Group for Research in Decision Analysis

Product-Line Pricing:Optimum or Pessimum?

Charles A. Ingene The University of Mississippi, United States

We consider two interesting classes of problems that arise when managing a product line. First, for a given a degree of demand interaction, what is the best way to price the line? Second, for a given pricing policy, what is the most profitable degree of product differentiation? We examine both problems from the viewpoint of the manufacturer, the retailer, and the channel by using a model of a bilateral-monopoly channel in which two substitutable products 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). 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 interest of the manufacturer (retailer) for both products to be produced (distributed) using PLP, no matter what the other player’s pricing policy is. Hidden beneath this PLP-oriented result are four non-obvious insights. First, when products in a decentralized channel are moderately-to-highly differentiated, NPLP maximizes profits of the channel, the manufacturer, and the retailer. 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 channel member’ individual interest is not in their collective interest. Second, whether the channel is centralized or decentralized, PLP encourages a broader product line than does NPLP at low degrees of product differentiation. Third, when the cost of product-line development is positively related to the degree of differentiation, either PLP or NPLP may lead to greater differentiation, depending on specific parametric values for cost. Fourth, consumers are worse off under PLP than under NPLP because prices are higher with PLP. Partially compensating for this price effect, the PLP product line is more differentiated at some parametric values. Thus, we find that while product-line pricing is the equilibrium, for a wide range of demand and cost conditions it is a channel “pessimum” relative to non-product line pricing.

Key Words: Distribution Channels; Product-Line Pricing; Product-Line Breadth; Game Theory