A dynamic model of advertising by the regulated firm

A profit-maximizing firm subject to price regulation typically seeks alternative variables to control if the regulatory constraint is binding. Advertising may be one such variable. By shifting the demand curve inward or outward between rate hearings, the firm may increase its earnings above the allowed level. Here, a simple discrete-time optimal-control model is proposed to examine the dynamic implications of advertising by the regulated firm. Our results indicate that, in the long run, the combined effect of regulation and advertising leads to a steady-state equilibrium that is closer to the minimum point on the firm's long-run average-cost curve than the original output level. Thus, an invisible-hand property is established that pushes the regulated firm to shift its demand curve toward the minimum point on its long-run average-cost curve in the presence of regulation. As a result, the well-known allocative inefficiency created by rate-of-return regulation (PMC), on which so much has been written over the past 100 years, is reduced (and, under certain conditions, eliminated) if the regulated firm is allowed to advertise.