Welfare Effect of Mergers and Multilateral Trade Liberalization
Abstract
In a two-country model where firms behave à la Cournot, we show that trade liberalization increases (decreases) the social desirability of those mergers that generate sufficiently large (small) reductions in marginal cost. There exists a range of intermediate levels of marginal cost savings such that marginal tariff reductions increase (decrease) the desirability of merger at sufficiently low (high) tariff levels. Moreover, in the neighborhood of free trade, we show that if trade liberalization increases the profitability of a merger, it necessarily also increases its desirability.
1. Introduction
During the past two decades, the world has been gradually moving closer to free trade.1 At the same time, mergers between firms have been on the rise.2 About 70% of all mergers are domestic, that is, mergers between different firms within the same country (Brakman et al., 2005).
Several explanations relating these two phenomena have been offered in the literature.3 Although not the only contender, trade liberalization remains one of the most-studied factors affecting firms' incentives to merge.4
This paper, in contrast, focuses on the impact of horizontal domestic mergers on social welfare when the merging firms are situated within a country undergoing trade liberalization.5 We say that a tariff reduction increases (decreases) the desirability of a merger when it increases (decreases) the merger-induced change in social welfare. We address two important questions: (i) Does trade liberalization render a domestic horizontal merger more desirable to society? (ii) Does trade liberalization move desirability and profitability in the same direction? In addressing these issues we simultaneously analyze the implications of trade liberalization for domestic competition policy.
We consider two countries, Home and Foreign, with segmented markets, identical demand conditions and two firms each. A “Home firm” is a firm that undertakes production in Home, and a “Foreign firm” is one that undertakes production in Foreign. All firms are assumed to produce a homogeneous good and compete à la Cournot in both markets. Within this context, we study the impact of equal bilateral tariff reductions6 (which, within our context is equivalent to multilateral trade liberalization) on the welfare effect in Home of a merger between the Home firms.
The existing literature categorizes the welfare effects of mergers into the following, both of which have been shown to be empirically relevant and both of which are incorporated in our model: (i) a negative effect of increased market power of the merger participants; (ii) a positive effect of reductions in the cost of production of the merger participants.7 The latter can arise, for example, if the merger results in the shutting down of one of the plants leading to fixed cost savings. Alternatively, it is possible that the merger participants vary in their productive efficiency and that the merger is motivated by the fact that the high cost firm wishes to gain access to the low cost firm's technology. Our model allows for lower fixed and marginal costs post-merger. We vary the level of merger-induced cost savings in order to distinguish between two main types of mergers: those with large merger-induced reductions in marginal cost that lead to greater productive efficiency and those with small merger-induced reduction in marginal cost that lead mainly to increased market power of the merger participants. We then investigate the impact of trade liberalization on each type of merger.
Given our setting, we generate two main findings about the impact of trade liberalization on the desirability of mergers. First, we show that trade liberalization increases (decreases) the desirability of mergers with sufficiently large (small) merger-induced reductions in marginal cost. Second, we show that there exists a range of intermediate levels of marginal cost savings from merger such that the desirability of merger is a non-monotonic function of the tariff level. Marginal trade liberalization increases (decreases) the desirability of merger at sufficiently low (high) tariff levels.
The direct policy implications of these findings are as follows. First, the accurate estimation of potential marginal cost savings of a merger rises in importance since inaccuracy in this measurement simultaneously leads to inaccurate predictions of the impact of trade liberalization on the desirability of the merger (thus magnifying the effect of the measurement error on the policy decision). An accurate estimation, however, can be directly used to accurately predict the impact of trade liberalization on the desirability of the merger. Second, the impact of marginal trade liberalization on the desirability of merger may fail to be a reliable indicator of the same when tariff changes are non-marginal. Thus, the formulation of the optimal merger policy in the face of trade liberalization cannot rely on marginal analyses. Rather, it requires the incorporation of the exact pre- and post-liberalization tariff levels.
As noted above, in the past decades, we have observed growing merger activity in parallel to important tariff reductions. A natural question that has arisen within this context is the following. When a merger's profitability increases with trade liberalization, does its desirability also increase? Or is it the case that competition authorities need to be more vigilant towards mergers that are encouraged by trade liberalization? We show that the latter is not the case when the pre-liberalization tariff level is sufficiently small. In particular, we show that in the neighborhood of free trade, if trade liberalization increases the profitability of a merger, then it necessarily increases its desirability.
2. The Model and Preliminaries
(1)
in Foreign. Firm 2 sells x2 in Home and 
in Foreign.
Each country imposes an import tariff. It is assumed that the tariffs imposed by Foreign and Home are identical, denoted by t. We focus on the case where both countries simultaneously reduce t by the same amount, that is, equal bilateral tariff reduction.
The Market Equilibrium
Let the total quantity sold in Home be Q ≡ x1 + x2 + 2y and that in Foreign be 
The profits of Home firm i and Foreign firm f are given by (2) and (3) respectively.
(2)
(3)
(4)A Merger
Subsequent to the merger of firms 1 and 2, the new entity and the Foreign firms compete à la Cournot. The cost of production of the new entity is assumed to correspond to the lower of the two marginal costs, that is, c2. The merger, thus, generates a reduction in the marginal cost of production of one of the merger participants by the amount z. Henceforth, we refer to z as the reduction in marginal cost due to the merger. In addition, we allow the merged entity to have a fixed cost, ΦM, different from the pre-merger fixed costs of the merger participants, Φ1 and Φ2. Thus, the merger generates “fixed cost savings,” denoted by φ ≡ Φ1 + Φ2 − ΦM.11 The subscript, M, denotes post-merger values throughout the rest of the paper.
denote the quantities sold by the merged entity in Home and Foreign respectively. Let yM and
denote the post-merger quantities sold by each Foreign firm in Home and Foreign respectively. For interior solutions, the post-merger equilibrium quantities sold are given by:
(5)
. It holds that all pre- and post-merger equilibrium quantities, as given by (4) and (5), are strictly positive iff t ∈ [0, tmax(z)), where
(6)
.12 In the following sections, we proceed with the analysis.3. Trade Liberalization and Desirability of Merger
(7)
(8)
(9)Marginal trade liberalization is said to increase (decrease) the desirability of the merger (from the social viewpoint) at t = t0 iff 
.
A non-marginal tariff reduction from t1 to t0 is said to increase (decrease) the desirability of the merger iff 
.
Marginal Trade Liberalization
(10)Proposition 1. We have the following:
- (i)
For sufficiently small merger-induced reductions in marginal cost, z ∈ [0, a/9], marginal trade liberalization decreases the desirability of a merger for all t ∈ [0, tmax(z)).
- (ii)
For an intermediate range of merger-induced reduction in marginal cost, z ∈ (a/9, 11a/92), marginal trade liberalization increases the desirability of a merger iff the pre-liberalization tariff level is sufficiently low, i.e. t ∈ [0, tw(z)).
- (iii)
For sufficiently large merger-induced reductions in marginal cost,
, marginal trade liberalization increases the desirability of a merger for all t ∈ [0, tmax(z)).
(11)
where tw(z) < tmax(z) iff z ∈ [0, 11a/92) and tw(z) > 0 iff z ∈ [a/9, zmax).The question of interest is the following: how should a competition authority respond to mergers that are proposed in the face of trade liberalization? As per Proposition 1, we show that the answer depends on the level of marginal cost savings (see Proposition 1(i) and 1(iii)), and also on the pre- and post-merger tariffs (see Proposition 1(ii)). More specifically, Proposition 1(i) and 1(iii) together state that marginal trade liberalization decreases the desirability of those mergers which yield small reductions in marginal cost whilst increasing the desirability of those which yield large reductions in marginal cost. Proposition 1 determines the sign of ∂F/∂t. We use a numerical example (setting a = 100 and φ = 230)13 to further illustrate that trade liberalization can change the sign of F itself.
In Figure 1, a merger yielding marginal cost savings of z = 10 is desirable at t0, but becomes undesirable with a move to free trade. At higher levels of marginal cost savings (e.g. z = 13), the desirability of merger increases monotonically with trade liberalization.
Desirability of Merger as a Function of t for Different Values of z
The analysis in Proposition 1 can be used to give important new insights to the role of merger-induced reductions in marginal cost in determining the effect of trade liberalization on the desirability of mergers, as illustrated by Corollary 1. Let zw(t) ≡ (16a + 7t)/144 > 0.
Corollary 1. At any given tariff level t ∈ (0, tmax(z)), marginal trade liberalization decreases the desirability of a merger iff z ∈ (0, zw(t)).
.Corollary 1 is illustrated by Figure 1. In this example, for z = 13, we have that z > zw(t) for all t ∈ (0, tmax(z)). Therefore, a marginal tariff reduction, at any given tariff level, makes the merger more desirable. In contrast, for z = 10, we have that z < zw(t) for all t ∈ [0, tmax(z)). Therefore, a marginal tariff reduction has the reverse effect.
The driving force behind this result is the effect of trade liberalization on the merger-induced change in consumers' surplus. Consumers' surplus in Home is given by 
. Since the merger causes a discrete fall in Q, it causes consumers' surplus to fall more than proportionately. Trade liberalization partially offsets this harmful effect of the merger by causing post-merger output levels of firms to rise.14 The higher is z, the lower the merger-induced fall in Q at any given tariff level, and the greater the beneficial impact of trade liberalization through the above mentioned channel due to the fact that consumers' surplus is increasing and strictly convex in Q.
The role of the competition bureau in the face of trade liberalization, thus, depends on the level of marginal cost savings from merger. At sufficiently high levels of marginal cost savings, the competition bureau need not be concerned about the impact of marginal trade liberalization. If the merger would have been allowed pre-liberalization, then it will necessarily be allowed post-liberalization. This does not hold at sufficiently low marginal cost saving levels, as shown by Figure 1 for z = 10.
It is interesting to note that zw(t) is increasing in t. Thus, for any t > 0, it holds that zw(t) > zw(0). That is, a marginal trade liberalization is less likely to increase the desirability of a given merger the higher is the pre-liberalization tariff level. The role played by the pre-liberalization tariff level is further elaborated in Proposition 1(ii).
An interesting case arises for intermediate values of z. From (10) it follows that for a range of marginal cost savings, z ∈ (a/9, 11a/92), we have tw(z) ∈ [0, tmax(z)). Consequently, F is non-monotonic in t, as shown in Figure 2.
Desirability of Merger as a Non-monotonic Function of t
Figure 2 illustrates Proposition 1(ii). Using a = 100, z = 11.5 and φ = 185,15 we show that a marginal tariff reduction at any t > tw (11.5) such as t1, makes the merger lessdesirable. At any t > tw (11.5) such as t2, however, a marginal tariff reduction has the reverse effect on the desirability of merger.
Proposition 1(ii), thus, highlights the importance of taking into account, not only the level of marginal cost savings, but also the pre-liberalization tariff level, when the competition bureau is assessing potential mergers. The same merger that would be optimal to allow in the face of a marginal trade liberalization at t = t2, would not be optimal to allow at t = t1.
Trade Liberalization: A Global Analysis
We now turn our attention to an interesting implication of Proposition 1(ii). Since a marginal analysis can lead to different results at different levels of tariff, a marginal analysis may not be a reliable predictor of the effects of non-marginal tariff reductions. For a merger with a given level of marginal cost savings, we seek to determine the conditions under which the impact of marginal and non-marginal trade liberalization differ.
Given marginal cost savings from merger, z, if trade liberalization increases the desirability of merger in the neighborhood of free trade, then, by Proposition 1(ii), it will increase the desirability of the merger for any pre-liberalization tariff level, t2 such that t2 < tw(z). It can also be concluded that a non-marginal change in tariff from t = t2 < tw(z) to t = 0 will increase the desirability of a merger: that is, for a given level of marginal cost savings, z, if t2 < tw(z) then F(t2, z) < F(0, z).
An interesting case arises when the pre-liberalization tariff level is sufficiently large: t = t0 > tw(z). Given z, it holds that 
and 
. Let
Proposition 2. For
and
, it holds that
and yet F(0, z) > F(t, z).
This can be seen from the fact that the function F(t, z) − F(0, z) is a convex quadratic function of t with roots at t = 0 and 
Therefore, for 
it holds that F(t, z) − F(0, z) < 0 and for 
it holds that F(t, z) − F(0, z) > 0. This, together with Proposition 1(ii), implies that Proposition 2 holds.
Proposition 2 identifies a range of pre-liberalization tariff levels, 
, at which marginal trade liberalization decreases the desirability of merger whereas a complete removal of a tariff increases the desirability of merger. This brings us to one of the main conclusions of this paper regarding merger policy under trade liberalization. Proposition 2 implies that in order to derive accurate policy decisions, the competition bureau must take into consideration the exact pre- and post-liberalization tariff levels rather than relying on marginal analyses. Starting from a tariff level, 
at which the merger is desirable, a jump to free trade necessitates that the competition bureau allow the merger. If, however, the move to free trade is gradual, as is typically the case subsequent to the signing of international trade treaties, it becomes relevant to investigate the effect of reducing the tariff level marginally. As illustrated by Proposition 2, this could lead to the merger becoming undesirable in the period immediately following the free trade agreement. The competition bureau would then need to compare the costs of allowing the merger in the short run and the benefits of allowing the merger in the longer run when the tariff level eventually approaches zero.
4. Profitability and Desirability of Merger
We now combine the analysis of the desirability of a horizontal merger with the analysis of the profitability of such a merger to address the second important question addressed by the paper: does trade liberalization move the social and private responses to a potential merger in the same direction? This has implications for whether merger policy needs to actively prevent or encourage mergers in the face of trade liberalization. Let P(t, z) ≡ ΠM − Π1 − Π2, t*(z) ≡ (7a − 48z)/91 and 
The Role of Cost Savings
Proposition 3. We have the following:
- (i)
For sufficiently small merger-induced reductions in marginal cost
and t ∈ (max{0, tw(z)}, min{t*(z), tmax(z)}), a marginal tariff reduction decreases both the profitability and the desirability of the merger. - (ii)
For sufficiently large merger-induced reductions in marginal cost
and t ∈ (max{0, t*(z)}, min{tw(z), tmax(z)}), a marginal tariff reduction increases both the profitability and the desirability of the merger.
The proof of Proposition 3 is available in the Appendix. Proposition 3 shows that given values of pre-liberalization tariff levels lying between tw(z) and t*(z), the need for competition policy to actively disallow or encourage the merger in response to trade liberalization is reduced. If trade liberalization renders the merger more (less) desirable, the merger is naturally more (less) likely to be realized since it simultaneously becomes more (less) profitable.
In our previous numerical example (a = 100, φ = 230), we have 
, and for z = 10, we have tw(z) < 0 and t*(z) = 2.42. Therefore, in Figure 3, for t ∈ (0, 2.42), we have that trade liberalization decreases both the profitability and the desirability of the merger. For z = 13, we have tw(z) > tmax(z) = 16 and t*(z) = 0.84. Therefore, in Figure 3, for t ∈ (0.84, 16), trade liberalization increases both the profitability and the desirability of the merger. Note that tw(z) is increasing in z while t*(z) is decreasing in z. This implies that for mergers yielding higher marginal cost savings, Proposition 3(ii) is more likely to apply.
Desirability and Profitability of Merger as Functions of t
Figure 3 also illustrates that cases do arise for which the desirability and profitability of the merger move in opposite directions as trade is liberalized. For example, for z = 10 and t ∈ (2.42,20), trade liberalization increases the profitability but decreases the desirability of the merger. The conditions under which this occurs are formalized in Proposition 4.
Proposition 4. We have the following:
- (i)
For
and t ∈ [0, min{t*(z), tw(z)}), trade liberalization increases the desirability and decreases the profitability of the merger. - (ii)
For z ∈ [0, a/7) and t ∈ (max{tw(z), t*(z)}, tmax(z)), trade liberalization decreases the desirability and increases the profitability of the merger.
This can be seen from the fact that t*(z) > 0 iff z < 7a/48 and tw(z) > 0 iff z > a/9. Also, it is straightforward to show that for any z ∈ [0, zmax), it cannot be that both t*(z) < 0 and tw(z) < 0. This, together with Proposition 1, implies that Proposition 4 (i) holds. We have that both t*(z) < tmax(z) and tw(z) < tmax(z) iff z < a/7. This, together with Proposition 1, implies that Proposition 4 (ii) holds.
Proposition 4 shows that, for a range of intermediate levels of marginal cost savings from merger, there does exist a range of pre-liberalization tariffs, t ∈ [0, min{t*(z), tw(z)}), for which trade liberalization increases the desirability of merger but reduces its profitability, so that competition policy might be needed to actively encourage the merger. For tariff levels higher than max{tw(z), t*(z)}, however, the need for competition policy to actively prevent potential mergers with low marginal cost savings in the face of trade liberalization increases. Although the merger becomes more profitable to the merger participants, and therefore, is more likely to be realized, it becomes less desirable to society.
The analysis in Propositions 3–4 depends on the level of cost-savings which, in reality, is difficult to ascertain. Moreover, the potential marginal cost savings from a proposed merger are even harder for the competition bureau to measure. Therefore, in Proposition 5, we derive policy prescriptions independent of the level of marginal cost savings from merger.
The Role of the Tariff Level
Proposition 5. Let
.
- (i)
For
, if trade liberalization increases the profitability of merger then it necessarily increases its desirability. - (ii)
For
, if trade liberalization decreases the profitability of merger then it necessarily decreases its desirability.
The proof of Proposition 5 is available in the Appendix. Given the growing merger activity that has been observed in parallel to important tariff reductions in the past decades, a natural question that has arisen is the following. Should competition authorities be more vigilant towards those mergers that are encouraged by trade liberalization? Proposition 5(i) shows that the latter is not the case when the pre-liberalization tariff level is sufficiently small, i.e. 
. In particular, in the neighborhood of free trade, Proposition 5(i) shows that, regardless of the marginal cost savings from the merger, the need for competition policy to actively disallow mergers in the face of trade of liberalization is reduced since those mergers that are more likely to be proposed are also the ones that become more desirable.
Proposition 5(ii), however, shows that, regardless of the marginal cost savings from merger, when the tariff level is sufficiently high, the need for competition policy to actively encourage the merger in the face of trade liberalization is reduced. This is because those mergers that are less likely to be proposed are also the ones that become less desirable. We note that 
for all z < 53/224.
Proposition 5 is further useful because it provides conditions under which the competition bureau can formulate the optimal merger policy without having to determine the impact of trade liberalization on the desirability of merger. It is sufficient to have information about the desirability of merger at the prevailing tariff level at the time of the merger proposal and the impact of trade liberalization on the profitability of merger only. The latter is easier to determine since it is implicitly included in firms' decision to propose mergers in the face of trade liberalization. For example, Proposition 5 (i) tells us that if a merger that is proposed in the face of trade liberalization is desirable at the current tariff level, it will become more so post-liberalization.
Figure 4 summarizes our results in this section, setting a = 100 in line with our previous numerical examples, and compares the different thresholds of the tariff level that are used in Propositions 3–5.
Threshold Tariff Levels tw(z), tmax(z), and t*(z) as functions of z
In Figure 4, region A represents those combinations of t and z for which a marginal tariff reduction decreases both the profitability and the desirability of the merger, that is, t and z which satisfy Proposition 3(i). Region B represents those combinations of t and z for which a marginal tariff reduction increases both the profitability and the desirability of the merger, that is, t and z which satisfy Proposition 3(ii). Region C represents those combinations of t and z for which trade liberalization increases the desirability and decreases the profitability of the merger, that is, t and z which satisfy Proposition 4(i). Region D represents those combinations of t and z for which trade liberalization decreases the desirability and increases the profitability of the merger, that is, t and z which satisfy Proposition 4(ii). Also, in Figure 4, for tariffs below 
, if trade liberalization increases the profitability of merger then it necessarily increases its desirability. For tariffs above 
, if trade liberalization decreases the profitability of merger then it necessarily decreases its desirability. This is in line with Proposition 5.
5. Conclusion
The main message of this paper is that trade liberalization can alter the optimal merger policy of a given country. This becomes relevant given the proliferation of regional trade agreements in recent years.
Since this paper shows that the welfare effect induced by a merger changes in response to trade liberalization, our first contribution is to demonstrate the need for competition bureaus to account for this when deciding whether to allow a potential merger. Moreover, we highlight two factors which deserve particular attention within this context because they alter the way in which trade liberalization affects the desirability of a merger.
First, the level of marginal cost savings yielded by a merger is shown to take on an additional role in the face of trade liberalization. An integral part of merger policy enforcement is the estimation of the potential cost savings to be generated by the merger. Our analysis shows that this information can directly be used to predict whether trade liberalization will increase or decrease the desirability of the merger. In particular, we show that trade liberalization increases (decreases) the desirability of mergers with sufficiently high (low) marginal cost savings.
Second, we show that different levels of pre- and post-liberalization tariff and magnitudes of the tariff reductions involved may lead to very different policy implications regarding a given merger with a given level of cost savings. Previous studies have mostly restricted their analyses to either the neighborhood of free trade or of the optimal tariff level. By considering all non-prohibitive tariff levels, we are able to determine conditions under which although marginal trade liberalization increases the desirability of merger in the neighborhood of free trade, the reverse holds at sufficiently high tariff levels. We also determine the conditions under which, the impact of marginal trade liberalization on the desirability of merger fails to be a reliable indicator of the same when tariff changes are non-marginal.
Moreover, we determine the conditions under which desirability and profitability of merger move in the same and in opposite directions in response to trade liberalization. For example, in the neighborhood of free trade, for sufficiently high marginal cost savings from merger, trade liberalization increases the desirability of merger whilst decreasing the profitability. Thus, a scenario is illustrated where competition policy might be called upon to actively encourage domestic mergers rather than preventing them, in response to trade liberalization.
Finally, we also show that it is possible for the competition bureau to use the process of trade liberalization to determine conditions under which it does not need to actively disallow mergers. For example, we are able to compute ranges of tariff levels, independent of the level of merger-induced marginal cost savings, for which if trade liberalization increases the profitability of merger then it necessarily increases its desirability. This is important because potential costs savings from merger are often difficult to evaluate in reality. Our finding thus shows that it is possible for the competition bureau to reduce its reliance on this imperfectly observed variable by using an alternative source of information, the tariff level, which is directly observable, when formulating optimal merger policy in the face of trade liberalization.
These results have been obtained using a few simplifying assumptions such as identical linear demand, number of firms and tariff reductions across countries. While we acknowledge that the exact roles played by marginal cost savings and magnitudes of tariff reductions may differ for alternative model specifications, our simplifying assumptions serve our main purpose: that is, to illustrate, as clearly as possible, that these factors do affect the impact of trade liberalization on merger policy and can be expected to do so under more general conditions. Furthermore, even within this simple framework, we are able to show that the relationship between trade liberalization and merger policy is quite complex and therefore merits further investigation under more general settings. It would also be useful to investigate how the welfare effects of cross border mergers respond to trade liberalization.
Appendix
Proof of Proposition 3
Marginal trade liberalization increases (decreases) the profitability of a merger iff t > t*(z) (t < t*(z)) (see Corollary 1 of Benchekroun and Ray Chaudhuri (2006)). It can be shown that 
, with tw(z) − t*(z) linear and increasing in z. Thus, for 
, it holds that tw(z) < t*(z) and for 
, it holds that tw(z) > t*(z). Since 
, it follows that for 
, we have tw(z) < tmax(z) and t*(z) > 0. This, together with Proposition 1, completes the proof for Proposition 3(i). It is straightforward to show that for 
, t*(z) < tmax(z) and tw(z) > 0. This, together with Proposition 1, completes the proof for Proposition 3(ii).□
Proof of Proposition 5
1. Let z*(t) = t*−1(z). Marginal trade liberalization increases (decreases) the profitability of a merger iff z > z*(t) (z < z*(t)) (see Proposition 1 of Benchekroun and Ray Chaudhuri (2006)). It can be shown that 
, with zw(t) − z*(t) linear and increasing in t. Thus, for 
, it holds that zw(t) < z*(t) and for 
, it holds that zw(t) > z*(t).
If trade liberalization increases the desirability of merger then, from Corollary 1, it follows that z > zw(t). For 
, since zw(t) > z*(t), it follows that for any z > zw(t), marginal trade liberalization increases the profitability of merger.
In contrast, if trade liberalization decreases the profitability of merger then, it follows that z < z*(t). For 
, since zw(t) > z*(t), it follows that, for any z < z*(t), marginal trade liberalization decreases the desirability of the merger.
2. Similar to proof of (i).□
