Trade Policy and Economic Integration in a Cournot Duopoly Model

Transcription

1 The Pakstan Development Revew 43 : 3 (Autumn 004) pp Trade Polcy and Economc Integraton n a Cournot Duopoly Model YU-TER WANG, BIH-JANE LIU, and PAN-LONG TSAI Ths paper nvestgates the polcy and welfare mplcatons of formng an economc regon n the context of a Cournot duopoly model. Some theoretcal results are obtaned. Frst, the economc regon lowers the external tarff (aganst non-partner countres) less than ts pre-ntegraton level when a suffcently large subsdy on the mports from the partner s carred out. Second, economc ntegraton reduces the non-partner country s welfare. Thrd, although the regon stll gans from ntegraton even under some partal trade lberalsaton regmes, complete trade lberalsaton wthn the regon leads to hgher regonal welfare. Fnally, trade lberalsaton wthn the regon mproves the welfare of the world as a whole.. INTRODUCTION The resurgence of regonal economc ntegraton snce the late 980s has caught the attenton of many economsts. Consequently, there have been many mportant contrbutons, both theoretcal and emprcal, that have been concerned wth the mpacts and perspectves of economc ntegraton. For nstance, Rchardson (993) shows that a small home country wll lower the tarff aganst the nonpartner f a free trade agreement (FTA) causes the FTA partners prce to fall below the nonpartner s tarff-nclusve prce. Panagarya and Fndlay (994) demonstrate that a FTA may lead to hgher tarffs between blocs snce the workers that prevously lobbed for protecton aganst the FTA partner countres wll be used to lobby for protecton aganst the rest of the world. Bond and Syropoulos (996) study the effects of bloc sze on market power and world welfare, and fnd that suffcently large ncreases n the relatve sze of a bloc enhance ts relatve market power and cause the welfare of ts members to rse above the free trade level. Levy (997) uses a medan-voter model, showng that whle blateral free-trade agreements may Yu-Ter Wang s based at the Department of Economcs, Mng Chuan Unversty, Taoyuan, Tawan. Bh-Jane Lu s based at the Department of Economcs, Natonal Tawan Unversty, Tawan. Pan-Long Tsa s based at the Department of Economcs, Natonal Tsng Hua Unversty, Tawan. Authors Note: We wsh to thank an anonymous referee for very valuable comments and suggestons. The usual dsclamer apples.

2 40 Wang, Lu, and Tsa undermne poltcal support for further multlateral trade lberalsaton, they can never enhance poltcal support for multlateral free trade. Utlsng a verson of the model adopted by Bond and Syropoulos (996); Bond, et al. (00) derve condtons under whch the deepenng of ntegraton wthn a customs unon, accompaned by a Kemp-Wan reducton n ts external tarff, wll be ncentvecompatble both for the unon and outsde countres. Nevertheless, n spte of ths, the ssue concerned wth the mplcatons of Artcle XXIV of the GATT has not been satsfactorly analysed, though t has been extensvely studed [e.g., McMllan (993)]. Ths artcle requres that () trade restrctons aganst nonpartner countres should not be ncreased after ntegraton, and () that trade barrers wthn the regon n whch economc ntegraton takes place should eventually be completely elmnated. It s qute clear that the ntenton behnd the frst part s to prevent the nonpartner countres from beng harmed by the formaton of economc blocs. As for the second requrement, t would be of nterest to know whether nternal trade lberalsaton wll mprove the welfare for an economc regon. In other words, we would lke to know whether there s any economc ratonale for the requrement of complete trade lberalsaton wthn a regonal economc bloc. These are the questons we are nterested n and wll attempt to answer n ths paper. We employ the famlar Cournot-Nash framework and compare two sub-game perfect equlbra, one for the pre-ntegraton case and the other for the post-ntegraton one. The pre-ntegraton case conssts of two stages. In the second stage, the exportng frms choose ther optmal output levels, takng the tarffs mposed by the mportng country as gven. In the frst stage, the government of the mportng country decdes the level of the tarffs, knowng how the second-stage Cournot equlbrum between the frms s affected by the frst-stage polcy choces. The post-ntegraton case conssts of three stages. The thrd stage s exactly the same as the second stage of the pre-ntegraton case except that the tarffs are set by the economc regon under consderaton. In the second stage, the economc regon determnes the optmal external tarff (aganst the nonpartner countres), takng nto account ts mpact on the frms behavour and the gven nternal tarff. The nternal tarff (aganst the partner countres) s decded n the frst stage, agan takng nto account ts mpact on the latter two stages. The rest of ths paper s organsed as follows. Secton sets up the basc model to nvestgate the pre-ntegraton case. Secton 3 frst examnes the relatonshp between the nternal and external tarffs after the economc regon s formed, and then goes on to study the welfare mpact of the economc ntegraton on the nonpartner countres. Secton 4 analyses the ncentve for the economc ntegraton to take place and also the welfare mpact of the economc ntegraton on the whole world. Secton 5 summarses our man results.

3 Trade Polcy and Economc Integraton 4. THE PRE-INTEGRATION MODEL Assume that two exportng frms and, whch are located n countres A and B, respectvely, produce dfferentated goods, q and q, and export them to country C. Followng the famlar framework, let U(q, q, M) be country C s utlty: U (q, q, M) = V (q, q, M) () where V ( q, q) = αq + αq β( q + q ) δqq denotes the utlty from consumng the dfferentated goods, and M s the utlty from consumng the numerare good whose prce s set to one. The demand functons for the two goods can then be derved as follows: P = α βq δq j, j,, j=,, () where P s the prce of good q, and α, β, and δ are assumed to be postve, wth β δ. Let c and f denote frm s margnal cost and fxed cost, respectvely, and t be the mport tarff mposed by country C on frm. Frm s proft functon can then be wrtten as π = ( P c t ) q f, =, (3) Country C s welfare functon w conssts of the consumer s surplus CS, and tarff revenue t q + t q : w = CS + t + (4) q tq where CS = V ( q, q) P q P q. The structure of the game s as follows. In the frst stage, country C chooses optmal tarffs. Once the tarffs are determned, two exportng frms wll compete wth each other n a Cournot-Nash fashon. The equlbrum can be solved by applyng the backward nducton method. Gven the tarffs, frm wll choose the optmal level of output to satsfy the followng frst-order condton: A typcal duopoly example s the European arcraft maker Arbus and ts U.S. rval Boeng Co. n the producton of large arlners. In addton, the duopoly model s used wdely n the strategc trade lterature, such as n Brander and Spencer (984, 985); Eaton and Grossman (986); Dxt (988); Colle (99, 994); Levy and Nolan (99) and Bhattacharjea (995) etc. Note that α ndcates the sze of market whle a postve δ can be used to measure the degree of substtuton between the two dfferentated goods. A hgher δ mples a hgher degree of substtuton. When δ = β, q and q are homogeneous goods. The assumpton β > δ also ensures that the second-order condtons and stablty condtons dscussed n the followng sectons are satsfed.

4 4 Wang, Lu, and Tsa π = P + q P c t = 0, =, (5) Usng (), the equatons n (5) can be solved smultaneously to derve the Nash equlbrum output q and prce P : q = [( α c t ) β ( α j c j t j ) δ], j,, j =, ; (6a) Η P = α [(β δ )( α c t ) + βδ( α j c j t j )], j,, j =,, (6b) Η where * denotes the equlbrum value under the pre-ntegraton case, and H 4β δ > 0. From (6a) and (6b), the followng comparatve statc results can be obtaned: β = < 0, Η j δ = Η > 0, j,, j =, ; (7a) P 0 < β δ = Η <, P j βδ = > 0, Η j,, j =,. (7b) Thus, a decrease n tarff t rases frm s exports whle lowerng those of frm j, and the prce of good decreases by a smaller extent than the change n tarff t. By takng the exportng frms reactons to mport tarffs nto consderaton, country C wll choose a set of tarffs, t ( =,), to maxmse ts welfare. By substtutng (6a) and (6b) nto Equaton (4), and totally dfferentatng w wth respect to t and settng t to zero, we obtan: βx t =, =, (8) 9β δ where X (α c ) δ(α j c j ) > 0, j. 3 Equaton (8) ndcates that the optmal tarffs on mports are postve when economc ntegraton does not occur [see also Brander and Spencer (984)]. We wll compare the pre-ntegraton tarffs wth the post-ntegraton ones that wll be derved n the followng secton and explore the polcy and welfare mplcatons of economc ntegraton. 3 A postve q ( =,) wll ensure a postve X. For q > 0,, the followng condtons must be satsfed: () α c t > 0, =, ; () α t [β(α t )/δ] + (βc /δ) < c < α t [δ(α t )/β] + (δc / β).

5 Trade Polcy and Economc Integraton TARIFF POLICIES UNDER ECONOMIC INTEGRATION In ths secton, we assume that countres C and A decde to ntegrate economcally. Apparently, wthout a transfer scheme, country C may not have an ncentve to lower or even elmnate a tarff on the mports from country A. However, f a transfer scheme exsts so that a loser from ntegraton can be compensated by the ganer, then an economc regon may emerge. 4 In such a case, the regon s jont welfare wll be the man concern n the formaton of an economc regon, and the nternal tarff t and the external tarff t wll be chosen to maxmse the regonal welfare. The ncentve for the economc ntegraton to exst wll be presented n Secton 4. Let W denote the regon s jont welfare whch conssts of country C s welfare and partner frm A s proft: W = CS + t q + t q + π. (9) Assume that the nternal tarff t s determned pror to the external tarff t. 5 The structure of the game here therefore s a three-stage sub-game perfect equlbrum. That s, t wll be chosen frst and then followed by the determnaton of t n the second stage. Gven t and t, frms wll compete n the output market n the last stage. Agan, the model can be solved backwards. Snce the solutons to the last stage are the same as those n Secton, Equatons (6)-(7) are stll applcable n ths secton. Takng Equatons (6) and (7) nto account and gven the nternal tarff t, the optmal external tarff t whch maxmses the regon s jont welfare can be derved: 6 δ + = t t α c 3, (0) where the superscrpt ** ndcates the post-ntegraton case. From Equaton (0), the effect of a change n the nternal tarff on the optmal external tarff s 0 < < δ =. () Thus, whle lowerng the nternal tarff wll lead to a lower external tarff, t s optmal for the economc regon to lower the external tarff to a smaller extent than the nternal tarff. In fact, the external tarff can be reduced at most by /3 of the reducton n the nternal tarff when the two goods are homogeneous and demand s lnear. 4 Kemp and Wan (976) and Wooton (988), for example, also dscuss customs unon ssues from the perspectve of regonal welfare, assumng that some ncome redstrbuton mechansm exsts. 5 It s worth notng that t does not matter whether the nternal or external tarff s set frst, or whether they are set smultaneously. The ratonale s dentcal to the case where a monopolstc frm determnes two varables sequentally or smultaneously. The proof can be found n Appendx A. 6 Here, the second-order condton s satsfed: W/ = /H < 0.

6 44 Wang, Lu, and Tsa Moreover, by usng (8) and (9) we have δ t t = ( t + t ). () Recall that the pre-ntegraton tarffs t * and * t are postve. Therefore, the nterrelatonshp between the nternal trade polcy and the external trade polcy can be llustrated n Fgure. Ths Fgure ndcates that the provson of a suffcently large subsdy on the mports from the partner by the economc regon s necessary for the external tarff to be lowered to a level less than ts pre-ntegraton level ** * (.e. t < t ). Proposton. In the Cournot duopoly model, the economc regon wll lower the external tarff from ts pre-ntegraton level only f a suffcently large subsdy on the mports from the partner s granted. Fg.. Knowng the effect of a change n the nternal tarff on the external tarff, we now examne ts mpact on the post-ntegraton proft of the nonpartner frm. By totally dfferentatng π wth respect to t, we obtan d π d t π = π + > 0. (3) The frst and second terms n (3) are, respectvely, the drect and ndrect effects of a change n the nternal tarff on the nonpartner frm s proft. The drect effect s:

7 Trade Polcy and Economc Integraton 45 π = ( P c t ) + q P > 0. (4a) It s postve because a decrease n the nternal tarff serves to swtch country C s demand for goods away from the nonpartner frm to the partner frm and thus lowers the nonpartner frm s proft. The ndrect effect (the second term n Equaton (3)) s negatve, as > 0 and π = ( P c t ) + q ** P ( ) < 0. (4b) Usng (6a) and (6b), t can be shown that the drect effect domnates the ndrect effect. The sgn of (3) s therefore postve. Thus we have Proposton. Economc ntegraton wth tarff barrers aganst partners beng lowered or elmnated wll reduce the nonpartner country s welfare. We now turn to the frst stage of the game,.e. the determnaton of the nternal tarff. Totally dfferentatng the regon s welfare wth respect to t yelds: d W d t = ( P + t c)( ( + + t ). ) q P [ P + ( ) The three terms n Equaton (5) respectvely capture the effects of a change n the nternal tarff on the partner frm s profts, the consumer s surplus, and the tarff revenue. Snce the second-order condton s satsfed (.e. d W/ dt ( δ )/H < 0), the optmal nternal tarff can be obtaned by settng (5) equal to zero: < t = βq 0. (6) The optmal nternal tarff s negatve. In other words, f the regon were to maxmse ts jont welfare, a subsdy on the mports from the partner country would be the frst best polcy. In fact, such a subsdy polcy wll lead the partner country to produce at the pont where P = c (see (5)) and thus reach the Pareto optmum. In a way smlar to Dxt (988), the subsdy serves to correct the dstorton caused by the mperfect competton n the commodty market. 7 Usng (6a), (8), (0), and (6), we have: 7 See also Syropoulos (996) (5) ]

8 46 Wang, Lu, and Tsa βδ t t = t < 0. (7) δ Thus, subsdsng the partner frm whle at the same tme reducng the tarff mposed on the nonpartner frm wll be the optmal strategy for the economc regon to adopt. Thus we have: Proposton 3. In the Cournot duopoly model, the optmal polcy package for the ntegratng regon s to subsdse the mports from the partner country and to reduce tarff barrers on the mports from the nonpartner country. 4. THE INCENTIVE FOR ESTABLISHING THE ECONOMIC REGION The prevous sectons assume that countres A and C have ndeed agreed to form an economc regon. However, for the two countres to have such an ncentve, the jont welfare of the economc regon must ncrease after the ntegraton. Ths secton attempts to demarcate the range for the nternal tarff over whch the regon s welfare ncreases after ts formaton. An nterestng by-product of ths analyss s that we are able to show that the second-best polcy s free trade among the member countres when the optmal subsdy polcy s not practcally feasble. Through a complcated calculaton process, t can be shown that δ W ( t, t ) W ( t, t ) = ( t + Rt S), (8) 6βΗ βx β (β + δ ) X where R, S. Therefore, the regon s jont δ ( δ )(9β δ ) welfare ncreases after ntegraton (.e. W ( t, t ) W ( t, t ) > 0 ) f and only f the nternal tarff satsfes R R R R t ( [( ) + S], + [( ) + S] ) = ( t L, t U ), (9) U L where t and t are the upper and lower bounds. Under such crcumstances, countres A and C wll have ncentves to form an economc regon, provded that an U approprate compensaton mechansm exsts. Snce > L t 0 and t < 0, the regon s jont welfare can be mproved when the mports from the partner country are subsdsed or even only partally lberalsed. Moreover, t can be shown that t =, and R L t t t = t U = [( R ) + S] > 0. (0)

9 Trade Polcy and Economc Integraton 47 That s, the post-ntegraton optmal nternal tarff (subsdy), t, wll fall at the mdpont of the range ( t L, ). The results can be llustrated n Fgure, where the ( U t welfare functon W t, t ) s strctly concave wth respect to t snce dw( t, t dt ) δ = ( t t Η ), (a) and thus d W ( t, t dt ) < 0. (b) The regonal welfare reaches the maxmum at wth t when > ( < ) t t. t = t, and decreases (ncreases) Fg.. Although the jont welfare reaches the maxmum level when the optmal subsdy ( t ) s granted, such a polcy s not usually feasble [Bhattacharjea (995)]. If for some reason a subsdy polcy s not avalable, Fgure shows that complete elmnaton of the nternal tarff wll result n the hghest level of welfare. Notce also that the partner countres could stll jontly beneft from a partal lberalsaton as

10 48 Wang, Lu, and Tsa long as the post-ntegraton nternal tarff falls wthn the range 0, t ). Thus we conclude: Proposton 4. Barrng mport subsdy, countres can beneft from economc ntegraton even under a partal trade lberalsaton regme, but complete abolshment of the tarff barrers among partner countres wll result n the hghest regonal welfare. In addton, defnng the world welfare as W T = W + π and usng (), (5) (7) (3) and (5), we get ( U d W dt T β δ + 3δ T = ( t t ), () 9βH where t T = [ (β δ )( α c) βδ(8β δ )( α c)] ( 36β δ + 3δ ). T 4 4 Snce d W dt = (36β δ + 3δ ) 9βH < 0, W T s also a strctly concave functon of t. Moreover, t can be shown that t < t < 0 and π > 0 so that we have the graph of Fgure. Clearly, the world welfare ncreases when the tarff aganst partner countres s lowered. In other words, the welfare gans to the economc regon are hgher than the welfare losses to the nonpartner country. As a result, we arrve at the followng proposton: Proposton 5. The world s net welfare s lkely to ncrease wth the formaton of economc ntegraton. If mport subsdes among the partner countres are not allowed, the welfare gans are the largest when free trade prevals wthn the economc regon. An mportant lesson emerges from Proposton 4 and Proposton 5. When mport subsdes are not avalable n an economc regon, not only does free trade wthn the regon lead to the hghest regonal welfare, but t also results n the hghest net gans of the world welfare. Consequently, our results fully support the wsdom of the GATT s Artcle XXIV, whch requres trade barrers wthn any economc regon be completely elmnated eventually. T CONCLUSION The resurgence of economc ntegraton snce the late 980s has led to a flurry of studes regardng ther mplcatons. From an economc vewpont, there s no doubt that most attempts at economc ntegraton have led to the adopton of polces amng at reducng trade barrers aganst partner countres n the hope of achevng producton effcency, explotng economes of scale, as well as acceleratng economc growth. On the other hand, due to the concerns over the potentally negatve mpacts of economc ntegraton on nonpartner countres, the GATT has endeavoured to regulate economc ntegraton through ts well-known Artcle XXIV.

11 Trade Polcy and Economc Integraton 49 In partcular, ths Artcle requres that () trade restrctons aganst nonpartner countres not be rased after ntegraton, and () that trade barrers wthn the economc regon eventually be completely elmnated. Apparently, the frst requrement s to prevent the nonpartner countres from beng harmed by the emergence of economc ntegraton, whle the second s based on the concept that free trade n part of the world s better than no free trade at all. Besdes nvestgatng the mpact of economc ntegraton on both the partner and nonpartner countres, t s also nterestng and mportant to see the mplcatons of the requrements of Artcle XXIV. In attemptng to answer the questons mentoned above, we employ n ths paper the Cournot duopoly model á la Brander and Spencer (985) to study the welfare mpacts of the formaton of an economc bloc, wth specal attenton beng pad to the nterdependence between the nternal and external tarffs. Our major results are as follows: () the economc regon wll lower the external tarff (aganst nonpartner countres) from ts pre-ntegraton level when a suffcently large subsdy on the mports from the partner s granted; () the formaton of an economc bloc wll reduce the nonpartner country s welfare; (3) an economc regon can gan from economc ntegraton even trade s partally lberalsed between partner countres though complete trade lberalsaton wthn the regon wll lead to hgher regonal welfare; (4) trade lberalsaton wthn the regon wll mprove the welfare of the world as a whole. Above all, our results seem to support the above-mentoned second requrement of Artcle XXIV of the GATT. Admttedly, economc ntegraton s a very complex phenomenon, mxng economc and geopoltcal consderatons. Therefore, t s mpossble for our smple model to capture all the nterestng aspects of ths phenomenon. However, we stll hope that our analyss has shed some lght n furtherng our knowledge about economc ntegraton. APPENDIX A If the nternal tarff t and the external tarff t are determned n the same stage, the followng two equatons wll be solved smultaneously: W q P q = ( P c) q + t, (A.) W q P q = ( P c) q + t + q, (A.) and usng (5) (7) we obtan β = [( α )], (A.3) δ ** c t

12 50 Wang, Lu, and Tsa β = [ β( α c) δ( α )]. (A.4) δ ** c t Alternatvely, f t s determned n stage and t n stage, we wll solve W/ =0 frst and get δ = t ( α β ), (A.5) ** c t Based on (A.5), n the settng ** t s a functon of t and hence dw q q = P c + dt t t t ( )( ) q P P q q ( ) ( ). + + t + (A.6) Lettng dw/dt = 0 and usng (5) (7) and (A.5) yelds (A.4). Next, (A.3) wll be obtaned by substtutng (A.4) nto (A.5). Smlarly, we can also obtan (A.3) by substtutng (8) nto (7) and can arrve at (A.4) by substtutng (A.3) nto (0). REFERENCES Bhattacharjea, A. (995) Strategc Tarffs and Endogenous Market Structures: Trade and Industral Polces under Imperfect Competton. Journal of Development Economcs 47, Bond, E. W., and C. Syropoulos (996) The Sze of Tradng Blocks: Market Power and World Welfare Effects. Journal of Internatonal Economcs 40, Bond, E. W., C. Syropoulos, and L. A. Wnter (00) Deepenng of Regonal Integraton and Multlateral Trade Agreements. Journal of Internatonal Economcs 53, Brander, J. A., and B. J. Spencer (984) Trade Warfare: Tarffs and Cartels. Journal of Internatonal Economcs 6, 7 4. Brander, J. A., and B. J. Spencer (985) Export Subsdes and Internatonal Market Share Rvalry. Journal of Internatonal Economcs 8, Colle, D. R. (99) Export Subsdes and Countervalng Tarffs. Journal of Internatonal Economcs 3, Colle, D. R. (994) Endogenous Tmng n Trade Polcy Games: Should Governments Use Countervalng Cutes? Weltwrtschaftlches Archv 30, Dxt, A. K. (988) Ant-Dumpng and Countervalng Dutes under Olgopoly. European Economc Revew 3,

13 Trade Polcy and Economc Integraton 5 Eaton, J., and G. M. Grossman (986) Optmal Trade and Industral Polcy under Olgopoly. Quarterly Journal of Economcs 0, Kemp, M., and H. Wan (976) Elementary Proposton Concernng the Formaton of Custom Unons. Journal of Internatonal Economcs 6, Levy, S., and S. Nolan (99) Trade and Foregn Investment Polces under Imperfect Competton. Journal of Development Economcs 37, 3 6. Levy, P. I. (997) A Poltcal-Economc Analyss of Free Trade Agreements. Amercan Economc Revew 87, McMllan, J. (993) Does Regonal Integraton Foster Open Trade Economc Theory and GATT s Artcle XXIV. In K. Anderson and R. Blackhurst (eds.) Regonal Integraton and the Global Tradng System. London: Wheatsheaf Harvester. Panagarya, A., and R. Fndlay (994) A Poltcal-Economy Analyss of Free Trade Areas and Customs Unons. (World Bank Polcy Research Workng Paper No. 6.) Rchardson, M. (993) Endogenous Protecton and Trade Dverson. Journal of Internatonal Economcs 34, Syropoulos, C. (996) Implcatons of Preferental Trade Arrangements for Polcy and Market Access. Canadan Journal of Economcs S40 S405. Wooton, I. (988) Towards a Common Market: Factor Moblty n a Customs Unon. Canadan Journal of Economcs,