The Gain-from-Merger function for a merger between two domestic firms is shown to be .... m foreign firms sells y in the home country and y* in the foreign.
THE EFFECTS OF NON-MARGINAL CHANGES IN THE TARIFF LEVEL ON HORIZONTAL MERGERS H. Benchekroun∗ and A. Ray Chaudhuri∗
First Draft. Very Preliminary. Please do not quote without authors’ authorization.
Abstract This paper analyses the effects of tariff reductions on cost-reducing horizontal mergers in a Cournot oligopoly in a two-country world. The Gain-from-Merger function for a merger between two domestic firms is shown to be strictly concave and non-monotone in the tariff level. For sufficiently large cost savings from merger, Long and Vousden (1995) show that marginal bilateral reductions in the tariff level lead to increases in the Gain-from-Merger function in the neighborhood of free trade, i.e. for tariff levels sufficiently close to zero. This result is generalized for the case of non-marginal tariff reductions and for high initial tariff levels in this paper. For sufficiently small cost savings from merger, Long and Vousden show that marginal tariff reductions lead to decreases in the gains from merger. We show in this paper that this does not necessarily hold in the neighborhood of positive tariffs and for non-marginal tariff reductions. For sufficiently small cost savings from merger there exists a positive value of the tariff level such that gains from merging are maximized. Thus, given initial tariff levels lower than this critical value, marginal bilateral reductions in the tariff rate will increase the profitability of high-cost-saving mergers and decrease the profitability of low-cost-saving ones. Given initial tariff levels higher than the critical value, both types of mergers become more profitable, a result very different from that obtained for tariff levels sufficiently close to zero. Thus analyses of marginal tariff reductions around the area of free trade may not lead to adequate recommendations for competition policy.
(∗) Department of Economics, McGill University
1
1
Introduction
During the period 1981-98 there were 70,000 mergers proposed across North America and Europe, each worth over $1 million, of which approximately 45,000 were realized, the average value of firms being $2 million. (Gugler, Mueller, Yurtoglu, Zulehner, 2003)). Given that globalization affects merger activity across countries, often the merging firms being some of the largest multinational companies, policy measures taken by antitrust authorities based on the predictions of the existing models of merger analysis affect the welfare of billions of consumers across the world. As pointed out by Kofi Annan, Secretary General of the United Nations, ”a freer market - and particularly the emerging global market for enterprises - calls for greater vigilance” (World Investment Report, UNCTAD). Trade liberalization in Europe, North America and Australia has been accompanied by the formation of a growing number of mergers, mainly domestic in Australia and the Canada-U.S. free trade area, including many cross-border cases in Europe (Long and Vousden, 1995). The effects of changes in trade policy on the industry structure and competition policy of the trading partners has been studied by many researchers from various perspectives. Dixit (1984), one of the first studies in this area, shows that trade liberalization, by increasing competition in the domestic market, reduces the need for active competition policy. Rysman (2000) sets up a Cournot model in which a country first selects the number of firms in the industry and then the optimal trade policy (in this case, an export subsidy). Since the model only considers the case where home and foreign firms compete in a third market, so that consumer surplus is not an issue for the two producing countries, each country can be shown to choose a monopoly and then to provide export subsidies. If agreements such as GATT limit the level of subsidies, it can be shown that competition rises in the producing countries, so that these results support those of Dixit. Neven and Seabright (1997) also obtain these results by examining the changes in firms’ incentives to merge post-trade-liberalisation, instead of focusing on the choices made by the governments to maximize social welfare. Horn and Levinson (2001) disagree. They investigate the effect of international agreements like GATT on merger policies (in this case represented by the level of industry concentration) that are chosen at a national level. Trade liberalization results in stricter standards for competition policy in this model. Countries are shown to be
2
substituting competition policy for trade policy in the use of promoting their own welfare at the expense of that of others. Richardson (1999) sets up a similar model in which countries strategically choose both the trade and merger policies and obtains similar results. Although not the focus of our study in this paper, a particularly interesting area of study involves the examination of the benefits of setting up international antitrust authorities. Since 1996, the WTO has been paying close attention to competition policy, and the EU has set up a supra-national level antitrust authority. Head and Ries (1997) summarize the international welfare effects of cross-border mergers and point out that given the large volume of cross-border mergers today, world welfare could be significantly increased were there to exist international bodies for the implementation of global antitrust laws. The related literature include Bhagwati (1991), Gatsios and Seabright (1990) and Neven (1992). Bond (1997) sets up a political economy model to examine the differences in the decision to allow particular mergers between the federal government and the state governments. Dixit (1984), Horn and Levinsohn (2001), Rysman (2000), Neven and Seabright (1997) and Richardson (1999), all study the effect of marginal changes in the tariff level on the gains from domestic mergers. The model presented in this paper is based on another paper in the same area, namely Long and Vousden (1995). Long and Vousden analyze the effects of marginal tariff reductions in the neighborhood of free trade on horizontal mergers in a Cournot oligopoly in a two country world. For mergers between two domestic heterogeneous firms unilateral tariff reductions encourage mergers which concentrate market power at the expense of mergers which reduce cost, while bilateral tariff reductions have the opposite effect, encouraging mergers which significantly reduce cost. The merger induced cost savings in their model arise from differences in the marginal costs of production across firms, with a merged firm producing at the lowest marginal cost of its constituents. The analysis is carried out by focusing on the gains from trade as a function of the cost differential between the merging firms and then doing comparative statics to see the effect of marginal changes in the tariff level. The only existing study of the effects of non-marginal changes in the tariff level, to our knowledge, is one conducted by Gaudet and Kanouni (2001). The equilibria that occur before and after the abolition of the tariff are compared, for different levels of the tariff. The merging firms are assumed to have no variable costs but do have identical fixed costs. This is similar to the assumptions made by Ross (1988), who examines the effect of marginal tariff reductions on gains from merger. The savings on fixed cost from the merger makes mergers
3
profitable. The threshold value of fixed costs that would make the merger just profitable is found. It is then examined how this threshold value changes with changes in the tariff level. The threshold values for different levels of tariff (relative to the prohibitive one) are compared to that under free trade. The larger the threshold value relative to the free trade threshold value, the larger the fixed cost savings from merger must be to make the merger profitable. In this setting, it is shown that when the tariff is not prohibitive, trade liberalization increases the profitability of the merger. When the tariff is prohibitive, trade liberalization always reduces the profitability of merger. Our paper uses the same framework as Long and Vousden (1995) to set up its basic model but focuses on how the gains from merger between heterogeneous domestic firms change as the tariff level is increased progressively from zero to the prohibitive level (the prohibitive tariff being the minimum tariff level sufficiently high so as to reduce imports to zero). ‘Thus we are able to analyze the effects of non-marginal changes in the tariff level. In particular, the gains- from-merger function is shown to be non-monotone (and strictly concave) in the preliberalisation tariff level. For sufficiently small cost savings from merger, Long and Vousden show that marginal tariff reductions lead to decreases in the gains from merger. That this does not necessarily hold for non-marginal tariff reductions, and that for sufficiently high initial tariff levels even the marginal changes in the tariff level push the gains from merger in the opposite direction is shown in this paper. The effects of marginal and non-marginal changes in the tariff level on the gains from merger are studied in detail in this paper and it is shown that analyses of marginal tariff reductions around the area of free trade may not lead to accurate prescriptions for competition policy.
2
The Model and Preliminaries
We consider two countries: Home and Foreign1 . Foreign has m identical firms and Home has n + 2 firms. All firms produce a homogenous product. Each foreign firm has a constant marginal cost given by cF . Each of the m foreign firms sells y in the home country and y ∗ in the foreign. In Home, we assume that n firms (firm 3 to firm n + 2) are identical with marginal cost c. The non-identical domestic firms, firm 1 and firm 2 have different 1 In order to make the comparison between our results and those of Long and Vousden easier we follow their setting and notation closely.
4
marginal costs (at least one different from c). Without loss of generality let us assume that c1 > c2 . Firm 1 sells x1 in the domestic market and x∗1 in the foreign market. Firm 2 sells x2 in the domestic market and x∗2 in the foreign market. Each of the n identical domestic firms sells x in the domestic market and x∗ in the foreign market. In each market firms compete in quantities, i.e. a la Cournot. Both countries have identical linear demand curves given by: p = a − bQ where a, b > 0 and p and Q are the price and total quantity sold in the country.
Each country imposes an import tariff. Since the two countries are identical we study the case where the tariffs imposed by Foreign and Home are identical: a symmetric bilateral tariff denoted t. The model examines the case when both countries simultaneously reduce t by the same amount, i.e. bilateral tariff reductions.
2.1
The market equilibrium:
The profits of firm i in Home from its sales in Home are given by:
πi =
⎧ ⎪ ⎪ ⎨
xi (a − b(x1 + x2 + nx + my)) − ci xi if i = 1, 2
(1)
⎪ ⎪ ⎩ x (a − b(x1 + x2 + nx + my)) − cx, if i = 3, 4..., n + 2
The profits of firm i in Home from its sales in Foreign are given by:
πi∗ =
⎧ ⎪ ⎪ ⎨
x∗i
(a −
b(x∗1
+
x∗2
∗
∗
+ nx + my )) − (ci +
t)i x∗i
if i = 1, 2
⎫ ⎪ ⎪ ⎬
⎪ ⎪ ⎪ ⎭ ⎩ x∗ (a − b(x∗1 + x∗2 + nx∗ + my ∗ )) − (c + t)x∗ , if i = 3, 4..., n + 2 ⎪
(2)
The profits of firm f in Foreign from its sales in Home are given by:
πf = y (a − b(x1 + x2 + nx + (m − 1) y + yf )) − (cF + t)yf , for f = 1, 2..., m The profits of firm f in Foreign from its sales in Foreign are given by: 5
(3)
πf∗ = y ∗ (a − b(x∗1 + x∗2 + nx∗ + my ∗ )) − cF y ∗ , for f = 1, 2..., m
(4)
Each of Home’s firm i takes the quantity chosen by the other (n + m + 1) firms as given and chooses the quantities xi and x∗i that maximize (1) and (2) respectively and similarly each of Foreign’s firm f takes the quantity chosen by the other (n + m + 1) firms as given and chooses the quantities yi and yi∗ that maximize (3) and (4) respectively. The Cournot equilibrium quantities for the two markets are computed. We have the interior equilibrium quantities sold in Home:
x1
=
x2
=
x = y
=
µ
¶ 1 [a + c2 + nc + m (cF + t) − (m + n + 2) c1 ] b (m + n + 3) µ ¶ 1 [a + c1 + nc + m (cF + t) − (m + n + 2) c2 ] b (m + n + 3) µ ¶ 1 [a + c1 + c2 + m (cF + t) − (m + 3) c] b (m + n + 3) µ ¶ 1 [a + c1 + c2 + nc − (n + 3) (cF + t)] b (m + n + 3)
The equilibrium quantities sold in Foreign are given by
x∗1
=
x∗2
=
x∗
=
y∗
=
µ
¶ 1 [a + (c2 + t) + n(c + t) + m (cF ) − (m + n + 2) (c1 + t)] b (m + n + 3) µ ¶ 1 [a + (c1 + t) + n(c + t) + m (cF ) − (m + n + 2) (c2 + t)] b (m + n + 3) µ ¶ 1 [a + (c1 + t) + (c2 + t) + m (cF ) − (m + 3) (c + t)] b (m + n + 3) µ ¶ 1 [a + (c1 + t) + (c2 + t) + n(c + t) − (n + 3) (cF )] b (m + n + 3)
It is straightforward to obtain the profits for each firm at the equilibrium by substituting the quantities above
into (1), (2) , (3) and (4) . The profits of Firms 1, 2 at the equilibrium can be written as
6
³ ´ 2 2 πi = b (xi ) + (x∗i ) , i = 1, 2 In this paper we want to study the effect of trade policy on antitrust policy towards mergers. In particular we seek to determine the impact of trade policy on firms’ incentive to merge. In a closed economy, under Cournot oligopoly mergers are not always profitable. In fact, as shown by Salant, Switzer and Reynolds (1983) a noncost-reducing merger is only profitable if the merging firms constitute 80% of the post-merger market. The case studied in SSR can be retrieved from the model at hand by for example setting t = 0 and c1 = c2 = cF = c, or alternatively setting t at a prohibitive level such that no exchange takes place.
2.2
A merger:
In this paper we focus on the case of the merger of only two firms, firm 1 and firm 2 in Home. When two firms merge, the new entity and the n + m + 1 other firms compete a la Cournot. In the SSR framework, such a merger results in a Cournot equilibrium between n + m + 2 symmetric firms. Unless it’s a merger to monopoly, a merger is always unprofitable for the two firms who merge: the profits of the new entity are smaller than the profits of the two firms in the premerger competition. Although in the SSR framework, firms are symmetric, the result can be generalized to the case of asymmetric firms. In the case of asymmetric firms, with constant marginal costs, we assume that the cost of the new entity corresponds to the lowest cost of the firms merging: there are cost savings. In our case, the merging firms are firm 1 and firm 2 and the marginal cost of the new entity is c2 (since we assumed c2 < c1 ).
2.2.1
The closed economy case
For the case of a closed economy: the merger of firm 1 and firm 2 is profitable iff
¡ ¢ G ≡ πM − π1 − π2 = b X 2 − x21 − x22 > 0
(5)
where G is the gains from a merger, πM the profit of the merged firm and X the Cournot equilibrium quantity produced by the merged firm. Note that even if G denotes the gains from merger it can take negative values: a
7
merger is then unprofitable. After substitution of X, x1 and x2 and after simplification the gains from a merger, G, can written G=(
α 2 α − (2 + n) z 2 α+z 2 ) −( ) −( ) n+2 3+n 3+n
(6)
where z ≡ c1 − c2 and α ≡ a − c2 + n(c − c2 ). If c1 = c2 then (6) gives G=(
after simplification (5) gives α
2
Ã
α 2 α 2 ) − 2( ) n+2 3+n
1 − 2n − n2 2
(n + 2) (3 + n)
2
!
< 0 for all n > 0
a merger of two equals is never profitable regardless of how c2 compares to c; unless n = 0 then we have a merger to monopoly. This generalizes the conclusion of SSR to the case of two types of firms: a first group of outsider firms with a marginal cost c and a group of insiders with a marginal cost c2 not necessarily equal to c. When c1 6= c2 we have 1 G= b
õ
α − (n + 2) z (n + 2) (3 + n)
which after simplifications yield G=
where z1 ≡
α (n+2)
and z2 =
−α(1−2n−n2 )
¶µ
α α+z + n+2 3+n
³ ´ 2 1 + (2 + n) 1 b
(n+2)(1+(2+n)2 )
(3 + n)
2
¶
−
µ
α − (2 + n) z 3+n
¶2 !
(z − z2 ) (z1 − z)
.
It can be seen from above that the gains from merger are quadratic in the level of the cost differential between the merging firms, i.e. c1 − c2 . This also becomes evident by examining the partial derivatives of the gain function with respect to c1 and c2 . In particular we have
which after simplification gives
¢ ¡ −α 1 − 2n − n2 α ³ ´ z1 − z2 = − (n + 2) (n + 2) 1 + (2 + n)2 z1 − z2 =
α 6 + 2n >0 (n + 2) 1 + (2 + n)2 8
If α > 0 and z2 < z1 then we have G > 0 iff 0 < z2 < z < z1
This suggest that there is an optimal cost differential level where the gains from merger are maximized (and positive). This can all be generalized to the case of trade with a bilateral import tariff.
3
Profitability of mergers and Trade policy
We now turn to the case of interest of this paper: the impact of import tariffs on the profitability of mergers. In the setup described in Section 2 above, we consider the merger of firm 1 and firm 2 in Home. We compute the postmerger equilibrium quantities sold in Home and Foreign respectively. For interior solutions we find:
µ
¶ 1 [a + nc + m (cF + t) − (m + n + 1) c2 ] b (m + n + 2) µ ¶ 1 x = [a + c2 + m (cF + t) − (m + 2) c] b (m + n + 2) µ ¶ 1 y = [a + c2 + nc − (n + 2) (cF + t)] b (m + n + 2)
X
=
and
X
∗
x∗ y∗
µ
¶ 1 = [a + n(c + t) + m (cF ) − (m + n + 1) (c2 + t)] b (m + n + 2) µ ¶ 1 = [a + (c2 + t) + m (cF ) − (m + 2) (c + t)] b (m + n + 2) µ ¶ 1 = [a + (c2 + t) + n(c + t) − (n + 2) (cF )] b (m + n + 2)
where X and X ∗ denote the quantities sold by the merged entity in Home and Foreign respectively. The profits of the merged firm, indexed by the subscript M , from sales in Home and Foreign are respectively given by: 9
2
2
∗ πM = b (X) and πM = b (Xi∗ ) .
The merger will thus be profitable if and only if:
∗ − (π1 + π2 ) − (π1∗ + π2∗ ) ≥ 0 G ≡ πM + πM
G represents the gains from the merger. We are particularly interested in the impact of the tariff t on the G. We can first note that G is a quadratic function of t. Computing the second derivative of G with respect to t gives:
2 −1 + 2n + n2 + 2m2 n2 + 8m2 n + 3m2 + 6mn + 4m3 n + 6m3 + 2mn2 + 2m4 ∂2G = − < 0 for all n, m > 0. ∂t2 b (m + n + 2)2 (m + n + 3)2 G is thus a strictly concave quadratic function of t. Let tˆ denote the tariff rate such that
−1 + 2n + n2 + 2m2 n2 + 8m2 n + 3m2 + 6mn + 4m3 n + 6m3 + 2mn2 + 2m4 ¢ ∂G ¡ t = tˆ = 0 ∂t i.e. G reaches a unique global maximum at t = tˆ. The gains from merging G is a function of t and the other parameters of the model (a, b, c, cf , c1 , c2 ). It is a very heavy expression and determining the sign of G in general proves to be too difficult. A first attempt is to analyze the sign of G in the neighborhood of a given tariff level t0 . Long and Vousden (1995) study the case t0 = 0. This case is very interesting: it constitutes a study of the profitability of a merger in the neighborhood of free trade.
PROPOSITION 1: Let z ≡ c2 −c1 be the cost differential between the merging firms, there exists a positive level of cost differential, denoted by z ∗ , above which marginal bilateral reductions in t, in the neighborhood of free trade (t0 = 0), lead to increases in the gains from merger and below which the same leads to decreases in the gains from merger.
10
In the neighborhood of free trade, equal marginal bilateral tariff reductions encourage previously unprofitable mergers with high cost savings. Thus bilateral tariff reductions encourage mergers which primarily reduce cost rather than those which increase market concentration.
In this paper we wish to check the reliability of this conclusion when we want to determine the profitability of mergers away from free trade: i.e. when the benchmark scenario or outcome is not free trade, but some other tariff level t0 > 0. Moreover, we also wish to determine the impact of a non-marginal change in tariff. This approach seems more in line with reality, since typically, tariffs are initially strictly positive between countries and then lowered through free trade agreements. Moreover, while short term changes in tariffs are gradual and their impact can be approximated by a local analysis (in the neighborhood of a given tariff), in the long-run, free trade agreements set non-marginal changes in the level of tariffs, and the results from a local analysis could be unreliable.
3.1
The case of large cost savings from merger
We begin by examining the case when z > z ∗ . For sufficiently large cost savings from merger, Long and Vousden (1995) show that marginal bilateral reductions in the tariff level lead to increases in the Gain-from-Merger function, ∂G ∂t |t=0
< 0. This result is shown to be true around tariff level zero. In this paper we generalize this result for the
case of non-marginal tariff reductions and for the case of marginal tariff reductions for any positive tariff level, not just in the neighborhood of free trade.
PROPOSITION 2: For any given positive tariff level t, for z > z ∗ , as the tariff level is reduced from t, gains from merger increase ∂G ∂t
< 0. Proof: The Gain-from-Merger function, as defined earlier, can be written as: ³ ´2 ³ ´2 a+nc+m(cF +t)−(m+n+1)c2 a+n(c+t)+mcF −(m+n+1)(c2 +t) 1 G(t, z) = + b b(m+n+2) b(m+n+2) ³ ´2 ³ ´2 a+nc+m(cF +t)−(m+n+1)c2 −(m+n+2)z a+nc+m(cF +t)−(m+n+1)c2 +z − − − b(m+n+3) b(m+n+3) 11
³
a+n(c+t)+mcF −(m+n+1)(c2 +t)−(m+n+2)z b(m+n+3)
´2
−
³
a+n(c+t)+mcF −(m+n+1)(c2 +t)+z b(m+n+3)
For any z, G (., z) is a strictly concave function of t,
´2
2 −1 + 2n + n2 + 2m2 n2 + 8m2 n + 3m2 + 6mn + 4m3 n + 6m3 + 2mn2 + 2m4 ∂2G = − < 0 for all n, m > 0. ∂t2 b (m + n + 2)2 (m + n + 3)2
Therefore, for any given z : ∂ ∂ (G(t, z)) < (G(0, z)) for all t > 0 ∂t ∂t Since
∂ ∂t
(G(0, z)) < 0 for all z > z ∗ (by Proposition1), we have
∂ ∂t
(G(t, z)) < 0 for all z > z ∗ and for all t > 0
Bilateral tariff reductions increase the profitability of a merger of two firms at any tariff level t. An implication of the proposition above is that for t > 0
G (t, z) < G (0, z) for all z > z ∗ When cost savings are high enough ( z > z ∗ ), if a merger is not profitable under free trade it is not going to be profitable when the tariff level is positive. Moreover, since G (., z) is a strictly concave quadratic function of t we have : for any given z there exists tz such that G (t, z) < 0 for any t > tz . The following situation can arise
for all z ∗ < z < z1 , G (t, z) < 0 < G (0, z) for t > tz
A merger that is not profitable under trade protection can become profitable under free trade.
Example:
Consider the case where the following parameter values hold: The choke price is given by a = 300, the slope of the demand curve is b = 1, the marginal cost of each of the identical domestic firms is c = 10, the marginal cost of the least efficient domestic firm is c1 = 19.5, the marginal cost of the most efficient domestic firms is c2 = 0, that of each of the identical foreign firms is cF = 10, the number of foreign firms is m = 16, and the number of identical domestic firms is n = 10. Fig. 1 shows the gains from merger as a function of the tariff level. 12
SEE F IGU RE 1
Fig. 1 shows the gains from merger as a function of the tariff level for the case z = 19.5 > z ∗ . For all positive tariff levels the gain function is decreasing in t.
It is tedious but straightforward to show that z ∗ is given by:
z
∗
=
¢ ¡ ¢ ¡ a −1 + 2mn + m2 + 2m + n2 + 2n + c2 1 − 6mn − 3mn2 − 3m2 n − m − n − m3 − 3m2 − n3 − 3n2 +
(m + n + 2)2 (m + n + 1) ¡ ¢ ¡ ¢ c −n + 2nm + nm2 + 2n2 m + n3 + 2n2 + cF −m + 2mn + mn2 + 2m2 n + m3 + 2m2 (m + n + 2)2 (m + n + 1)
For the given parameter values z ∗ = 19. 233. In our example, z = 19.5 > z ∗ . As per the definition above, in this example, tz = 1. 218 2. The gains from merger are maximized at the negative tariff level : t = −1. 427 5 × 10−2 . The prohibitive tariff level, T , (the tariff level at which imports fall to zero), is given by:
T =
1 (−c1 − a − cn − c2 + cF n + 3cF ) −n − 3
Beginning from the prohibitive tariff level, in this case, 22. 315, where the gains from merger are negative, if bilateral tariff reductions cause the tariff level to fall below tz , the gains from merger change from being negative to positive. As the tariff level is reduced further all the way down to zero, the gains from merger keep increasing. Does this necessarily imply that as soon as tariff levels fall below tz , competition policy should be made stricter? A direct implication of Proposition 2 is that for z > z ∗ bilateral tariff reductions encourage those mergers which have high cost-savings and therefore might be welfare-improving, and discourage the low cost-saving mergers. A detailed analysis is therefore required to evaluate the welfare effects of the mergers that become possible as a result of trade liberalization before the implications for competition policy can be accurately determined.
13
3.2
The case of small cost savings from merger
For sufficiently small cost savings from merger, Long and Vousden (1995) show that marginal bilateral reductions in the tariff level lead to decreases in the Gain-from-Merger function,
∂G ∂t |t=0
> 0 in the area of free trade, i.e. for
t sufficiently close to zero. In this paper we show that for the case of non-marginal tariff reductions this result may be reversed in the sense that the (bilateral) abolition of a sufficiently large tariff may lead to an increase in the gains from merger. Also, even for sufficiently high initial tariff levels a marginal bilateral reduction in t leads to an increase in the gains from merger.
PROPOSITION 3: For all z < z ∗ , we have:
0
tˆ ∂t ∂t where tˆ is such that
∂ ∂t
Proof:
¡ ¢ G(tˆ, z) = 0.
For any given z :
∂ ∂ (G(t, z)) < (G(0, z)) for all t > 0 ∂t ∂t Since
∂ ∂t
(G(0, z)) > 0 for all z < z ∗ and G (., z) is strictly concave quadratic function of t, for a given t > 0 we
can have two cases: 0
tˆ ∂t ∂t where tˆ is such that
∂ ∂t
¡ ¢ G(tˆ, z) = 0. 14
If 0
G (0, z) for any t ∈ 0, tˆ . For t > tˆ, we have
0
tˆ. We then have
∂ ∂t
(G(t, z)) < 0
tˆ results in an increase in the profitability of a merger, whereas a marginal a reduction of a tariff in the neighborhood of free trade would predict the opposite.
Example:
Consider the case where the following parameter values hold: The choke price is given by a = 300, the slope of the demand curve is b = 1, the marginal cost of each of the identical domestic firms is c = 10, the marginal cost of the least efficient domestic firm is c1 = 19.85, the marginal cost of the most efficient domestic firms is c2 = 0, that of each of the identical foreign firms is cF = 10, the number of foreign firms is m = 12, and the number of identical domestic firms is n = 10. Fig. 2 shows the gains from merger as a function of the tariff level.
SEE F IGU RE 2
Fig. 2 shows the gains from merger as a function of the tariff level for the case z = 19.85 < z ∗ = 20.685.
Beginning from the prohibitive tariff level, in this case, 22. 296, where the gains from merger are negative,
15
bilateral tariff reductions cause the gains from merger to increase until the tariff level tˆ = 6.709 4 × 10−2 (the tariff level at which the gains from merger are maximized). Any further tariff reductions beyond tˆ, causes a decrease in the gains from merger. Thus, the effect of bilateral tariff reductions on the gains from merger depends on the initial value of the tariff level. If the initial tariff level is sufficiently high (i.e. above tˆ) then trade liberalization may need to be accompanied by stricter competition policy if the mergers that are encouraged by it are welfarereducing. If the initial tariff level is below tˆ then trade liberalization discourages domestic mergers so that stricter competition is not required.
The analysis above has another implication regarding the reliability of a local analysis (in the neighborhood of a tariff level) and the analysis of the impact of a non marginal tariff reduction. In particular, since
∂ ∂t
(G(0, z))
> 0 for all z < z ∗ and G (., z) is strictly concave quadratic function of t, there exists tz such that G (t, z) < 0 for t > tz and tz0 such that G (t, z) = G(tz0 , z).For any z > 0 and t > 0 we have G (t, z) < G(t˜, z) for all t˜ ∈ (tz0 , t) and G (t, z) > G(t˜, z) for all t˜ < tz0 . In the latter case we can have the following situation: ¡ ¢ ∂ G (t, z) > G t˜, z with t˜ < t whereas (G(t, z)) < 0 ∂t A local analysis (in the neighborhood of t) gives that a marginal reduction of the tariff level will increase the ∂ (G(t, z)) < 0) where as a nonmarginal tariff reduction from t to t˜ will reduce the profitability of a merger ( ∂t
profitability of a merger.
Example: Consider the case where the following parameter values hold: The choke price is given by a = 300, the slope of the demand curve is b = 1, the marginal cost of each of the identical domestic firms is c = 10, the marginal cost of the least efficient domestic firm is c1 = 20.9115, the marginal cost of the most efficient domestic firms is c2 = 9, that of each of the identical foreign firms is cF = 10, the number of foreign firms is m = 12, and the number of identical domestic firms is n = 10. For these parameter values the prohibitive tariff level is given by T = 23.07 and z ∗ = 12.451. In this example z = 11.9115 < z ∗ .
SEE F IGU RE 3 16
Fig. 3: The initial tariff level is t,where gains from merger are positive. Marginal reductions in t lead to increases in gains from merger. A non-marginal change from t to t˜2 reduces gains from merger, although they do remain positive. A non-marginal change from t to t˜1 reduces gains from merger from positive to negative.
SEE F IGU RE 4
Fig. 4: The initial tariff level is t,where gains from merger are negative. Marginal reductions in t lead to increases in gains from merger, and could lead to the gains changing from being negative to positive. Non-marginal tariff reductions to tariff levels below tz0 cause the gains from merger to become more negative. Fig. 3 shows that marginal reductions in the tariff level in the neighborhood of t will lead to increases in the gains from merger. However, a non-marginal reduction in the tariff level from t to t˜2 decreases the gains from merger below G (t, z). A reduction in the tariff level from t to t˜1 leads to the gains from merger changing from being positive to negative. It might be justifiable to make competition policy stricter for marginal tariff reductions in the neighborhood of t, since they encourage mergers with low cost-savings. Again, the welfare effects of these mergers need to be computed before the implications for competition policy can be accurately determined. However, sufficiently large tariff reductions, as shown in Fig. 3, discourage mergers themselves so that competition policy need not be made stricter.
Fig. 4 considers a case where the initial tariff level, t, results in losses from merger. Marginal tariff reductions could change these losses to gains. But if there was a jump to free trade (or to any tariff level less than tz0 ), then the process of trade liberalization would result in greater losses from mergers than before.
Instead of relying on the analysis of marginal tariff reductions in the neighborhood of free trade, it thus becomes imperative for the policy maker to understand the movement along the gain from merger function resulting from the particular change in the tariff level in question in order to make the welfare-maximising changes to competition policy.
17
4
Conclusion
This paper is one of very few which analyze the effect of non-marginal reductions in the tariff level on the gains from horizontal mergers. For sufficiently large cost savings from merger, Long and Vousden (1995) show that marginal bilateral reductions in the tariff level, in the neighborhood of free trade, lead to increases in the Gainfrom-Merger function,
∂G ∂t |t=0
< 0. Using a two-country model in which domestic and foreign firms compete
both in the Home and Foreign markets to reach Cournot equilibria we generalize this result for the case of nonmarginal tariff reductions and for the case of marginal tariff reductions for any positive tariff level, not just in the neighborhood of free trade. For sufficiently small cost savings from merger, Long and Vousden (1995) show that marginal bilateral reductions in the tariff level lead to increases in the Gain-from-Merger function,
∂G ∂t |t=0
> 0 in
the area of free trade, i.e. for t sufficiently close to zero. In this paper we show that for the case of non-marginal tariff reductions this result may be reversed in the sense that the (bilateral) abolition of a sufficiently large tariff may lead to a decrease in the gains from merger. It might be useful to supplement the analysis in this paper with a detailed study of the conditions under which mergers with high cost-savings and low cost-savings become more profitable and of the welfare effects of each type. This would complete the analysis required to prescribe any changes to competition policy that might increase welfare in the presence of bilateral trade liberalization. All of these results are obtained for the case where two heterogenous domestic firms merge, and given that all bilateral tariff reductions are equal for the two countries. It would be interesting to study cross-border mergers and unilateral tariff reductions in order to investigate the implications for competition policy.
5
References:
Bhagwati, J., ”Fair Trade, Reciprocity and Harmonisation: The Novel Challenge to the Theory and Policy of Free Trade,” 1991, Paper presented to the Conference on Analytical and Negotiating Issues in the Global Trading System, University of Michigan, Ann Arbor. Bond, E., ”Competition Policy in Customs Unions: A Natural Experiment using State Level Antitrust Enforcement,” 1997, Penn State University, Department of Economics, mimeo. 18
Collie, D. R., ”Mergers and Trade Policy under Oligopoly,” 2003, Review of International Economics, 11(1), 55-71. Dixit, A., ”International Trade Policy for Oligopolistic Industries,” 1984, Economic Journal, 94 Supplemental Issue: 1-16. Gatsios, K. and P. Seabright, ”Regulation in the European Community,” Oxford Review of Economic Policy, 5(2), 37-60. Gaudet, G. and R. Kanouni, ”Trade Liberalisation and Profitability of Domestic Mergers,” 2000, Département de sciences économiques and Centre de recherche et développement en économie, Université de Montréal; Département d’économie, Université Laval. Gugler, K., D. C. Mueller, B. B.Yurtoglu and C. Zulehner, ”The Effects of Mergers: An International Comparison,” 2003, International Journal of Industrial Organization, 21 (5), 625-53. Head, K. and J. Ries, ”International Mergers and Welfare under Decentralised Competition Policy,” 1997, The Canadian Journal of Economics 30, 1104-1123. Horn, H. and J. Levinsohn, ”Merger Policies and Trade Liberalisation,” 2001, Economic Journal, 111 (470), 244-76. Long, N.V. and N. Vousden, ”The Effects of trade Liberalisation on Cost-Reducing Horizontal Mergers,” 1995, Review of International Economics 3 (2), 141-155. Neven, D., ”Regulatory Reform in the European Community,” 1992, American Economic Review, 82 (2), 98-103. Neven, D. and P. Seabright, ”Trade Liberalisation and the Coordination of Competition Policy,” 1997, In Competition Policy in the Global Economy, Modalities for Cooperation, eds. L. Waverman, W. Comanor, and A. Goto. London: Routledge: 381-406. Richardson, M., ”Trade and Competition Policies, Concordia Discors?” 1999, Oxford Economic Papers, 51(4), 649-664. Ross, T. W., ”On the Price Effects of Mergers with Freer Trade,” 1988, International Journal of Industrial Organisation, 6, 233-46. Rysman, M. ”Competition Policy and trade Policy-Mediating the Interface,” Journal of World Trade, 30(4).
19
71-105. Salant, S.W., S. Switzer and R. J. Reynolds, ”Losses from Horizontal Merger: The Effects of an Exogenous Change in Industry Structure on Cournot-Nash Equilibrium,” 1983, The Quarterly Journal of Economics, 98 (2), 185-199. World Investement Report 2000, UNCTAD (United Nations Conference on Trade and Development), New York.
20
