Can Horizontal Mergers Without Synergies Increase Consumer Welfare? Cournot and Bertrand Competition Under Uncertain Demand

For instance, Tony Blair, former British prime minister and current Middle East peace envoy, attempted in September 2012 to help smooth the way for this Glencore merger. See The Economist for a series of reports related to Glencore and Xstrata, including “Merger of Equals,” February 2, 2012; “Ore Inspiring,” February 11, 2012; “Happy Ending,” September 10, 2012; and “Miner Irritations,” September 15, 2012.

See Xstrata’s 2011 annual report at http://www.xstrata.com/assets/reports/ar11/strategic-review/ceo-strategic-review/glencore-merger/.

As the “Ore Inspiring” report in The Economist (February 11, 2012) states: “It is possible that the world’s antitrust authorities may not like the look of a merger that unites a dominant commodity trader and a leading miner of lead and zinc as well as coal and copper.”

Noting that antitrust authorities emphasize the issue of uncertainty related to proposed efficiency gains, Choné and Linnemer (2008) characterize the curvature of the expected social welfare function in a general framework and offer significant suggestions regarding the way antitrust authorities view the inevitable uncertainty.

U.S. Department of Justice and Federal Trade Commission (2010).

There is a fine distinction between our study and that of Vives (1984), though. Vives considers information sharing between two duopoly firms, while we consider information sharing between two plants of a merged entity in the contexts of quantity and price setting (see Section 3 of the present paper for a complete treatment).

U.S. Department of Justice and Federal Trade Commission (2010). See, for example, Section 6.1 (p. 20).

U.S. Department of Justice and Federal Trade Commission (2010).

In Section 3, we discuss further why this is the case in our model.

Footnotes 11 and 12 provide details for the derivation of this assumption. Other papers considering uncertainty, such as Stennek (2003), Banal-Estañol (2007), and Hamada (2012), also impose similar conditions to ensure interior solutions.

We have iff , , iff , and iff . The intersection of these conditions on θ is .

We have iff , , iff , and iff . The intersection of these conditions on θ is .

It is straightforward to show that , which is smaller than . Thus, information sharing indeed yields greater expected profits for the merged entity. Note that the solutions given in (21) are strictly positive iff , which is a subset of the parameter space considered in the present paper. For simplicity of exposition, in this section we focus on these solutions, noting that this simplified discussion does not affect our result presented in Proposition 1, which holds for all.

Gal-Or (1988) also finds that when the effects of information sharing under positive and negative shocks go in opposite directions, the effect from positive shocks dominates.

Using expressions in (25), we have , which is smaller than . Thus indeed, information sharing results in greater expected profits for the merged entity. Note that the solutions given in (25) are strictly positive iff , where Again, for simplicity of exposition, we focus here on the solutions in (25), knowing that our result presented in Proposition 3 holds for all.

Under a good state, by plugging into (17), we have the average price of the merged entity , which is greater than the average price of the price-setting hypothetical monopoly derived from (25). The associated outputs and are similarly obtained. Substituting for yields corresponding values under a bad state, .

From (8) and (22), we have .

U.S. Department of Justice and Federal Trade Commission (2010); see, for example, Section 6.1.

With b approaching 1, the degree of product differentiation is getting so small that the two products are close to homogeneous. One can then regard the case of homogeneous products as a limiting case of differentiated products.

Mathematically, we have , which is greater than .

Indeed, from (6) and (7) we have , which is smaller than , which we derive from (17).

U.S. Department of Justice and Federal Trade Commission (2010); see, for example, Section 6.1.

The responsiveness of Q^M to θ is given by , which is larger when b is smaller (i.e., more differentiated).

From (14) and (26), we have , such that the market power effect is indeed bad for social welfare.

From (12) and (13), we have . It is straightforward to show that .

See Footnote 13 in Section 3.1.

See Footnote 15 in Section 3.2.

See, for example, Figure 2.

According to Chen et al. (2012), alternative suitable conditions include the following: π₂ being normally distributed, π₂ being a monotonic linear function of a single random variable, π₂ being endowed with some truncated probability distribution, the distribution of π₂ being elliptical, or the distribution of π₂ being slightly nonnormal, etc. In our model with , it is suitable to assume that π₂ is endowed with some truncated probability distribution.