Discrete Dynamics in Nature and Society, 2014, vol. 2014, 1-8

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.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:137090

DOI: 10.1155/2014/137090

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