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Review of Industrial Organization

13-02-2023

Simulating Vertical Mergers

Published in: Review of Industrial Organization | Issue 2/2023

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Abstract

We study the effects of a vertical merger in a standard setting with a single upstream supplier of a critical input and two downstream customers that compete with each other. Initially, the upstream supplier first announces prices, then the two downstream customers announce their retail prices. We show that this pre-merger timing does not survive a vertical merger. The merged firm may choose to be either a first mover or a second mover in the post-merger pricing game with its unintegrated rival. Our results suggest that a vertical merger is unlikely to lead to a significant upstream price increase unless the downstream firm involved in the merger is relatively large. In such a case, an upstream price increase is to be expected. For vertical mergers involving a large downstream firm, in most simulations the merged firm reduces its downstream price. Its rival often increases its price. In all simulations, the rival is caught in a price squeeze. This calls into question the rival’s long-term viability.

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Appendix
Available only for authorised users
Footnotes
1
See Slade (2021) for a good summary of these views.
 
2
Note that Chen’s model depends on there being at least two upstream firms, with downstream firms incurring switching costs when changing upstream suppliers.
 
3
United States v. AT&T, Inc. (2018) and United States v. AT&T, Inc. (2019).
 
4
New York v. Deutsche Telekom AG (2019). One of the authors (Sibley) advised the FCC on its analysis of the merger.
 
5
See Slade (2021) and Beck and Scott Morton (2021).
 
6
Prominent examples are Ordover et al. (1990), Salinger (1988), and Chen (2001).
 
7
For the use of the vGUPPI in the T-Mobile–Sprint merger analysis, see Israel et al. (2019), paragraphs 16–20.
 
8
See Rogerson (2020) for the overview of the standard assumptions in vertical mergers.
 
9
This statement is based on the authors’ experience analyzing vertical pricing in the antitrust context.
 
10
We are grateful to the Editor for pushing us in the direction of Theorem 1.
 
11
The reader may consider the possibility that Firm 1 tires of waiting and announces \(P_1\) before Firm 2 announces \(P_2\). Although this is hypothetically possible, it will not occur in equilibrium. This is because Firm 1 always has the option to be a first mover by announcing \(\left( w_2,P_1\right)\) simultaneously. For it to wait some period of time and then be a first mover is inferior to doing so at once. Therefore, in equilibrium it will not occur.
 
12
See “Appendix 1”.
 
13
We did not exclude any observations based on negative profits.
 
14
Lu et al. (2007) show that \(w_2\) will not change in a linear symmetric model.
 
15
Because we assume linear demand curves, the Das Varma and De Stefano (2020) results imply that Firm 2’s post-merger demand curve is more price elastic than is true pre-merger. This effect would also lead to decreases in \(w_2\).
 
16
To be sure, we do not model entry or exit in this paper. However, to do so would not be hard. Suppose, for example, that to begin with there is no Firm 2. In this setting, the only impact of the vertical merger is to solve the double markup problem. However, suppose that there is a potential entrant—Firm 2—and that there is a sunk cost of entry. If Firm 2 were to enter, the merged firm would react in the way we have described. If there is a sufficiently large sunk cost of entry, then entry will be deterred.
 
17
The informed reader will note that our results differ from those implied by the vGUPPI approach to vertical merger analysis. See Moresi and Salop (2013). We discuss this further in Sect. 4.
 
18
We are grateful to a referee for suggesting that we do this.
 
19
The result with \(^{\gamma _1}/_{\gamma _2}=1\) is due to Lu et al. (2007). For a complete analysis, see Das Varma and De Stefano (2020).
 
20
When Firm i increases its price, the diversion ratio from i to j measures the fraction of the resulting lost sales that is diverted to some other Firm j. To be clear: If \(Q_i\left( P_i,P_j\right)\) is the demand curve that faces Firm i and \(Q_j\left( P_i,P_j\right)\) is the demand curve that faces Firm j, then the diversion ratio from i to j is: \(D_{ij}\equiv \frac{\partial Q_j / \partial P_i}{-\partial Q_i / \partial P_i}\).
 
21
We will be happy to provide details to the interested reader.
 
22
See “Appendix 1”.
 
23
Note that these criteria differ from those that are used in the linear case: non-negativity requirements. This is because negative prices and quantities do not arise in logit models.
 
24
In fact, some of the simulations show small decreases in \(w_2\). This is obscured in Fig. 3b by the scaling of the vertical axis.
 
25
The vGUPPI was first developed by Moresi and Salop (2013).
 
26
This does not apply to the BLR index that was proposed by Rogerson (2020), which we have not analyzed.
 
27
In a previous version of this paper, we focused on the numerical accuracy of the vGUPPI upstream and downstream indices in the linear case. We found that the downstream vGUPPI correctly predicted a fall in \(P_1\) 82% of the simulations. As expected, the upstream vGUPPI index had no predictive ability; it always predicted increases.
 
28
See equation (4) in Moresi and Salop (2013).
 
29
The source code is available upon request.
 
Literature
Cournot, A. A. (1838). Recherches sur les principes mathématiques de la théorie des richesses. L. Hachette.
Israel, M., Katz, M., & Keating, B. (2019). Declaration of Compass Lexecon. Joint Opposition of T-Mobile US, Inc. and Sprint Corporation.
Lu, S., Moresi, S., & Salop, S. (2007). A note on vertical mergers with an upstream monopolist: Foreclosure and consumer welfare effects. Charles River Associates, Georgetown University Law Center.
Moresi, S., & Salop, S. C. (2013). vGUPPI: Scoring unilateral pricing incentives in vertical mergers. Antitrust Law Journal, 79(1), 185–214.
New York v. Deutsche Telekom AG. 419 F. Supp. 3d 783 (S.D.N.Y. 2019).
Ordover, J. A., Saloner, G., & Salop, S. C. (1990). Equilibrium vertical foreclosure. The American Economic Review, 80(1), 127–142.
U.S. Department of Justice, & Federal Trade Commission. (2020). Draft vertical merger guidelines (Technical Report). DOJ, FTC.
United States v. AT&T, Inc. 916 F.3d 1029 (D.C. Cir. 2019).
United States v. AT&T Inc. 310 F. Supp. 3d 161 (D.D.C. 2018).
Warren-Boulton, F. R. (1974). Vertical control with variable proportions. Journal of Political Economy, 82(4), 783–802.CrossRef
Metadata
Title
Simulating Vertical Mergers
Publication date
13-02-2023
Published in
Review of Industrial Organization / Issue 2/2023
Print ISSN: 0889-938X
Electronic ISSN: 1573-7160
DOI
https://doi.org/10.1007/s11151-023-09896-z