## Abstract

If one firm buys inputs from a competitor, the input price may be used to internalize the competition between the firms. Thus, positive unilateral pricing effects may arise if one firm starts to buy inputs from a competitor. Conversely, unilateral pricing effects may be small if two firms with vertical relations merge, as pre-merger competition is partly internalized through the input price. We present a method for adjusting the formula of Hausman et al. (Econ Lett 111(2):119–121, 2011), in order to predict correct unilateral pricing effects not only for horizontal mergers, but also for structural changes in markets where one firm sells inputs to a rival.

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## Notes

In the case of two vertically integrated firms, it is reasonable to assume that the two firms will utilize the most efficient production technology post-merger. In this sense, the high-cost firm will experience an efficiency gain, as it can produce at a smaller marginal cost post-merger. Such an efficiency gain assumes that the low-cost firm has no binding capacity constraints.

Competition authorities have access to detailed financial accounts for the merging parties, thus allowing them to estimate these quantities. Alternatively, if only relative margins are observable, the UPE-equations can be rewritten in terms of margins, in order to facilitate quantification.

Using that the diversion ratio is defined as \(D_{12} \equiv - \dfrac{\dfrac{\partial Q_2}{\partial p_1}}{\dfrac{\partial Q_1}{\partial p_1}}\).

As \(D_{21} \equiv -\dfrac{\partial Q_1 / \partial p_2}{\partial Q_2 / \partial p_2}\), and \(\partial Q_2 / \partial p_2\) is much greater than \(\partial Q_1 / \partial p_1\), \(D_{21}\) will become small. Note that in order for \(D_{21}\) to approach zero and \(D_{12}\) to approach one, we need \(\partial Q_2 / \partial p_2 \rightarrow - \infty\) and \(\partial Q_1 / \partial p_1 \rightarrow 0\). However, it is not necessary that \(D_{21}= 0\), as the condition also holds when \(D_{21}\) is sufficiently small.

This assumes that there are no binding upstream capacity constraints.

Note that the assessment of potential unilateral effects is not the only concern in an assessment of a merger. A merger that leads to high concentration and/or firm symmetry may increase the possibility of coordination. In practice, the analysis of coordinated effects is treated separately from the analysis of unilateral effects, and is beyond the scope of this paper.

Note that, given the vertical structures between the firms, it is not possible for them to internalize diversion completely. Even if firm 1 chooses

*w*optimally in order to maximize joint profits, the result will be that firm 1 sets a price that is slightly lower than its post-merger price. Firm 2 will set a pre-merger price that is higher than the post-merger price. Consequently, firm 2 will have a*negative*unilateral pricing effect if*w*is set optimally in the pre-merger situation. Despite this being an interesting result, the discussion of it is beyond the scope (and purpose) of this paper.As a simplification, we assume zero fixed costs. This assumption does not alter the first-order conditions, and thus does not affect the optimal allocation of the firms. We also assume that firm 2 has no marginal costs, other than the wholesale price

*w*. It is possible to adjust the calculations further, in order to include other marginal cost (and other cost-structures). However, the mechanisms that are presented in this article are still valid.The method and substitutions are equivalent to those that were used in Sect. 2; thus they are not discussed in further detail here.

In the expressions, we have made the following simplifications in notation: \(c_i^0= c_i\), \(p_i^0= p_i\), \(Q_i^0=Q_i\) for \(i=1,2\).

Symmetric in the sense that the expressions for the two firms’ unilateral pricing effects are symmetric. However, if the firms are not symmetric, diversion rates, prices, and costs will also differ. Consequently, also the firms’ unilateral pricing effects will not be the same.

Furthermore, this allows us to assess the unilateral pricing effect formulas that we calculated in the previous section. By considering the introduction of a vertical relation step 1, and a merger with vertical relations (as seen in the previous section) step 2, we can test the result of our model against the traditional Hausman formula.

Note that in order for firm 2 to participate in the vertical arrangement, its post-change margin must be at least as large as its margin prior to the structural market change: \(w-\varDelta p_2 \le c_2\). However, this condition may be violated if the merger also significantly reduces fixed costs. This is because a sufficiently large reduction in fixed costs may compensate for a reduction in the post-change margin.

We again substitute for \(c_1= c_1^0 + \varDelta c_1\) \(p_i= p_i^0 + \varDelta p_i\) for \(i=1,2\), and we utilize the expressions for \((Q_i-Q_i^0) , i=1,2\). Rearranging by the two unknowns \(\frac{\varDelta p_1}{p_1^0}\) and \(\frac{\varDelta p_2}{p_2^0}\) then allows us to use Cramer’s rule.

## References

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*The BE Journal of Theoretical Economics,**10*(1), 1–41.Hausman, J., Moresi, S., & Rainey, M. (2011). Unilateral effects of mergers with general linear demand.

*Economics Letters*,*111*(2), 119–121.Oledale, A., & Padilla, J. (2013). EU merger assessment of upward pricing pressure: Making sense of UPP, GUPPI, and the like.

*Journal of European Competition Law and Practice*,*4*(4), 375–381.Werden, G. (1996). A robust test for consumer welfare enhancing mergers among sellers of differentiated products.

*Journal of Industrial Economics*,*44*, 409–413.Williamson, O. E. (1968). Economies as an antitrust defense: The welfare tradeoffs.

*The American Economic Review*,*58*(1), 18–36.Willig, R. (2011). Unilateral competitive effects of mergers: Upward pricing pressure, product quality, and other extensions.

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## Acknowledgements

The authors gratefully acknowledge the financial support of The Price Regulation Fund (det alminnelige prisreguleringsfond) administrated by the Norwegian Competition Authority (*Konkurransetilsynet*). The model in Sect. 3 was presented at the ACE (Association of competition economics) conference in 2015, as a part of a presentation about the Tele 2/TeliaSonera merger case. The authors would like to thank Lars Sørgard and Frode Steen for their valuable comments on early versions of the model.

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Asphjell, M.K., Bergh, H.N., Merker, T. *et al.* Unilateral Effects of Horizontal Mergers with Vertical Relations Between Firms and Other Structural Market Changes.
*Rev Ind Organ* **51**, 381–394 (2017). https://doi.org/10.1007/s11151-017-9566-z

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DOI: https://doi.org/10.1007/s11151-017-9566-z