Delocation and Trade Agreements in Imperfectly Competitive Markets (Preliminary)

Transcription

1 Delocation and Trade Agreements in Imperfectly Competitive Markets (Preliminary) Kyle Bagwell Stanford and NBER Robert W. Staiger Stanford and NBER June 20, 2009 Abstract We consider te purpose and design of trade agreements in imperfectly competitive environments featuring rm-delocation e ects. In bot te segmented-market Cournot and te integrated-market monopolistic competition settings were tese e ects ave been identi ed, we sow tat te only rationale for a trade agreement is to remedy te ine ciency attributable to te terms-of-trade externality, te same rationale tat arises in perfectly competitive markets. Furtermore, and again as in te perfectly competitive bencmark case, we sow tat te principle of reciprocity is e ciency enancing, as it serves to undo te terms-of-trade driven ine ciency tat occurs wen governments pursue unilateral trade policies. Our results terefore indicate tat te terms-of-trade teory of trade agreements applies to a broader set of market structures tan previously tougt. We tank Ralp Ossa and seminar participants at Princeton for very useful comments.

2 1 Introduction A central question in te study of commercial policy is wy governments form international trade agreements. Answers to tis question provide te foundation from wic to evaluate and interpret te design of trade agreements in ligt of te underlying problems tat tey exist to solve. An establised literature argues tat governments ave a reason to form a trade agreement wen an international externality is associated wit teir trade-policy coices. Wen a country is large in world markets, it can reduce te world (o sore) price of its imported goods by raising its tari s. Te country ten enjoys an improvement in its terms of trade; owever, its trading partners su er a negative terms-of-trade externality. As Jonson ( ) argues, wen governments maximize national income and markets are perfectly competitive, te associated non-cooperative equilibrium is ine cient, and a problem is tereby identi ed. An appropriately designed trade agreement can ten enance te welfare of all governments by reducing or eliminating tis ine ciency. Tese arguments are extended by Bagwell and Staiger (1999) and Grossman and Helpman (1995) to allow tat governments ave political-economic preferences. Allowing for a wide class of government preferences, Bagwell and Staiger (1999) demonstrate tat te non-cooperative equilibrium is ine cient relative to government preferences if and only if governments are motivated by te terms-of-trade consequences of teir respective trade policies. Building from tis nding, tey ten explore te form tat an e ciency-enancing trade agreement migt take. Tey sow tat te principle of reciprocity (and in a multi-country setting, non-discrimination) can elp to undo te terms-of-trade driven ine ciency and guide governments toward e cient policies. A model wit perfectly competitive markets o ers a valuable bencmark for understanding te purpose of trade agreements. For many markets, owever, rms possess market power. It is tus important to know weter te purpose of trade agreements migt cange in some fundamental sense once te model is extended to allow for te realistic possibility of imperfect competition. Tis extension introduces several novel issues. In particular, as is well known, imperfectly competitive markets can give rise to pro t-sifting and rm-delocation e ects tat provide novel motives for trade policy intervention. At a minimum, tis suggests tat oter international externalities in addition to te terms-of-trade externality may also be present in markets wit imperfect competition. In tis paper, we move beyond perfectly competitive markets and extend te analysis to imperfectly competitive markets tat feature te rm-delocation motive for trade policy intervention. In settings were te rm-delocation e ect is present, we examine te rationale for a trade agreement, and we also consider te form tat an e ciency-enancing trade agreement migt take. Venables (1985) rst identi ed te rm-delocation e ect, according to wic an import tari or export subsidy can produce te surprising result of bene ting a country s consumers, by stimulating entry of domestic rms and tereby reducing domestic prices troug enanced competition. Tis bene t, owever, comes at te expense of foreign consumers, wo experience iger prices as a result of foreign- rm exit and diminised competition in te foreign market. Venables identi ed tis e ect in a model were rms produce a omogeneous good and compete in a Cournot fasion 1

3 for sales in segmented markets under conditions of free entry. Venables (1987) ten sowed tat tis e ect extends to a setting of free-entry monopolistic competition were markets are integrated and rms compete to sell di erentiated products. In te model of monopolistic competition used by Venables, it is te savings on transport costs implied by te rm-delocation e ect rater tan te impacts on competition tat can enance te welfare of te intervening country. As Venables demonstrates, if te ome country raises barriers to its imports or subsidizes its exports, ten foreign rms can be delocated to te ome market. Home consumers ten save on trade costs in te form of a lower overall price index, at te expense of foreign consumers wose price index rises. 1 Wen tis novel motive for trade policy intervention is present, it migt be expected tat a novel rationale for a trade agreement would likewise be present. In line wit tis expectation, we sow tat new international externalities indeed arise wen te rm-delocation e ect is present: in addition to te terms-of-trade externality tat travels troug te world price, tere are also local price externalities tat travel troug domestic and foreign local prices. Te key question for our purposes, owever, is weter governments internalize tese international externalities in an appropriate fasion from a world-wide perspective wen tey make teir unilateral policy coices. In bot te Cournot and te monopolistic competition settings were te rm-delocation e ect as been sown to arise, we address tis question and establis a surprising answer: te only rationale for a trade agreement is to remedy te ine ciency attributable to te terms-of-trade externality, te same rationale tat arises in perfectly competitive markets. Furtermore, and again as in te bencmark model wit perfect competition, te principle of reciprocity is e ciency enancing, as it serves to undo te terms-of-trade driven ine ciency tat occurs wen governments pursue unilateral trade policies. To establis tese results, we caracterize te non-cooperative and e cient policy coices, and we ten evaluate te precise reasons for any divergence between tem. To tis end, we follow Bagwell and Staiger (1999) and evaluate politically optimal tari s, de ned as tose tari s tat would ypotetically be cosen by governments unilaterally if tey did not value te pure international rent-sifting associated wit te terms-of-trade movements induced by teir unilateral tari coices. We do tis rst for te Cournot model of rm delocation (Section 2) and ten for te monopolistic competition model (Section 3). In eac setting, we sow tat te noncooperative tari s are ine cient and tat te politically optimal tari s are e cient. In particular, starting at te noncooperative tari s, bot countries could gain by reducing te total trade impediment on any trade ow. We tereby establis tat te only rationale for a trade agreement is to remedy te iger-tan-e cient tari s tat arise as a consequence of te value tat governments place upon te terms-of-trade movements induced by teir unilateral tari coices. 1 More recently, te rm-delocation e ect of trade policy intervention as it arises in a monopolistic competition setting as been featured in Baldwin and Robert-Nicoud (2000), Melitz and Ottaviano (2008) and Ossa (2009). Baldwin and Robert-Nicoud extend te analysis of tis e ect to an economic geograpy setting in wic capital is internationally "footloose," and consider trade liberalization rules tat prevent rm-delocation in tis setting. Melitz and Ottaviano extend te analysis of tis e ect to a eterogeneous- rm setting. Ossa considers te rationale for trade agreements wen rm-delocation e ects are present. We relate our paper furter to Ossa s work below. 2

4 We also sow tat te Cournot and monopolistic competition models exibit an interesting and overlooked feature: in eac model, te terms-of-trade e ects of import tari s and export taxes are asymmetric. Te asymmetry is most pronounced in te Cournot delocation model. In tat model, a country can in standard fasion improve its terms of trade by levying an import tari ; owever, an export tax worsens te terms of trade in te model, contrary to te standard case. By implication, an export subsidy improves a country s terms of trade in te Cournot delocation model. Tis features distinguises te Cournot delocation model from oter models of commercial policy. Te monopolistic competition delocation model tat we utilize is similar to tat developed in Helpman and Krugman (1989). As Helpman and Krugman (1989) observe, in tis model, a country is unable to alter its terms of trade by using an import tari. We include export policies in our analysis as well, owever, and observe tat a country can generate a somewat extreme (dollar-for-dollar) improvement in its terms of trade by applying an export tari. Our paper is most closely related to te recent paper of Ossa (2009). Utilizing a monopolistic competition model of rm delocation, Ossa argues tat te rm-delocation e ect provides a new rationale for a trade agreement, and a rationale tat is especially relevant for (two-way) trade between similar countries. Ossa ten goes on to o er a novel interpretation of reciprocity and nondiscrimination as simple rules tat can neutralize te rm-delocation e ect. Our result concerning te rationale of a trade agreement in tis setting is at odds wit Ossa s rst observation, and so it is important to explore te di erences across te two papers. Tere are two substantive di erences between te monopolistic competition model employed by Ossa and te one we utilize below. A rst di erence is tat Ossa allows income e ects on te demand for di erentiated products, wile our (quasi linear) speci cation of utility ensures tat tere will be no suc income e ects. Te second di erence is related to te rst: due to income e ects, Ossa s model becomes intractable wen trade taxes imply revenue, and so Ossa assumes tat trade taxes do not ave revenue consequences; and importantly, tis assumption requires Ossa to abstract from export (subsidy) policies in is analysis. By contrast, te revenue consequences of trade taxes are simple to andle in our quasi-linear setting, and so we can and do allow for bot import tari s and export taxes/subsidies; and as we explain below, allowing for bot import and export policies is crucial for our result. 2 If te presence of te rm-delocation e ect introduces new international externalities tat are transmitted troug non-terms-of-trade cannels, and we con rm below tat it does, ten ow can te problem tat a trade agreement must solve still boil down to providing an avenue of escape from a terms-of-trade driven Prisoners Dilemma? Broadly speaking, te reason is tis: trade agreements do not expand te set of feasible policy instruments available to governments, and so any e ciency gains generated by a trade agreement must derive from canges in te level of intervention acieved wit te existing policy instruments; and as we demonstrate below, even in tis more complicated environment it is te international rent-sifting/cost-sifting associated wit 2 Te GATT/WTO restricts te use of export subsidies, and in tis ligt Ossa s (2009) nding can be interpreted as caracterizing a problem tat arises wen export subsidies are banned. At te same time, tis interpretation would fall sort of delivering a fundamental rationale for a trade agreement, because it appeals to te existence of a trade agreement (on export subsidies) to explain wy governments need a trade agreement. 3

5 te terms-of-trade externality and tis externality alone tat accounts for te ine cient level of intervention under unilateral policy coices. Te analysis in tis paper maintains te assumption tat free entry eliminates pro ts in equilibrium even toug rms are not price-takers. Tis allows us to focus on te rm-delocation e ect, and on te novel role for trade policy intervention in te presence of tis e ect. An alternative role for government intervention can arise wen te number of producers in eac country is xed and invariant to trade policy. In tis case, tere may exist pro table rms, and te pursuit of tose pro ts eiter converted into tari revenue or sifted from one rm to anoter combined wit te relaxation of te assumption of price-taking beavior can provide an alternative pro t sifting role for trade policy intervention. In a companion paper (Bagwell and Staiger, 2009), we consider tis alternative by exploring models in wic rms are not price takers but were te number of rms is xed, and we again ask weter a novel role for trade agreements can be identi ed. For te models of pro t-sifting, our main nding is again tat te terms-of-trade externality continues to provide te only rationale for a trade agreement. 2 Delocation wit Cournot Competition and Segmented Markets In tis section we consider a model wose underlying structure is essentially tat contained in Venables (1985). 3 We refer to tis model as te Cournot delocation model. Te industry under consideration is comprised of rms wo produce a omogeneous good and compete in a Cournot fasion for sales in a domestic and foreign market under conditions of free entry. Te markets are segmented, and two-way trade in identical products arises as a consequence. Tere are transport costs between te markets, and eac government may also impose a trade tax/subsidy on trade ows in and/or out of its market. Tis environment exibits a rm-delocation e ect tat as important implications for te impacts of trade policy, as Venables rst empasized. Our main purpose ere, owever, is to identify and interpret te sources of ine ciency tat arise wen governments set teir trade policies unilaterally, and tereby to explore te potential role and design of a trade agreement in tis environment. 2.1 Model Setup Tere are two countries (ome and foreign), eac endowed wit a large amount of labor wic is te only factor of production. In te background, a competitively supplied numeraire good is produced wit labor alone according to a constant-returns-to-scale production function common across countries (1 unit of labor produces 1 unit of te numeraire). Te numeraire good enters linearly into te utility of eac country, is always produced and consumed in positive amounts by eac country (due to te large supply of labor in eac country), and is freely traded across countries, so tat its price (and ence te wage of labor) is xed and equalized (and normalized to 3 Te model we develop ere imposes additional symmetry across countries relative to Venables (1985), but tis symmetry serves only to simplify te exposition and is not necessary for our main results. 4

6 one) everywere in te world. Tis structure permits a partial equilibrium treatment of te second, imperfectly competitive, industry tat is our main focus. Te ome country as n Cournot rms in tis industry, and te foreign country as n f Cournot rms, all producing te same good at a (common) marginal cost c and xed cost F under conditions of free entry. If te good sells in te ome country at price P, ten ome consumers demand D(P ) units; likewise, if te good sells in te foreign country at price P, ten foreign consumers demand D (P ) units. We assume tat D(P ) and D (P ) are positive and downward sloping. Te markets are segmented, so tat te ome and foreign market prices P and P are determined by separate ome and foreign market-clearing conditions, and te problem of output coice for eac rm is separable across te ome and foreign markets. As sown by Brander (1981), an implication of te segmented markets setting is tat in general trade will occur in bot directions. 4 Trade in eiter direction is costly in tis industry, and we let ' denote te cost of transporting one unit of te good between countries (measured in units of te numeraire). We assume tat eac country as bot import and export policies at its disposal, and we express all trade taxes in speci c terms: for exports from te ome country to te foreign country, t is te export tax imposed by te ome country (t < 0 if an export subsidy) and t f is te import tari imposed by te foreign country; and for exports from te foreign country to te ome country, t f is te export tax imposed by te foreign country (t f < 0 if an export subsidy) and t is te import tari imposed by te ome country. We maintain a focus trougout on non-proibitive trade taxes. For convenience we de ne te total trade impediments facing ome and foreign imports, respectively, by ' + t + t f ; and (1) ' + t + t f : In wat follows, we assume te existence of positive transport costs so tat ' > 0, implying tat under free-trade policies (t = 0, t f = 0, t = 0, t f = 0) we ave > 0 and > 0. In e ect as will become clear, tis assumption ensures tat, beginning from free trade, a rm s pro ts are more sensitive to canges in te price it receives for its domestic sales tan for its export sales. As discussed in Venables (1985), it is tis feature tat delivers te rm-delocation e ects of trade policy exibited by te model. Consider next te problem faced by ome rm i. coose output destined for te ome market q i For xed n and n f, ome rm i must to maximize its ome-market pro t in ligt of te (n 1) oter (symmetric) ome rms ome-market output coices (n 1)q and te n f (symmetric) foreign rms ome-market output coices n f q f. Te industry output destined for te ome market is Q q i + (n 1)q + n f q f, and Q ten determines P troug te ome 4 For analyses of trade policies in te presence of segmented markets wit an exogenously xed number of rms, see Brander and Spencer (1984) and Dixit (1984). For an analysis of trade agreements in te segmented-market- xed-number-of- rms setting, see Bagwell and Staiger (2009). 5

7 market-clearing condition q i + (n 1)q + n f q f = D(P ): (2) to maximize its foreign- Home rm i must also coose output destined for te foreign market q i market pro t in ligt of te (n 1) oter (symmetric) ome rms foreign output coices (n 1)q and te n f (symmetric) foreign rms foreign output coices n f qf. Te industry output destined for te foreign market Q q i + (n 1)q + n f qf ten determines P troug te foreign market-clearing condition q i + (n 1)q + n f q f = D (P ): (3) Using (2) and (3), we may terefore de ne te ome and foreign market-clearing prices P (q i + (n 1)q + n f q f ) and P (q i + (n 1)q + n f qf ), or equivalently P (Q) and P (Q ). Notice tat, owing to te segmented market assumption, P and P do not depend on trade taxes directly, but may depend indirectly on trade taxes to te extent tat trade taxes alter respectively Q and Q. We may now write ome rm i 0 s ome-and-foreign-market pro ts as i (q i ; q ; q f ; q i ; q ; q f ; n ; n f ; ) = [P (q i + (n 1)q + n f q f ) c]q i +[P (q i + (n 1)q + n f q f ) (c + )]q i F: For eac market, ome rm i 0 s rst-order condition equates te marginal revenue generated from a sligt increase in its output in tat market wit its marginal cost of delivery to tat market. Using (2) to derive dp dq = 1 dp 1 D 0 (P ) and using (3) to derive dq = D 0 (P ), tese rst-order conditions can be expressed as q i + [P () c]d0 (P ()) = 0; and (4) q i + [P () (c + )]D 0 (P ()) = 0; were we use P () to denote P (q i +(n 1)q +n f q f ) and P () to denote P (q i+(n 1)q +n f qf ) to reduce notation. Tese conditions de ne ome- rm i 0 s reaction curve for te ome and foreign markets, respectively. 5 Under our assumption tat demand functions are downward sloping, we may observe from (4) tat ome rm i s markups (inclusive of trade costs) must be positive in bot markets. Wit analogous steps, we may write foreign rm i 0 s ome-and-foreign-market pro ts as fi (qf i ; q ; q f ; qf i ; q ; q f ; n ; n f ; ) = [P (qf i + (n f 1)qf + n q ) c]qi f +[P (q i f + (n f 1)q f + n q ) (c + )]q i f F: As before, in eac market, foreign rm i 0 s rst-order condition equates te marginal revenue gen- 5 We assume tat te second-order conditions old. Tese conditions are given by 2[ D 0 (P ())] > [P () c]d 00 (P ()) and 2[ D 0 (P ())] > [P () (c + )]D 00 (P ()), and tey are sure to old, for example, if te demand functions D(P ) and D (P ) are log concave. 6

8 erated from a sligt increase in its output in tat market wit its marginal cost of delivery to tat market. Tese rst-order conditions can be expressed as q i f + [P () c]d 0 (P ()) = 0; and (5) q i f + [P () (c + )]D0 (P ()) = 0: Tese conditions de ne foreign- rm i 0 s reaction curve for te foreign and ome markets, respectively. 6 Again, given our assumption tat demand functions are downward sloping, we see from (5) tat foreign rm i s markups (inclusive of trade costs) must be positive in bot markets. Finally, wen all ome and foreign rms are on teir respective reaction curves, we ave te Cournot-Nas equilibrium. After imposing symmetry across ome rms (q i = q and q i = q ) and across foreign rms (qf i = q f and qf i = q f ), we may solve for te ome-market output levels for a representative ome rm and a representative foreign rm. We denote tese Nas quantities in te ome market by q N (n ; n f ; ) and q N f (n ; n f ; ), respectively, wit Q N (n ; n f ; ) n q N + n f q N f. Similarly, we may solve for te foreign-market output levels for a representative ome rm and a representative foreign rm. We denote tese Nas quantities in te foreign market by (n ; n f ; ) and qf N (n ; n f ; ), respectively, wit Q N (n ; n f ; ) n q N impose te condition q N + n f qf N. We also q N f P 00 (Q N ) + P 0 (Q N ) < 0 and q N P 00 (Q N ) + P 0 (Q N ) < 0; (6) wic ensures tat a rm s marginal revenue falls in a market wen oter rms output increases in tat market, and amounts to an assumption tat reaction curves are downward sloping. 7 For a broad family of demand functions (including linear demands), wen n and n f are eld xed an increase in reduces te sales of eac foreign rm into te ome market, q N f (n ; n f ; ), raises te sales of eac ome rm in te ome market, q N (n ; n f ; ), and reduces total sales in te ome market Q N (n ; n f ; ), wit P (Q N (n ; n f ; )) rising but by less tan. 8 And similarly, wit n and n f eld xed, an increase in reduces te sales of eac ome rm into te foreign market, q N(n ; n f ; ), raises te sales of eac foreign rm in te foreign market, qf N (n ; n f ; ), and reduces total sales in te foreign market Q N (n ; n f ; ), wit P (Q N (n ; n f ; )) rising but by less tan. We encefort assume tat tese properties old. We may now write te maximized pro ts of a representative ome rm as (n ; n f ; ; ) = [P (Q N (n ; n f ; )) c]q N (n ; n f ; ) (7) +[P (Q N (n ; n f ; )) (c + )]q N (n ; n f ; ) F: 6 We again assume tat te second-order conditions old. 7 Condition (6) clearly olds wen demand is linear. More generally, condition (6) is ensured if te demand functions D(P ) and D (P ) are log concave. 8 For te linear-demand case, see, for example, Bagwell and Staiger (2009a). We note tat, for su ciently convex demand functions, an increase in may induce P (Q N (n ; n f ; )) to rise by more tan, wen n and n f are eld xed. We abstract from suc demand functions ere. 7

9 And similarly, we may write te maximized pro ts of a representative foreign rm as f (n ; n f ; ; ) = [P (Q N (n ; n f ; )) c]q N f (n ; n f ; ) (8) +[P (Q N (n ; n f ; )) (c + )]q N f (n ; n f ; ) F: We assume tat (n ; n f ; ; ) and f (n ; n f ; ; ) are eac decreasing in n and n f. assumption olds for a broad family of demand functions (including linear demands). Under free entry, n and n f adjust to ensure tat te maximized pro ts of ome and foreign rms de ned in (7) and (8) respectively are equal to zero, or Tis (n ; n f ; ; ) = 0 = f (n ; n f ; ; ); (9) wic ten de nes n N ( ; ) and n N f ( ; ). Our focus on non-proibitive trade taxes ensures tat bot n N ( ; ) and n N f ( ; ) are positive, but condition (9) ignores te fact tat n and n f can only take on integer values. Neverteless, we will follow standard practice and treat n N ( ; ) and n N f ( ; ) as continuous and di erentiable functions, wic is a good approximation if te number of rms is large. We assume tat n N ( ; ) is increasing in and decreasing in wile n N f ( ; ) is increasing in and decreasing in. Tis assumption olds if te determinant of te Jacobian matrix associated wit (9) is positive; for example, it is straigtforward to verify tat tis assumption olds wen demand is linear. Intuitively, under our assumptions, an increase in wit n and n f eld xed will result in positive pro ts for ome rms and negative pro ts for foreign rms. Te equilibrium zero-pro t condition in (9) can ten be restored if foreign rms exit (n N f falls) and ome rms enter (n N rises). Similarly, an increase in wit n and n f eld xed will result in positive pro ts for foreign rms and negative pro ts for ome rms, and te equilibrium zero-pro t condition in (9) can ten be re-establised if ome rms exit (n N falls) and foreign rms enter (nn f rises). As we will illustrate sortly, te canges in n N and nn f induced by canges in tari s underlie te rm-delocation e ects of trade policy intervention featured in tis model. Finally, using n N ( ; ) and n N f ( ; ), we may write te ome and foreign market prices respectively as ~P N ( ; ) P (Q N (n N ( ; ); n N f ( ; ); )); and (10) ~P N ( ; ) P (Q N (n N ( ; ); n N f ( ; ); )): Similarly, we may write te ome and foreign market sales of a representative ome and foreign 8

10 rm as ~q N ( ; ) q N (nn ( ; ); n N f ( ; ); ); (11) ~q N f ( ; ) q N f (nn ( ; ); n N f ( ; ); ); ~q N ( ; ) q N (nn ( ; ); n N f ( ; ); ); and ~q N f ( ; ) q N f (n N ( ; ); n N f ( ; ); ): According to (10) and (11), all Nas equilibrium prices and quantities can be expressed as functions of te total trade impediments and. 2.2 Te Firm-Delocation E ect At tis point, we evaluate te impacts of tari s on te Nas local prices ~ P N ( ; ) and ~ P N ( ; ), and tereby furter igligt te importance of te rm-delocation e ect. To tis end, we substitute (4) into (7) and (5) into (8) to rewrite (9) as [P () c] 2 [ D 0 (P ())] + [P () (c + )] 2 [ D 0 (P ())] F = 0; and (12) [P () c] 2 [ D 0 (P ())] + [P () (c + )] 2 [ D 0 (P ())] F = 0; were wit a sligt abuse of notation we now use P () to denote P (Q N (n ; n f ; )) and P () to denote P (Q N (n ; n f ; )). Te top equation in (12) traces out a locus of ome and foreign prices (P and P ) tat, for any, is consistent wit te ome- rm zero-pro t condition; similarly, te bottom equation of (12) traces out a locus of ome and foreign prices tat, for any, is consistent wit te foreign- rm zero-pro t condition. Di erent values of n and n f trace out te locus of (P; P ) combinations described by eac of te two equations in (12), and te equilibrium values n N ( ; ) and n N f ( ; ) and ence ~ P N ( ; ) and ~ P N ( ; ) are determined were te two loci cross and ence te two equations in (12) are satis ed. Di erentiating eac equation in (12) wit respect to P and P and solving for dp dp j =0 and dp dp j f =0, it is straigtforward to establis tat eac locus of (P; P ) combinations is negatively sloped under te second-order conditions. Moreover, using (6), it can be sown tat at te equilibrium point te foreign- rm zero-pro t condition is steeper tan te ome- rm zero-pro t condition dp (i.e., dp j f =0 < dp dp j =0 < 0) as long as > 0 and > 0, wic is guaranteed beginning from free-trade policies (t = 0, t f = 0, t = 0, t f = 0) under our assumption of positive transport costs (' > 0). Starting wit an initial set of policies, suc as te free-trade policies, at wic > 0 and > 0, consider now te impact of a small increase in, triggered by an increase in eiter t or t f. Figure 1 illustrates. Wit P on te vertical axis and P on te orizontal axis, te solid lines labelled 0 = 0 and f 0 = 0 depict, respectively, te ome- rm and foreign- rm zero pro t loci described by (12) under te initial policies. As discussed above, wit positive transport costs, te two loci cross as depicted in te gure, wit te f 0 = 0 locus cutting te 0 = 0 locus from above, and 9

11 te point at wic tey cross corresponds to an initial equilibrium price combination denoted in te gure by P ~ 0 N and P ~ 0 N. As can be con rmed from (12), a small increase in triggered by an increase in eiter t or t f leaves te = 0 locus una ected, but it sifts out te f = 0 locus. 9 In Figure 1, tis new locus is depicted by te dased line and labeled f 1 = 0, and te new equilibrium prices are denoted by P ~ 1 N and P ~ 1 N. Recall tat, wit n and n f eld xed, P (Q N (n ; n f ; )) rises wen is increased but by less tan te rise in, wile P (Q N (n ; n f ; )) is una ected. To restore zero-pro ts for bot ome and foreign rms, tere must be entry of ome rms (n must rise) and exit of foreign rms (n f must fall); and as Figure 1 illustrates, te competitive e ects of tis entry and exit must be su cient to ensure tat ~ P N ( ; ) ultimately falls and ~ P N ( ; ) ultimately rises. In oter words, a small increase in results in a pro-competitive (entry) e ect wic reduces te price in te ome market and an anti-competitive (exit) e ect wic raises te price in te foreign market. A corresponding analysis establises tat a small increase in, triggered by an increase in eiter t or t f, will decrease ~ P N ( ; ) and increase ~ P N ( ; ). Tese surprising price impacts of tari intervention are te allmark of te rm-delocation e ect. As Venables (1985) empasizes, tese impacts arise wen trade costs are positive, since a rm ten as greater sales in its domestic market tan abroad, all else equal, and so adjustments in te domestic price bear te primary burden for restoring zero pro ts following any trade policy intervention. As Venables (1985) establises, te rm-delocation e ect gives rise to a novel motive for trade policy intervention: an import tari or export subsidy can bene t a country s consumers, by stimulating entry of domestic rms and tereby reducing domestic prices troug enanced competition; tis bene t, owever, comes at te expense of foreign consumers, wo experience iger prices as a result of foreign- rm exit and diminised competition in te foreign market. We next introduce a complete representation of welfare, so tat we may explore te implications of te rm-delocation e ect for optimal unilateral trade policy coices and te nature of trade agreements. 2.3 Representation of Welfare To proceed, we now develop expressions for te welfare of eac country. We begin wit te ome welfare function. Because te free-entry condition (9) ensures tat oligopoly pro ts are zero, we can write ome welfare as te sum of consumer surplus and net trade tax revenue, or CS( ~ P N ) + t n N f ~qn f + t nn ~qn ; were we note tat n N f ~qn f corresponds to ome-country imports and nn ~qn corresponds to omecountry exports. To re ne te expression for ome welfare, we next introduce a number of furter price de nitions. First, at te Cournot-Nas equilibrium, let us denote te world price for exports to te ome 9 Tis follows from te second-order conditions. 10

12 market by ~P wn (t ; ; ) = ~ P N ( ; ) t (13) and te world price for exports to te foreign market by ~P wn (t f ; ; ) = ~ P N ( ; ) t f : (14) We also de ne R ~ N ( ; ) = P ~ wn (t f ; ; ) ' t as te price received by te ome rm for foreign sales (te segmentation of markets implies tat in general R ~ N 6= P ~ N ), and similarly ~R N ( ; ) = P ~ wn (t ; ; ) ' t f as te price received by te foreign rm for ome-country sales (te segmentation of markets implies tat in general R ~ N 6= P ~ N ). Notice using (1) tat ~P N R ~ N = and P ~ N R ~ N =. We may tus regard te equilibrium numbers of rms de ned in (9) and ence te Cournot-Nas quantities de ned in (11) as functions of local price di erences. Wit tese observations in place, we now represent ome-country imports M and exports E respectively as M( ~ P N ~ R N ; ~ P N ~ R N ) = n N f ( ~ P N ~ R N ; ~ P N ~ R N )~q N f ( ~ P N ~ R N ; ~ P N ~ R N ); and E( ~ P N ~ R N ; ~ P N ~ R N ) = n N ( ~ P N ~ R N ; ~ P N ~ R N )~q N ( ~ P N ~ R N ; ~ P N ~ R N ); allowing ome country welfare to be expressed as a direct function of prices: W ( ~ P N ; ~ R N ; ~ P wn ; ~ P N ; ~ R N ; ~ P wn ) = CS( ~ P N ) (15) +[ ~ P N ~ P wn ]M( ~ P N ~ R N ; ~ P N ~ R N ) +[ ~ P wn ~ R N ']E( ~ P N ~ R N ; ~ P N ~ R N ): Next consider te foreign welfare function. Foreign welfare is given by te sum of consumer surplus and net trade tax revenue, or CS ( ~ P N ) + t f n N f ~qn f + t f nn ~qn : We may terefore represent foreign country welfare by W ( P ~ N ; R ~ N ; P ~ wn ; P ~ N ; R ~ N ; P ~ wn ) = CS ( P ~ N ) (16) +[ P ~ wn R ~ N ']M( P ~ N R ~ N ; P ~ N R ~ N ) +[ P ~ N P ~ wn ]E( P ~ N R ~ N ; P ~ N R ~ N ): Hence, by (15) and (16), we may express te welfare of eac country as a function of ome and foreign local prices and te terms of trade (as re ected in te two world prices). Notice an interesting feature of te Cournot delocation model: te terms-of-trade e ects of import tari s and export taxes are asymmetric. To see tis, consider rst te impact of an increase in te ome import tari t on te world prices P ~ wn and P ~ wn. Using te de nitions of te world 11

13 = ~ P wn t + ~ P wn = P ~ wn = prices given in (13) and (14), we ave d P ~ wn dt = P ~ N 1 < 0 and d P ~ wn dt > 0, and ence te ome import tari improves te ome terms of trade by lowering te ~ P N world price of ome imports and raising te world price of ome exports. An analogous statement olds for te foreign import tari. Te terms-of-trade e ect of an import tari in te Cournot delocation model is tus te standard e ect expected from competitive models for a country tat is large in world markets, and tis provides a second motive (in addition to rm delocation) for import tari s in te model: international cost-sifting. 10 Now consider te impact of an increase in te ome export tax t on te world prices ~ P wn and P ~ wn. In tis case we ave d P ~ wn dt = P ~ wn = P ~ N > 0 and d P ~ wn dt = P ~ wn = P ~ N < 0, and ence, contrary to te standard e ect in competitive models, te ome export tax worsens te ome terms of trade by raising te world price of ome imports and lowering te world price of ome exports. Again an analogous statement olds for te foreign export tax. Intuitively, a ome export tax worsens te ome terms-of-trade because of te domestic exit and foreign entry tat te export tax induces: as noted above in section 2.2, te anti-competitive e ect of te domestic exit induced by te ome export tax is su cient to raise te price for sales in te ome market, wic must be paid for ome imports; and te pro-competitive e ect of te induced foreign entry is su cient to lower te price for sales in te foreign market, wic ome rms receive for teir exports. Te terms-of-trade e ect of an export tax in te Cournot delocation model is tus opposite te standard e ect expected from competitive models for a country tat is large in world markets. By implication, an export subsidy improves a country s terms of trade, and tis provides a second motive (in addition to rm delocation) for export subsidies in te model, namely, international cost-sifting. 11 At tis point it is useful to pause and compare te expressions for welfare in (15) and (16) wit te expressions tat arise in a perfectly competitive (integrated markets) bencmark setting. Under conditions of perfect competition in tis single-good setting, eac country s welfare can be expressed as a function of its local price (P or P ) and te world price (P w ), so tat ome country welfare can be written as W (P; P w ) and foreign country welfare can be written as W (P ; P w ). 12 Compared to te perfectly competitive bencmark, te presence of segmented markets is one reason for te proliferation of prices in te expressions for welfare in (15) and (16). Wen markets are segmented, identical products may trade in two directions. If te con guration of tari s (or transport costs) is di erent along one direction of trade tan te oter, ten te associated world prices may di er as well. Tus, we may ave tat ~ P wn 6= ~ P wn. Te segmentation of markets also implies tat in general te price tat a rm receives for a unit destined for export may di er from te price tat it receives wen te unit is sold locally. In oter words, wen markets are segmented, we generally ave tat ~ R N 6= ~ P N and ~ R N 6= ~ P N. But te ome and foreign welfare expressions in 10 Speci cally, some of te tari revenue is being collected from foreigners. 11 Speci cally, foreigners are paying for some of te subsidy to domestic exporters. 12 See Bagwell and Staiger (1999, 2001, 2002) on te general validity of tis structure and its importance for trade agreements. 12

14 (15) and (16) reveal a furter and crucial distinction between te perfectly competitive bencmark and te setting we consider ere: in te present setting, eac country s welfare depends not only upon its own local prices and te world prices, but also on te local prices tat prevail in te markets of its trading partner. Tis is because it is te di erence between local prices at ome and abroad tat determines Nas equilibrium trade volumes and terefore trade tax revenues. Hence, as (15) and (16) con rm, tere is a new international externality present for eac government as compared to te competitive bencmark setting: for te ome government, in addition to te terms-of-trade externalities tat travel troug ~ P wn and ~ P wn, tere are also (foreign) local price externalities tat run troug ~ R N and ~ P N ; and similarly, for te foreign government, in addition to te terms-of-trade externalities tat travel troug ~ P wn and ~ P wn, tere are also (ome-country) local price externalities tat run troug ~ R N and ~ P N. Tis indicates a more complex international policy environment tan exists under te competitive bencmark, and it raises te possibility tat te task of a trade agreement may be more complicated in tis environment as a result. Neverteless, te fundamental question for our purposes ere is weter governments would make unilateral policy coices tat internalize tese international externalities watever form tese externalities migt take in an appropriate fasion from a world-wide perspective, and if not, wy not. To answer tis question, we need to examine te non-cooperative and e cient policy coices in detail and evaluate te precise reasons for any divergence between tem. 2.4 Nas Policies and Ine ciency We next caracterize te Nas policy coices, wic we interpret to be tose policies tat governments would coose in te absence of a trade agreement. Using (15) and te fact tat d dt = 1 = d dt by (1), te rst-order conditions tat de ne te optimal unilateral policy coices for te ome country are given by 13 W ~P N ~ P N + W ~R N ~ R N + W ~P wn d ~ P wn dt P + W ~ N ~P N R + W ~ N ~R N P + W ~ wn ~P wn d = 0; (17) W ~P N ~ P N + W ~ R N ~ R N + W ~ P wn ~ P wn + W ~P N ~ P N + W ~R N ~ R N + W ~P wn ~ P wn = 0. (18) Similarly, using (16) and te fact tat d dt = 1 = d f dt f by (1), te rst-order conditions tat de ne te optimal unilateral policy coices for te foreign country are given by 14 W ~ P N ~ P N + W ~ R N ~ R N + W d P ~ wn P ~ wn dt f + W ~ P N ~ P N + W ~ R N ~ R N + W ~ P wn ~ P wn = 0, (19) W ~ P N ~ P N + W R ~ N R ~ N + W P ~ wn P ~ wn + W ~ P N ~ P N + W ~ R N ~ R N + W P ~ wn P ~ wn = 0. (20) 13 We assume tat second-order conditions are met. 14 Again we assume tat second-order conditions are met. 13

15 Te Nas policies, wic we denote by t N, tn, tn f four rst-order conditions. and t N f, are de ned by te solution to tese Beginning from free trade and under our assumption of positive transport costs, it can be sown tat eac country gains wen it imposes a small import tari and/or a small export subsidy. 15 Intuitively, as we ave observed, tere are two reinforcing motives in te model tat drive governments to restrict imports wit import tari s and to promote exports wit export subsidies: a rm-delocation motive, wereby eac government seeks to reduce te prices faced by consumers in its local market; and a terms-of-trade motive, wereby eac government can sift some of te costs of its intervention on to foreigners. In ligt of tese motives, it migt seem natural to expect tat te Nas policies caracterized by (17) troug (20) would ten involve eac country taxing its imports and subsidizing its exports. In Bagwell and Staiger (2009a), owever, we focus on te case of linear demand and identify a furter consideration: a tari -complementarity e ect exists for any country between its import and export tari s. Intuitively, wen a country raises its import tari, te resulting rm-delocation e ect generates entry and tus expanded export volume. From te perspective of trade tax revenue, tis makes an export subsidy less attractive and an export tax more attractive. For te linear-demand case, we sow in Bagwell and Staiger (2009a) tat te tari -complementarity e ect is su ciently strong to ensure tat te Nas equilibrium entails a positive import tari and an export tax. More generally, wile it can be expected tat te Nas import policy is an import tari in tis model, te sign of te Nas export policy is di cult to pin down witout imposing additional assumptions on te model. In wat follows, we terefore make no assumptions on te signs (taxes or subsidies) of Nas policies. In any event, we now con rm te ine ciency of te Nas policy coices. As a preliminary step, we caracterize e cient policy coices. An e cient or joint-welfare maximizing agreement would maximize te sum of W and W. Notice from (15) and (16), toug, tat te world prices ( ~ P wn and ~ P wn ) cancel from tis summation: te world price a ects te distribution of rents across countries, but does not in itself a ect e ciency. Tis observation provides one simple way of understanding wy tari policies tat are motivated by terms-of-trade e ects lead to ine ciencies. But we may still ask weter any oter sources of ine ciency are present. To tis end, we express joint welfare as J( ~ P N ; ~ R N ; ~ P N ; ~ R N ) W ( ~ P N ; ~ R N ; ~ P wn ; ~ P N ; ~ R N ; ~ P wn ) + W ( ~ P N ; ~ R N ; ~ P wn ; ~ P N ; ~ R N ; ~ P wn ) = CS( ~ P N ) + [ ~ P N ~ R N [ ~ P N ~ R N ']M( ~ P N ~ R N ; ~ P N ~ R N ) + ']E( ~ P N ~ R N ; ~ P N ~ R N ) + CS ( ~ P N ): Using te expression for joint welfare above, and noting tat ~ P N, ~ R N, ~ P N and ~ R N are eac functions of and only and ence only functions of te total tari s t + t f and t + t f it follows tat tere are only two independent conditions tat de ne e cient coices of t, t, t f and 15 See Venables (1985) for a demonstration of tis point. Venables does not, owever, caracterize te Nas equilibrium policies, wic we discuss next. 14

16 t f, and tey are given by [W ~P N +W P ~ N ] P ~ N +[W R ~ N +W R ~ N ] R ~ N +[W P ~ N +W P ~ N ] P ~ N +[W ~R N +W ~ R N ] R ~ N = 0; (21) [W ~P N +W ~ P N ] ~ P N +[W ~ R N +W ~ R N ] ~ R N +[W P ~ N +W P ~ N ] P ~ N +[W ~ R N +W ~ R N ] ~ R N = 0: (22) For te case of linear demands, it can be sown tat e ciency requires t + t f = 0 and t + t f = 0, despite te Cournot environment (see Bagwell and Staiger, 2009a). Wit general demands, e cient trade policy intervention may entail eiter net trade restrictions or net trade promotion. We now formally establis tat te Nas policy coices are ine cient. Adding te Nas conditions (17) and (20) togeter, using (15) and (16) to con rm tat W ~P wn = E = W ~ P wn and W ~ P wn = M = W ~ P wn, and noting tat d ~ P wn dt = ~ P wn 1 yields [W ~P N + W P ~ N ] P ~ N + [W R ~ N + W R ~ N ] R ~ N + [W P ~ N + W P ~ N ] P ~ N + [W ~R N + W ~ R N ] R ~ N = M N ; (23) were we use M N to denote te Nas ome-country import volume. Similarly, adding te Nas conditions (18) and (19) togeter, and noting tat d P ~ wn dt = P ~ wn f 1 yields [W ~P N + W P ~ N ] P ~ N + [W R ~ N + W R ~ N ] R ~ N + [W P ~ N + W P ~ N ] P ~ N + [W R ~ N + W R ~ N ] R ~ N = E N ; (24) were we use E N to denote te Nas ome-country export volume. Comparing (23) wit te e ciency condition (21), and under te assumption tat te second-order conditions for jointwelfare maximization old, it is apparent tat for any te level of implied by te Nas tari condition (23) is ine ciently ig. Similarly, comparing (24) wit te e ciency condition (22), it is apparent tat for any te level of implied by te Nas tari condition (24) is ine ciently ig. Tus, in tis environment te Nas policy coices result in trade barriers tat are too ig Politically Optimal Policies and E ciency To determine te reason for te ine ciency of te Nas tari coices, we now follow Bagwell and Staiger (1999, 2001) and de ne politically optimal tari s as tose tari s tat would ypotetically be cosen by governments unilaterally if tey did not value te pure international rent-sifting associated wit te terms-of-trade movements induced by teir unilateral tari coices. Speci cally, we suppose tat te ome government acts as if W ~P wn 0 and W ~P wn 0 wen coosing its politically optimal tari, wile te foreign government acts as if W ~ P wn 0 and W ~ P wn 0 wen coosing its politically optimal tari. We terefore de ne politically optimal tari s as tose tari s 16 In particular, beginning from te Nas equilibrium tari levels, a reduction in will increase joint welfare and tereby move countries toward te international e ciency frontier. A similar interpretation applies for (24) and (22) and te Nas level of. 15

17 tat satisfy te following four conditions: W ~P N W ~P N W ~ P N W ~ P N P ~ N R + W P ~R N + W R ~P N + W ~R N = 0; (25) P ~ N + W R ~ N R ~ N + W P ~ N R P ~ N + W ~R N = 0; P ~ N + W R ~ N R ~ N + W P ~ N P ~ N + W R ~ N R ~ N = 0; and P ~ N + W R ~ N ~ R N + W P ~ N ~ P N + W R ~ N ~ R N = 0. Wit politically optimal tari s de ned in tis way, we may ask weter politically optimal tari s are e cient, and tereby explore weter te Nas ine ciencies identi ed above can be given a terms-of-trade interpretation, according to wic te fundamental problem faced by governments in designing teir trade agreement is to nd a way to eliminate terms-of-trade manipulation. Wit regard to te nature of te tougt experiment envisioned in te politically optimal tari s, tere is an important distinction between te perfectly competitive environment considered in Bagwell and Staiger (1999, 2001) and te imperfectly competitive setting tat we analyze ere. 17 In te perfectly competitive setting, domestic welfare can be written as W (P; P w ) as we ave observed, and te politically optimal tari for te domestic government ten satis es W P dp dt = 0. Tus, in te case of perfect competition, it is immaterial weter te tougt experiment associated wit politically optimal tari s is interpreted to mean tat te government acts as if W P w 0 or rater tat te government acts as if dp w dt 0, because eiter way we ave W P w dp w dt Notice tat, under te second interpretation, politically optimal tari s are te tari s tat governments would coose unilaterally if tey were small in world markets. In te presence of imperfectly competitive rms, owever, tis second interpretation is not valid. To see wy, consider te ome country, and recall tat te ome welfare function now includes ~P N and ~ R N. And observe as well tat te relationsip ~ P wn (t f ; ; ) = ~ P N ( ; ) t f implies d ~ P N dt = d ~ P wn dt, wile te relationsip ~ R N ( ; ) = ~ P wn (t ; ; ) ' t f implies d ~ R N dt Consequently, if te ome government were to act as if d ~ P wn dt ten by necessity also act as if d ~ P N dt = d P ~ wn dt. 0 and d P ~ wn dt 0, it would 0, and so its unilaterally cosen import 0 and d R ~ N dt = 0, wic di ers from te expression for te politically tari would satisfy W P ~ N ~P N + W R ~ N ~R N optimal ome import tari in te rst condition of (25). An analogous statement applies for te oter ome policy instrument and for eac policy instrument of te foreign government. In e ect, in te presence of imperfect competition, it no longer makes sense to tink of a ypotetical situation in wic governments act as if tey were small in world markets, because teir rms are not small. We now proceed to o er a formal evaluation of te e ciency properties of politically optimal tari s as de ned by (25). Tis is easily done: te rst and fourt conditions in (25), wen summed 17 Tis distinction is sared as well wit te xed-number-of- rms imperfectly competitive environment considered in Bagwell and Staiger (2009). 18 Bagwell and Staiger (1999, footnote 11) stress te rst of tese interpretations in teir formal analysis, but bot interpretations are valid in te competitive markets setting. 16

18 togeter, imply te e ciency condition (21); and te second and tird conditions in (25), wen summed togeter, imply te e ciency condition (22). Politically optimal tari s are tus e cient. Put di erently, if governments could be induced not to value te pure international rent-sifting associated wit te terms-of-trade movements caused by teir unilateral tari coices, ten tey would set e cient tari s. Evidently, te rm-delocation motive for trade-policy intervention provides no independent source of international ine ciency in te Cournot delocation model. It is interesting to compare te Nas and politically optimal trade policies, so tat we may understand te nature of te import and export policy commitments tat government must make if tey are to move from te Nas to te political optimum in te Cournot delocation model. A complete comparison is di cult to undertake witout furter structure, owever. Wit te restriction of linear demand, we sow in Bagwell and Staiger (2009a) tat te politically optimal policy is free trade. As we note above, for te linear-demand case, we also sow in Bagwell and Staiger (2009a) tat te Nas import policy is an import tari and te Nas export policy is an export tax. As we observe above, it is also true tat, beginning from free trade, eac government as a unilateral incentive to subsidize its exports. For te linear-demand case, we tus argue in Bagwell and Staiger (2009a) tat te e cient political optimum (free trade) requires tat governments be restrained from imposing import tari s and export subsidies, despite te fact tat te unilateral incentive to subsidize exports does not arise in te model until import tari s are restrained to su ciently low levels. A nal point wort empasizing is te important role played by bot import and export policies in establising te e ciency of te political optimum. If, for example, governments were assumed only to ave import tari s (t for te ome country and t f for te foreign country) at teir disposal, ten it is still te case tat e ciency would be de ned as in (21) and (22) above, owing to te redundancy of te export instruments t and t f in terms of teir impacts on te total trade taxes and, and ence on ~ P N, ~ R N, ~ P N and ~ R N. Te e cient total trade taxes would ten be acieved entirely troug t and t f. But as can be seen from te conditions for te political optimum in (25), te politically optimal setting of t and t f alone could not in general acieve e ciency. Terefore, te e ciency of te political optimum and ence te ability to interpret te problem tat a trade agreement can solve as a terms-of-trade problem inges importantly on te assumption tat governments ave su cient trade-tax instruments at teir disposal. If tey did not, ten oter non-terms-of-trade problems migt also be addressed by a trade agreement (in tis setting, just as more generally). But viewed in tis way, it is also clear wat te associated non-terms-of-trade problem would be: a trade agreement could elp substitute for missing trade policy instruments (e.g., export policies) wic, if available, would ten convert te role of a trade agreement back to te standard terms-of-trade driven Prisoners Dilemma. 19 We summarize te results of tis section wit: We empasize tat wat is required for te e ciency of te political optimum in tis setting is tat eac country as a complete set of trade tax instruments, in te sense tat eac government as available te use of an import tari and an export tax/subsidy, not tat eac country as a complete set of (trade and domestic) tax instruments wit wic to acieve te rst best. 20 In reality, political economy concerns are an important reason for trade policy intervention. According to te 17