Effects of fixed and continuously distributed delays in a monopoly model with constant price elasticity
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In this paper, we analyze the dynamics of a monopoly model with constant elasticity in which the monopolist faces a form of bounded rationality due to limited accessibility to information. We assume the firm adopts a gradient mechanism to adjust the output level, and we investigate how the introduction of fixed and continuously distributed delays within the resulting continuous-time system may affect the long-run dynamics. We find that the stability of the equilibrium depends on the weighting function adopted to model continuously distributed delays, and the convergence of the realized output toward the steady state is crucially affected by the choice of the delay type which, in turn, reflects the availability and the weight assigned to information. Indeed, depending on the assumptions on modeling delays, the equilibrium point may undergo a Hopf bifurcation after which a limit cycle arises.
KeywordsMonopoly Time delays Fixed and continuously distributed delays Hopf bifurcation Bounded rationality
JEL ClassificationD42 C62 D84 C02
We wish to thank two anonymous reviewers for useful comments and suggestions. The usual caveats apply.
Compliance with ethical standards
Conflicts of interest
The authors declare that they have no conflict of interests.
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