Review of Industrial Organization 17: 277–284, 2000. © 2000 Kluwer Academic Publishers. Printed in the Netherlands.
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Cournot Oligopoly Conditions under which Any Horizontal Merger Is Profitable DAVID A. HENNESSY? Department of Economics, Iowa State University, Ames, Iowa 50011-1070, U.S.A.
Abstract. Findings in economic theory suggest that horizontal mergers involving firms with aggregate market share less than 50% are unlikely to be motivated by the consequent reduction in competitivity. The results arise because, absent cost efficiencies, quantity-setting firms in small mergers are impoverished by the merger. We demonstrate that this conclusion is a consequence of the strong restrictions imposed on the demand function, and we identify a well-behaved demand function such that any set of merging firms benefits from the reduction in competition even when there are no cost efficiencies. Key words: Demand function, endogenous merger, equilibrium, market power. JEL Classifications: D43, L13, L40.
I. Introduction Evolving market environments provide new impetus for industry re-organization and so determine the nature of decisions to be made by the overseers of competition policy. Recent trends in market conditions suggest that horizontal merger policy will not recede in importance during the first decades of the 21st century. Within the U.S.A., telecommunications markets have consolidated while the pace of bank amalgamations has also accelerated since passage of the Interstate Banking and Branching Efficiency Act of 1994. Impending nationwide competition in electricity production and distribution may transform the oversight problem in that industry from regulated monopoly to keenly watched oligopoly. The single market program in the European Union is posing similar problems as national standard bearers in the provision of electricity, gas, water, and telecommunications respond to market competition. Increasingly, alignments are of a transnational or even global concern. For example, the Boeing acquisition of McDonald-Douglas had to pass a review by the European Commission even though neither firm was incorporated in the European Union. Also, international telecommunications and airline markets seem set to become dominated by four or five major alliances. ? Phone: (515) 294-6740, Fax: (515) 294-0221, E-mail:
[email protected] The paper has
benefited from helpful comments by John Schroeter.
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In other ways, innovations in communications may reduce the number of players in large markets to a few in number. The large fixed costs and constant marginal costs that may represent the cost structures of Internet-based firms may reduce the number of online retailers in the travel agency, auto-trade, print, music, and stock brokerage sectors to a few significant firms in large, perhaps global, markets. When viewed together, innovations, deregulation, and globalization suggest that horizontal merger laws may have to be substantially re-written or re-interpreted. But doing so may not be easy. There are at least two reasons why difficulties may arise in legislative adjustments. First, merger policy tends to possess inertia while enforcement depends upon the will of politicians. In the U.S., the 1890 Sherman Act was passed with intent to discourage industrial combinations. But in the eyes of Scherer and Ross (1990), it was to be a decade before a President seriously enforced the anti-merger provisions when Theodore Roosevelt derailed a railroad merger. Recognizing that the Sherman Act did not prohibit all mergers that were considered to substantially lessen competition, the U.S. Congress passed the Clayton Act in 1914. But while this act did not allow horizontal mergers that substantially lessened competition, horizontally competing firms could effectively merge by trading assets. In 1950, the Celler-Kefauver Act finally plugged this obvious escape clause. Concerning the acquisitions Section in Clayton, the minority opinion on United States vs. du Pont (1957) asserted that a consequence of the Celler-Kefauver legislation was that “. . . over 40 years after the enactment of the Clayton Act, it now becomes apparent for the first time that Section 7 has been a sleeping giant all along”. Audretsch (1983), among others, documents how the Celler-Kefauver amendments appear to have altered the nature of merger activity towards conglomerate rather than horizontal mergers. A second reason why problems may arise is that market definition is usually problematic, and so disagreement is likely concerning the degree of post-merger concentration. The benchmark 1,800 Herfindahl-Hirshman Index (HHI) value suggests that U.S. competition authorities are prepared to tolerate five equally sized firms in a market, and the minimum number should increase as the dispersion of market share increases. As reported in Shepherd (1997), many commentators concur with the proximate number five. Porter (1990) expressed the opinion that several large economies had become too lax in refusing to block horizontal mergers. But of course market concentration policy can be wise only to the extent that the market can be defined in the first place. Kaserman and Zeisel (1996), and also Glick et al. (1997), have delineated some problems with existing methods for defining the market. Essentially, market bounds are diffuse. Adherence to the notion of well-defined bounds is a convenience maintained in order to facilitate understanding, communication, and regulation. In recent years, a literature on endogenous mergers has arisen. Game theoretic in flavor, this research suggests that regulators seeking to maximize social welfare ought not be concerned about mergers involving less than 50% of market share
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because these are unlikely to enhance post-merger profitability unless cost reductions are sufficiently large to improve social welfare. These results are, of course, predicated upon several assumptions including those of pre- and post-merger profit maximization. In the main, Cournot price-dependent inter-firm interactions are assumed. The endogenous merger literature will be discussed in more detail in Section II. The Chicago school of economic thought is largely skeptical about the existence of tacit collusion as embodied in Cournot-type pricing behavior, and so would be inclined to allow more concentration than the five firm benchmark. In particular, Posner (1976, Chapter 4) and Bork (1978, p. 175) suggest that the profit opportunities from breach of any tacit agreement by pricing at marginal cost will likely be too large to ignore unless there is a formal agreement to collude. The endogenous merger literature accepts the notion of tacit collusion, and yet suggests the same policy conclusion: Mergers are not a concern unless the HHI value is well in excess of 1,800. Together, the lines of thought suggest that regardless of one’s opinions on tacit collusion, if there is little evidence to suggest an environment conducive to formal collusion then it is best to prohibit only mergers that would give rise to a market structure that is just short of monopoly. The purpose of this note is to suggest that, even if one accepts the other assumptions underlying the endogenous merger literature, the laissez faire implication with regard to horizontal merger policy is not robust with regard to the assumed attributes on demand. In particular, for Cournot-type interactions we demonstrate that plausible firm-level cost functions and industry-level demand functions exist such that any horizontal merger reduces consumer welfare. Thus, if tacit collusion reflects actual market behavior then it is necessary to be quite precise about the nature of demand before one can advocate a relaxed horizontal merger policy. After a brief review of the literature on endogenous horizontal mergers, our analysis identifies a demand structure such that any horizontal merger is profitable when firm behavior is Cournot before and after mergers. Then monopolization would be inexorable, and market structure will converge to a firm number that is one larger than the largest number the antitrust regulators will not tolerate. The analysis first motivates the nature of the demand function such that market power generated gains from mergers are always positive. Then the existence, stability, and uniqueness of the Cournot equilibrium are considered. We conclude with simulations to ascertain the nature and determinants of private gains from merging.
II. Literature on Horizontal Mergers While useful and not without intuitive appeal, the traditional paradigm whereby market structure implies market conduct which, in turn, implies market performance may have promoted the notion that market structure is by-and-large exogenous. Salant et al. (1983) have challenged the premise by showing that while mergers in a Cournot oligopoly may reduce competition, the merging firms may
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not be the better for the merger. This is because, although the industry profit pie may grow, the merging firms are surrendering seats at the table. Studying a linear demand function when constant, common, marginal costs represent the technology, they show that if less than 80% of firms merge and all firms are Cournot in behavior both before and after the merger, then merging firms would have been better off before the merger. Cheung (1992) assumes that industry revenue is concave in industry output, and concludes that if less than 50% of firms with constant, common, marginal costs merge, then the profitability of that set falls. Levin (1990) also identifies an important role for mergers between a set of firms with aggregate market share of less than 50% of output. He finds that if such a merger is profitable then it would be welfare enhancing. The result cannot be considered jointly with that of Cheung because Levin makes different assumptions on the nature of the demand curve, and he also does not require a firm resulting from a merger to adhere to Cournot behavior. Levin does not answer the question of whether such mergers will be profitable. Kamien and Zang (1990, 1991) introduce strategic richness into the analysis by allowing merged firms to operate units in a decentralized manner so that a merger does not imply the loss of a seat at the table. Their’s are three-stage games where the first stage involves bidding to acquire other firms and where industry revenue is concave in industry output. With and without this strategic capability, Kamien and Zang conclude that significant increases in market power through merger is unlikely to occur. In fact, if the initial number of firms is sufficiently large then a monopoly outcome to the game is impossible. Like Cheung (1992), they assume that industry revenue is concave in industry output. III. Model Following Cheung (1992), Farrell and Shapiro (1990) and others, we assume that all firms in an industry observe Cournot behavior both before and after any merger of m among the n firms. We further assume that marginal costs are constant, at level c, and common among all firms while fixed costs are zero. Under these symmetry conditions, it is well-known that firms which arise from mergers behave in the same way as the firms which do not merge. Denote total industry profit when there are r firms by V (r), and let per firm profit be T (r) = V (r)/r. Then the gain to the merged entity from an m-firm merger is G(m, n) = T (n − m + 1) − mT (n) =
V (n − m + 1) V (n) −m . n−m+1 n
(1)
Were it possible, then an infinitesimal merger would be beneficial if dG(m, n)/dm > 0 when evaluated at m = 1. That is, −T 0 (n − m + 1)|m=1 − T (n) > 0,
(2)
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where the prime indicates a differentiation and the subscripted vertical bar provides the point of evaluation. Were the inequality an equality, then the solution would be of the form T (n) = A e−k(n−m+1) with A being some positive constant of integration and k = 1. This provides the starting point for our analysis. Turning to the n-firm Cournot oligopolyPmodel where firm j produces xj , for the inverse demand function P (X), X = nj=1 xj , symmetry requires that each optimum satisfies P (X) + xj P 0 (X) = c.
(3)
With reference to the expression for T (n), set P (X) = A e−λX where we assume that A > c so that positive industry profit is feasible. When c = 0, condition (3) solves as xj = 1/λ, ∀j ∈ {1, 2, . . ., n}. For future reference, when we will permit c 6 = 0, we describe the symmetric n-firm optimum choice by x(n, c). For the demand function in question, the requirement that the private gains from the merger be positive is given by the condition G(m, n) = x(n − m + 1, c){A e−λ(n−m+1)x(n−m+1,c) − c} − mx(n, c){A e−λnx(n,c) − c} > 0.
(4)
When c = 0, the inequality reduces to em−1 > m. Expanding, we have em−1 − m =
(m − 1)2 (m − 1)3 + + ··· > 0 2! 3!
(5)
for m > 1. So, notwithstanding invariance to an infinitesimal merger [Limm↓1 G(m, n) = 0], there are private gains to horizontal mergers regardless of the number of firms, n, the number of merging firms, m > 1, and the demand parameters, A and λ. Further, the gains increase with m. IV. Nature of Equilibrium Issues of concern in Cournot oligopoly analysis are the existence and stability of equilibria. It is shown in an appendix available from the author that a unique equilibrium exists and that this solution is stable under commonly assumed behavior in states of disequilibrium. To characterize the nature of this equilibrium, we will study the solution to (3) for our negative exponential demand specification. If c ≥ 0, then application of the first-order condition yields the straightforward results that an increase in the number of firms causes a nonincreasing shift in firm output and a nondecreasing shift in industry output. It can also be shown that industry output is nonincreasing in the level of marginal costs. Our analysis suggests that if c = 0 then a prohibition on mergers between any set of firms larger than two will not preclude a sequence of myopically profitimproving mergers that will ultimately lead to a monopoly. The problem can be
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Table I. Firm output solutions to L(x) = 0 Number of firms
c = 0.00001
c = 0.0001
c = 0.001
c = 0.01
n=8 n=7 n=6 n=5 n=4 n=3 n=2 n=1
0.977199935 0.989623988 0.996375524 0.998524821 0.999475749 0.999806076 0.999923875 0.999972818
0.8835 0.9322 0.9670 0.9862 0.9947 0.9980 0.9993 0.9997
0.7092 0.7742 0.8429 0.9068 0.9545 0.9810 0.9927 0.9973
0.4912 0.5453 0.6104 0.6881 0.7766 0.8657 0.9351 0.9735
modified so as to allow the results to hold for strictly positive marginal costs by letting P (X) = c + A e−λX . Even with P (X) = A e−λX , it is likely that all mergers are profitable when c is very small. We now investigate the profitability of an infinitesimal merger when c > 0. Differentiating (4) with respect to m, using the first-order condition, evaluating at m = 1, and conducting some simple algebra yields that dG(m, n)/dm|m=1 has the sign of [1 − λx(n, c)]/[1 + n − nλx(n, c)]. Because 1 ≥ λx(n, c), it follows that the only case where an infinitesimal merger does not reduce the profitability of the merged entity is when 1 = λx(n, c), i.e., when c = 0. But in reality, m ≥ 2 and so all mergers may be profitable even if c > 0.
IV. Simulations In our simulations, we will assume the negative exponential form for P (X). Without loss of generality, we set A = λ = 1. Table I presents the x(n, c) solutions to L(x) = e−nx −xe−nx −c = 0 for n ∈ {1, 2, . . ., 8} and for each of c ∈ {0.00001, 0.0001, 0.001, 0.01}. The sensitivities of x(n, c) and nx(n, c) with respect to n and c are as expected. For low c, the impact on x(n, c) is small. Table II presents the values of G(m, 5); that is the change in joint profitability for m merging firms when there are initially five symmetric Cournot firms. Only when c = 0.01 is the two-firm merger unprofitable. All mergers of three or more firms are profitable. Table III presents the values of G(m, 8) for various values of c. Here all mergers are profitable when c ≤ 0.0001. But endogenous mergers between small numbers of firms will not occur at larger values of c. Then merging firms lose seats at the table whereas the gains from reduced competition are shared among all remaining firms.
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Table II. Gains from merging in a five firm industry n=5
c = 0.0001
c = 0.001
c = 0.01
m=2 m=3 m=4 m=5
0.00447 0.02882 0.10725 0.33267
0.00236 0.02424 0.10001 0.32273
−0.00335 0.01031 0.07405 0.28216
Table III. Gains from merging in an eight firm industry n=8
c = 0.00001
c = 0.0001
c = 0.001
c = 0.01
m=2 m=3 m=4 m=5 m=6 m=7 m=8
0.00019 0.00136 0.00523 0.01642 0.04749 0.13265 0.36480
0.00000 0.00083 0.00436 0.01519 0.04590 0.13068 0.36246
−0.00080 −0.00066 0.00192 0.01138 0.04036 0.12324 0.35306
−0.00294 −0.00466 −0.00379 0.00329 0.02738 0.10155 0.32009
VI. Summary Existing research on horizontal mergers suggests that enhancing market power is unlikely to be a motive for mergers between a small fraction of the firms in a Cournot oligopoly. This conclusion would be reassuring if only because it suggests that cost efficiencies might be the motive and so regulation concerning marginal increases in market concentration might impede efficiency. We show that this favorable interpretation of horizontal mergers may be a consequence of assumptions on the demand curve and that industry demand curves exist, with well-behaved Cournot equilibrium properties, such that welfare-reducing mergers occur endogenously between a small fraction of firms even if there are no cost efficiencies.
References Audretsch, David B. (1983) The Effectiveness of Antitrust Policy towards Horizontal Mergers. Ann Arbor, MI: UMI Research Press. Bork, Robert H. (1978) The Antitrust Paradox: A Policy at War with Itself. New York: Basic Books. Cheung, Francis K. (1992) ‘Two Remarks on the Equilibrium Analysis of Horizontal Mergers’, Economics Letters, 40, 119–123.
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Farrell, Joseph, and Carl Shapiro (1990) ‘Horizontal Mergers: An Equilibrium Analysis’, American Economic Review, 80, 107–126. Glick, Mark A., Duncan J. Cameron, and David G. Mangum (1997) ‘Importing the Merger Guidelines Market Test in Section 2 Cases: Potential Benefits and Limitations’, 42, 121–150. Kamien, Morton I., and Isreal Zang (1990) ‘The Limits of Monopolization through Acquisition’, Quarterly Journal of Economics, 105, 465–499. Kamien, Morton I., and Isreal Zang (1991) ‘Competitively Cost Advantageous Mergers and Monopolization’, Games and Economic Behavior, 3, 323–338. Kaserman, David L., and Hans Zeisel (1996) ‘Market Definition: Implementing the Department of Justice Merger Guidelines’, Antitrust Bulletin, 41, 665–690. Levin, Dan (1990) ‘Horizontal Mergers: The 50-Percent Benchmark’, The American Economic Review, 80, 1238–1245. Porter, Michael E. (1990) The Competitive Advantage of Nations. New York: Free Press. Posner, Richard A. (1976) Antitrust Law: An Economic Perspective. Chicago: University of Chicago Press. Salant, Stephen W., Sheldon Switzer, and Robert J. Reynolds (1983) ‘Losses from Horizontal Merger: The Effects of an Exogenous Change in Industry Structure on Cournot-Nash Equilibrium’, 98, 185–199. Scherer, F. M., and David Ross (1991) Industrial Market Structure and Economic Performance. 3rd edn. Boston: Houghton Mifflin. Shepherd, William G. (1997) “Dim Prospects: Effective Competition in Telecommunications, Railroads and Electricity’, Antitrust Bulletin, 42, 151–175. United States v. du Pont de Nemours and Co. et al. (1957), United States Reports, 353, 586–611.
