On the timing of vertical relationships

Etienne Billette de Villemeur (1) , Richard Ruble (2) , Bruno Versaevel (2)

1 GREMAQ - Groupe de recherche en économie mathématique et quantitative
2 EM - EMLyon Business School

In a real option model, 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 to serve a growing but incertain demand, 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-type index, and we show how market growth rate and volatility affect the extent of the distortion. If the initial market demand is high, greater volatility increases the effective investment cost and results in lower value for both firms. Vertical restraints can restore efficiency. For instance, the upstream firm can induce entry at the correct investment threshold by selling a call option on the input. Otherwise, if two downstream firms are engaged in a preemption race, the upstream firm sells the input to the first investor at a discount which is chosen in such a way that the race to preempt exactly offsets the vertical distortion, and this leader invests at the optimal time.

Mots clés: investment timing; preemption; real options; vertical relations

Domaines: Economies et finances

Etienne Billette de Villemeur, Richard Ruble, Bruno Versaevel. On the timing of vertical relationships. 2011. ⟨halshs-00585557⟩