A multiscale time model with piecewise constant argument for a boundedly rational monopolist. Issue 10 (2nd October 2016)

• Record Type: Journal Article
• Authors: Cavalli, F.; Naimzada, A.
• Is Part Of: Journal of difference equations and applications. Volume 22:Issue 10(2016)
• Page Start: 1480
• Page End: 1489
• Publication Date: 2016-10-02
• Subjects: Boundedly rational monopolist -- multiscale -- piecewise continuous differential equations -- nonlinear difference equation -- stability -- bifurcation; Difference equations -- Periodicals; 515.625
• DOI: 10.1080/10236198.2016.1202940
• Languages: English
• ISSNs: 1023-6198

Abstract

Abstract : We present a dynamic model for a boundedly rational monopolist who, in a partially known environment, follows a rule-of-thumb learning process. We assume that the production activity is continuously carried out and that the costly learning activity only occurs periodically at discrete time periods, so that the resulting dynamical model consists of a piecewise constant argument differential equation. Considering general demand, cost and agent's reactivity functions, we show that the behavior of the differential model is governed by a nonlinear discrete difference equation. Differently from the classical model with smooth argument, unstable, complex dynamics can arise. The main novelty consists in showing that the occurrence of such dynamics is caused by the presence of multiple (discrete and continuous) time scales and depends on size of the time interval between two consecutive learning processes, in addition to the agent's reactivity and the sensitivity of the marginal profit.