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Product Line Pricing in a Supply Chain

Olin Business School, Washington University in St. Louis, St. Louis, Missouri 63130
Olin Business School, Washington University in St. Louis, St. Louis, Missouri 63130
Department of Industrial Engineering and Logistics Management, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
dong{at}wustl.edu
narasimhan{at}wustl.edu
kzhu{at}ust.hk

A vertically integrated channel would prefer to coordinate the pricing of its products. In this paper, we investigate drivers of product line pricing decisions in a bilateral monopoly where a manufacturer produces and sells two substitutable or complementary products to a retailer. In a two-stage game, each firm commits credibly in the first stage to a pricing scheme within its own organization: product line pricing (PLP) or nonproduct line pricing (NPLP). In the second stage, depending on the relative balance of power in the supply chain, the firms engage in either a Nash or a leader-follower pricing game. We study the equilibrium of the two-stage game under a general symmetric demand function. With strategic interaction between firms, a firm may choose NPLP as the equilibrium pricing strategy. In particular, when the second stage is a leader-follower game, the price leader chooses PLP, and the follower may choose NPLP only if the inefficiency of using NPLP empowers the follower by increasing the demand sensitivity to the leader's margin. When the second stage is a vertical Nash game, whether NPLP occurs in equilibrium depends on the nature of coupling between demand interdependence and vertical strategic dependence: NPLP can be an equilibrium only if products are demand substitutes (complements) and vertical strategic dependencies are complementary (substitutable). We find that prisoner's dilemma exists in the first stage for both types of second-stage pricing games. In those cases, one firm may have the incentive to commit to a pricing scheme in the first stage prior to its channel partner and steer the supply chain away from prisoner's dilemma.

Key Words: marketing; product line pricing; substitute; complement; equilibrium; vertical strategic interaction
History: Received: August 8, 2007; accepted: May 3, 2009.