This paper examines the profitability of horizontal merger in an open economy. We find that duopoly is a necessary, but not sufficient,condition for domestic merger to be profitable. A cross-border merger, however,can be profitable from any market structure

Chalkley, Martin

Stewart, Geoff

English

University of Dundee Online Publications

                                                              University of DundeeInternational trade and the incentive for mergerChalkley, Martin; Stewart, GeoffPublication date:2004Link to publication in Discovery Research PortalCitation for published version (APA):Chalkley, M., & Stewart, G. (2004). International trade and the incentive for merger. (Dundee Discussion Papersin Economics; No. 175). University of Dundee.General rightsCopyright and moral rights for the publications made accessible in Discovery Research Portal are retained by the authors and/or othercopyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated withthese rights. • Users may download and print one copy of any publication from Discovery Research Portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain. • You may freely distribute the URL identifying the publication in the public portal.Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Download date: 19. Mar. 2016                                                     Department of Economic Studies, University of Dundee, Dundee. DD1 4HN   Dundee Discussion Papers in Economics           International Trade and the Incentive for Merger    Martin Chalkley  and  Geoff Stewart                                                                                                                                                                        Working Paper  No. 175 November 2004 ISSN:1473-236X        International Trade and the Incentive forMergerMartin ChalkleyUniversity of DundeeGeo¤ StewartUniversity of Southampton15 November 2004AbstractThis paper examines the protability of horizontal merger in an open econ-omy. We nd that duopoly is a necessary, but not su¢ cient, condition fordomestic merger to be protable. A cross-border merger, however, can beprotable from any market structure.JEL classication: L4, F2Keywords: merger, international trade, oligopoly.1 IntroductionIn an important contribution to the literature on incentives for rms to merge, Salant,Switzer and Reynolds (1983) establish that a bilateral merger from an initial Cournotequilibrium with linear demand is unprotable, except in the case of duopoly. Onestrand of subsequent research has explored conditions that might augment the prof-itability of merger, such as the existence of cost savings (Perry and Porter, 1985),product di¤erentiation advantages (Deneckere and Davidson, 1985) or more complex(non-linear) demand functions (Cheung, 1992 and Faulí-Oller, 1997). In this paperwe revert to Salant, Switzer and Reynoldss constant cost, homogeneous product,1linear demand framework to examine the protability of merger in an open econ-omy. More specically, we ask: for what congurations of market structure and tradecosts, if any, will merger be protable? Using a two-country model, we considerboth within-country (domestic) and cross-border (international) mergers. Wend that, under trade conditions, duopoly is a necessary, but no longer su¢ cient,condition for protable domestic merger, but international merger can be protablefrom any market structure.12 The ModelWe consider a homogeneous product which can be produced and consumed in either,or both, of two countries, i; j = 1; 2; i 6= j: We suppose that each country has anidentical linear inverse demand functionPi = a Qi: (1)Production costs comprise a constant marginal cost which is the same for all rmsand, for simplicity, set to zero. In addition, exports are subject to a trade cost, t,per unit of output. We let ni and nj denote the number of rms located in countriesi and j respectively. We assume that the outcome of competition between rms is aCournot equilibrium in quantities and that there is no arbitrage. This implies thatthe price prevailing in country i can di¤er from that in country j by more than t.Prots for a representative rm based in country i are given byi = Piyi + (Pj   t)xi; (2)1A related, but di¤erent, issue is the change in the protability of merger that would result froma change in trade cost or unilateral tari¤. This question has been examined by Long and Vousden(1995), Falvey (1998) and Gaudet and Kanouni (2004).2where yi denotes the sales of a rm in country i to its home market and xi its exportsto country j.The problem of a representative rm in country i is to maximise (2), holdingoutputs of rival rms xed and subject to non-negativity constraints on xi and yi.We assume, henceforth, that domestic output is strictly positive in equilibrium. Therst order conditions, using an asterisk to denote Cournot equilibrium values, for thisproblem areP i   yi = 0 (3)andP j   t  xi  0xi  09>=>; ; (4)where a right hand brace indicates a pair of complementary inequalities, one of whichmust hold with equality.Noting that P i is a function of yi and xj alone, whilst Pj is a function of yj andxi alone, conditions (3) and (4) can be solved simultaneously to yieldxi (ni; nj) = max0;a  (nj + 1)tni + nj + 1(5)andyi (ni; nj) = (a+ njt)=(ni + nj + 1), xj(ni;nj) > 0;yi (ni; nj) = a=(ni + 1); xj(ni;nj) = 0:(6)In the case where exports from both countries are zero, (5) - (6) reduce to thestandard conditions for Cournot equilibrium in each country in which rms makeprots ofAi (ni) =ani + 12: (7)By inspection of (5), the maximum trade cost compatible with international trade3taking place (i.e. xi ; xj > 0) is given byt < maxani + 1;anj + 1 t (8)and for the symmetric case where ni = nj = n this threshold level of trade cost ist =an+ 1: (9)For an equilibrium involving trade, substitution from (5) and (6) into (1) and (2),after some rearrangement, yields:i (ni; nj; t) =2a2 + 2n2j t2   2anjt2 + t2ni + nj + 1: (10)It is convenient to decompose this prot into the elements deriving from the homeand overseas markets. For a rm located in country i, we denote these prots asii(ni; nj; t) and ji (ni; nj; t) respectively and note that i(ni; nj; t)  ii(ni; nj; t) +ji (ni; nj; t): Substitution from (5) and (6) into (1) yieldsii(ni; nj; t) =a+ njtni + nj + 12(11)andji (ni; nj; t) =a  (nj + 1)tni + nj + 12: (12)Similarly for a rm in country j; j(ni; nj; t)  jj(ni; nj; t) + ij(ni; nj; t); wherejj(ni; nj; t) =a+ nitni + nj + 12(13)andij(ni; nj; t) =a  (ni + 1)tni + nj + 12: (14)42.1 Merger under TradeWe consider rst an initial equilibrium with trade taking place and consider twopossible forms of merger. In what we term a domestic merger two rms in country iform a single rm and in what we term an international merger one rm in countryi joins with one rm in country j:With a domestic merger two rms forgo their individual prots i(ni; nj; t) buttake a share of prots that are enhanced through the reduction in domestic competi-tion. Thus, the gain to a domestic merger in a trade equilibrium in which ni = nj = n,can be written asGD(n; t) = ii(ni   1; nj; t) + ji (ni   1; nj; t)  2ii(ni; nj; t)  2ji (ni; nj; t): (15)With an international merger, we need to consider three types of rms. Followingsuch a merger there will be n   1 rms located wholly in country i, n   1 rmslocated in country j and one newly merged rm which has a production base ineach country. The newly merged rm is not the same as existing rms in that itcan supply either market from a domestic production unit. Therefore, in setting itsoutput in each country it can act like a domestic rm in that country; there is noincentive for it to produce for export because by producing domestically it can savetrade costs. The multinational rms impact on total production can therefore bededuced by analogy with a Cournot equilibrium in which domestic output in countryi is determined as if there are n domestic Cournot competitors and n   1 overseascompetitors, whilst output for export from country i is determined as if there aren   1 rms competing over exports facing n overseas competitors. The position incountry j is symmetric to this. International merger, therefore, has the e¤ect ofreducing by one the number of exporters serving each market but leaving the numberof domestic producers unchanged. Thus, the gain to an international merger in a5trade equilibrium in which ni = nj = n, can be written asGI(n; t) = ii(ni; nj   1; t) + jj(ni   1; nj; t)  i(ni; nj; t)  j(ni; nj; t): (16)In their autarky setting, Salant, Switzer and Reynolds (1983) demonstrate thata merger is protable only if there are two rms in the initial Cournot equilibrium.Does this result hold under trade? Proposition 1 addresses this question in regard todomestic and international merger.Proposition 1 For domestic merger, GD(n; t) < 0 for all n and 0  t < t whilstfor international merger there exists a threshold level of trade costs, btI(n) such thatGI(n; t) < 0 when t < btI(n), but GI(n; t) > 0 when btI(n) < t < tProof. Setting ni = nj = n, substituting from (11) and (12) into GD(n; t) anddi¤erentiating with resect to t the resulting rst order condition implies that GD(n; t)is maximised at a trade cost of t(n) = a2n2+2n+1. Substitution of this value of t intoGD(n; t) shows that the latter is negative for n  2 thus establishing the result fordomestic merger. After setting ni = nj = n, substituting from (11) and (12) intoGI(n; t) and equating to zero, the critical (zero-gain) value of trade cost can be solvedfor as btI(n) = 8an3 10an 2a2(4n4+12n3+7n2 2n 1) : For all n  2, btI(n) lies in the range (0; t): Since,as can readily be conrmed, GI(n; t) is negative at t = 0, concave and approaches zerofrom above as t approaches t it follows that btI(n) constitutes a threshold such thatGI(n; t) < 0 when t < btI(n), but G1(n; t) > 0 when btI(n) < t < t, thus conrmingthe result for international merger.The Proposition establishes that from an initial equilibrium in which there isinternational trade then, whatever the market structure, there is no incentive fordomestic merger. However, with an international merger the situation is somewhatdi¤erent. Specically, the Proposition admits the possibility that mergers from even62Number of firms in initial equilibrium (n)15trade cost (t)0.40GI < 0GI > 010t*50.10.30.2It?relatively competitive markets may be protable provided that trade costs are of anappropriate magnitude. The following gure illustrates this in the case of a = 1 whereit can be seen that for combinations of trade cost and initial concentration betweenthe locus t and the locus btI ; international mergers are protable.2.2 Merger Initiating TradeWhen a merger takes place from autarky (i.e. t > t) the resulting change in marketstructure may initiate trade. To understand this e¤ect, let Xi and Xj denotethe total volume of exports from i to j and j to i respectively. Using (5) for therepresentative rm in i; and an equivalent expression for that in j, these are given byXi (ni; nj; t) =ni(a  t(nj + 1))ni + nj + 1(17)and7Xj (ni; nj; t) =nj(a  t(ni + 1))ni + nj + 1: (18)With a symmetric initial structure with n rms in each country, the ows ofexports from i to j and j to i following a domestic merger in country i are, respectively,XDi (n; t) = max0;(a  t(n+ 1))(n  1)2n(19)andXDj (n; t) = max0;a  nt2: (20)Inspection of (19) and (20) reveals that the former is positive for t < t whilst thelatter is positive for t < tA wheretA  an: (21)Thus, if t lies in the range t < t < tA a domestic merger in country i will initiatea one-way ow of trade from j to i.Consider now an international merger. As explained above, this has the e¤ect ofreducing by one the number of exporters serving each market but leaving the numberof domestic producers unchanged. Assuming a symmetric initial structure with nrms in each country and using, (17) and (18), we can write the post-merger tradeows asXIi (n; t) = max0;(a  t(n+ 1))(n  1)2n(22)and8XIj (n; t) = max0;(a  t(n+ 1))(n  1)2n: (23)For either of these ows to be positive requires t < t, which is the same conditionthat pertained pre-merger. An international merger will thus neither initiate, norcause the cessation of, trading.We may thus consider whether from a position of autarky, but where t < tA, adomestic merger is protable. The gain from such a merger isGDA(n; t) = ii(ni   1; nj; t)  2A(ni) (24)and, in rather special circumstances, this may be positive as the following Propositionestablishes.Proposition 2 For n = 2 there exists a threshold level of trade costs, btD, such thatGDA(n; t) > 0 when btD < t < tA(n): In all other circumstances, GDA(n; t) < 0.Proof. After setting ni = nj = n, substituting from (11) and (7) into GDA(n; t)reveals directly that this is negative for n > 2: Setting n = 2 and solvingGDA(n; t) = 0for t yields a critical (zero-gain) value for trade cost of btD = a(4p2 3)6: Since GDA(n; t)is increasing in t it follows that for btD < t < tA(n) it is positive, thus establishing theclaim.The Proposition demonstrates that for trade costs in the range where a domesticmerger would initiate trade, duopoly is a necessary but not su¢ cient condition forthe merger to be protable. This contrasts to the position under autarky where,as established by Salant Switzer and Reynolds, a bilateral merger from duopoly isalways protable.93 ConclusionsIn their autarky setting, Salant, Switzer and Reynolds (1983) demonstrated that amerger would be protable if there were two rms in the initial Cournot equilibrium,but not if there were three or more rms. We show that in an open economy withinternational trade, the condition for a domestic merger to be protable becomesmore restrictive. Specically, duopoly is no longer a su¢ cient condition for a mergerto be protable; an additional requirement is that trade costs exceed a threshold level.An international merger, by contrast, can be protable from any market structure,provided again that trade costs lie in a certain range.References[1] Cheung, F.K. (1992). Two remarks on the equilibrium analysis of horizontalmerger.Economics Letters, 40, 1, 119-123.[2] Falvey, R. (1998). Mergers in open economies.World Economy, 21, 1061-1076.[3] Faulí-Oller, R. (1997). On merger protability in a Cournot setting.EconomicsLetters, 54, 1, 75-79.[4] Gaudet, G. and Kanouni, R. (2004). Trade liberalization and the protability ofdomestic mergers.Review of International Economics, 12, 3, 353-358.[5] Long, N.V. and Vousden, N. (1995). The e¤ects of trade liberalization on cost-reducing horizontal mergers.Review of International Economics, 3, 2, 141-155.[6] Salant, S., Switzer, S. and Reynolds, R. (1983). Losses from horizontal merger:the e¤ects of an exogenous change in industry structure on Cournot-Nash equi-librium.Quarterly Journal of Economics, 98, 2, 185-199.10

Losses from horizontal merger: the e¤ects of an exogenous change in industry structure on Cournot-Nash equilibrium.Quarterly

Mergers in open economies.World

On merger pro tability in a Cournot setting.Economics

The e¤ects of trade liberalization on costreducing horizontal mergers.Review of

Trade liberalization and the pro tability of domestic mergers.Review

Two remarks on the equilibrium analysis of horizontal merger.Economics

Dundee Discussion Papers in Economics 175:International trade and the incentive for merger

                                                                    University of DundeeDundee Discussion Papers in Economics 175Chalkley, Martin; Stewart, GeoffPublication date:2004Link to publication in Discovery Research PortalCitation for published version (APA):Chalkley, M., & Stewart, G. (2004). Dundee Discussion Papers in Economics 175: International trade and theincentive for merger. (Dundee Discussion Papers in Economics; No. 175). University of Dundee.General rightsCopyright and moral rights for the publications made accessible in Discovery Research Portal are retained by the authors and/or othercopyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated withthese rights.Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Download date: 25. Nov. 2023                                                     Department of Economic Studies, University of Dundee, Dundee. DD1 4HN   Dundee Discussion Papers in Economics           International Trade and the Incentive for Merger    Martin Chalkley  and  Geoff Stewart                                                                                                                                                                        Working Paper  No. 175 November 2004 ISSN:1473-236X        International Trade and the Incentive forMergerMartin ChalkleyUniversity of DundeeGeo¤ StewartUniversity of Southampton15 November 2004AbstractThis paper examines the protability of horizontal merger in an open econ-omy. We nd that duopoly is a necessary, but not su¢ cient, condition fordomestic merger to be protable. A cross-border merger, however, can beprotable from any market structure.JEL classication: L4, F2Keywords: merger, international trade, oligopoly.1 IntroductionIn an important contribution to the literature on incentives for rms to merge, Salant,Switzer and Reynolds (1983) establish that a bilateral merger from an initial Cournotequilibrium with linear demand is unprotable, except in the case of duopoly. Onestrand of subsequent research has explored conditions that might augment the prof-itability of merger, such as the existence of cost savings (Perry and Porter, 1985),product di¤erentiation advantages (Deneckere and Davidson, 1985) or more complex(non-linear) demand functions (Cheung, 1992 and Faulí-Oller, 1997). In this paperwe revert to Salant, Switzer and Reynoldss constant cost, homogeneous product,1linear demand framework to examine the protability of merger in an open econ-omy. More specically, we ask: for what congurations of market structure and tradecosts, if any, will merger be protable? Using a two-country model, we considerboth within-country (domestic) and cross-border (international) mergers. Wend that, under trade conditions, duopoly is a necessary, but no longer su¢ cient,condition for protable domestic merger, but international merger can be protablefrom any market structure.12 The ModelWe consider a homogeneous product which can be produced and consumed in either,or both, of two countries, i; j = 1; 2; i 6= j: We suppose that each country has anidentical linear inverse demand functionPi = a Qi: (1)Production costs comprise a constant marginal cost which is the same for all rmsand, for simplicity, set to zero. In addition, exports are subject to a trade cost, t,per unit of output. We let ni and nj denote the number of rms located in countriesi and j respectively. We assume that the outcome of competition between rms is aCournot equilibrium in quantities and that there is no arbitrage. This implies thatthe price prevailing in country i can di¤er from that in country j by more than t.Prots for a representative rm based in country i are given byi = Piyi + (Pj   t)xi; (2)1A related, but di¤erent, issue is the change in the protability of merger that would result froma change in trade cost or unilateral tari¤. This question has been examined by Long and Vousden(1995), Falvey (1998) and Gaudet and Kanouni (2004).2where yi denotes the sales of a rm in country i to its home market and xi its exportsto country j.The problem of a representative rm in country i is to maximise (2), holdingoutputs of rival rms xed and subject to non-negativity constraints on xi and yi.We assume, henceforth, that domestic output is strictly positive in equilibrium. Therst order conditions, using an asterisk to denote Cournot equilibrium values, for thisproblem areP i   yi = 0 (3)andP j   t  xi  0xi  09>=>; ; (4)where a right hand brace indicates a pair of complementary inequalities, one of whichmust hold with equality.Noting that P i is a function of yi and xj alone, whilst Pj is a function of yj andxi alone, conditions (3) and (4) can be solved simultaneously to yieldxi (ni; nj) = max0;a  (nj + 1)tni + nj + 1(5)andyi (ni; nj) = (a+ njt)=(ni + nj + 1), xj(ni;nj) > 0;yi (ni; nj) = a=(ni + 1); xj(ni;nj) = 0:(6)In the case where exports from both countries are zero, (5) - (6) reduce to thestandard conditions for Cournot equilibrium in each country in which rms makeprots ofAi (ni) =ani + 12: (7)By inspection of (5), the maximum trade cost compatible with international trade3taking place (i.e. xi ; xj > 0) is given byt < maxani + 1;anj + 1 t (8)and for the symmetric case where ni = nj = n this threshold level of trade cost ist =an+ 1: (9)For an equilibrium involving trade, substitution from (5) and (6) into (1) and (2),after some rearrangement, yields:i (ni; nj; t) =2a2 + 2n2j t2   2anjt2 + t2ni + nj + 1: (10)It is convenient to decompose this prot into the elements deriving from the homeand overseas markets. For a rm located in country i, we denote these prots asii(ni; nj; t) and ji (ni; nj; t) respectively and note that i(ni; nj; t)  ii(ni; nj; t) +ji (ni; nj; t): Substitution from (5) and (6) into (1) yieldsii(ni; nj; t) =a+ njtni + nj + 12(11)andji (ni; nj; t) =a  (nj + 1)tni + nj + 12: (12)Similarly for a rm in country j; j(ni; nj; t)  jj(ni; nj; t) + ij(ni; nj; t); wherejj(ni; nj; t) =a+ nitni + nj + 12(13)andij(ni; nj; t) =a  (ni + 1)tni + nj + 12: (14)42.1 Merger under TradeWe consider rst an initial equilibrium with trade taking place and consider twopossible forms of merger. In what we term a domestic merger two rms in country iform a single rm and in what we term an international merger one rm in countryi joins with one rm in country j:With a domestic merger two rms forgo their individual prots i(ni; nj; t) buttake a share of prots that are enhanced through the reduction in domestic competi-tion. Thus, the gain to a domestic merger in a trade equilibrium in which ni = nj = n,can be written asGD(n; t) = ii(ni   1; nj; t) + ji (ni   1; nj; t)  2ii(ni; nj; t)  2ji (ni; nj; t): (15)With an international merger, we need to consider three types of rms. Followingsuch a merger there will be n   1 rms located wholly in country i, n   1 rmslocated in country j and one newly merged rm which has a production base ineach country. The newly merged rm is not the same as existing rms in that itcan supply either market from a domestic production unit. Therefore, in setting itsoutput in each country it can act like a domestic rm in that country; there is noincentive for it to produce for export because by producing domestically it can savetrade costs. The multinational rms impact on total production can therefore bededuced by analogy with a Cournot equilibrium in which domestic output in countryi is determined as if there are n domestic Cournot competitors and n   1 overseascompetitors, whilst output for export from country i is determined as if there aren   1 rms competing over exports facing n overseas competitors. The position incountry j is symmetric to this. International merger, therefore, has the e¤ect ofreducing by one the number of exporters serving each market but leaving the numberof domestic producers unchanged. Thus, the gain to an international merger in a5trade equilibrium in which ni = nj = n, can be written asGI(n; t) = ii(ni; nj   1; t) + jj(ni   1; nj; t)  i(ni; nj; t)  j(ni; nj; t): (16)In their autarky setting, Salant, Switzer and Reynolds (1983) demonstrate thata merger is protable only if there are two rms in the initial Cournot equilibrium.Does this result hold under trade? Proposition 1 addresses this question in regard todomestic and international merger.Proposition 1 For domestic merger, GD(n; t) < 0 for all n and 0  t < t whilstfor international merger there exists a threshold level of trade costs, btI(n) such thatGI(n; t) < 0 when t < btI(n), but GI(n; t) > 0 when btI(n) < t < tProof. Setting ni = nj = n, substituting from (11) and (12) into GD(n; t) anddi¤erentiating with resect to t the resulting rst order condition implies that GD(n; t)is maximised at a trade cost of t(n) = a2n2+2n+1. Substitution of this value of t intoGD(n; t) shows that the latter is negative for n  2 thus establishing the result fordomestic merger. After setting ni = nj = n, substituting from (11) and (12) intoGI(n; t) and equating to zero, the critical (zero-gain) value of trade cost can be solvedfor as btI(n) = 8an3 10an 2a2(4n4+12n3+7n2 2n 1) : For all n  2, btI(n) lies in the range (0; t): Since,as can readily be conrmed, GI(n; t) is negative at t = 0, concave and approaches zerofrom above as t approaches t it follows that btI(n) constitutes a threshold such thatGI(n; t) < 0 when t < btI(n), but G1(n; t) > 0 when btI(n) < t < t, thus conrmingthe result for international merger.The Proposition establishes that from an initial equilibrium in which there isinternational trade then, whatever the market structure, there is no incentive fordomestic merger. However, with an international merger the situation is somewhatdi¤erent. Specically, the Proposition admits the possibility that mergers from even62Number of firms in initial equilibrium (n)15trade cost (t)0.40GI < 0GI > 010t*50.10.30.2Itrelatively competitive markets may be protable provided that trade costs are of anappropriate magnitude. The following gure illustrates this in the case of a = 1 whereit can be seen that for combinations of trade cost and initial concentration betweenthe locus t and the locus btI ; international mergers are protable.2.2 Merger Initiating TradeWhen a merger takes place from autarky (i.e. t > t) the resulting change in marketstructure may initiate trade. To understand this e¤ect, let Xi and Xj denotethe total volume of exports from i to j and j to i respectively. Using (5) for therepresentative rm in i; and an equivalent expression for that in j, these are given byXi (ni; nj; t) =ni(a  t(nj + 1))ni + nj + 1(17)and7Xj (ni; nj; t) =nj(a  t(ni + 1))ni + nj + 1: (18)With a symmetric initial structure with n rms in each country, the ows ofexports from i to j and j to i following a domestic merger in country i are, respectively,XDi (n; t) = max0;(a  t(n+ 1))(n  1)2n(19)andXDj (n; t) = max0;a  nt2: (20)Inspection of (19) and (20) reveals that the former is positive for t < t whilst thelatter is positive for t < tA wheretA  an: (21)Thus, if t lies in the range t < t < tA a domestic merger in country i will initiatea one-way ow of trade from j to i.Consider now an international merger. As explained above, this has the e¤ect ofreducing by one the number of exporters serving each market but leaving the numberof domestic producers unchanged. Assuming a symmetric initial structure with nrms in each country and using, (17) and (18), we can write the post-merger tradeows asXIi (n; t) = max0;(a  t(n+ 1))(n  1)2n(22)and8XIj (n; t) = max0;(a  t(n+ 1))(n  1)2n: (23)For either of these ows to be positive requires t < t, which is the same conditionthat pertained pre-merger. An international merger will thus neither initiate, norcause the cessation of, trading.We may thus consider whether from a position of autarky, but where t < tA, adomestic merger is protable. The gain from such a merger isGDA(n; t) = ii(ni   1; nj; t)  2A(ni) (24)and, in rather special circumstances, this may be positive as the following Propositionestablishes.Proposition 2 For n = 2 there exists a threshold level of trade costs, btD, such thatGDA(n; t) > 0 when btD < t < tA(n): In all other circumstances, GDA(n; t) < 0.Proof. After setting ni = nj = n, substituting from (11) and (7) into GDA(n; t)reveals directly that this is negative for n > 2: Setting n = 2 and solvingGDA(n; t) = 0for t yields a critical (zero-gain) value for trade cost of btD = a(4p2 3)6: Since GDA(n; t)is increasing in t it follows that for btD < t < tA(n) it is positive, thus establishing theclaim.The Proposition demonstrates that for trade costs in the range where a domesticmerger would initiate trade, duopoly is a necessary but not su¢ cient condition forthe merger to be protable. This contrasts to the position under autarky where,as established by Salant Switzer and Reynolds, a bilateral merger from duopoly isalways protable.93 ConclusionsIn their autarky setting, Salant, Switzer and Reynolds (1983) demonstrated that amerger would be protable if there were two rms in the initial Cournot equilibrium,but not if there were three or more rms. We show that in an open economy withinternational trade, the condition for a domestic merger to be protable becomesmore restrictive. Specically, duopoly is no longer a su¢ cient condition for a mergerto be protable; an additional requirement is that trade costs exceed a threshold level.An international merger, by contrast, can be protable from any market structure,provided again that trade costs lie in a certain range.References[1] Cheung, F.K. (1992). Two remarks on the equilibrium analysis of horizontalmerger.Economics Letters, 40, 1, 119-123.[2] Falvey, R. (1998). Mergers in open economies.World Economy, 21, 1061-1076.[3] Faulí-Oller, R. (1997). On merger protability in a Cournot setting.EconomicsLetters, 54, 1, 75-79.[4] Gaudet, G. and Kanouni, R. (2004). Trade liberalization and the protability ofdomestic mergers.Review of International Economics, 12, 3, 353-358.[5] Long, N.V. and Vousden, N. (1995). The e¤ects of trade liberalization on cost-reducing horizontal mergers.Review of International Economics, 3, 2, 141-155.[6] Salant, S., Switzer, S. and Reynolds, R. (1983). Losses from horizontal merger:the e¤ects of an exogenous change in industry structure on Cournot-Nash equi-librium.Quarterly Journal of Economics, 98, 2, 185-199.10

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Dundee Discussion Papers in Economics 175:International trade and the incentive for merger

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