Finite Brand Loyalty and Equilibrium Price Promotions

Abstract

The extant literature on price promotions typically assumes that consumers loyal to a brand never switch to a competing brand, with Shilony (1977) and Raju et al (1990) being exceptions. Extending the Narasimhan (1988) model, we allow loyal consumers to hold finite brand loyalty. Our unique equilibrium splits into three types, depending upon configurations of consumer reservation utility, brand strength and switcher population. The type of equilibrium for high brand loyalty corresponds to the one in Narasimhan (1988). The remaining two types for intermediate and low brand loyalty demonstrate strikingly different properties. First, the strong brand has a higher price range and a higher regular price. Second, the strong brand has a higher (lower) average promotional depth than the weak brand when the switcher population is small (large). Third, both brands promote equally frequently when brand loyalty is relatively low. Therefore, this analysis hopefully provides a more complete picture about firms’ promotional decisions for all possible levels of brand loyalty and switcher pupulation.