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Article Excerpt
In this article, the effect of downstream horizontal mergers on the upstream producer's capacity choice was studied. Contrary to conventional wisdom, I find a nonmonotonic relationship: horizontal mergers induce a higher upstream capacity if the cost of capacity is low, and a lower upstream capacity if this cost is high. This result is explained by decomposing the total effect into two competing effects." a change in holdup and a change in bargaining erosion.
1. Introduction
* A growing debate in the antitrust arena concerns the negative long-term effects of downstream horizontal integration on upstream producers' investment incentives. For example, the position held by the European Commission in two recent decisions on mergers of leading retailers, Kesko/Tuko and Rewe/Meinl, created jurisprudence in merger control: competitive assessment should no longer be restricted to the downstream market but should also look for adverse effects on input markets. (1)
The present article studies how downstream horizontal mergers affect the capacity choice of an upstream producer. It seems intuitive that following a merger the producer's bargaining power vis-a-vis the downstream firms is weakened and, because the producer then gets a lower share of the surplus, his incentives to invest in capacity are also reduced. Perhaps surprisingly then, working from fundamentals, I find a nonmonotonic relationship between downstream horizontal integration and the upstream equilibrium capacity.
A two-stage game is studied. In the first stage, the upstream producer chooses capacity and pays for its cost. In the second stage, the producer bargains with downstream firms over input supply. Because the solution concept determines the allocation of the bargaining surplus, and therefore investment incentives, this choice is a crucial step. Like other authors studying the effects of integration, I use the Shapley value (e.g., Hart and Moore, 1990; Inderst and Wey, 2003; Segal, 2003).
The main result is that the cost of capacity provides a simple criterion for evaluating claims about the effect of downstream horizontal mergers on the producer's capacity choice: a downstream merger induces a higher equilibrium capacity upstream if the cost of capacity is low, and the converse is true if the cost of capacity is high.
I explain this result by decomposing the total effect into two effects. On the one hand, as expected, the merger decreases the share of the surplus accruing to the producer, that is, the extent to which downstream firms are able to holdup the producer is increased. On the other hand, for any given market configuration, increasing capacity erodes the bargaining power of the producer because competition for an input gets weaker when this input becomes more abundant. A downstream merger reduces the rate at which this bargaining erosion takes place. This latter effect counteracts the former, and will dominate when the cost of capacity is low.
Surprisingly, although the holdup literature has studied the effect of vertical integration, there exists little formal analysis of the investment effects of downstream horizontal integration--the growing literature on buyer power has focused on mergers' distributive effect. The paper closest to ours is Hart and Moore (1990) who, assuming that marginal contributions are independent of the level of investment, find that "as one might expect, if two competing traders merge, this will worsen the incentives of the owner-manager of a firm that trades with them" (Hart and Moore, 1990). Other papers studying continuous investment choices find a similar negative relationship between downstream mergers and upstream investment (e.g., Chae and Heidhues, 1999; Inderst and Shaffer, 2007). The present article shows precisely that this result may change significantly when the above-mentioned assumption is not satisfied.
A few other papers look at discrete technology choices. Stole and Zwiebel (1996a, 1996b) find that a firm dealing with independent workers has a preference for technologies which give rise to more concave surplus functions because this leverages its bargaining power; this bias is absent when the workforce is unionized. Inderst and Wey (2003, 2006) show that downstream horizontal mergers reduce a similar bias, inducing the producer to focus on value creation itself. The work extends this analysis in two ways. First, and similar to the property rights literature, I focus on a continuous investment choice and show that downstream horizontal mergers may result in more upstream investment (not a discrete change in technology). Second, I account for the problem of producer's opportunism in related output markets studied in the vertical contracting literature (e.g., McAfee and Schwartz, 1994; Segal and Whinston, 2003).
Most of the above-mentioned literature uses linear bargaining solutions--for example, the Shapley value. Recent work has shown that results derived using a linear bargaining solution may not be robust in settings with nonlinear bargaining solutions (e.g., Chiu, 1998; de Meza and Lockwood, 1998; Inderst and Wey, 2005). Although the results remain valid in examples with nonlinear bargaining solutions, the present article is, to my knowledge, the first using a linear bargaining solution which finds that the integration of competing players may actually increase the level of investment made by a complementary player.
The remainder of the article is organized as follows. In Section 2, the main ideas of this article are illustrated with a simple example. I present the model in Section 3 and the analysis in Section 4. In Section 5, I extend the model to related output markets and conclude in Section 6. All proofs can be found in the Appendix.
2. A simple example
* Suppose a producer p chooses, at date 0, a capacity Q [member of] {0, 1, 2}. The cost of each unit of capacity is c. There are two outlets, each in a distinct market. At date 1, in each outlet, one unit can be sold for a value of 1, but there is no demand for a second unit. Denote the maximal revenue obtained with m outlets and a capacity of Q by [phi] (Q, m) (e.g., 4, (1, 1) = [phi] (1, 2) = 1).
No contracts are signed at date 0, and at date 1 gains from trade are split according to each player's Shapley value. Let Z denote the industry configuration and [S.sub.Z](Q) denote the producer's Shapley value in industry Z when the producer's capacity is Q. (Below two situations are compared, A and B, so Z [member of] {A, B}.)
The producer's problem is to maximize its date 1 revenue minus date cost of capacity:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
He will choose an additional unit of capacity at stage if the incremental benefit of capacity is larger than the cost c, that is, if
[DELTA][S.sub.Z](Q) [equivalent to] [S.sub.Z](Q) - [S.sub.Z](Q - 1) > c.
First focus is on the producer's date 1 revenue. A well-known interpretation of the Shapley value has all players in the game being randomly set in an ordered sequence, with each sequence being equally likely. Suppose each player gets his marginal contribution to the coalition formed by those players who precede him in the sequence. The Shapley value is the expectation taken over all possible sequences.
In situation A, each of the two downstream firms, i and j, owns one outlet. There are six possible sequences: pij, pji, ipj, jpi, ijp, and jip. In two of them the producer comes first, so his marginal contribution is 0. In two others he comes second, so his marginal contribution is equal to [phi] (Q, 1)--the value of allocating all capacity to a single outlet. Finally, there are two sequences in which the producer comes last, so he gets [phi] (Q, 2)--the total industry surplus. Taking expectations I get [S.sub.A](0) = 0,
[S.sub.A](1) = 2 1/6(0) + 2 1/6(1) + 2 1/6(1) = 2/3
and
[S.sub.A](2) = 2 1/6(0) + 2 1/6(1) + 2 1/6(2) = 1.
In situation B the downstream firm i owns both outlets. In this case, there are only two possible sequences: pi and ip. So [S.sub.B](0) = 0,
[S.sub.B](1) = 1/2(0) + 1/2(1) = 1/2,
and
[S.sub.B](2) = 1/2(0) + 1/2(2) = 1.
To study the extent to which downstream firms are able to holdup the producer, I also define the share of the industry surplus accruing to the producer as
[[alpha].sub.Z](Q) [equivalent to] [S.sub.Z](Q)/[phi](Q, 2).
I have
[[alpha].sub.A](1) = 2/3, [[alpha].sub.A](2) = 1/2, and [[alpha].sub.B](1) = [[alpha].sub.B](2) = 1/2.
The share of date 1 surplus accruing to the producer is (weakly) higher in situation A, so the holdup is more severe in situation B. I could therefore expect the incremental benefit of capacity to be larger in A than in B. Things are in fact not so simple, however. Although this is true from Q = to Q = 1, as
[DELTA][S.sub.A](1) = 2/3 and [DELTA][S.sub.B](1)= 1/2,
it is not true from Q = 1 to Q = 2, as
[DELTA][S.sub.A](2) = 1/3 and [DELTA][S.sub.B](2)= 1/2.
The table below represents the equilibrium choice of capacity, [Q.sup.*.sub.Z], as a function of c: upstream equilibrium capacity is larger in B when the cost of capacity is low, and lower when this cost is high (it is zero in both cases if the cost is too high, i.e., c [greater than or equal to] 2/3):
c [Q.sup.*.sub.A] [Q.sup.*.sub.B] [member of] [0, 1/3] 2 2 [member of] [1/3, 1/2 1 2 [member of] [1/2, 2/3] 1
To understand...
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