Empirical Analysis of Competitive Pricing Strategies with Complementary Product Lines

We build an econometric model of a household's purchase incidence and brand choice decisions in complementary product categories to account for cross-category dependence in demand. Complementarity is modeled as the additional utility that a household derives from the joint consumption of brands in complementary categories. We estimate the proposed multi-category demand model using scanner panel data on cake mix and frosting categories. Using the estimated demand model as an input, we investigate whether the observed retail prices in the two categories are consistent with joint-category profit maximization behavior on the part of the retailer. We also investigate whether manufacturers' pricing behavior is consistent with maximizing the sum of profits from their brands (bearing the same umbrella name) in both complementary categories. Lastly, we investigate the nature of vertical channel interactions between the manufacturers and the retailer. We find that our proposed multi-category demand model fits households' purchasing outcomes better than traditional single-category demand models (which yield significantly under-stated within-category price elasticities). While each brand in one category is a complement for every brand in the other category, the cross-category complementarity and cross-category price elasticity are found to be strongest with respect to the umbrella brand name in the other category. We find that the data are consistent with joint-category profit maximization behavior by the retailer across the two categories, and with a Vertical Nash game between the retailer and the manufacturer. Finally, we find that the data are consistent with a Bertrand-Nash pricing game among manufacturers maximizing the sum of their brands' profits in the two categories. In fact, joint-category profit maximization is found to be a dominant strategy for each manufacturer.