Complex dynamics of monopolies with gradient adjustment

Akio Matsumoto and Ferenc Szidarovszky

Economic Modelling, 2014, vol. 42, issue C, 220-229

Abstract: This paper aims to show that delay matters in continuous- and discrete-time framework. It constructs a simple dynamic model of a boundedly rational monopoly. First the existence of the unique equilibrium state is proved under general price and cost function forms. Conditions are derived for its local asymptotical stability with both continuous and discrete time scales. The global dynamic behavior of the systems is then numerically examined, demonstrating that the continuous system is globally asymptotically stable without delay and in the presence of delay if the delay is sufficiently small. Then stability of the continuous system is lost via Hopf bifurcation. In the discrete case without delay, the steady state is locally asymptotically stable if the speed of adjustment is small enough, then stability is lost via period-doubling bifurcation. If the delay is one or two steps, then stability loss occurs via Neimark–Sacker bifurcation.

Keywords: Gradient dynamics; Boundedly rational monopoly; Continuous and discrete dynamics; Time delay (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecmode:v:42:y:2014:i:c:p:220-229

DOI: 10.1016/j.econmod.2014.06.013

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