A Model of Monopoly with Lags in the Planning and Production Activity

Abstract

In this note, departing from the traditional static and fully rational economic agent setting, I study a dynamic model of a boundedly rational monopolist who, in a partially known environment, follows a rule of thumb learning process. Instead of considering the classical differential model with smooth argument, the proposed dynamic model consists of a piecewise constant argument differential equation, in order to take into account the more realistic assumption of a lag between the Learning activity and the output production activity. It is shown how this simple first order differential equation can be rephrased into a nonlinear difference equation which, differently from the classical model with smooth argument, can exhibit complex behaviors. The aim of the paper is to illustrate, from a methodological point of view, the potential applications and the dynamical effects of piecewise constant argument differential equations in economics.

Keywords: Monopoly, lags, bounded rationality, piecewise constant argument differential equations, complex dynamics

JEL Classification: D42, L12, C02, C62, C63, C65