Leading and merging: convex costs, Stackelberg, and the merger paradox.

AuthorHeywood, John S.
PositionEvlauating acquisitions and mergers impact on business
  1. Introduction

    In the canonical model of the merger paradox, two firms with linear costs never have an incentive to merge as long as there remains even a single rival (Salant, Switzer, and Reynolds 1983). The reduction in quantity by the newly merged firm is outweighed by the combination of a loss of "a seat at the table" and the increase in quantity by excluded rivals such that the merger cannot be profitable. Perry and Porter (1985) show that with sufficiently convex costs, two firms can profitably merge. Yet, Heywood and McGinty (2007) emphasize that even when such a merger is profitable, the profit gained by the excluded rivals exceeds that of the merger participants. Thus, although the introduction of convex costs provides an incentive for merger, it does not eliminate the free-rider aspect of the merger paradox: namely, each firm would rather have other firms merge than do so itself.

    Attempts to further resolve the paradox have moved in a wide variety of directions, but we pick up the threads of those following Daughety (1990), who examined models of Stackelberg leadership. (1) Thus, Huck, Konrad, and Muller (2001) examine firms with linear costs, showing that if a leader merges with a follower, the merged firm earns more profit than its two premerger component firms. Feltovich (2001) also produces this result and shows that such a merger results in a decrease in total welfare. These results have sufficient currency that they have found their way into current textbooks (Pepall, Richards, and Norman 2003). Yet, as is the case with convex costs but without leadership, the gain to remaining an excluded follower exceeds the gain from merging with the leader. Thus, the free-rider portion of the merger paradox remains stubbornly intact.

    We combine for the first time the assumption of convex costs from Perry and Porter (1985) with that of Stackelberg leadership. We show that for most market structures, there is a wide range of convexity such that a merger between the leader and a follower increases profit and causes the gain to participating in the merger to exceed that of remaining an excluded follower. Thus, in comparison with the canonical model, the two firms can profitably merge, and there exists no free-rider incentive that might otherwise stop them from merging. Interestingly, there also exists a range not only in which the free-rider problem vanishes, as the profit gain from merging exceeds that from being excluded, but also a range in which the excluded firms actually suffer reduced profit because of the merger and the resulting lower price. Farrell and Shapiro (1990, p. 112) emphasize that such a result can be generated only if a merger yields cost efficiencies (synergies) and point out that such efficiencies do not exist in the case of identical firms with convex costs. Two Cournot competitors with convex costs produce equal quantities and, once merged, cannot produce their premerger output at any lower cost. Yet, a Stackelberg leader and a follower with convex costs produce very different quantities in equilibrium and, once merged, can produce their premerger quantity at lower cost by equalizing production between the two plants. Indeed, the resulting harm to the excluded firms might well result in their entreaties that antitrust officials investigate the competitive consequences of the merger. As White (1988) points out, excluded rivals are the most common source of antitrust complaints regarding mergers. In sum, the combination of convex costs and Stackelberg leadership provides a series of outcomes that help resolve important parts of the merger paradox.

    Our emphasis on convex costs sets us apart from Huck, Konrad, and Muller (2004) and Creane and Davidson (2004), who examine the possibility of Stackelberg leadership among plants but within the firm. Both begin with a standard simultaneous move oligopoly but assume that after the merger, the merged firm can sequence the output decisions of its constituent parts. Although somewhat in the vein of Daughety (1990), in that the merger changes the ability to commit, these models allow a resolution of the merger paradox that retains linear costs and allows excluded rivals to be hurt. Importantly, our introduction of convex costs dramatically limits the profitability of sequencing output across plants within the firm. The differing output levels across plants that result from the internal sequencing generate a cost inefficiency with convex costs that is absent with linear costs. Thus, to focus on the importance of convex costs, we ignore the possibility of internal sequencing.

    Our presentation also firmly fits within the mainstream of the merger literature by taking the original number of firms as exogenous. We exclude entry and assume that the extent of convexity is sufficient that fixed cost savings from simply closing plants do not drive merger dynamics. We recognize that the resulting model should be viewed as either short-run or as having high entry barriers. We also recognize the existence of a small literature on mergers with free entry (Cabral 2003; Spector 2003; Davidson and Mukherjee 2007).

    Beyond being a theoretical exercise, the case of merger involving a leading and dominant firm commands special policy interest. Historically, the dominant market shares of the Standard Oil trust and the sugar trust were maintained through the purchase of much smaller rivals (Leeman 1956; Zerbe 1956). Later in the 1960s, the Court prohibited the takeover of even very small market share firms if the suitor was a dominant firm. Thus, Alcoa, the leading producer of aluminum conduit with nearly 30% of the market, was prohibited in 1964 from purchasing Rome Cable, which had only 1.3% of the market (Shepherd 1985, p. 231). Even today, the merger guidelines add emphasis to markets with dominant firms, as the resulting asymmetry of market shares results in a larger Herfindahl Index and so increase the chance for initial scrutiny. A recent antitrust case in the UK nicely illustrates many of the dimensions of our theoretical inquiry. The UK Competition Commission found that IMS Health Inc. was the leading provider of pharmaceutical business information services in the UK. These services enable pharmaceutical firms to monitor their competitive position, identify areas of product development, focus their marketing, and remunerate sales personnel. In 1997, IMS had a market share between 37 and 85%, depending on how narrowly the product was defined. They wished to merge with Pharmaceutical Marketing Services Inc., which had an 8% market share under the narrow definition. Excluded firm Taylor, Nelson, Sofres objected to the merger, citing that it would reduce their profits and viability. The commission found that the merger "could be expected to have adverse effects on efficiency" and "operate against the public interest" (UK Competition Commission 2006).

    In the next section, we model the case of a merger between a leader and a single follower in a market in which all firms have convex costs. We isolate the profit consequences of the merger for the merger participants and for the excluded followers. We also isolate the welfare consequences. The third section generalizes the model to consider multiple followers merging with a leader. Again, the profit consequences for participants and excluded rivals are identified. We isolate the range of convexity that resolves the key components of the paradox as the merger size is varied. The welfare consequences of such multiple mergers are isolated through simulation. The final section draws conclusions, makes policy observations, and suggests future research.

  2. Merger between the Leader and Single Follower

    We consider a market with one leader and n followers and examine a merger between the leader and one follower. The merged firm remains the leader after merger, and all excluded followers prior to merger remain followers after merger. (2) By assuming that the roles of the firms remain what they were prior to merger, we explicitly exclude the case in which two followers merge to become a leader (Daughety 1990). As in other models of merger and Stackelberg (Huck, Konrad, and Muller 2001), we take the leadership as given. We note that a substantial literature has examined the conditions under which leadership can emerge endogenously in duopolies of otherwise similar firms (Saloner 1987; Hamilton and Slutsky 1990; Robson 1990; Pal 1996). Moreover, recent laboratory experiments have suggested that followers can emerge even among identical agents (Fonseca, Muller, and Normann 2006). Nonetheless, we recognize that leadership in our model is an assumption. We will show, however, that the profit of the leader after merging with an existing firm exceeds that earned by the leader after building a new plant. (3)

    Following previous work, we assume a linear demand curve, P = a - Q, where Q = [q.sub.l] + [n.summation over (i=1)] [q.sub.i] is the sum of the leader's and the...

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