Abstract
Policy authorities are pushing non-equilibrium arguments (“untethered vertical math,” or “UVM”) to challenge vertical mergers. The typical UVM argument: if the merging upstream firm has a dominant market share but a low profit share, it has (1) the power to foreclose, and (2) the incentive to foreclose because the profit lost from foreclosing downstream rivals is low relative to the profit gained from the induced diversion to the merged downstream division. The flaw in this logic, analogous to flaws exposed in the Lucas Critique, is that it does not consider how rival suppliers and downstream buyers respond to the foreclosure attempt. Logically, a low upstream profit share is direct evidence that downstream buyers would respond to foreclosure by purchasing substantially less from the dominant supplier (presumably more from rivals), otherwise the dominant supplier would have raised the pre-merger price. We modify standard foreclosure analysis to account for these responses. Using equilibrium relationships, we “tether” the departure rate—the rate at which sales of foreclosed firms depart in response to foreclosure—to pre-merger observables. The tethered departure rate is decreasing in the merging supplier’s market share and may increase or decrease with its profit share, undermining UVM logic. We use our approach to provide necessary and sufficient conditions for profitable foreclosure that depend on the upstream profit share, the dominant firm’s market share, the input and final product diversion ratios, and pass-through rates.
Available here: https://ssrn.com/abstract=4726861.