Working paper

Timing Vertical Relationships

Richard Ruble, Bruno Versaevel, and Étienne de Villemeur


We show that the standard analysis of vertical relationships transposes directly to investment timing. Thus, when a firm undertaking a project requires an outside supplier (e.g. an equipment manufacturer) to provide it with a discrete input, and if the supplier has market power, investment occurs too late from an industry standpoint. The distortion in firm decisions is characterized by a Lerner index, which is related to the parameters of a stochastic downstream demand. When feasible, vertical restraints restore efficiency. For instance, the upstream firm can induce entry at the correct investment threshold by selling a call option on the input. Otherwise, competition may substitute for vertical restraints. In particular, if two firms are engaged in a preemption race downstream, the upstream firm sells the input to the first investor at a discount that is chosen in such a way that the race to preempt exactly offsets the vertical externality, and this leader invests at the optimal market threshold.

JEL codes

  • C73: Stochastic and Dynamic Games • Evolutionary Games • Repeated Games
  • D43: Oligopoly and Other Forms of Market Imperfection
  • D92: Intertemporal Firm Choice, Investment, Capacity, and Financing
  • L13: Oligopoly and Other Imperfect Markets

See also

Published in

TSE Working Paper, n. 10-181, June 23, 2010