A General Theory of Pass-Through in Channels with Category Management and Retail Competition

I provide a general formulation of the channel pass-through problem as a comparative static of the retail price equilibrium, and I analyze the impact of category management and retail competition on pass-through, focusing on brand and retailer differences, and the nature of the cost change being passed through—whether it is brand specific, retailer specific, both, or neither. With category management, a retailer's response to a brand-specific cost change is not limited to that brand; in general, a retailer will also change the prices of other brands. The cross-brand effect can be positive or negative, and, depending on its sign, it either enhances or attenuates pass-through. I explain the cross-brand effect as an interaction between two forces: a demand-substitution force that pushes for a negative cross-brand effect, and a strategic-complementarity force that pushes for a positive cross-brand effect. Retail competition adds another layer of strategic complementarity, causing other retailers to respond even for retailer-specific cost changes and increasing pass-through of categorywide cost changes. But its effect for brand-specific cost changes is ambiguous. I apply the theory to two commonly used demand functions—linear demand and nested logit—and show that they have significantly different pass-through properties. The paper concludes with a discussion of how the theory relates to the empirical literature, including the companion piece by Besanko et al. (Besanko, D., J-P. Dubé, S. Gupta. 2005. Own-brand and cross-brand retail pass-through. (1) 123–137.)