Pricing and Marketing Rules with Brand Loyalty
Many firms face a dynamic trade-off: if price is reduced, the firm attracts new customers who will yield profits in the future, but it also forgoes the opportunity to squeeze profits now from loyal customers. This paper identifies a rule that represents the optimal resolution of this trade-off, in terms of an intuitive modification to the static Lerner rule. We find that the “effective” price elasticity depends on the discount rate used by the firm, on the rate of depreciation of the clientele through exit from the stock of repeat purchasers, and on a weighted sum of the price elasticities of the flow of entries into the stock of repeat-purchasers and the flow of exits from the stock of repeat-purchasers. None of these factors enter the optimal pricing strategy for a firm facing a conventional demand function with instantaneous adjustment, i.e. where consumers are “fast switchers”, rather than repeat-purchasers. We also find optimal rules for marketing investment and for quality of service, which are extensions of the Dorfman-Steiner conditions. The paper shows that our rules, with suitable modifications, are valid for many market structures, including monopolistic competition, pure monopoly and strong cartels, dominant firms and oligopolists that have full commitment ability. In the case of dominant firms and oligopolists that cannot commit to their strategy paths, these simple optimal pricing and marketing rules do not apply.