Product-Line Pricing: Its Impact on Horizontal and Vertical Externalities in Distribution Channels

We consider three interesting classes of problems that arise regarding a product line. First, for a given a degree of demand interaction, what is the best way to price the line? Second, what is the relationship between the pricing policy and product-line breadth? Third, for a given pricing policy, what is the most profitable degree of product differentiation? We examine these problems from the viewpoint of manufacturer, retailer, and channel with a bilateral-monopoly model in which two demand-related goods may be produced and distributed. We allow the channel to sell (a) only the ith product, (b) only the jth product, (c) both products with non-product-line pricing (NPLP), or (d) both products with product-line pricing (PLP). For substitute goods, we prove that PLP is the profit-maximizing solution in a centralized channel. We also prove that PLP is the equilibrium solution in a decentralized channel that is organized as Vertical-Nash or as Stackelberg-Leader. By equilibrium we mean that it is in the manufacturer's (retailer's) interest for both products to be produced (distributed) using PLP, no matter what pricing policy the other channel member chooses. Hidden beneath this PLP-oriented result are four non-obvious insights. First, if products in a decentralized channel are moderately-to-highly differentiated, NPLP maximizes profits for the channel, manufacturer, and retailer. In contrast, PLP is more profitable only for minimally-differentiated products. Divergence between the profit-maximizing strategy and the equilibrium strategy occurs because the PLP vs. NPLP choice creates a prisoner's dilemma over most parametric values: what is in a channel member's individual interest is not in the channel's collective interest. Second, for both centralized and decentralized channels, PLP leads to a broader product line than does NPLP when products are not too differentiated. Third, because prices are higher with PLP, consumers are worse off under PLP than under NPLP even though a PLP product line is broader at some parametric values. Fourth, when differentiation is costly, optimal product-line differentiation is greater under NPLP than under PLP. While product-line pricing is the equilibrium pricing policy for substitutes, for a wide range of demand and cost conditions it is a channel pessimum relative to non-product-line pricing. We also briefly address complementary goods. While the mathematics remains the same, we show that certain key conclusions differ from the case of substitute products.