Investigating the Sensitivity of Equilibrium Profits to Advertising Dynamics and Competitive Effects

Abstract

The author investigates the validity of the “flat maximum principle”—the insensitivity of a firm's profits to changes in its optimal advertising level—in a duopolistic market in which advertising by the two firms has carryover effects. Two alternative competitive scenarios are examined (i) in which total industry sales are allowed to vary over time, and (ii) where firms are engaged in market share rivalry. For (i), the open-loop Nash equilibrium advertising strategies for the firms are derived assuming a specific sales response function and an infinite time horizon. A numerical analysis of the sensitivity of firms' profit functions to advertising expenditures is performed at different levels of the (a) discount rate, (b) advertising elasticity, and (c) advertising decay rate. An empirical illustration from the pharmaceutical industry is provided. Special cases of the model formulation are examined analytically in order to highlight the intuition behind the flatness of the maximum and to study the sensitivity of results obtained to choice of equilibrium strategy (closed-loop vs. open-loop). For the market share game, closed-loop policies are considered and the flat maximum principle is illustrated in the context of Coke–Pepsi rivalry in the soft drinks market.