Optional fixed fees in multilateral vertical relations
Introduction
The main result in the literature on vertical contracting has been to demonstrate how ex post opportunism constrains an upstream monopolist's ability to leverage its market power downstream. Starting from ‘efficient’ supply contracts consistent with an integrated monopoly outcome, an upstream monopolist has an incentive to act opportunistically by discounting to selected downstream firms. Anticipating this, other downstream firms will only sign agreements consistent with a more oligopolistically competitive outcome.
There have been several different statements of these results. Hart and Tirole (1990), O'Brien and Shaffer (1992), McAfee and Schwartz (1994), Segal (1990), Segal and Whinston (2003), and de Fontenay and Gans (2005) all demonstrate how private information may give rise to secret discounting. In contrast, one of the central results of McAfee and Schwartz (1994) [hereafter MS] was to demonstrate how a similar outcome could occur even with perfect information; a particularly strong challenge to Chicago School presumptions.
The result that arms-length vertical contracting may not maximise industry profits has, of course, motivated analyses of alternative practices that could achieve this. For instance, vertical integration allows the downstream externalities to be partially internalised by the upstream firm (Hart and Tirole, 1990) while exclusive dealing may directly reduce downstream competition (Rey and Tirole (2003)).
Here we demonstrate, however, that efficiency in the complete information variant explored by MS may be more easily achieved. We reconsider an implicit but, it turns out, far from innocuous assumption that downstream firms must pay fixed fees upfront (prior to learning information about the contract terms of others). We demonstrate that an upstream firm has an incentive to make such fees optional, thus, providing a means for downstream firms to back out of contracts if they have been the victim of opportunistic behaviour. This, in turn, removes the upstream firm's incentive to act opportunistically; restoring efficiency. The simplicity and the realistic nature of optional fees lead us to conclude that imperfect information or downstream bargaining power are necessary ingredients to motivate inefficiencies in vertical contracting.
Section snippets
Model set-up
We consider the environment of MS where an input monopolist faces n (> 1) competing downstream firms that can use that input. The monopolist has no fixed costs and a constant marginal cost, z > 0. To firm i, the monopolist offers a two part tariff, Ti(q) = fi + riqi where fi is the fixed fee, and ri is the unit price. Interestingly, McAfee and Schwartz (1994) impose a requirement that the fixed fee is upfront. That is, as soon as a downstream firm accepts a supply contract, it is liable for the fixed
Upfront fees
To build intuition, we begin with the case of MS where the monopolist is constrained to set Ti(0) = fi for all i. In this case, they find that there is no equilibrium that achieves a payoff to the monopolist of G* ≡ maxrΠ(r) where r is the vector of all marginal prices and:
The reason is simple: let ri* be the marginal price to i and r− i* the vector of marginal prices to firms other than i consistent with achieving G*. Suppose that the monopolist had offered and had
Optional fees
Now consider the polar case where the monopolist cannot charge an upfront fee so that Ti(0) = 0. In this case, when it comes to offering firm n a lower marginal price, this will at least be another downstream firm to make a loss if they choose qi > 0. As such, assuming only one downstream firm 1 chooses to become inactive, the monopolist will earn (ignoring the possibility that (rn > rn*)):
Conclusion and future directions
Recent analyses of inefficiency in vertical contracting have involved models with imperfect and perfect information. The perfect information stream—where firms are assumed to learn each other's marginal costs prior to choosing production levels—has received additional attention as it is the natural setting to consider the role of facilitating practices such as non-discrimination clauses. The efficacy of such practices is an unresolved issue in the literature (Marx and Shaffer, 2004a).
This paper
Acknowledgement
We thank Stephen King, Leslie Marx and Martin Byford for helpful discussions and comments. Of course, responsibility for all errors lies with the authors.
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