Asymmetric Integration *

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1 Fung and Shneider, International Journal of Applied Eonomis, (, September 005, Asymmetri Integration * K.C. Fung and Patriia Higino Shneider University of California, Santa Cruz and Mount Holyoke College Abstrat We use a standard repeated game framework and assume imperfet ompetition to eamine how the feasibility of trade agreements is affeted by the presene of asymmetries in market size, wage levels and labor produtivities. The results regarding asymmetries in market size are onsistent with the traditional literature: the ountry with the larger market is more likely to defet and transfers from the small to the large ountry an improve the feasibility of the trade agreement. When ost asymmetries are introdued in the model, we an identify situations in whih either ountry is likely to defet on the agreement. In partiular, the smaller and lesseffiient ountry may not always benefit from the trade agreement and we might atually observe transfers from the more effiient to the less effiient ountry. Keywords: Trade integration, asymmetri eonomies, imperfet ompetition JEL Classifiations: F, F, F5 Introdution Regional Trade Agreements (RTAs have beome a major feature of our urrent multilateral trading system. They have substantially epanded over the past deade and their proliferation has even aelerated in reent years, leading Crawford and Fiorentino (005 to all the period between January 004 and February 005 the most prolifi RTA period in reorded history with 4 RTAs notified to the World Trade Organization (WTO. As of January 005, over 00 RTAs have been notified to the WTO and 70 of those are still urrently in fore. One main trend in this proess is that developed-developing ountries RTAs are on the rise, suggesting that an important proportion of RTAs takes plae among rather asymmetri eonomies. Traditional eamples of suh agreements are the integration of Spain and Portugal into the European Union (EU or Meio's integration with the United States and Canada in the North-Amerian Free Trade Agreement (NAFTA. They represent eamples of integration between a larger, riher and more advaned area with a smaller, poorer and developing eonomy. Table presents a omparison of GNP and population for the above regional agreements at their initial stages of integration. Table shows that in 990 Portugal's GNP was % and Spain's GNP was 8% of the EC-0's GNP; while Meio's GNP was.9% of the US GNP. Table presents a omparison of per apita inome and wages. Note that in 990, Portugal's per apita inome was.9% and Spain's per apita inome was 49.4% of Germany's per apita inome. Also Meio's per apita inome was.4% of the US per apita inome. In terms of hourly labor osts, Spain's

2 Fung and Shneider, International Journal of Applied Eonomis, (, September 005, was 54% and Portugal's was 7% of Germany's, while Meio's was % of the US hourly labor osts in 990. The EU's enlargement with the inlusion of Eastern European eonomies, as well as the negotiations towards the Central Amerian Free Trade Agreement (CAFTA agreement are additional and more reent eamples of trade integration that follows the above pattern. Another interesting eample of asymmetri integration is the Mainland China and Hong Kong Closer Eonomi Partnership Arrangement (CEPA. In this ase, there is eonomi integration between a smaller, but riher area with a bigger, but less-advaned region. It is important to note that this kind of integration an also be observed in RTAs among developing ountries. In the ase of MERCOSUR, for eample, Brazil and Argentina have signifiantly larger market sizes than Paraguay and Uruguay as Table indiates. It shows, for instane, that in 995 Paraguay's GDP was % of Merosur's GDP, while Brazil's GDP was 70% of Merosur's GDP. A vast literature has been developed to study the impat of the formation of regional trade agreements on the ability of ountries to maintain low ooperative multilateral tariffs. However, most ontributions to this literature adopt models portraying perfetly symmetri ountries 4. While this approah produes tratable models and provides valuable insights, it does not provide a formal framework in whih one an investigate the gains from ooperation between a large ountry and a small ountry, or a low-produtivity eonomy and a highprodutivity eonomy, for eample. Another harateristi of most of these models is that they adopt the assumption of perfet ompetition. We argue that in developing ountries, imperfet ompetition may be a more appropriate assumption. Aording to Ros (987, for instane, Meian industries traditionally have been oligopolisti. Also Rodrik (988 presents evidene of oligopolisti market struture for many developing ountries. The purpose of this paper is to develop a framework that more realistially desribes the nature of trade agreements as desribed in this introdution. This paper differs from the previous literature in two respets. First, we onsider at least three kinds of asymmetries: size, wage levels, and labor produtivities. Seond, we eamine integration assuming that the produt market is oligopolisti. In the papers that we review in the net setion, the benefits of being a large ountry are related to inreased bargaining power through terms-of-trade effets. Large ountries have an inentive to limit imports (and eports to improve their terms of trade, even if it is in their olletive interest not to do so. Aording to Krugman (997, however, this optimal tariff argument plays almost no role in real world disputes over trade poliy. By introduing imperfet ompetition into the model, we abstrat from the terms-of-trade effet and introdue elements of strategi behavior (rent shifting among ountries. In this senario, a hange in profits that results from a hange in the tariff rate, affets the feasibility of the trade agreement. The approah used in this paper is an infinitely repeated game. The paper is organized as follows. Setion presents a review of the literature. Setion disusses the basi model. We then proeed to disuss variants of this basi model that depend on speifi assumptions about the kind of asymmetries onsidered. Setion 4 assumes that the only kind of asymmetry in the model is with respet to market size. Setion 5 onsiders the ase in whih ountries are asymmetri only with respet to their ost strutures (wage rates and/or labor produtivities. And in setion 6, we allow for asymmetries both in market sizes and ost strutures. Finally, setion 7 onludes the paper.

3 Fung and Shneider, International Journal of Applied Eonomis, (, September 005, Review of the literature The following review fous on studies that have used stati and dynami games to eamine the feasibility of trade agreements and their impat on the multilateral trading system. These studies have portrayed perfetly symmetri ountries as well as asymmetri eonomies. Among the studies that portray perfetly symmetri ountries, we an ite Krugman (99 and Bagwell and Staiger (997a, 997b 5. Overall, these studies look at how the formation of regional trade agreements might impat ooperation, i.e., low multilateral tariff levels. Krugman (99, for eample, suggests that although a world that onsolidates into trading blos ould simultaneously redue tariffs so as to avoid trade diversion, the optimal nonooperative behavior of the blos is atually to inrease eternal tariffs. Thus a redution in interblo trade is the normal outome of the formation of regional trading blos. Bagwell and Staiger (997a also argue that the formation of free trade areas an interfere with the ability to maintain low multilateral tariffs, both before the proess of free trade area formation begins and speially, one the proess has begun, during the transition to the fully implemented regional agreements. Their model suggests that these heightened multilateral tensions should be temporary, and that greater multilateral ooperation an reemerge one the new trading patterns are more firmly established. Using a similar model that fouses on the formation of ustoms unions, Bagwell and Staiger (997b find that the transition period in this ase is haraterized by a temporary honeymoon for liberal multilateral trade poliies. Eventually, however, as the impat of the ustoms union on market power beomes more prominent, these poliies annot be sustained. Even though this approah has produed tratable models and provided valuable insights, it has not offered a formal framework in whih we an investigate the gains from ooperation between eonomies that depit asymmetries. Among the studies that onsider asymmetries when studying the formation (and breakdown of international poliy ooperation we highlight Riezman (98, 99, Kennan and Riezman (988,990, Jensen (994, Bond and Syropoulos (996, Choi (998, Park (000 and Bond and Park (00. The general result in these studies is that the eistene of asymmetries among trading partners makes ooperation (free trade harder. Riezman (98 and Kennan and Riezman (988,990 adopt stati models based on Johnson (95. Riezman (98 develops a stati game of omplete information and eamines if free trade will be obtained when ountries take into aount the strategi nature of the tariff poliy problem. The asymmetry in his model is related to the elastiities of demand and supply those elastiities determine the outome of a tariff war by affeting the terms of trade. He finds that when ountries play nonooperatively, they will selet the strategy of harging the optimal tariff, hene free trade will not be reahed. In the ooperative ase (with no transfer payments allowed, free trade as a pure strategy is never hosen if one ountry is better off as a result of a trade war. If ountries are symmetri, free trade will be hosen. More generally, when the gains from moving to free trade are similar for both ountries then free trade is likely to be hosen. When the gains are unevenly distributed, the attainment of free trade is less likely 6. Kennan and Riezman (988 show that if one ountry is substantially bigger it an epet to gain from a tariff war, despite retaliation. The asymmetry in their model is size and they suggest that big ountries win tariff wars. Kennan and Riezman (990 etend the previous model to show that when more than two ountries trade with eah other, the advantage obtained by being part of a large trading unit an help eplaining the formation of ustoms unions. Riezman (99, Jensen (994, Bond and Syropoulos (996, Choi (998 Park (000

4 Fung and Shneider, International Journal of Applied Eonomis, (, September 005, and Bond and Park (00 approah the question from a dynami perspetive. In Jensen (994 the asymmetry is population size. He uses an infinitely repeated game and finds that national heterogeneity unambiguously redues trigger strategies' support for poliy ooperation. In other words, the more ountries differ the harder it is to sustain poliy ooperation. Cooperation is onsidered in terms of spending levels, so that the international spillover effet of unilateral poliy measures works through the terms of trade. The asymmetry in Bond and Syropoulos (996 is also size. They look at how the struture and size of regional blos an affet multilateral tariff negotiations. The overall result is that trade agreements are more diffiult to support as blo size inreases. In Riezman (99 and Choi (998 the asymmetry is related to the fat that ountries imperfetly observe other ountries' protetion poliies. And the presene of asymmetries also makes ooperation harder. Park (000 analyzes trade agreements between ountries of asymmetri size, fousing on self-enforing agreements between a small and a large ountry in a repeated trade relationship. His results suggest that asymmetri ountries may have onfliting interests in hoosing the fous of trade negotiations. Using the autarky punishment sheme instead of the interior Nash punishment may provide the small ountry with greater bargaining power in trade negotiations, in the sense that it only epands the set of self-enforing trade agreements in a diretion that is favorable to the small ountry. By negotiating reiproal tariff redutions instead, the small ountry improves its bargaining position regarding its worst possible outome of the negotiation. Bond and Park (00 look at how a gradual approah to tariff liberalization an ontribute to an effiient self-enforing agreement between a large and a small ountry. They show that non-stationary agreements (where tariffs and transfers are not onstant over time may be optimal in the ase of symmetri ountries or when asymmetries in the ountries' bargaining powers lead to asymmetri ountries' payoffs. In all of the above models, with or without asymmetries, the sustainability of the trade agreement is ultimately affeted by hanges in the terms of trade. And the advantage of being a large ountry implies more bargaining power and redues the sustainability of the agreement 7. Basi Model In this paper, we eamine trade integration between two ountries. For simpliity, we refer to them as the North (denoted by asterisks and the South. We view trade agreements as requiring self-enforement. Unlike domesti ontratual agreements, international agreements are not baked up by a binding international ourt. The natural framework is one where ooperation (trade agreement is baked up by redible threats. Eah ountry will balane its one-period gain of defeting from the agreement with the future punishment of nonooperation. The approah that we use is one of nonooperative repeated game (Diit 987, Fung 987, Bagwell and Staiger 990. In eah ountry, we highlight one eport industry and one import-ompeting industry. There is one firm in eah industry. There is a large setor that onstitutes the rest of the eonomy. The industries are oligopolisti with the firms ompeting in a Cournot-Nash fashion. Eah government is supposed to maimize its national welfare NW and NW that equals the sum of firms' rents, onsumer surplus and government revenue. Demands in eah ountry are

5 Fung and Shneider, International Journal of Applied Eonomis, (, September 005, P y and P u v, ( where Southern domesti output in ompetition with Northern eport y, u Southern eport to the North, and v domesti prodution in the North, 0 and 0 are the market sizes in eah ountry, and are the slopes of the ountries' demands. Goods are assumed to be homogeneous, even though the introdution of produt differentiation is not likely to hange the onlusions. The assumption of speifi funtional forms allows us to derive epliit results in the model and to find an analytial solution 8. Prodution is arried out solely by labor l and l, with prodution funtions as f l, y f l, u g l, v g l. Wage rates are w and w in the South and in the North, respetively. Profit funtions for the Southern import-ompeting industry and the Northern eporting industry are: i i Π = P C(, w, Π = Py C( y, w ty ( For the Southern eport industry and the Northern import-ompeting industry the profit funtions are: e e Π = P u C( u, w t u, Π = P v C( v, w, ( where C,w, C y, w, C u,w, C v,w are total ost funtions and C w/f l,c y w /f l, C u w/g l, C v w /g l are marginal osts. The Cournot-Nash outputs are obtained by maimizing ( and ( with respet to outputs: ( t ( t ( t ( t =, y =, u =,and v = (4 where w/f l 0, w /f l 0, w/g l 0, w /g l 0, and t and t are the Southern and Northern tariffs respetively. Nonooperative Tariffs and Outputs Under nonooperative behavior, eah ountry seeks to maimize its welfare assuming that outputs are desribed by (4 and that the other ountry's tariff is given. we omit the omplete desription of the maimization problem, sine it is straightforward, and move diretly to the results. Lemma With no trade agreement, eah ountry sets its optimal strategi tariffs aording to N N t = > 0 and t = > 0 (5 with assoiated outputs being N 6 N 4 N 4 N 6 =, y =, u = and v = (6 Proof. Eah ountry maimizes its national welfare NW CS t.y y i e t.y and

6 Fung and Shneider, International Journal of Applied Eonomis, (, September 005, NW CS t.u u v i e t.u, with outputs given by (4 and given that the other ountry's tariff is set. The solution to those maimization problems yields t N and t N. By definition, and are greater than zero, therefore, t N and t N are positive. By substituting t N and t N into (4, we get N 6, y N 4,u N 4, and v N 6. 9 The nonooperative tariff is independent of the domesti industry's osts. It depends only on the size of the domesti market and on the osts of the industry that eports to that market. A positive tariff is optimal here beause of the shifting of eonomi rents and inrease in tariff revenue, whih ompensates for the drop in onsumer welfare. Note that in a perfetly N symmetri ase = = = = = α. Therefore both tariffs are given by t = t N = > 0. Cooperative Tariffs C With a free trade agreement, we assume that ooperative tariffs an be hosen to maimize joint welfare ( NW + NW. As before, the maimization problem is straightforward and we proeed to report the results. Lemma Under ooperation (trade agreement and assuming no import subsidies, the optimal tariffs are t C = 4 5 > or < 0 and t C = 4 5 > or < 0 (7 with assoiated outputs being C ( C 4 C 4 C ( =, y =, u =, v = (8 Proof. The solution to Ma t, t ( NW + NW yields t C 4 5 and t C 4 5. Reall that w/f l, w /f l, w/g l, and w /g l. Therefore, the ooperative tariffs an be positive or zero depending on speifi assumptions about asymmetries in market size and/or ost strutures. Finally, by substituting (7 into (4, we get the ooperative outputs. In a perfetly symmetri ase both ooperative tariffs are zero ( t C t C 0. Also, the hange in national welfare assoiated with ooperation is always positive for both ountries 7 ( NW = NW = > 0. 6 Feasibility of the trade agreement 9 Following Bagwell and Staiger (997a,997b and Fung (987, 99, we adopt an infinitely repeated game. In this setting, ountries have the possibility of supporting a

7 Fung and Shneider, International Journal of Applied Eonomis, (, September 005, ooperative tariff, sine any attempt to raise the urrent-period tariff will be greeted with the retaliatory (Nash tariff from the trading partner in future periods. Intuitively, a ooperative tariff an be supported in equilibrium if the one-time inentive to heat is suffiiently small relative to the future value of maintaining a ooperative relationship with the trading partner. For the agreement to be sustainable, we need that N C C [ NW ( t, t NW ] NW < 0 i s C N C and [ NW ( t, t NW ] NW < 0, i n (9 where NW t N,t C NW C is the one-time gain of heating, NW is the future disounted punishment for the South, NW t C,t N NW C is the one-time gain of heating and NW is the future disounted punishment for the North. Finally, i s and i n are the interest i n rates for the South and the North, respetively. We an rewrite (9 as is i s < NW C C [ NW ( t, t NW ] N = i s NW and i i, (0 n < C N C = [ NW ( t, t NW ] n where i s and i n are the ritial interest rates for the South and the North, i.e., the maimum interest rates that keep the ountries from defeting. We define, as it is standard in the literature, that ooperation is more (less likely if the ritial rates beome larger (smaller 0. Note that in a symmetri setting, the ritial rates are equal and there is no binding onstraint on the feasibility of the agreement. In this ase, i n i s i and a hange in any parameter that inreases i will lead to an inrease in the feasibility of the trade agreement. However, in an asymmetri ase, there are two ritial interest rates i n i s. We fous on the smaller one as the smaller one is the binding onstraint on the feasibility of the agreement. Then, min( i, n we an define ooperation to be more likely if s i min( i, n > 0 and less likely if s i < 0 where is any arbitrary parameter. Asymmetri market sizes model In this setion, we assume that ountries are asymmetri only with respet to their market sizes. That is, α α, = and C = C = C = C C. Moreover, we assume that the φ y u v = North has the larger market size, i.e.,. The results show that both ooperative tariffs are zero. If the North has the larger market, the South always benefits from the trade agreement. The North, however, may not benefit from the agreement depending on how wide market size disrepanies are. Transfers from the small to the large ountry may be neessary in order to make the agreement feasible. With respet to the ritial rates, the North always imposes the binding onstraint as long as it has the larger market. φ

8 Fung and Shneider, International Journal of Applied Eonomis, (, September 005, Nonooperative tariffs and outputs As before, the nonooperative tariffs are given by (5. However, for ountries that are asymmetri only with respet to their market sizes, = = = α C and = = = α C. Therefore, their optimal strategi tariffs are set aording to N N t = > 0 and t = > 0 ( By definition, and are greater than zero, therefore, t N and t N are positive. By N substituting = N t and t = into (4, we get the assoiated outputs N 4 N N 4 N =, y =, u = and v = ( Both ountries impose positive nonooperative tariffs, however, the North's nonooperative tariff is larger t N t N, sine. Fousing on the Southern tariff, a smaller market in the South means a smaller strategi tariff. Domesti and eporting industries are smaller in the South N v N, y N u N. For the ountry with the larger market size, the import-ompeting prodution is higher than the N N prodution of the eporting industry ( v < y. For the ountry with the smaller market, it depends on how muh larger is the foreign market N u N. Cooperative tariffs and outputs Proposition Under ooperation (trade agreement and assuming no import subsidies, the optimal tariffs for ountries with asymmetri market sizes are t C C = 0 and t = 0 ( with assoiated outputs being C C C C = y = and u = v = Proof. As before, the solution to Ma t, t C ( NW + NW yields t = 4 5 and t C 4 5. Now reall that, by assumption, C and C. Therefore, t C and t C. However, by definition, C 0 and C 0 whih implies t C 0 and t C 0. So both ooperative tariffs are zero. We get the ooperative outputs by substituting ( into (4. Note that both domesti and import-ompeting outputs are the same in eah ountry, however they are higher in the North, i.e., the ountry with the larger market size has higher output levels.

9 Fung and Shneider, International Journal of Applied Eonomis, (, September 005, Who benefits from the trade agreement? Proposition When ountries are asymmetri with respet to their market sizes, the hange in national welfare assoiated with ooperation is given by ΔNW and ΔNW for the South and the North, respetively. Assuming that the North has the larger market, the South will always benefit from the trade agreement ( ΔNW 0. For the North, the hange in national welfare assoiated with ooperation an be positive or negative depending on how wide market size disrepanies are ( ΔNW Proof. NW = +. Now reall that = =, = = and 8 8 (6 9. Therefore, NW = 6 > 0. Sine,ΔNW 0 always, i.e., the South will always benefit from the trade agreement. 4 5 For the North, NW =. And sine α α, = and 8 C C y C u C v C, ΔNW, Note that ΔNW 0 if α < (4α C, i.e., the market in the North annot be too muh larger than the market in South. In this sense, the results are similar to the terms-of-trade effet results. The small ountry always benefits from the agreement, the large ountry may not, depending on how wide market size disrepanies are. In the ase in whih the domesti market is muh larger than the foreign market, we should observe transfers from the small to the large ountry in order to make the agreement feasible. The minimum transfer to ensure that the large ountry will go along is ^ T 6 ( Note that large ountries usually benefit from onessions with respet to intelletual property protetion, environmental and labor legislation, as well as foreign investment liberalization. These onessions an be viewed as transfers from the small to the large ountry. Additionally, either a smaller market in the South or a larger market in the North means that the South is more likely to gain. NW / α = 9 ( α C < 0 6 NW = ( α C > 0 Critial Rates / α 8 Proposition When ountries are asymmetri with respet to their market sizes, their ritial rates are given by 6 6 i s = and i = n (4 9 9 for the South and the North respetively. 8

10 Fung and Shneider, International Journal of Applied Eonomis, (, September 005, s ( 9 i s 8 Proof. Using (0, the South is likely to heat when i > 5 =, where i s the ritial interest rate for the South. But sine, and, 6 8 i =. Similarly, the North is likely to heat when i > 5 =, where i n s 9 n ( 9 i n represents the North's ritial interest rate. But sine, and, i n 6 9 If i s i s, the South is indifferent between heating or not. And if i s i s, the South does not heat. If i n i n, the North is indifferent between heating or not. And if i n i n, the North does not heat. Corollary When ountries are asymmetri with respet to their market sizes, the ountry with the larger market size always imposes the binding onstraint on the agreement. Proof. Assume that i n i s i world's interest rate. Therefore, we have that i n i s So i n i s 0 if C 4 C 4. By assumption, then i n i s 0 i n i s, i.e., the North always imposes the binding onstraint. Comparative Statis: Change in Market Sizes Reall from before that, in an asymmetri ase, we an define ooperation to be more min( i, n likely if s i min( i, n > 0 and less likely if s i < 0 where is any arbitrary parameter. φ φ Proposition 4 When ountries are asymmetri with respet to their market sizes, an inrease in the size of the larger market redues the feasibility of the trade agreement and an inrease in the size of the smaller market inreases it: i n < 0 and > 0 α α Proof. Taking first derivatives of the northern ritial interest rates given by (4 with respet to and yields < i n i 0 and n > 0. We determine the signs of the previous = α 9 α = 9 epressions using the fat that = ( α C > 0 and = ( α C > 0. Then reall that the North always imposes the binding onstraint, so that ooperation is more (less likely if a hange in the market size inreases (dereases the ritial rate of the North. An inrease in market size of the North dereases the Northern ritial interest rate and redues the feasibility of the trade agreement. Other things equal, an inrease in the market size N of the North reates an inentive for the North to impose the nonooperative tariff ( t, shifting rents from abroad towards the Northern import-ompeting industry. An inrease in the market size of the South, inreases the Northern ritial interest rate and the feasibility of the trade agreement. Sine both ountries have symmetri osts and assuming no transportation osts, an inrease in the North's eporting market ( α inreases its is

11 Fung and Shneider, International Journal of Applied Eonomis, (, September 005, inentive to keep tariffs low and maintain its position in that market. The North benefits from a larger eport market. The overall onlusion is that the ountry with the larger market has the smaller ritial rate and imposes the binding onstraint on the agreement. Therefore, an inrease in the size of the larger market redues feasibility and an inrease in the size of the smaller market inreases feasibility. These results are in line with the results obtained by Kennan and Riezman (988: the larger ountry wants to defet. Also the results support the general notion that asymmetries make ooperation harder and that making ountries more similar might inrease ooperation. In fat, an inrease in the asymmetry between the two ountries ( α beomes even larger redues the feasibility of the agreement, while a derease in the asymmetry ( α beomes larger inreases the feasibility of the agreement. Asymmetri osts model Now onsider a situation in whih ountries are asymmetri with respet to their ost strutures; i.e., assume that =, α = α and C C y Cu Cv. Different situations an arise depending on speifi assumptions about eah ountry's relative ost strutures. If we assume that osts are higher in the South; i.e., C > C y and C u > C v, and that eah ountry has the same osts for both domesti and eport industries ( C = Cu and C y = C v, the results show that the ooperative tariff for the South is zero ( t C = 0, while the ooperative tariff for the North an be positive or zero t C depending on how wide osts disrepanies are. The higher ost ountry always benefit from the agreement, while the lower ost ountry may not always benefit from ooperation. The North always imposes the binding onstraint on the agreement. Nonooperative tariffs and outputs As stated in Lemma, with no trade agreement, ountries set their optimal strategi tariffs aording to (5. If we assume that ountries are asymmetri with respet to their ost strutures, and the nonooperative tariffs are given by N N t = > 0 and t = > 0 (5 By substituting (5 into (4 we get the assoiated outputs 6 N 4 N 4 N 6, y =, u = and v = N = (6 where C 0, C y 0, C u 0, C v 0. As before, both nonooperative tariffs are positive and independent from the domesti

12 Fung and Shneider, International Journal of Applied Eonomis, (, September 005, industry's osts. They only depend on the size of the market ( α and on the osts of the industry that eports to that market. N Fousing on the Southern tariff t, a higher wage rate in the North leads to a smaller N strategi tariff, but a higher labor produtivity in the North implies a higher t. A positive tariff is optimal here beause of the shifting of eonomi rents and inrease in tariff revenue, whih ompensates for the drop in onsumer welfare. Cooperative tariffs and outputs Proposition 5 Under ooperation (trade agreement and assuming no import subsidies, the optimal tariffs for the ase where ountries have different ost strutures and the osts in the South are always higher are C C = 0 and t = 4 5 t (7 with assoiated outputs being C Proof. The solution to,y C Ma, t t,u C 4,v C C C ( NW + NW yields t = 4 5 and t = 4 5. Reall that by assumption and C C y C u C v so that w/f l, w /f l, w/g l, and w /g l. Therefore, with lower osts in the North, w/f l w /f l and w/g l w /g l, or and respetively. And sine t C 0, the Southern ooperative tariff rate is zero. For the North, the ooperative tariff an be positive or zero, depending on how wide the osts disrepanies are. In C 5 fat, t > 0 if > 4. Finally, by substituting (7 into (4, we get the ooperative outputs. What are the benefits from a trade agreement? Proposition 6 When two ountries are asymmetri with respet to their ost strutures and one of them has a ost disadvantage in both domesti and eporting industries, the less effiient ountry will always benefit from ooperation ( NW > 0, while the more effiient ountry may or may not depending on how wide osts disrepanies are ( ΔNW 0. Corollary In the event in whih the North does not benefit from ooperation ( NW < 0, transfers should be observed from the less effiient to the more effiient ountry in order to make the agreement feasible. Proof. When ountries are asymmetri with respet to their ost strutures, the hange in 80 national welfare assoiated with ooperation is given by NW = + (4 8 8

13 Fung and Shneider, International Journal of Applied Eonomis, (, September 005, ( and NW = + for the South and the North respetively. For the South, (4 NW = +. Now reall that = so that 8 8 NW = 6 ( 9 60(4 +. (Note that the domesti ost in the South ( C doesn't matter here. Therefore, NW > 0 if 60(4 9 0, i.e., NW > 0 if > 60 or 4 > ( And 4 > 60 > ( 4 > that > ( Hene, in order for NW > 0, we need implies that or > Note that sine we assume lower osts in the North, C > C y and C u > C v, whih implies that < and <, we annot determine if > However, if we assume that eah ountry has the same osts for both domesti and eport industry, that is, C = Cu = C and C y = Cv = C, where C > C, then C and C. Also,. In this ase, ΔNW 0 if This ondition is satisfied if we use the fat that the nonooperative outputs have to be positive 4. Therefore, NW > 0. 8 For the North, ( NW = Now reall that so { ( 4 NW = (5 + }. Then, ΔNW 0 if ( 4 0. (5 8 If we assume, as before, that = < =, ΔNW 0 > if Again, in the event in whih ΔNW 0, we should observe transfers from the small to the large ountry in order to make the agreement feasible. The minimum transfer to ensure that the more effiient ountry will go along is Critial Rates ^ T Proposition 7 When ountries are asymmetri with respet to their ost strutures and the South has higher osts in both domesti and eport industries, the ritial rates are given by 60 (4 (5 i s = and i = n (8 9 8 (4 where, and the North always imposes the binding onstraint on the agreement ( i n i s. 5 Proof. In order to determine whih ountry imposes the binding onstraint, we need to (5 60 (4 determine the sign of i i =. Note that n s 8 (4 9

14 Fung and Shneider, International Journal of Applied Eonomis, (, September 005, i n i s By using the fat that C and C, we an determine that , whih implies i n i s. 6 Comparative Statis: Changes in Costs Proposition 8 When ountries are asymmetri with respet to osts, an inrease (derease in the marginal osts for the more effiient ountry redues (inreases the feasibility of the trade agreement, while an inrease (derease in the osts of the less effiient ountry inreases (redues it. This inrease (derease in marginal osts results from an inrease (derease in the wage rate and/or a derease (inrease in the labor produtivities. < 0, < 0, > 0, and > 0 y v u Proof. By taking first derivatives of (8 and using the fat that the nonooperative outputs have to be positive ( 0, 4 0, 4 0, and 0, we 0 (5 + 4 (5 + obtain < 0, <, = > 0, and > 0. = y 8(4 = 0 v (4 u 9(4 = 6(4 An inrease in the marginal osts for the Northern industries leads to greater losses and redues the sustainability of the agreement. So the agreement is less likely beause the benefits it provides to the ountry most likely to defet are smaller. Other things equal, an inrease in marginal osts for the Southern industries, inreases the ritial interest rate for the North and the feasibility of the trade agreement. The North has inreased its advantage over its trading partner and therefore has an inentive to maintain the agreement. Note that in this ase, a redution in eisting ost asymmetries makes the agreement less feasible. So making ountries more alike may not always inrease ooperation. Asymmetri Model In this setion, we assume that ountries are asymmetri with respet to both their market sizes and ost strutures ( =, α α and C C C C. We later assume that the South has higher osts in both domesti and eport industries. Non-Cooperative Tariffs and Outputs As before, with no trade agreement, ountries set their optimal strategi tariffs aording to (5. If we assume that ountries are asymmetri with respet to their market sizes and ost strutures, and the nonooperative tariffs are given by y u v

15 Fung and Shneider, International Journal of Applied Eonomis, (, September 005, N N t = > 0 and t = > 0 (9 By substituting (9 into (4 we get the assoiated outputs N 6 N 4 N 4 N 6 =, y =, u = and v = (0 where C 0, C y 0, C u 0, C v 0. As before, the nonooperative tariff only depends on the size of the domesti market and N on the osts of the industry that eports to that market. Fousing on the Southern tariff t, (9 implies that: a smaller Southern market means a smaller strategi tariff, a higher wage rate in the N N North also translates into a lower t, but a higher produtivity in the North implies a larger t. A positive tariff is optimal here beause of the shifting of eonomi rents and inrease in tariff revenue, whih ompensates for the drop in onsumer welfare. Cooperative Tariffs Proposition 9 Under ooperation (trade agreement and assuming no import subsidies, the optimal tariffs for asymmetri ountries are C t = 0 and t C = 5 > or 0 ( with assoiated outputs being C Proof. The solution to 4 <,y C Ma t, t,u C 4,v C C C ( NW + NW yields t = 4 5 and t = 4 5. Reall that = α w / f ( l, = α w / f ( l, = α w / g ( l, and = α w / g ( l. Therefore, with lower osts in the North, w / f ( l > w / f ( l and w / g ( l > w / g ( l, or < and < respetively. And sine t C 0, the Southern ooperative tariff rate is zero. For the North, the ooperative tariff an be positive or C 5 zero, depending on how wide the osts disrepanies are. In fat, t > 0 if > 4. Finally, by substituting ( into (4, we get the ooperative outputs. Note that the zero ooperative tariff depends not on size, but on relative osts. Does the South always benefit from a trade agreement? Net, we investigate the ase in whih the Southern welfare is smaller under ooperation and transfers may be needed in order to make the trade agreement feasible.

16 Fung and Shneider, International Journal of Applied Eonomis, (, September 005, Proposition 0 In the event that the Southern national welfare is smaller under ooperation, an agreement annot be reahed ΔNW 0. This an be indued by transfers from the larger to ^ the smaller ountry. The minimum transfer T to ensure that the small ountry will go along is: ^ T Proof. Let NW C and NW N denote national welfare in the South under ooperation and national welfare under non-ooperation. Also let C NW NW N NW. Reall that NW CS t.y y i e t.y or NW y y P. C,w P.u C u,w t.u t.y or NW y t.y u u uv t u. C Using t = 0, 4 C t = 5 and ooperative outputs, we get 8 C (9 6 (4 N NW = + +. Using = N t, t = and non- N ooperative outputs, we get NW = ( (4. Therefore, 6 8 ΔNW ( The first term in ( denotes the loss in national welfare in the import-ompeting industry as the tariffs are eliminated, while the seond term denotes the gain in profits in the eport industry. The NW annot be signed unambiguously beause the market sizes and osts in eah setor are not idential. Therefore, the South does not always benefit from a free trade agreement. Note that this result relates to the Brander and Spener (984 results: with no eports, free trade an be worse than protetion. In the ase in whih national welfare in the South is smaller under ooperation, transfers an be used as a way to stabilize the agreement. The minimum per period transfer is a funtion of the market sizes, the wage rates, the prodution funtions and demand onditions. Tables 4 and 5 illustrate how transfers may have been used to sustain Portugal and Spain's entry in the European Union. Table 4 shows that the net finanial flow (as a perentage of GDP between Portugal and the EC inreased onsistently from 986 to 99. In 99, it represented.5% of Portugal's GDP. Also Table 5 shows a onsistent inrease in EC transfers to Spain from 986 to 989. This evidene is onsistent with the results in the model. Proposition A smaller Southern market or a larger Northern market imply that the South is more likely to gain: ΔNW/ 0 and ΔNW/ 0. Proof. Taking first derivatives of ( with respet to and yields NW / α = / < 0, sine 0, and ( 80 (4 NW α = > 0, sine in order to assure positive nonooperative tariffs ( 4 > 0. Critial Rates > / 8

17 Fung and Shneider, International Journal of Applied Eonomis, (, September 005, The ritial rates are given by 7 60 (4 4 (5 i s = and i = n ( 9 7 (4 In order to determine whih ountry imposes the binding onstraint, we need to determine the sign of i n i s The above epression annot be unambiguously signed beause the market sizes and osts in eah setor are not idential. Therefore, both the North or the South an impose the binding onstraint on the agreement, depending on how wide ost and market disrepanies are. Comparative Statis Analysis We now proeed to present the omparative stati results from the home ountry's perspetive. Note that the following omparative statis results are based on the assumption that the North is the lower-ost ountry and has the larger market. They provide useful insights by introduing elements of rent shifting into the disussion on the feasibility of trade agreements. Change in Market Sizes Proposition From the home ountry's perspetive, an inrease in the size of the domesti market redues the feasibility of the trade agreement and an inrease in the size of the foreign market inreases it: is is < 0, < 0, > 0, and > 0. α α α α Proof. Taking first derivatives of the ritial interest rates given by ( with respet to α and i α yields s 0 (4 α = < 0, i n (5 = 7 (4 α > 0. i n 4 (5 = α (4 < 0, i s 0 (4 = α > 0 We determine the signs of the previous epressions using the fat that the nonooperative outputs have to be positive: > 0, 4 > 0, 4 > 0, and > 0. Then reall that the ritial interest rate is the future punishment divided by the one-time gain, so the higher the ritial interest rate, the more feasible is the trade agreement. An inrease in market size of the South dereases the Southern ritial interest rate and redues the feasibility of the trade agreement. Other things equal, an inrease in the Southern N market size reates an inentive for the South to impose the nonooperative tariff ( t, shifting rents from abroad towards the Southern import-ompeting industry. Similarly, an inrease in the Northern market size reates an inentive for the North to impose the strategi tariff and shift rents from abroad towards its import-ompeting industry. and

18 Fung and Shneider, International Journal of Applied Eonomis, (, September 005, Assuming lower osts in the North, an inrease in the market size of the South, inreases the Northern ritial interest rate and the feasibility of the trade agreement. Sine the North is the ountry with lower osts, an inrease in its eporting market ( α inreases the North's inentive to keep tariffs low and maintain its position in that market. The North benefits from a larger eport market. From the South's perspetive, an inrease in the Northern market size also inreases the feasibility of the trade agreement, sine the South now benefits from a larger eport market. The overall onlusion is that an inrease in the domesti market redues feasibility and an inrease in the foreign market inreases feasibility. Changes in Marginal Costs Changes in Marginal Costs for the domesti import-ompeting and eporting industries. Proposition From the home ountry's perspetive, an inrease (derease in the marginal osts of the domesti import-ompeting industry or in the marginal osts of the domesti eporting industry redues (inreases the feasibility of the trade agreement. This inrease (derease in marginal osts results from an inrease (derease in the wage rate and/or a derease (inrease in the labor produtivities. is is = 0, < 0, < 0 and < 0 u y v Remark Note that a hange in marginal osts for the Southern domesti industry ( C does is not affet the South's ritial interest rate ( = 0. Therefore, it does not affet the feasibility of the trade agreement. This is related to the fat that both tariffs for the South N C not depend on C ( t depends on C y and t = 0. N t and C t do Proof. By taking first derivatives of ( and using the fat that the nonooperative outputs have to be positive ( 0, 0, 0, and 0, we obtain is = 0, > is 0 (4 = u 4 > < 0, 4 > ( 0 = y 8 (4 < 0 > (5 = v (4 < 0. An inrease in the marginal osts for the South means either an inrease in the Southern wage rate ( w or a derease in labor produtivities ( f ( l, g ( l, or both. From the South's perspetive, an inrease in the Southern marginal osts for the eporting industry dereases the gains from eports and makes the agreement less feasible. Similarly, for the North, an inrease in the marginal osts for its eporting industry, redues the gains from eports. So the agreement is less likely beause the benefits it provides are smaller. Finally, an inrease in the marginal osts for the Northern import-ompeting industry leads to greater losses in that industry, and redues the feasibility of the agreement.

19 Fung and Shneider, International Journal of Applied Eonomis, (, September 005, Changes in Marginal Costs for the foreign import-ompeting and eporting industries. Proposition 4 From the home ountry's perspetive, an inrease (derease in the marginal osts of the foreign eporting industry or in the marginal osts of the foreign import-ompeting industry inreases (dereases the feasibility of the trade agreement. is is > 0, > 0, > 0, and > 0 y v u Proof. By taking first derivatives of ( and using the fat that the nonooperative outputs have to be positive ( 0, 0, 0, and 0, we obtain i s y 0 (4 = > and = 6 (4 > 0, 4 > is v > 0. 0 (4 = 9 4 > i > 0, > n 4 u = (5 > 0, (4 From the South's perspetive, an inrease in marginal osts for the Northern eporting industry has a positive effet on the feasibility of the trade agreement. The South's ompetitor is at disadvantage, so the feasibility of the agreement inreases. Similarly, when we onsider an inrease in marginal osts for the Northern import-ompeting industry, the effet on i s is a positive one, that is, it inreases the feasibility of the trade agreement. Again, the South benefits from its ompetitor's disadvantage. From the perspetive of the North, an inrease in the marginal osts for the Southern eporting industry inreases the feasibility of the trade agreement. The North wants to maintain the agreement beause its trading partner is at disadvantage. Also, other things equal, an inrease in marginal osts for the Southern importompeting industry, inreases the ritial interest rate for the North and the feasibility of the trade agreement. Again, the North has an advantage over its trading partner and therefore wants to maintain the agreement. Changes in domesti wage rates Proposition 5 From the home ountry's perspetive, an inrease (derease in the domesti wage rate auses a derease (inrease in the feasibility of the trade agreement is < 0 and < 0. w w Proof. Following a proedure similar to the one in the previous proof, we obtain i s 80 (4 ( (4 ( 0 6 ( (5 i ( ( n f l g l w = < 0 and = 0. g ( l 8 < (4 w From the perspetive of the South, an inrease in the Southern wage rate inreases the marginal osts for both eporting and import-ompeting firms in the South. The intuition is similar to the one in proposition : an inrease in the South's wage rate redues the gains for the eporting industry and dereases the feasibility of the trade agreement. From the Northern perspetive, the gains from eports are smaller and the North loses the domesti market too.

20 Fung and Shneider, International Journal of Applied Eonomis, (, September 005, Changes in foreign wage rates Proposition 6 From the home ountry's perspetive, an inrease (derease in the foreign wage rate auses an inrease (derease in the feasibility of the trade agreement: i 0 n and 0. w i s w Proof. Following a proedure similar to the one in the previous proof, we obtain is 0 = { ( (4 + ( (4 } > 0 and w g ( l = 4 8 (4 f ( l in {(/ f ( l(4 + 8(/ g ( l(5 (4 } > 0 w From the South's perspetive, an inrease in the Northern wage rate has a positive effet on the feasibility of the trade agreement. The South wants to maintain the agreement beause its ompetitor is at disadvantage. From the North's perspetive, an inrease in wage rate of the South inreases the feasibility of the trade agreement. The North wants to sustain the agreement beause its ompetitor is at disadvantage. The results relate to the ones in proposition 4. Summarizing the results from the home ountry's perspetive, we have that:. An inrease in the size of the domesti market redues the feasibility of the trade agreement, while an inrease in the size of the foreign market inreases it.. An inrease (derease in the marginal osts of the domesti industry or in the marginal osts of the eporting industry redues (inreases the feasibility of the trade agreement. 9 This inrease (derease in marginal osts results from an inrease (derease in the wage rate and/or derease (inrease in the labor produtivities.. When looking solely at the effet of a hange in the domesti wage rate, the onlusion is similar: an inrease (derease in the domesti wage rate auses a derease (inrease in the feasibility of the trade agreement. 4. On the other hand, an inrease (derease in the marginal osts of the foreign eporting industry or in the marginal osts of the foreign import-ompeting industry inreases (dereases the feasibility of the trade agreement. 5. Similarly, an inrease (derease in the foreign wage rate auses an inrease (derease in the feasibility of the trade agreement. The overall result with respet to marginal osts is that if the home ountry's industries beome more (less effiient relative to the foreign ountry's industries, the gains from ooperation inrease (derease for the home ountry and, therefore, the sustainability of the agreement inreases (dereases. Conluding Remarks Despite the growth in importane of the WTO, regional trade agreements have been a entral feature in the development and evolution of the post-war trading system rather than the eeption. Moreover, the number of regional trade agreements has grown substantially in the past deade. We argue that most ontributions to the literature regarding the ability of ountries to sustain ooperation adopt models that portray symmetri ountries interating in a perfetly

21 Fung and Shneider, International Journal of Applied Eonomis, (, September 005, ompetitive environment. However, sine most integration agreements are haraterized by asymmetri eonomies, we emphasize the importane of looking at integration in a framework with asymmetries. In this paper, we eamine the sustainability of trade agreements between asymmetri eonomies, whih differ with respet to market sizes, wage levels and labor produtivities. We also onsider integration in an imperfetly ompetitive framework, whih allows us to abstrat from the usual terms-of-trade effets and to fous on other hannels affeting the feasibility of trade agreements (e.g., rent-shifting motives. First, we develop a basi infinitely repeated game and then we eamine how the results are affeted by the introdution of different kinds of asymmetries. When we onsider market size asymmetries, the results show that the ountry with the larger market is more likely to defet. In the ase in whih the domesti market is muh larger than the foreign market, we should observe transfers from the small to the large ountry in order to make the agreement feasible. These transfers from the small to the large ountry an take plae in the form of onessions with respet to intelletual property protetion, environmental and labor legislation, as well as foreign investment liberalization. In this ase, an inrease in the eisting asymmetry redues ooperation, while a derease in the asymmetry inreases ooperation. Therefore, the general notion that asymmetries make ooperation harder and that making ountries more similar is likely to inrease ooperation, might be right. However, when we onsider asymmetries with respet to osts, we find that making ountries more alike may atually redue ooperation. In this ase, the more effiient ountry is more likely to defet and a redution in the osts of the less effiient ountry is likely to redue the feasibility of the agreement. A point worth emphasizing is that the general notion that asymmetries make ooperation harder might be right, however making ountries more alike does not neessarily improve ooperation. Finally, when we onsider asymmetries in both market sizes and ost strutures, we find that either ountry is likely to defet on the agreement depending on how wide market size and ost disrepanies are. In this ase, the smaller and less-effiient ountry may not always benefit from the trade agreement and we might observe transfers from the North to the South, like the ones observed during Portugal and Spain's integration into the EU. Furthermore, we find that an inrease in the size of the domesti market redues the feasibility of the trade agreement, while an inrease in the size of the foreign market inreases it. Also if the home ountry's industries beome more (less effiient relative to the foreign ountry's industries, the gains from ooperation inrease (derease for the home ountry and, therefore, the sustainability of the agreement inreases (dereases. The approah used in the paper is useful in showing the importane of onstruting alternative modeling strutures in response to the rapid formation of trade agreements aross signifiantly heterogeneous ountries. These different frameworks are of great importane in offering a broader set of situations that an be taken into onsideration by poliymakers. Endnotes * The authors would like to thank an anonymous referee for useful omments. Patriia H. Shneider would also like to thank the Brazilian Ministry of Eduation - CNPq Ageny for finanial support in developing this projet.. See Crawford and Fiorentino (005 for more details.

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