Pouring cold water on the waterbed effect

Impossibility in the baseline Hotelling model

This week’s newsletter originally appeared on Truth on the Market, a website full of scholarly commentary on law, economics, and more.

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A familiar concern in antitrust-adjacent debates goes like this: when a company such as Walmart grows large enough, it can strong-arm suppliers into steep discounts. Suppliers, in turn, recoup those lost margins by charging smaller grocery stores more. Those smaller stores raise prices. The big chain’s gains come at everyone else’s expense—prices fall on one end because they rise on the other. That’s the “waterbed effect.”

It’s a—maybe not compelling—but a story. A 2023 New York Times op-ed argued that this mechanism drives high grocery prices, noting that “as suppliers cut special deals for Walmart and other large chains, they make up for the lost revenue by charging smaller retailers even more, something economists refer to as the water bed effect.” The Organisation for Economic Co-operation and Development (OECD) has raised concerns about it for years. The United Kingdom’s Competition Commission has investigated it.

Regulators that have actually examined the waterbed effect tend to be skeptical. In its 2008 groceries investigation, the UK Competition Commission considered the theory and declined to rely on it, finding the evidence insufficient. Two years earlier, the UK Office of Fair Trading concluded that “there are theoretical questions that would need to be resolved before concluding that the price differentials observed are evidence of a waterbed effect.” As Eric Fruits put it on this blog, the waterbed was a notion without a model—and without a model, it was headed the same way as the real-world waterbed.

Then it got a model.

In 2011, Roman Inderst and Tommaso Valletti published a paper in the Journal of Industrial Economics that gave the waterbed a formal theoretical foundation. Their model features a supplier selling to a large buyer and smaller rivals. The large buyer’s scale gives it bargaining leverage, so the supplier compensates by charging the smaller rivals more. In the model, that is exactly what happens: the large buyer pays less, and the smaller rivals pay more. That result is straightforward.

The paper goes further. It claims the waterbed harms consumers—not just smaller firms, but shoppers at the checkout, who face higher prices on average. That is the result that matters for antitrust, which turns on consumer harm. It is also how the authors close their abstract.

I have a new working paper that shows consumer harm is impossible in their model, which is a Hotelling model. Seems relevant to the discourse? So let me explain.

The Waterbed Breaks Before Consumers Do

The waterbed operates through the small firm’s wholesale price. More precisely, it does not turn on the supplier needing to “make up” lost profits. It turns on bargaining. Once the small firm faces a lower-cost rival, its bargaining position with the supplier weakens, and the supplier can charge it more.

But the small firm is not captive. It can reject the offer and source inputs elsewhere. The supplier may want to squeeze harder, but push too far and the small firm walks.

For the waterbed to harm consumers overall, the squeeze has to be extreme. The small firm’s retail-price increase must outweigh the large firm’s price decrease. The walk-away option blocks that outcome. The supplier hits a ceiling before the waterbed grows strong enough to raise average prices.

In the Inderst and Valletti model, these forces pull in opposite directions. The small firm’s cost disadvantage must stay limited so the firm prefers the supplier’s deal over walking away—that is what keeps the waterbed in place. But consumer harm requires a large enough disadvantage that the small firm’s price increase swamps the large firm’s decrease. The first constraint caps the disadvantage below what the second requires. The waterbed and consumer harm cannot coexist.

This is not a math error. Inderst and Valletti’s consumer-harm result takes the form of an if-then: if a certain condition holds, then consumers are worse off. The logic is sound. The condition never holds. No equilibrium in the model satisfies the “if.” Nowhere in their model does the waterbed harm consumers.

The wholesale waterbed is real in their setup. Large buyers pay less, and smaller rivals pay more. The model even allows the small firm to raise its retail price—despite competing against a lower-cost rival, it still chooses to do so.

You can call that a waterbed. But a higher price at the small firm is not the same as consumers being worse off.

The Policy That Outruns Its Math

A throwaway line in a 15-year-old paper would not usually matter. This one does. The waterbed effect has hovered over antitrust for two decades. As Eric Fruits has noted on this blog in the context of the proposed Kroger-Albertsons merger, it surfaces in merger review and policy debates. It came up repeatedly in congressional hearings on that deal.

Its largest policy footprint may be the push to revive the Robinson-Patman Act. The RPA prohibits suppliers from charging competing buyers different prices for the same goods. That is the waterbed: a supplier charges Walmart less and the corner grocery more. If that price discrimination harms consumers, you have a consumer-welfare case for enforcement.

The logic chain runs like this: the waterbed harms consumers; supplier price discrimination is the mechanism; RPA enforcement is the fix. If the waterbed does not harm consumers in the very model that supplies its theoretical foundation, the first link in the chain breaks. What remains is a statute that bars supplier discounts to large buyers without a consumer-welfare rationale. As Alden Abbott has argued, reinvigorated RPA enforcement risks raising prices for the consumers it is supposed to protect.

None of this proves the waterbed could never harm consumers. A different model, with different assumptions, might get there. You could all a simple price discrimination model that raises average prices “waterbed” if you want.

The point is narrower. The specific claim that this model—the one people cite—shows consumer harm does not hold. The general idea that there is this tension in waterbed-type effects between squeezing retailers and them also being able to exit is hard to avoid. Hard is not impossible.