The Price and Variety Effects of Vertical Mergers

54 Pages Posted: 28 Aug 2016 Last revised: 7 Feb 2020

See all articles by Awi Federgruen

Awi Federgruen

Columbia Business School - Decision Risk and Operations

Ming Hu

University of Toronto - Rotman School of Management

Date Written: January 26, 2020


Vertical mergers within a multi-echelon market result in equilibrium price changes, for wholesalers and retailers, alike. They may also impact the product variety that is available to the consumer, i.e., the equilibrium product assortment sold in the market. In this paper, we consider the simultaneous price and variety effects of vertical mergers in a general two-echelon base model, in which an arbitrary number of firms compete at each echelon; each of the upstream suppliers offers one or multiple products to some or all of the retailers or directly to the end consumer. We assume linear price contracts, with prices selected sequentially, in a sequence of oligopolistic price competitions: the process starts with the firms at the upper echelon, followed by simultaneous price selections by the retailers in the downstream echelon. To assess the impact on product variety, we employ a demand model with the characteristic that, depending on the selected retail prices, a smaller or larger subset of all potential products is sold in the market.

For an arbitrary merger of a supplier with a group of retailers, we characterize the post-merger equilibrium behavior and show how the changes of all performance measures of interest, i.e., wholesale and retail price equilibria, product assortment, sales volumes, the firms' profit levels and consumer welfare, can be computed efficiently. When the merger is strictly vertical, i.e., involves a single retailer (organization) with whom the supplier deals on an exclusive basis, we prove that the merger results in a (weak) reduction of all equilibrium prices, along with a (weak) shrinkage of the product assortment.

Keywords: Vertical Merger, Oligopoly Pricing, Product Variety, Antitrust Law, Supply Chain Network, Industrial Structure and Structural Change, Linear Complementarity Problem

JEL Classification: C68, C72, D43, D51, D58, K21, L11, L13, L16, L4

Suggested Citation

Federgruen, Awi and Hu, Ming, The Price and Variety Effects of Vertical Mergers (January 26, 2020). Columbia Business School Research Paper No. 16-63, Available at SSRN: or

Awi Federgruen

Columbia Business School - Decision Risk and Operations ( email )

New York, NY
United States

Ming Hu (Contact Author)

University of Toronto - Rotman School of Management ( email )

105 St. George st
Toronto, ON M5S 3E6
416-946-5207 (Phone)


Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Abstract Views
PlumX Metrics