NBER WORKING PAPER SERIES PROFIT SHIFTING AND TRADE AGREEMENTS IN IMPERFECTLY COMPETITIVE MARKETS. Kyle Bagwell Robert W. Staiger

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1 NBER WORKING PAPER SERIES PROFIT SHIFTING AND TRADE AGREEMENTS IN IMPERFECTLY COMPETITIVE MARKETS Kyle Bagwell Robert W. Staiger Working Paper NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambrige, MA March 2009 We thank Henrik Horn, Giovanni Maggi an Xenia Matschke as well as seminar participants at Princeton University an the Braneis WTO an International Trae Research Conference for their helpful comments. The views expresse herein are those of the author(s) an o not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulate for iscussion an comment purposes. They have not been peerreviewe or been subject to the review by the NBER Boar of Directors that accompanies official NBER publications by Kyle Bagwell an Robert W. Staiger. All rights reserve. Short sections of text, not to excee two paragraphs, may be quote without explicit permission provie that full creit, incluing notice, is given to the source.

2 Profit Shifting an Trae Agreements in Imperfectly Competitive Markets Kyle Bagwell an Robert W. Staiger NBER Working Paper No March 2009 JEL No. F12,F13 ABSTRACT When markets are imperfectly competitive, trae policies can alter the terms of trae, shift profits from one country to another, an moerate or exacerbate existing istortions that are associate with the presence of monopoly power. In light of the various ways in which trae policies may influence welfare, it might be expecte that new rationales for trae agreements woul arise once imperfectly competitive markets are allowe. In this paper, we consier several trae moels that feature imperfectly competitive markets an argue that the basic rationale for a trae agreement is, in fact, the same rationale that arises in perfectly competitive markets. In all of the moels that we consier, an whether or not governments have political-economic objectives, the only rationale for a trae agreement is to remey the inefficient terms-of-trae riven restrictions in trae volume. Having ientifie the problem that a trae agreement might solve, we next evaluate the form that an efficiency-enhancing trae agreement might take. Here, too, our results parallel the results establishe previously for moels with perfectly competitive markets. In particular, we show that the principles of reciprocity an non-iscrimination (MFN) are efficiency enhancing, as they serve to "uno" the terms-of-trae riven restrictions in trae volume that occur when governments pursue unilateral trae policies. Kyle Bagwell Department of Economics Stanfor University Lanau Economics Builing 579 Serra Mall Stanfor, CA an NBER kbagwell@stanfor.eu Robert W. Staiger Department of Economics Stanfor University Lanau Economics Builing 579 Serra Mall Stanfor, CA an NBER rstaiger@stanfor.eu

3 1 Introuction Governments have a reason to form a trae agreement when an international externality is associate with their trae-policy choices. When countries are large, if a government raises its import tari, then the worl (o shore) price of the importe goo is reuce. The importing country then enjoys an improvement in its terms of trae, an the exporting country su ers a negative termsof-trae externality. As Johnson (1954) argues, when governments maximize national welfare an markets are perfectly competitive, the associate non-cooperative equilibrium is ine cient, an governments can achieve greater welfare by forming an appropriately esigne trae agreement. Bagwell an Staiger (1999) an Grossman an Helpman (1995) exten the moeling framework to allow that governments have political-economic preferences. Allowing for a wie range of possible political-economic motivations, Bagwell an Staiger (1999) show that the non-cooperative equilibrium is ine cient if an only if governments are motivate by the terms-of-trae consequences of their respective trae policies. Builing from this ning, they then characterize the form that an e ciency-enhancing trae agreement might take. They show that the principles of reciprocity an non-iscrimination (MFN) play a useful role in guiing governments towar e cient policies. In this paper, we move beyon the competitive-markets paraigm an expan the analysis to markets with imperfect competition, thereby introucing the realistic possibility that rms have market power. A rm with market power is itself large, in the sense that it oes not regar the market price as xe; instea, such a rm recognizes that its ecisions may in uence the price at which its output sells. The terms-of-trae externality is still present in markets with imperfect competition, but the well-known pro t-shifting role for trae policies in imperfectly competitive markets suggests that other international externalities might also be present. For a sequence of moels with imperfectly competitive markets, we examine the rationale for a trae agreement, an we also consier the form that an e ciency-enhancing trae agreement might take. When markets are imperfectly competitive, a government may be tempte to use trae policy as a means of extracting pro t from foreign exporters. This temptation arises as well, at least in the short run, when markets are perfectly competitive; however, the consieration of imperfectly competitive markets introuces several novel features. First, an unerstaning of the impact of trae policy on the worl price now requires a theory as to how price is etermine when rms possess market power. Secon, when omestic rms also participate in the oligopolistic market, trae policy may have strategic e ects in so far as it alters the oligopolistic interaction between omestic an foreign rms. While trae policy can again shift foreign pro ts to the omestic treasury in the form of tari revenue, it may now also shift some foreign pro t to omestic rms. Thir, when markets are imperfectly competitive, output levels are often istorte away from nationally or globally e cient levels. In the absence of omestic policies that irectly target such istortions, trae policies may serve as secon-best policies that iminish existing istortions. These an other motives for trae policy intervention are represente in an expansive literature that examines optimal unilateral trae policy uner imperfect competition. One of the main conclusions of this literature is that optimal unilateral trae policy is highly sensitive to market 1

4 structure. 1 Base on the nings of this literature, it might be expecte that the rationale for a trae agreement woul likewise vary markely with market structure. Consistent with this expectation, we show that new international externalities inee arise when market power is present: in aition to the terms-of-trae externality that travels through the worl price, there are also local-price externalities that travel through omestic an foreign local prices. These local-price externalities are associate with the oligopolistic pro t-shifting an istortion-in uencing a ects of trae policies. For our purposes, however, the key question is whether governments internalize these international externalities in an appropriate fashion from a worl-wie perspective when they make their unilateral policy choices. For a sequence of moels that feature imperfectly competitive market structures, we aress this question an establish a surprising answer: the basic rationale for a trae agreement is, in fact, the same rationale that arises in perfectly competitive markets. In particular, in all of the moels that we consier, an whether or not governments have political-economic objectives, the only rationale for a trae agreement is to remey the ine cient terms-of-trae riven restrictions in trae volume. Furthermore, an again as in the benchmark moel with perfect competition, the principles of reciprocity an MFN are e ciency enhancing, as they serve to uno the terms-of-trae riven restrictions in trae volume that occur when governments pursue unilateral trae policies. To establish these points, we consier the istinct motives for trae policy intervention that arise when there is a monopoly supplier in one country 2 (Section 2), when there is oligopolistic interaction between an exporting an an import-competing rm 3 (Section 3), an when there is oligopolistic interaction between two rms exporting from two i erent countries to a thir-country market 4 (Section 4). In each setting, our approach is to examine the non-cooperative an e cient policy choices in etail an evaluate the precise reasons for any ivergence between them. this en, we follow Bagwell an Staiger (1999) an evaluate politically optimal tari s, e ne as those tari s that woul hypothetically be chosen by governments unilaterally if they i not value the pure international rent-shifting associate with the terms-of-trae movements inuce by their unilateral tari choices. For each setting, we show that politically optimal tari s are e cient, an we thereby establish that the only rationale for a trae agreement is to remey the ine cient termsof-trae riven restrictions in trae volume. With this rationale for a trae agreement in han, we then procee to establish that the principles of reciprocity an (in the thir-country setting) MFN are e ciency enhancing in each setting as well. 1 For excellent summaries of the early literature on optimal trae policy uner imperfect competition, see Braner (1995) an Helpman an Krugman (1989). 2 Braner an Spencer (1981, 1984a) consier the role of import tari s as a means of extracting pro ts from non-competitive foreign suppliers. 3 In a setting with international oligopoly competition, trae policy may play a strategic role by altering the nature of oligopolistic competition, as the seminal papers of Spencer an Braner (1983) an Braner an Spencer (1985) have shown. These papers assume that international markets are integrate; Braner an Spencer (1984b) an Dixit (1984) explore relate moels with segmente markets. 4 International oligopoly competition now occurs between exporters from i erent countries. As Braner an Spencer (1985) show, ue to the pro t-shifting e ect of an export subsiy, the optimal unilateral export policy for a government in such a setting may be an export subsiy. To 2

5 If the presence of imperfectly competitive rms introuces new international externalities that are transmitte through non-terms-of-trae channels, as we con rm below, then how is it that the problem for a trae agreement to solve in this more complicate environment still boils own to proviing an avenue of escape from a terms-of-trae riven Prisoners Dilemma? Broaly speaking, the reason is that trae agreements o not expan the set of feasible policy instruments available to governments, an so any e ciency gains generate by a trae agreement must erive from changes in the level of intervention achieve with the existing policy instruments; an as we emonstrate below, even in this more complicate environment it is the international rent-shifting/cost-shifting associate with the terms-of-trae externality an this externality alone that accounts for the ine cient level of intervention uner unilateral policy choices. The analysis in this paper maintains the assumption that the number of proucers in each country is xe an invariant to trae policy. This gives rise to the existence of pro table rms in the moels we have escribe above, an it is the pursuit of those pro ts either converte into tari revenue as in the monopoly exporter moel of Section 2, or shifte from one rm to another as in the uopoly pro t-shifting moels of Sections 3 an 4 combine with the relaxation of the assumption of price-taking behavior that provies the novel role for government tari intervention in these moels. An alternative role for government intervention can arise when free-entry conitions serve to eliminate pro ts in equilibrium even though rms are not price-takers. This alternative centers on a rm elocation e ect of trae policy intervention that coul enhance the welfare of the intervening country: by triggering foreign exit an omestic entry, a omestic import tari can lea to greater competition in the omestic market an therefore lower prices for omestic consumers (Venables, 1985, 1987, Helpman an Krugman, 1989, Ossa 2008). In a companion paper (Bagwell an Staiger, 2009), we consier this alternative by exploring moels in which rms are not price takers but where entry is enogenous, an we again ask whether a novel role for trae agreements can be ienti e. For the moels of rm elocation, our main ning is again that the terms-of-trae externality continues to provie the only rationale for a trae agreement. 2 Trae Policies an Market Power We begin with a simple 2-country partial-equilibrium moel in which the goo uner consieration is prouce by a monopolist in the omestic country an consume in both the omestic an foreign countries. The omestic country thus exports this goo to the foreign country. We assume that the omestic an foreign markets are integrate, so that the omestic monopolist cannot price iscriminate across the two markets. Any i erence in prices across the two markets then erives from trae policies. The alternative case of segmente markets is consiere in the Appenix. 2.1 Basic Assumptions We assume that a monopolist resies in the omestic country, selling goo y to omestic consumers an also exporting goo y to foreign consumers. The local price in the omestic market is P an 3

6 the omestic eman function is D(P ); likewise, the local price in the foreign country is P an the foreign eman function is D (P ). Both eman functions are ownwar sloping an positive. The government of the omestic country has an export policy, t, where t > 0 inicates an export tari (expresse in speci c terms); an the government of the foreign country has an import policy, t, where t > 0 correspons to an import tari (expresse in speci c terms). The markets are integrate. This means that any wege between the prices P an P must equal the sum of the export an import tari s for non-prohibitive trae taxes: letting t + t, it then follows that P = P +. Let us e ne the worl (i.e., o shore) price as P w = P + t = P t. Since both governments may use trae policies, the worl price is istinct from both local prices. When markets are integrate an trae policies t an t are given, the monopolist chooses P (an thereby P = P + ) to maximize pro t in the omestic an foreign markets: (P; ) = [P c o ]D(P ) + [P c o ]D (P + ); where c o is the constant marginal cost of prouction for the monopolist. We assume that the secon-orer conition for pro t maximization hols. The associate rst-orer conition balances the e ect of a price increase across the integrate markets an may be written as follows: 5 P (P; ) = [P c o ]D 0 (P ) + D(P ) + [P c o ]D 0 (P + ) + D (P + ) = 0: (1) As (1) inicates, the pro t-maximizing or monopoly price epens on, the total tari on trae ows from the omestic to the foreign country, an so we represent the monopoly price function as P (). Given ownwar-sloping eman functions, (1) also implies that the monopoly price function entails a positive markup over unit prouction costs: P () > c o. Since P w = P + t = P t, we may use P () = P () + to enote the corresponing monopoly price function for foreign sales an P w (t; t ) to represent the corresponing worl price function. For a large family of eman functions, incluing linear eman functions, P () eclines as the total tari rises. 6 In this case of incomplete pass through, the monopolist absorbs some of the incience of trae taxes an thus reuces the price at which it sells. More generally, the nal price pai by foreign consumers, P (), rises with. 7 In what follows we therefore assume P rises an P falls with the total tari. Finally, we note that our assumptions ensure that the worl price, P w (t; t ), rises with the export tari t an falls with the import tari t. The omestic country thus enjoys a terms-of-trae improvement when the omestic export tari is increase or the foreign import tari is reuce, whereas the foreign country enjoys a terms-of-trae gain when the omestic export tari is reuce or the foreign import tari is increase. 5 In keeping with our focus on non-prohibitive tari s, we maintain the assumption here an throughout that it is optimal for the monopolist to sell strictly positive volume in each country for all relevant tari levels. 6 In particular, P () is ecreasing in if (P c o)d 00 (P ) + D 0 (P ) < 0 at the monopoly selection. For this conition, it is thus su cient if D 00 (P ) 0, but this inequality is clearly not necessary. 7 We n that P () is increasing in if (P c o)d 00 (P ) + 2D 0 (P ) < 0. This is the traitional secon-orer conition that woul apply if the monopolist sol only in the omestic market. This conition hols, for example, if D 00 (P ) 0, although this inequality is clearly not necessary. 4

7 2.2 Welfare Functions We next consier government welfare functions. To begin, we assume that each government maximizes the welfare of its country. Domestic country welfare is then [P c o ]D(P ) + CS(P ) + [P (c o + )]D (P ) + td (P ); where CS(P ) enotes omestic consumer surplus. The rst two terms represent omestic welfare on omestically sol units, the thir term captures (post-tari ) pro t on exporte units, an the nal term is omestic tari revenue. We may simplify an represent omestic country welfare as W (P; P ; P w ) = [P c o ]D(P ) + CS(P ) + [P w c o ]D (P ): (2) Domestic country welfare is ultimately a function of the unerlying tari s; however, for our purposes, it is more useful to write welfare as a function of prices (which are themselves etermine by tari s), as we can then ientify the speci c channels through which trae policies a ect welfare. Notice from (2) that omestic welfare epens on the foreign local price, P, since the omestic monopolist has market power an selects P an thus P, with the units exporte at the price P then etermine by the foreign eman function. This feature istinguishes the current setting from one in which omestic prouction takes place uner conitions of perfect competition. In that case, with price-taking rms, omestic welfare can again be written as the sum of proucer surplus, consumer surplus an tari revenue. But the omestic local price P then etermines the levels of omestic prouction an omestic consumption, an so P etermines as well omestic export volume, omestic proucer surplus an omestic consumer surplus. Given that t = P w P, it is then possible to express omestic tari revenue as a function of P an P w. As a consequence, with a competitive omestic prouction sector, all components of omestic welfare are etermine once P an P w are given, an so omestic welfare can be written as W (P; P w ) in that case. 8 Hence, as (2) con rms, there is a new international externality present for the omestic government when market power is present in the omestic export sector: in aition to the terms-of-trae externality that travels through P w, there is also a (foreign) local-price externality that runs through P. This inicates a more complex international policy environment when market power is present, an it raises the possibility that the task of a trae agreement may be more complicate in this environment as a result. Nevertheless, the funamental question for our purposes here is whether governments woul make unilateral policy choices that internalize these international externalities whatever form these externalities might take in an appropriate fashion from a worl-wie perspective. To answer this question, we nee to go further an fully characterize the remaining features of the moel, so that we may then examine the Nash an e cient policy choices in etail an evaluate the precise reasons for any ivergence between them. To this en, we complete our characterization of government welfare functions by consiering 8 For further iscussion of this case, see Bagwell an Staiger (1999, 2001). 5

8 the foreign country. Foreign country welfare takes the following simple form: W (P ; P w ) = CS (P ) + [P P w ]D (P ); (3) where CS (P ) enotes foreign consumer surplus an [P P w ]D (P ) is foreign tari revenue. As with omestic welfare, we express foreign welfare as a function of prices in orer to isolate the speci c channels through which trae policies a ect welfare. 2.3 Nash an E cient Tari s We may now characterize the Nash policy choices, which we take to be the optimal policies that the governments woul choose unilaterally in the absence of a trae agreement. We assume that the respective secon-orer conitions are satis e an focus on the associate rst-orer conitions for welfare maximization. Using the expressions for omestic an foreign welfare evelope above, an noting that t = 1 = t, the rst-orer conitions that jointly e ne the Nash choices of t an t, which we enote by t N an t N, are given by: P W P + W P P + w P W P P + W P = 0: = 0; an (4) Evaluating the Nash conitions in (4) using the explicit expressions for welfare in (2) an (3) an the monopolist s rst-orer conition (1), it is irect to show that the foreign government imposes an import tari in the Nash equilibrium, while the omestic government may impose either an export tax or an export subsiy in the Nash equilibrium epening on eman conitions. Intuitively, the Nash export policy t N for the omestic country maximizes W (P; P ; P w ) an thus internalizes the e ects of the inuce changes in P, P an P w on omestic welfare. omestic eman were nonexistent, then the Nash export tax woul be zero, because in that case the objectives of the omestic monopolist woul coincie with omestic welfare. In the presence of omestic eman, however, two aitional consierations arise. On the one han, an export tax has a bene cial e ect in lessening the existing monopoly istortion in the omestic market (i.e., it pushes P own towar c o ), an if this consieration ominates then the Nash export policy is an export tax. On the other han, uner an export subsiy foreign consumers pay a lower price than omestic consumers, an given appropriate eman conitions it is possible that facilitating the implie price iscrimination across markets for the omestic monopolist has a su ciently bene cial e ect on omestic welfare that the Nash export policy is an export subsiy. 9 9 In particular, we n that t N 0 if an only if [ D(P ) P t ] [(P co)d0 (P ) + D(P )] when t = 0 an t = t N. The left-han-sie of this conition is strictly positive. By examining the monopoly rst-orer conition (1), it can be seen that the right-han-sie of this conition is zero when the monopolist has no incentive to price-iscriminate across markets, an so the conition is met in that case; an it is negative when the monopolist woul like to priceiscriminate in favor of the omestic market, an so the conition is met in that case as well; but the right-han-sie is positive when the monopolist woul like to price-iscriminate in favor of the foreign market, an uner appropriate eman conitions it can be su ciently positive to violate the conition above an imply t N < 0. If 6

9 The Nash import tari t N for the foreign country maximizes W (P ; P w ) an thus internalizes the e ects of the inuce changes in P an P w on foreign welfare. The foreign local price etermines the level of foreign eman. It thereby etermines consumer surplus in the foreign country an also impacts foreign tari revenue. The worl price a ects welfare in the foreign country through its e ect on foreign tari revenue. The Nash import tari for the foreign country weighs the tari revenue collecte from the omestic monopolist against the loss in foreign consumer surplus, an it is positive provie that the eman function is such that the exporting monopolist oes not pass through the full tari (as we assume). 10 It is instructive at this point to consier more generally the interpretation of the Nash policy choices. Let us rst examine the tari choice of the foreign country. As we observe above, foreign welfare may be expresse in the form W (P ; P w ). Consier now Figure 1a. With the foreign import tari t on the vertical axis an the home export tax t on the horizontal axis, an initial tari pair is represente by the point A (t ; t). This pair is associate with a foreign iso-localprice line (i.e., an iso-tari -sum line), enote as P (A)! P (A), an an iso-worl-price line, epicte as P w (A)! P w (A). In light of the property establishe above that the foreign price can be written as P (), the iso-local-price line has slope 1. The iso-worl-price line has a positive slope, because the worl price can be hel xe only if an increase in the foreign export tax is balance against an increase in the omestic import tari. For a xe t, when t is increase to t 1, a new point C (t 1 ; t) is inuce. This point lies on new iso-price lines, represente as P (C)! P (C) an P w (C)! P w (C), an the foreign local (worl) price is now higher (lower) than it was originally at A. As the bottom equation of (4) suggests, the overall movement from A to C in Figure 1a can be isentangle into separate movements in the worl an foreign local prices, respectively. The movement from A to B re ects the inuce fall in the worl price, holing xe the foreign local price, an the associate welfare implications for the foreign country are re ecte in the bottom equation of (4) by the term WP w. Similarly, the movement from B to C isolates the foreign local price change, with the corresponing foreign welfare change re ecte in the bottom equation of (4) by the term WP. Exactly as in a competitive setting, the worl price movement from A to B can be interprete as a form of international rent-shifting/cost-shifting: if the foreign government wishes to implement a foreign local price corresponing to the iso-local-price line P (C)! P (C), then a unilateral increase in the foreign import tari passes some of the costs of this outcome to the omestic country, whose exports are sol at a lower worl price. Further, in our moel with export-sector market power, the omestic country also has a irect interest in the foreign local price that the foreign government wishes to implement. The foreign government, of course, ignores this interest when choosing its Nash import tari. We next turn to an examination of the tari choice of the omestic country. As we observe above, omestic welfare may be expresse in the form W (P; P ; P w ). The presence of both omestic an 10 Formally, W = (P P w )D 0 (P ) P D (P w. At t = 0, P = P w an so W t that P () an thus P w (t; t ) = P () + t is ecreasing in t. > 0, since we assume 7

10 foreign local prices in the omestic welfare function implies that the interpretation of the Nash tari choice that we evelop just above for the foreign country cannot be applie irectly to the omestic country tari choice. Nevertheless, an analogous interpretation oes apply once the appropriate observations are mae. To see why, consier Figure 1b. With the omestic export tax t now on the vertical axis an the foreign import tari t now on the horizontal axis, an initial tari pair is represente by the point A (t; t ) in Figure 1b. The key observation is that both P an P are tie own once the sum of t an t (an hence ) is tie own. Therefore, the tari pair at A is associate with a omestic-an-foreign iso-local-price line (i.e., an iso-tari -sum line), enote as P (A); P (A)! P (A); P (A), an an iso-worl-price line, epicte as P w (A)! P w (A). As before, the iso-local-price line has slope 1, while the iso-worl-price line has a positive slope. For a xe t, when t is increase to t 1, a new point C (t 1 ; t ) is inuce. This point lies on new iso-price lines, represente as P (C); P (C)! P (C); P (C) an P w (C)! P w (C), an the omestic local price is now lower than it was originally at A, while the foreign local price an the worl price are now each higher than they were originally at A. As the top equation of (4) suggests, the overall movement from A to C in Figure 1b can be isentangle into separate movements in the worl price, an in the omestic an foreign local prices, respectively. The movement from A to B re ects the inuce increase in the worl price, holing xe the omestic an foreign local prices, an the welfare implications of this change for the omestic country are associate in the top equation of (4) with the term W P w. Similarly, the movement from B to C isolates the omestic an foreign local price changes, with the corresponing omestic welfare change capture in the top equation of (4) with the terms W P an W P. Despite the ae complication of the extra term W P in the top equation of (4), it may now be seen that the omestic Nash tari choice amits an analogous interpretation to the foreign Nash choice. Speci cally, an exactly as in a competitive setting, the worl price movement from A to B can be interprete as a form of international cost-shifting: if the omestic government wishes to implement a omestic-an-foreign local price pair corresponing to the iso-local-price line P (C); P (C)! P (C); P (C), then a unilateral increase in its export tax passes some of the costs of this outcome to the foreign country, whose imports are purchase at a higher worl price. A novel feature of our moel with export-sector market power is that the foreign country also has a irect interest in one of the local prices (the foreign local price) that the omestic country wishes to implement. The omestic government ignores this interest when setting its Nash export tari. To formally evaluate the e ciency properties of the Nash tari choices, we rst nee to characterize the trae policy choices that woul be internationally e cient in this environment. Consier, then, an e cient or joint-welfare maximizing agreement that woul maximize the sum of W an W. The worl price cancels from this summation: the worl price a ects the istribution of rents across countries but oes not in itself a ect e ciency. This observation provies one simple way of unerstaning why tari policies that are motivate by terms-of-trae e ects lea to ine ciencies. But we may still ask whether any other sources of ine ciency are present. To aress this question, 8

11 we express joint welfare as J(P; P ) = W (P; P ; P w )+W (P ; P w ) = [P c o ]D(P )+CS(P )+[P c o ]D (P )+CS (P ): (5) As inspection of (5) con rms, joint welfare is maximize at the perfectly competitive prices: P = P = c o. 11 Governments, however, are unable to eliver these prices using only their export an import tari s. Uner free trae policies, the monopolist sets P = P > c o, an eaweight loss results. Using a positive total tari, governments coul steer supply towar the omestic market an push the omestic local price own to c o. But a positive introuces a wege between P an P, making it impossible that P coul also be set equal to c o. An e cient tari pair woul balance e ciency objectives across markets with the nal outcome satisfying c o < P an c o < P. 12 We next characterize the e cient tari s at a formal level. At the e cient tari s, it is impossible to increase joint welfare by changing the omestic export tari or the foreign export tari. Recalling that the worl price cancels from the joint welfare expression, an that the local prices P an P epen only on the tari sum, it follows that e ciency only ties own the sum of the two tari s. The rst-orer conition that e nes e cient choices of t an t is thus given by: P W P + W P P + W P P = 0: (6) E ciency requires only that t an t be chosen so that the total tari satis es (6). We may now formally con rm that the Nash tari choices are inee ine cient. This can be seen by aing the two Nash conitions in (4) together to obtain P W P + W P P + W P P + D (P w w ] = 0; where in writing (7) we have use the fact that (2) implies W P w = D (P ) an (3) implies WP w = D (P ). The term D (P ] is strictly positive, an so (7) implies that W P + + WP P must be negative when evaluate at Nash tari choices. But then, uner the assumption that the secon-orer conition for joint-welfare maximization hols, (6) implies that W P P the sum of the Nash tari s is above that require for e ciency: in the Nash equilibrium, trae volume (D (P )) is ine ciently low. 2.4 Politically Optimal Tari s To etermine the reason for the ine ciency of the Nash tari choices, we now follow Bagwell an Staiger (1999, 2001) an e ne politically optimal tari s as those tari s that woul hypothetically 11 If all units of goo y were sol omestically, then the omestic welfare function woul take the form [P c o]d(p )+ CS(P ). In this setting, as is well known, omestic country welfare is maximize at the perfect-competition outcome (i.e., when P = c o). The same logic applies as well for the foreign country. 12 Suppose, for example, that > 0 elivers P = c o. The term [P c o]d(p ) + CS(P ) is then maximize; thus, by reucing the total tari an raising P slightly, the reuction in this term woul only be secon orer. At the same time, a lower total tari woul reuce P an thus facilitate a rst-orer increase in the term [P c o]d (P ) + CS (P ). Likewise, if < 0, then it woul not be e cient to rive P to or below c o. 9

12 be chosen by governments unilaterally if they i not value the pure international rent-shifting associate with the terms-of-trae movements inuce by their unilateral tari choices. Speci cally, we suppose that the home government acts as if W P w 0 when choosing its politically optimal tari, while the foreign government acts as if WP w 0 when choosing its politically optimal tari. We therefore e ne politically optimal tari s as those tari s that satisfy the two conitions P W P + W P P WP P = 0; an (8) = 0: With politically optimal tari s e ne in this way, we may ask whether politically optimal tari s are e cient, an thereby explore whether the Nash ine ciencies ienti e above can be given a terms-of-trae interpretation, accoring to which the funamental problem face by governments in esigning their trae agreement is to n a way to eliminate terms-of-trae manipulation. With regar to the nature of the thought experiment envisione in the politically optimal tari s, there is an important istinction between the perfectly competitive environment consiere in Bagwell an Staiger (1999, 2001) an the imperfectly competitive setting that we analyze here. In the perfectly competitive setting, omestic welfare can be written as W (P; P w ), an the politically P optimal tari for the omestic government then satis es W P = 0. Thus, in the case of perfect competition, it is immaterial whether the thought experiment associate with politically optimal tari s is interprete to mean that the government acts as if W P w 0 or rather that the government acts as 0, because either way we have W P Notice that, uner the secon interpretation, politically optimal tari s are the tari s that governments woul choose unilaterally if they were small in worl markets. In the presence of imperfectly competitive rms, however, this secon interpretation is not vali. To see why, recall that the omestic welfare function now inclues P an observe as well that the relationship P w = P t = P. Consequently, if the omestic government were to act as 0, it woul then by necessity also act as if P P = 0, an so its unilaterally chosen tari woul satisfy W P = 0, which i ers from the expression for the politically optimal omestic tari in (8) above. In e ect, in the presence of imperfect competition, it no longer makes sense to think of a hypothetical situation in which governments act as if they were small in worl markets, because their rms are not small. We now procee to o er a formal evaluation of the e ciency properties of politically optimal tari s as e ne by (8). This is easily one: the two conitions in (8), when summe together, imply the conition in (6). We thus now have the following result: politically optimal tari s are e cient. Put i erently, if governments coul be inuce not to value the pure international rentshifting associate with the terms-of-trae movements inuce by their unilateral tari choices, then they woul set e cient tari s. To unerstan this result at a more speci c level, we refer to Figures 2a-c. In Figures 2a an 2b, 13 Bagwell an Staiger (1999, footnote 11) stress the rst of these interpretations in their formal analysis, but both interpretations are vali in the competitive markets setting. 10

13 we illustrate the manner in which the omestic government etermines its politically optimal export tari. Figure 2a isolates the e ects in the foreign market of a higher export tari. The bol lines ientify market values at initial export an import tari s, t an t, respectively, where we assume for now that both tari s are positive. The otte lines ientify the values that are etermine after an increase in the export tari. As Figure 2a illustrates, the omestic country initially enjoys tari revenue (enote as T R) in the amount (P w P )D (P ) an pro t on exporte units (enote as P S x ) in the amount (P c o )D (P ), so that the overall bene t that the omestic government enjoys from foreign sales is (P w c o )D (P ): The foreign country likewise enjoys tari revenue (enote as T R ) in the amount (P P w )D (P ) an consumer surplus (enote as CS ) as represente by the triangular area above P an below the eman curve. As the omestic government increases its export tari, local an worl prices change, an we illustrate these changes with arrows. In particular, the foreign local price P rises, leaing to a reuction in foreign eman an thus trae volume. Consequently, the omestic country su ers a loss in tari revenue an pro t, with each unit of lost sales being value at rate (P w c o ). In this way, a higher foreign local price generates a welfare loss (enote by L 1 an L 2 ) for the omestic government in the foreign market. Figure 2a thus ienti es a cost to the omestic government of a higher export tari. This cost is attributable to the reuce trae volume that arises as a consequence of the inuce higher foreign local price. The omestic government weighs this cost when etermining its politically optimal export policy. Figure 2a also illustrates two e ects that the omestic government oes not weigh when setting its politically optimal export policy. First, a higher export tari generates a termsof-trae gain (enote as G(T OT )) for the omestic government, which as Figure 2a illustrates amounts to a irect transfer from the foreign treasury (i.e., from T R ) to the omestic treasury (i.e., to T R). A government ignores pure international rent shifting of this nature when setting its politically optimal tari policy. Secon, when the omestic government sets its politically optimal export policy, it also ignores the fact that the inuce reuction in trae volume itself lowers foreign tari revenue when the foreign import tari is positive. This loss (enote as Z) to the foreign government ienti es a negative international externality that is associate with local-price movements an suggests that the politically optimal omestic export tari may be ine ciently high if the foreign import tari is positive. In Figure 2b, we isolate the e ect of a higher export tari in the omestic market. As illustrate, a higher export tari inuces a lower omestic local price P. Since the omestic market is initially istorte ue to the presence of monopoly power, the omestic government gains in the omestic market when the export tari is increase an greater omestic sales are generate. This gain correspons to the new consumer surplus (enote as G 1 ) an the new pro t (enote as G 2 ) that are enjoye on units that are omestically consume only after the higher export tari is impose. When setting its politically optimal export tari, the omestic government thus evaluates an increase in its export tari by balancing the losses in the foreign market (i.e., L 1 + L 2 ) against the gains in the omestic market (i.e., G 1 + G 2 ). The omestic government thus sets its politically optimal export policy so as to achieve an optimal balance in its attempt to iminish both markups. 11

14 The politically optimal export policy is therefore sensitive to the relative slopes of the omestic an foreign eman functions. We turn now to Figure 2c an consier the politically optimal import tari for the foreign government. Here, it is convenient to assume that the foreign import tari is initially zero an that the foreign government is contemplating an increase in the import tari. For simplicity, in Figure 2c, we assume that the omestic export tari is positive. If the foreign government raises its import tari to a positive level, then the foreign local price P rises an trae volume is again reuce. As well, the worl price falls, an the foreign country thus enjoys a terms-of-trae gain (enote as G (T OT )) that amounts to a pure rent transfer from the omestic treasury to the foreign treasury. When setting its politically optimal import policy, however, the foreign government ignores this terms-of-trae e ect an instea focuses on the fact that a higher import tari inuces a higher foreign local price an thus a loss in foreign consumer surplus (enote as L ). As Figure 2c suggests, then, the politically optimal import policy for the foreign government is a policy of free trae. In fact, this observation can be easily formalize at a general level. At the political optimum, we see from (8) that W P = 0. This conition implies in turn that P = P w, from which we conclue that the politically optimal tari for the foreign country is free trae: t P O = 0.14 At this point, we may return to consier the omestic government. When setting its politically optimal export policy, the omestic government internalizes all of the gains (i.e., G 1 + G 2 ) of a reuction in eaweight loss in the omestic market; however, it internalizes all of the losses (i.e., L 1 +L 2 +Z) of an increase in eaweight loss in the foreign market if an only if the foreign import tari is zero (i.e., if an only if Z = 0). But we have just argue that the politically optimal import tari for the foreign government is zero; therefore, the omestic government internalizes all of the gains an losses in joint welfare when setting its politically optimal export policy. In short, when the foreign government aopts a policy of free trae, the omestic government s export policy no longer generates an international externality through the inuce change in the foreign local price. For this reason, politically optimal tari s are e cient. A general perspective on this result is possible with reference to Figures 1a an 1b. Consier, for instance, the trae-o s face by the omestic government as epicte in Figure 1b. If the omestic government seeks to achieve a pair of omestic an foreign local prices corresponing to the iso-local-price line P (C); P (C)! P (C); P (C), then the attainment of this pair of local prices involves no worl-price externality when the omestic government s higher export tax is balance against a higher foreign import tari, so that the worl price is not altere. This correspons in Figure 1b to the movement from A to D. When the omestic government is not motivate by the terms-of-trae implications of its tari policy, it prefers choosing a higher export tax an inucing point C instea of selecting a lower export tax an inucing point A if an only if it also prefers 14 Given W (P ; P w ) = CS (P ) + [P P w ]D (P ) an the fact that the erivative of CS (P ) equals D (P ), we see that WP = [P P w ]D 0 (P ). Since D (P ) is a ownwar-sloping eman function, we conclue that WP = 0 if an only if P = P w. We note that the foreign country s politically optimal tari is thus inepenent of the home country s export tari. As we establish in the next section, this inepenence property isappears when we allow for prouction in the foreign country. 12

15 point D to point A. If both governments choose tari s in this fashion (so that in Figure 1a the foreign government prefers choosing a higher import tari an inucing point C instea of selecting a lower import tari an inucing point A if an only if it also prefers point D to point A), then a resulting consistent set of tari s is politically optimal. In this case, the tari s that governments select are not motivate by the cost-shifting e ects of movements in the terms of trae. While the omestic government s willingness to move from point A to point D in Figure 1b inuces no externality on the foreign country through the terms of trae, it will involve a change in the foreign local price. If the foreign government also selects a tari that is politically optimal, however, then a small change in the foreign local price will not alter the foreign welfare to the rst orer. 15 Similarly, the foreign government s willingness to move from point A to point D in Figure 1a inuces no externality on the omestic country through the terms of trae, but it will involve a change in both the omestic an the foreign local price. If the omestic government also selects a tari that is politically optimal, however, then this small change in the omestic an the foreign local price will not alter the omestic welfare to the rst orer. In sum, when governments aopt politically optimal tari s, they are not motivate to impose terms-of-trae externalities on one another, an the international externalities associate with local-price movements are eliminate. We thus now have a general perspective as to why politically optimal tari s are e cient. Builing from this perspective, let us now suppose that the omestic government chooses its export tax minful of the terms-of-trae externality associate with movements in the worl price (i.e., the movement from D to C in Figure 1b). It then recognizes that some of the costs of achieving the lower omestic an higher foreign local prices are shifte on to the foreign country through the resulting increase in the worl price. As a result, the omestic government can be expecte to choose a higher export tax (i.e., restrict trae volume more) than is jointly e cient. An analogous observation applies to the foreign government. This explains why Nash trae policies are always ine cient, with trae volumes that are necessarily too low. The broa conclusion that emerges is therefore that an ine ciency arises when governments set trae policies unilaterally if an only if they are motivate by terms-of-trae consierations, exactly as in the case of competitive markets analyze in Bagwell an Staiger (1999, 2001). 2.5 The Rationale for a Trae Agreement We can now explicitly consier the rationale for a trae agreement in the moel with export-sector monopoly power. To this en, we exten the moel slightly beyon the single-goo setting to allow that the foreign country is the mirror image of the omestic country. Thus, while the omestic country has a monopolist that sells goo y in omestic an foreign markets, the foreign country likewise has a monopolist that sells goo x in the foreign an omestic markets. The partialequilibrium moel can then be close to achieve general equilibrium in the usual way with the aition of a trae numeraire goo z that enters linearly into the welfare of each country an 15 Recall that WP = 0 when the foreign government sets its politically optimal tari. As we iscuss above, the foreign country s politically optimal tari is thus free trae, which ensures that the area Z in Figure 2a is eliminate. 13

16 which is always consume in positive amounts by the representative agent of each country. Within this extene 3-goo setting, if governments set their unilateral policies so as to maximize the welfare of their respective countries, then a trae agreement between the two governments woul o er scope for mutual gains if an only if the unilateral policies give rise to an ine cient outcome. As we argue above, when governments are motivate by the terms-of-trae consequences of their trae policies an set their unilaterally optimal tari s, an ine ciency is create in the resulting Nash equilibrium. An we have further shown that, if governments were not motivate by the terms-of-trae consequences of their trae policies, then the resulting politically optimal trae policies woul be e cient. Thus, in the moel with export-sector monopoly power, if each government maximizes the welfare of its country, we conclue that the only rationale for a trae agreement is to remey the ine cient terms-of-trae riven restrictions in trae volume. We next show that this conclusion continues to hol even when governments have politicaleconomic objectives. To this en, we return to the single-goo setting an now allow that the omestic government may value pro t more heavily than consumer surplus an tari revenue. Formally, we suppose that the omestic government maximizes the political-economic welfare function [P c o ]D(P ) + CS(P ) + [P (c o + )]D (P ) + td (P ); where 1 is a political-economy weight (see, e.g., Balwin, 1987, an Grossman an Helpman, 1994). The omestic government thus maximizes omestic country welfare when = 1 an values pro t more heavily than consumer surplus an tari revenue when > 1. As before, we may substitute for tari s an rewrite government welfare as a function of local an worl prices: W (P; P ; P w ; ) = [P c o ]D(P ) + CS(P ) + [P c o ]D (P ) + [P w P ]D (P ): (9) Holing xe the volumes of omestic an foreign consumption, an increase in P transfers surplus from omestic consumers (on omestically trae units) an tari revenue (on internationally trae units) to pro t. This reistribution has no e ect on omestic country welfare, but it raises the welfare of the omestic government when > 1. The welfare of the foreign government is again given by the sum of foreign consumer surplus an tari revenue as e ne in (3): in the foreign country, no rms prouce goo y, an so we o not inclue a political-economy parameter there. A key observation from (9) an (3) is that joint welfare (i.e., the sum of W (P; P ; P w ; ) an W (P ; P w )) is again inepenent of the worl price. Whether or not the omestic government has political-economic motivations, a change in the worl price amounts to a pure transfer across governments with the associate rent moving from one treasury to the other. We thus may again represent joint welfare as a function of local prices only: J(P; P ; ) = W (P; P ; P w ; ) + W (P; P ): (10) We may e ne e cient tari s relative to J(P; P ; ) as those satisfying the conitions in (6), an 14