A model of monopoly with lags in the planning and production activity

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.