CONVEX COSTS AND THE MERGER PARADOX REVISITED

I. INTRODUCTION A simple canonical model published in the early 1980s suggests that mergers are rarely profitable for potential participants. Salant, Switzer, and Reynolds (1983) examined a model of n-identical firms, of which m merged. The model demonstrates that only in the unlikely event of more than 80% of the firms merging could the participants earn additional profits as a result of the merger. In all other cases, the profit of the firm created by the merger is lower than the sum of premerger profits of the constituent firms that merge. This result has grown to take prominent places in textbooks such as that by Pepall, Richards, and Norman (1999, Chapter 8) and to take the name The Merger Paradox. While a variety of researchers have attempted to resolve the paradox, Perry and Porter (1985) used the simple modification of allowing for increasing marginal cost. They showed that for sufficiently convex costs, two firms do profit from merging. At issue in our study is the extent to which cost convexity actually relaxes the merger paradox. We show that any merger of m of n-identical firms (a merger of any market share) will be profitable to the participants with a sufficiently steep marginal cost structure and that this can be used to identify critical concentration measures for given degrees of convexity, which can be compared with the famous 80% figure. This allows us to specify the extent to which convexity relaxes the merger paradox. We also show that although convexity may reduce to some extent the critical degree of concentration needed to earn profit, it does nothing to relax the second crucial element of the merger paradox. Even with convex costs, firms remain better off being excluded from the merger than being a participant. Finally, we add realism by arguing that mergers of m of n firms may happen sequentially rather than simultaneously. Yet, the power of cost convexity to relax the merger paradox is greatly reduced in this realistic case of sequential mergers. In sum, we believe that we are the first to give cost convexity a thorough hearing as a potential solution to the merger paradox and that we find it of only marginal importance. The next section examines the literature on the merger paradox, defending the rationale for convex costs. The third section introduces the basic model, presenting the pre- and postmerger equilibria. The fourth section compares the equilibria isolating the central propositions and presents simulations for the case of a simultaneous merger of two or more firms. The remainder of the fourth section examines a sequence of firm-by-firm mergers comparing them to simultaneous mergers. A final section concludes and suggests additional research. II. MERGERS AND PROFITABILITY: THE PARADOX The basic insight of the merger paradox remains important. If firms merge to restrict quantity, then excluded Cournot competitors will increase their output. Moreover, this increase in output can frequently be sufficient to reduce the profit of the newly merged firms. In this sense, the paradox suggests that the primary beneficiaries of horizontal merger are the rivals excluded from the mergers. Certainly, this idea has received currency in both the popular press and the econometric work. Thus, the major beneficiary of the recent merger of U.S. banks Chase Morgan and Bank One was identified in the business press by Berenson (2004) as excluded rival Citigroup. In econometric work, a series of studies focus on the profit levels of excluded rivals as a test for whether or not the mergers hurt welfare. While Stillman (1983) found that excluded rivals did not benefit as judged by stock market data in the 1970s, Song and Walkling (2000) used more recent data confirming that excluded rivals do earn increased profit as a result of mergers in their industry. Recognizing the importance of the merger paradox, we further explore the Perry and Porter (1985) modification, which ensures that the newly merged firm retains the sum of its previous capital by allowing for convex costs (increasing marginal costs). …