Supervisory control for dynamic monopoly

A monopoly firm maximises profit by producing the quantity at which marginal revenue equals marginal cost. In order for a monopoly firm in a disequilibrium (non-profit-maximising) state to reach an equilibrium (profit-maximising) state, it usually adopts the following conventional strategy: when marginal revenue exceeds marginal cost, the firm increases output (the quantity of production), and when marginal cost exceeds marginal revenue, the firm decreases output. In this study, using supervisory control theory of discrete event systems, the authors study the dynamic monopoly problem: Does the monopoly firm’s conventional strategy always assure that the firm in disequilibrium eventually reaches an equilibrium state? The author show that the non-blocking property and controllability (which are the major concepts in supervisory control theory) are the necessary and sufficient conditions for the existence of a solution to the dynamic monopoly problem.