Are Loyalty Discounts Really Anticompetitive?

Josh Wright —  11 June 2008

I promised that I would write about why I think that Professor Elhauge’s claim in his new working paper, “Loyalty Discounts and Naked Exclusion,” that he has proven that loyalty discounts generally involve anticompetitive effects is mistaken. Let me begin by saying that this is a very provocative claim from a very serious antitrust analyst and deserves careful attention. Loyalty discounts are an important and highly controversial issue in antitrust at the moment and so economic analysis that enlightens us to their effects in the marketplace should be applauded. I should also note, as I made clear in the first post, that I admire Elhauge’s work and have a great deal of respect for him. Obviously, with that many caveats, you know what is coming next. I strongly disagree that Elhauge’s economic analysis lives up to his claims. First, here’s an excerpt from the abstract:

This article proves that loyalty discounts create anticompetitive effects, not only because they can impair rival efficiency, but because loyalty discounts perversely discourage discounting even when they have no effect on rival efficiency. The essential reason, missed in prior work, is that firms using loyalty discounts have less incentive to compete for free buyers, because any price reduction to win sales to free buyers will, given the loyalty discount, also lower prices to loyal buyers. This in turn reduces the incentive of rivals to cut prices, because there will exist an above-cost price that rivals can charge to free buyers without being undercut by the firm using loyalty discounts. These anticompetitive effects occur even if buyers can breach or terminate commitments, and even if the loyalty conditions require no contractual commitments and less than 100% loyalty. Further, I prove that these anticompetitive effects are exacerbated if multiple sellers use loyalty discounts. None of the results depend on switching costs, market differentiation, imperfect competition, or the loyalty discount bundling contestable and incontestable demand. Contrary to commonly held views, I prove these anticompetitive effects exist even when: (1) the price with the loyalty discount is above cost, (2) the rival has higher costs than the firm using loyalty discounts, (3) the rival prices above its own costs, (4) buyers voluntarily agree to the conditions, and (5) the discount and foreclosure levels are low. I derive formulas for calculating the inflated price levels in each situation.

In short, Elhauge claims that he has proven that loyalty discounts always or at least generally have anticompetitive effects. I don’t think he has. In fact, I don’t think the paper is really about loyalty discounts at all. And it certainly isn’t about “naked exclusion” as the title implies. I offer a somewhat lengthy critique of the economic analysis in the paper below the fold.

When I first saw Professor Elhauge’s paper claiming that loyalty discounts are generally anticompetitive, I was quite skeptical for several reasons. It is not that I do not accept the proposition that discounting practices can never be anticompetitive or exclude rivals and create market power. Anticompetitive equilbria under these types of contracts certainly exist. Indeed, there is a published academic literature on the possibility of loyalty discounts resulting in competitive harm that Elhauge curiously does not discuss. (See, e.g. Kolay, Shaffer and Ordover (2004); Greenlee & Reitman (2005) or Kobayashi (2005) for a survey of the literature). As a policy matter, I accept these possibility theorems as demonstrating that exclusionary contracts and loyalty discounts can generate anticompetitive effects under some possible set of conditions. It is an empirical question as to whether these conditions are satisfied in real world markets and whether these anticompetitive theories explain the use of the contracts in question. My answer, based on the existing theoretical and empirical literature, and a respect for the social costs associated with getting it wrong, is that the appropriate approach is for antitrust enforcement to be extremely cautious about attacking discounting behavior. Somewhat curiously, Professor Elhauge essentially agreed with this restrained approach in his well known Yale Law Journal article on above-cost predation.

But back to loyalty discounts and my skepticism about Elhauge’s claim that they generate anticompetitive effects under general conditions. Consider the following: the extreme case of a loyalty discount is when the firm sets the threshold to achieve the discount to 100% the buyer’s purchases. In this case, the loyalty discount = de facto exclusive dealing. And we know something about exclusive dealing in the economics literature. Namely, we know that exclusive dealing can be pro-competitive and use of exclusive dealing contracts can intensify manufacturer competition for distribution and result in lower equilibrium prices. (See, e.g. Mathewson & Winter (1987); Klein & Murphy (2008)).

So if in the extreme case loyalty discounts are like exclusive dealing, which certainly can be pro-competitive, and Elhauge is purporting to demonstrate that loyalty discounts generally (not just the extreme case) create this significant incentive to increase price which everybody has missed under all sorts of conditions and without foreclosure, my preliminary reaction was that something funny must be going on in the model.

I think I’m right. Something funny is going on. Specifically, Professor Elhauge’s model isn’t really about loyalty discounts. It isn’t about exclusive dealing either. Its about Most-Favored Nation (MFN) clauses. Let me explain while trying to avoid getting into the technical details of the proofs.

What Professor Elhauge is modeling here is the case where the incumbent offers contracts to loyal and non-loyal buyers of the form P-d where P = list price and d = discount. The key economic insight in the model is that any reduction in P changes the price to both the “loyal” guys (who get the discount) and the uncommitted buyers (who don’t). In other words, once the firm selects a P and a d and offers the contract to a bunch of customers, any reduction of P lowers the price to everybody (loyal customers and uncommitted buyers who don’t get the discount). It is this mechanism that generates the disincentive to lower price in Professor Elhauge’s Proposition 1 (on page 6).

So far so good. But there are some important points to make about what is going on in the model here to result in these higher prices. The first is the Elhauge’s model restricts the firm from offering the same contract to all buyers rather than on a customer-by-customer basis. As I understand loyalty discounts in practice, and in the published cases, the point is to offer discounts to different buyers. But it is important to recognize that the assumption that the seller can only offer the same contract to all buyers is driving the disincentive to reduce prices.

The second point to recognize is that the anticompetitive mechanism really doesn’t depend on the loyalty discount at all! Something else is going on. Elhauge writes:

“Strikingly, anticompetitive prices results even if the discount level is zero, which would be true if a particular loyalty discount did not assure any particular gap between committed and uncommitted prices, but simply guaranteed that the user would never charge committed buyers more than uncommitted buyers. Then the rival will charge Pr* = Pm – [(1-?)((Pm-C)2]½ = (1- (1-?)½)Pm + (1-?)½C, which always exceeds competitive level C if Pm > C. The reason for this result is that even this weak assurance to committed buyers means that the user will lose profits from the committed buyers if it cuts prices below this level to match the rival on uncommitted buyers.”

Ok. This is where the Most-Favored Nation clause point comes in. First, this anticompetitive effect depends on some sort of mechanism to constrain firms to reduce prices to all buyers or none at all. One way to do this is by assumption (see above), constraining the firm to offer the same contract to both loyal and uncommitted buyers. A second way is to do so contractually with a MFN clause. This appears to be what Elhauge is getting at in the passage above. The problem is that, again, the anticompetitive mechanism explicitly has nothing to do with the loyalty discount and everything to do with the MFN clause facilitating softening of price competition. A second problem is that, as an empirical matter, I’m not aware of any loyalty discount cases in the antitrust world involving such contractual provisions. This second problem is especially important given that Elhauge takes to task previous authors to task for creating models that involve sellers offering contracts that “one does not often observe in the real world.” This is a strange criticism to level given the assumptions in Elhauge’s model.

What is left is the observation that loyalty discounts that artificially restrict the seller from offering different contracts to different buyers (which we do not observe in the real world so far as I know and I’ve been presented no evidence to convince me that they exist) OR MFN clauses (which do exist) can cause an effective market division resulting in higher “collusive-like” prices above the competitive level. Because these are collusive-type mechanisms, they do not depend on foreclosure share or the size of the discount. Fair enough.

It is true that Professor Elhauge has demonstrated that some contracts involving loyalty discounts can be part of an anticompetitive equilibrium. But the mechanism in the model creating higher prices has very little to do with loyalty discounts as they are observed in the real world or even in the antitrust literature. Elhauge has shown that MFN clauses can, at least under certain conditions, facilitate collusive equilibria and result in anticompetitive effects. However, this point has long been understood in the industrial organization literature beginning with Salop (1986) who demonstrated that MFN clauses might make price reductions more costly by ensuring that those reductions must be given to all customers. Of course, this is not to say MFN clauses are “generally” anticompetitive. There is no evidence that they are always or even usually increase prices, and they can be efficient (see Crocker & Lyon (1994)).

At the end of the day, my conclusion is that Elhauge’s economic analysis cannot live up to the aggressive and provocative claims in the paper.


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  1. TRUTH ON THE MARKET » Daubert and Antitrust Economics, Or When Should An Antitrust Economist Have Training in Economics? - December 22, 2009

    […] ourselves on some of Professor Elhauge’s views on the related topic of loyalty discounts here.  If you’d like to get caught fully up to speed, read the briefs.  I’ll start you off […]