Integration of Complementary Multiproduct Firms

Hao Wang

doi:10.1515/rle-2020-0058

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Integration of Complementary Multiproduct Firms

Hao Wang

Veröffentlicht/Copyright: 4. November 2021

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Aus der Zeitschrift Review of Law & Economics Band 17 Heft 3

Abstract

Two firms offer product series from which multiple complementary pairs are formed. The firms engage in a price- or quantity-choosing game in the market. It is found that the integration of the two firms may not necessarily lower the equilibrium prices because it precludes “indirect competition” in the market. Therefore, the integration, which may appear as a vertical integration, could be an antitrust concern even in the absence of exclusionary purpose.

Keywords: antitrust; complement products; integration; multiproduct

JEL Codes: L1; L4

Corresponding author: Hao Wang, China Center for Economic Research, National School of Development, Peking University, Beijing 100871, China, E-mail: hwang@nsd.pku.edu.cn

Funding source: Ministry of Education of China

Award Identifier / Grant number: 16JJD790002

Appendix A. Market Outcomes of the Quantity-Choosing Games

In the case of a quantity-choosing game, the (symmetric and linear) inverse demands for the products can be represented by:

(16) p e q e , q E , q f , q F = B − η q e + κ q E − λ q f − μ q F ,

(17) p E q e , q E , q f , q F = B − η q E + κ q e − λ q F − μ q f ,

(18) p f q e , q E , q f , q F = B − η q f + κ q F − λ q e − μ q E ,

(19) p F q e , q E , q f , q F = B − η q F + κ q f − λ q E − μ q e ,

with B > 0, η ≥ 0, κ ≥ 0, and λ ≥ 0, but the sign of μ not definite. The costs of production are still assumed to be zero. The product relationships are shown in Figure 2.

Figure 2:

Product relationships (quantity-choosing game).

It can be checked that integration of the upstream firm U and downstream firm D lowers the equilibrium prices (i.e., p i U = p i D > p i I ) if and only if κ − μ > 0. The previous proposition still holds. Again, the integration strictly increases the industrial profits as long as κ − μ ≠ 0. In the parallel horizontal integration, the profits of the firms are

(20) π U = q e p e q e , q E , q f , q F + q f p f q e , q E , q f , q F ,

(21) π D = q E p E q e , q E , q f , q F + q F p F q e , q E , q f , q F .

The equilibrium outcome is

(22) q e U = q E D = q f U = q F D = B 2 η − κ + 2 λ + μ ,

(23) p e U = p E D = p f U = p F D = η + λ B 2 η − κ + 2 λ + μ ,

(24) π U = π D = 2 η + λ B 2 2 η − κ + 2 λ + μ 2 .

If the two firms integrate into a monopolist, the merged firm’s profits are

(25) π I = q e p e + q E p E + q f p f + q F p F .

The equilibrium outcome is

(26) q e I = q E I = q f I = q F I = B 2 η − 2 κ + 2 λ + 2 μ ,

(27) p e I = p E I = p f I = p F I = B 2 ,

(28) π I = B 2 η − κ + λ + μ .

Therefore, the integration lowers the equilibrium prices (i.e., p i U = p i D > p i I ) if and only if κ − μ > 0, and the integration strictly increases industrial profits as long as κ − μ ≠ 0.

References

Allain, M., Chambolle, C., and Rey, P. (2016). Vertical integration as a source of hold-up. Rev. Econ. Stud. 83: 1–25. https://doi.org/10.1093/restud/rdv035.Suche in Google Scholar

Bonanno, G. and Vickers, J. (1988). Vertical separation. J. Ind. Econ. 36: 257–265. https://doi.org/10.2307/2098466.Suche in Google Scholar

Chen, Y. (2001). On vertical mergers and their competitive effects. Rand J. Econ. 32: 667–685. https://doi.org/10.2307/2696387.Suche in Google Scholar

Chen, Y. and Riordan, M. (2007). Vertical integration, exclusive dealing, and ex post cartelization. Rand J. Econ. 38: 1–21. https://doi.org/10.1111/j.1756-2171.2007.tb00041.x.Suche in Google Scholar

Choi, J. (2008). Mergers with bundling in complementary markets. J. Ind. Econ. 56: 553–577. https://doi.org/10.1111/j.1467-6451.2008.00352.x.Suche in Google Scholar

Choi, J. and Yi, S. (2000). Vertical foreclosure with the choice of input specifications. Rand J. Econ. 31: 717–743. https://doi.org/10.2307/2696356.Suche in Google Scholar

Cournot, A. (1838). Recherches sur les principes mathematiques de la theorie des richesses. Paris, France: Hachette (English translation by N. Bacon in Economic Classics, New York: Macmillan, 1897).Suche in Google Scholar

Economides, N. and Salop, S. (1992). Competition and integration among complements, and network market structure. J. Ind. Econ. 40: 105–123. https://doi.org/10.2307/2950629.Suche in Google Scholar

Edgeworth, F. (1925). The pure theory of monopoly. In: Papers relating to political economy, Vol. 1. Burt Franklin, New York.Suche in Google Scholar

Grant, J. and Neven, D. (2005). The attempted merger between general electric and Honeywell: a case study of transatlantic conflict. J. Compet. Law Econ. 1: 595–633. https://doi.org/10.1093/joclec/nhi019.Suche in Google Scholar

Nocke, V. and Rey, P. (2018). Exclusive dealing and vertical integration in interlocking relationships. J. Econ. Theor. 177: 183–221. https://doi.org/10.1016/j.jet.2018.06.003.Suche in Google Scholar

Nocke, V. and White, L. (2007). Do vertical mergers facilitate upstream collusion? Am. Econ. Rev. 97: 1321–1339. https://doi.org/10.1257/aer.97.4.1321.Suche in Google Scholar

Normann, H. (2009). Vertical integration, raising rivals’ costs and upstream collusion. Eur. Econ. Rev. 53: 461–480. https://doi.org/10.1016/j.euroecorev.2008.09.003.Suche in Google Scholar

Ordover, J., Saloner, G., and Salop, S. (1990). Equilibrium vertical foreclosure. Am. Econ. Rev. 80: 127–142.Suche in Google Scholar

Rey, P. and Stiglitz, J. (1988). Vertical restraints and producers’ competition. Eur. Econ. Rev. 32: 561–568. https://doi.org/10.1016/0014-2921(88)90203-6.Suche in Google Scholar

Rey, P. and Stiglitz, J. (1995). The role of exclusive territories in producers’ competition. Rand J. Econ. 26: 431–451. https://doi.org/10.2307/2555997.Suche in Google Scholar

Riordan, M. (1998). Anticompetitive vertical integration by a dominant firm. Am. Econ. Rev. 88: 1232–1248.Suche in Google Scholar

Riordan, M. and Salop, S. (1995). Evaluating vertical mergers: a post-chicago approach. Antitrust Law J. 63: 513–568.Suche in Google Scholar

Salinger, M. (1991). Vertical mergers in multi-product industries and Edgeworth’s paradox of taxation. J. Ind. Econ. 39: 545–556. https://doi.org/10.2307/2098460.Suche in Google Scholar

Salop, S. and Scheffman, D. (1987). Cost-raising strategies. J. Ind. Econ. 36: 19–34. https://doi.org/10.2307/2098594.Suche in Google Scholar

Spengler, J. (1950). Vertical integration and antitrust policy. J. Polit. Econ. 58: 347–352. https://doi.org/10.1086/256964.Suche in Google Scholar

Received: 2020-11-04

Revised: 2021-09-16

Accepted: 2021-09-16

Published Online: 2021-11-04

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Artikel in diesem Heft

https://doi.org/10.1515/rle-2020-0058

Schlagwörter für diesen Artikel

antitrust; complement products; integration; multiproduct