Uniform Output Subsidies in Economic Unions versus Profit-shifting Export Subsidies

Transcription

1 nform Output Subsdes n Economc nons versus Proft-shftng Export Subsdes Bernardo Moreno nversty of Málaga and José L. Torres nversty of Málaga Abstract Ths paper focuses on the effect of output subsdes n an economc unon n the context of a thrdmarket model where there are two countres whch produce a homogeneous good consumed n a thrd country. We study the mportance of cost asymmetry between frms n dfferent countres, and the elastcty of demand n the case of countres that on an economc unon wth harmonzed output subsdes. We fnd that the optmal level of subsdy n the economc unon can be negatve a tax) f frms have dfferent costs and the demand s concave. We also compare the optmal subsdy n the economc unon wth the pre-unon export subsdes wth the result that the new polcy generally favours the less effcent countres. JEL Classfcatons: F Key Wor: Output Subsdes, Economc non *Correspondng address: Bernardo Moreno, José L. Torres, Department of Economcs, nversty of Málaga, El Edo s/n, 90 Malaga, Span, Tel: , Fax: , Emal: bernardo@uma.es, torres@uma.es

2 I. Introducton The European non has attempted to harmonse all ad beng gven by the governments of member states to the dfferent ndustral sectors. Ths was done to elmnate or reduce torton of competton wthn the Communty. In ths paper we analyse the effects of unform producton subsdes n an economc unon of two producng countres and a thrd consumng country, n an mperfectly compettve market, usng Brander and Spencer's [985] so-called thrd-market model. The am of the paper s to compare the prevous pre-unon stuaton, n whch each government, ndependently and smultaneously sets a proft-shftng export subsdy to ts frm, wth a stuaton n whch the three countres form an economc unon wth smlar subsdes for the two producng countres. Followng Balassa [96], we can tngush several stages or levels of economc ntegraton among countres, such as free trade areas, customs unons, common markets and monetary unons. In ths paper, we defne an economc unon as an area wth a common economc authorty whch decdes the same level of output subsdes for all the frms n an olgopolstc ndustry. Frst, we study the tradtonal problem n terms of the optmal subsdy level, n a pre-unon step. In the pre-unon case, we obtan the conventonal result that the lower cost frm obtans the hghest subsdy, as shown by Neary [994] and De Meza [986]. Brander and Spencer [985] were the frst to show that, n a Cournot duopoly settng, an export subsdy to a home frm s desrable because t rases the frm's market share and profts at the expense of ts foregn compettor. Neary [994] consders the problem n whch the socal cost of publc fun excee unty, followng Gruenspecht [988]. He fn that subsdes are optmal only for surprsngly low values of the socal cost of publc fun and, f subsdes are ustfed, they should be hgher the more cost compettve the domestc frms are. However, as s ponted out by Bandyopadhyay [997], ths result s reversed n the presence of nelastc demand. For an excellent survey about strategc trade polcy and the dfferent extensons of the thrd-market model see Brander [995]. Followng Brander and Spencer [985], we consder the exstence of three countres. We depart from the tradtonal case and wegh the exstence of an economc unon. Countres frms) and produce a homogeneous good n an mperfectly compettve market. There s no consumpton Followng Brander [995] a thrd-market model can be defned as one n whch frms from a domestc country and frms from a foregn country only compete n a thrd market, n other wor, they only produce to export. Ths smplfcaton turns out to be very useful n allowng the strategc effects of export subsdes to be seen n pure form and ths s the reason why ths model has been extensvely used n the lterature. See Hne [994] for a survey on the nternatonal economc ntegraton lterature.

3 n the producng countres. Country mports the mperfectly compettve good. We explore the case n whch the three countres on an economc unon wth a common economc authorty. Therefore, n ths case, the common economc authorty chooses the same level of subsdes for the two frms, n terms of welfare maxmzaton n the economc unon. We assume that the obectve of the common economc authorty s to maxmze socal welfare n the unon, takng both producers and consumers nto account. We fnd that the optmal output subsdy level can be negatve a tax) f the demand s concave when frms have dfferent cost. As a result, n the case of a lnear demand and symmetry n costs, the optmal level of subsdy n the economc unon yel a compettve market level of output. Comparng the economc unon wth the export subsdes case n the standard thrd-market model, the effects of the new polcy depend on the relatonshp between the new unform subsdy level and the prevous proft-shftng export subsdy levels settled by each country. We fnd that n the case of a lnear demand, the optmal subsdy n the economc unon s larger than the optmal subsdes n the pre-unon export subsdes case. We also fnd that, n the symmetrc cost case, the optmal subsdy level n the economc unon s larger than n the non-cooperatve pre-unon export subsdes stuaton, ndependently of the curvature of the demand functon. In order to compare both cases wth asymmetres n costs, we consder the two specal cases, when the optmal subsdy n the economc unon s equal to the optmal subsdy for each frm n the pre-unon noncooperatve export subsdy case. In both cases, the result s that the new polcy favours the less effcent frm. The structure of the paper s as follows. Secton II presents the model and analyses the standard case of two exportng countres, each usng export subsdes to mprove the relatve poston of ts frm. In Secton III, we derve the optmal subsdy level n an economc unon formed by the two exportng countres and the mportng country wth a common economc authorty that chooses the same level of subsdes for the two frms. We compare the results wth the proft-shftng export subsdes pre-unon stuaton. Secton IV concludes the paper. II. The model Followng Brander and Spencer [985], we use the thrd-market model of nternatonal trade under olgopolstc competton. The descrpton of the model s as follows. We analyse the market for a homogeneous good that s produced by two frms, each located n a dfferent country,.e., country and country, wth constant return to scale functons denoted by c x )c x,,, where

4 4 x s the output of frm. Let px +x ) be the nverse demand functon, where x s the output of frm country) and x s the output of frm country) and let xx +x, be the total output, s the subsdy per unt of output receved by frm and the proft of frm be gven by: ) x, x, s ) p x + x x c x + s x ) Wthout loss of generalty, we assume that, n general, the frm's costs n country are lower than those of the frm n country. Each country chooses a subsdy for the frm wth the obectve of ncreasng ts welfare net of subsdy. Assumpton : ) ε,. { } Assumpton : Margnal payoff functons are strctly decreasng n x and n x,. { } We consder a two-stage game where frms play a Cournot-Nash game regardng output levels. The frms move nto the second stage after the governments have announced ther subsdy level n the frst one. We assume that both producng countres ntervene, that s, both countres choose an export subsdy n order to maxmze the socal welfare n a non-cooperatve settng. Snce there s no domestc consumpton, we consder the profts of the frm net of subsdes as the socal welfare of each of the two producng countres. Wth a subsdy, s,,, provded by the government the optmal subsdy has been predetermned n stage and s therefore treated as exogenous), the frm's frst-order condton s: obtan: p p x c + s 0 ) + By totally dfferentatng the frst-order condtons of proft maxmzaton for both frms we p + αr) p [ + α R] + α [ α x] where s the market share of frm, x / {,} ), R s a measure of the concavty of demand defned as R p x / p, where + R 0 from stablty condtons, and + α ) + α R 4) Solvng the above two expresson we obtan: As has been ponted out by Brander and Spencer [985] the subsdy ncreases domestc welfare net of the subsdy so each country has a unlateral ncentve to offer an export subsdy to ts frm.

5 5 and + α R p [ + R] + α R p [ + R] > 0 < 0 On the other hand, we have that: + α R < 0 + α R 5) 6) 7) where + R > 0. It seems to be clear that the ntroducton of an export subsdy gven to frm α > + α R causes the output to frm to rse and the output of frm to fall. Ths s due to the fact that an export subsdy s equvalent to a reducton n the producton cost, and then, t makes the frm ncrease producton for a gven producton of the other frm. From that we also obtan that total producton rses, prce falls, profts of the subsdzed frm rse and profts of the rval frm fall. Once we have solved stage of the game, we turn off to solve stage. In ths stage the government chooses an output subsdy n order to maxmze socal welfare. Snce there s no consumpton n the producng countres, the socal welfare s defned as the home frm's proft net of the value of the subsdy payments. The problem for country can then be defned as: max { s } x s, s ), x s, s ), s ) s x s, s ) 8) The frst-order condton s: d x + x + s x s 0 9) Snce x 0, and that s x, the above expresson s reduced to: x s 0 0) Therefore, the optmal subsdy level for frm country) s, s ) x Substtutng expresson 7) n ) and takng nto account that x x p ), we x obtan the same results gven by Neary [994]. The optmal subsdy level for frm s: s + α R εp α ) + α R

6 6 where ε p' x p x) s the elastcty of the demand functon. Gven symmetry, the optmal subsdy for frm s: s + αr εp α ) + αr The optmal subsdy s an ncreasng functon of the market share of each frm. Ths means that the optmal subsdy s ncreasng n the relatve cost advantage of the frm. As Brander [995] ponted out, frms that need help to compete wth foregn rvals are the least attractve targets for strategc assstance from a welfare-maxmzng government's pont of vew. Wth symmetrc costs, snce α α /, the subsdy s the same for both frms and t s gven by + R s s ε p x) 4) 4 + R As we can observe, n ths case the subsdy s postve for any stable value of the curvature of the demand functon R>-). However, n the case of asymmetres n cost the subsdy of the hgher cost frm can be negatve a tax) f the demand s convex enough. If frm s the hgher cost frm, expresson ) s negatve f α R. < Combnng ) and ), the dfference between both subsdes s: s α α + R α + α ) + R α α α α s εp x) 5) 4 + R + αα R dependng on the market share of each frm and on R. If frm s the low cost frm, the above dfference s postve. Therefore, we obtan the tradtonal results gven by Brander and Spencer [985], De Meza [986] and Neary [994]: the low cost frm obtans the hgher subsdy. When the demand functon s lnear the subsdy dfferental equals the cost dfferental. If the demand s non lnear the subsdy dfferental ncreases. As t s shown by Brander and Spencer [985], under symmetry, the game has the general form of a prsoner's dlemma, as both producng countres are worse off than under free trade, but each country has a unlateral ncentve to ntervene. Colle [99] uses a lnear verson of the model to prove that only wth sgnfcant cost dfferences t s possble that the more effcent country wll be better off at the Nash equlbrum n export subsdes than under free trade. Obvously, ths trade polcy ncreases the welfare of country. 4 ) 4 As Brander and Spencer [985] state, f countres and wsh to subsdze country to consume the goo they produce, so much the better for country.

7 7 III. Economc non Next we call nto queston the case of an economc unon of both producng countres plus the thrd mportng country, so now the whole producton of the two frms s consumed nsde the economc unon. We assume that the new economy has a common central authorty that chooses the same subsdy levels for both countres. Ths ntroduces an mportant dfference as regar to the tradtonal case consdered n the lterature. In fact, f each country chooses the subsdy level n a non-cooperatve way, n the case of asymmetrc costs, the optmal subsdy for each frm s dfferent. In our case, n spte of asymmetry n costs, we assume that the subsdy level for the two frms s the same. 5 Therefore, the motve for subsng n ths model s not to rase home profts at the expense of foregn compettors, but to maxmze total welfare n the unon. Obvously, n ths case the producton subsdy cannot be consdered as an export subsdy. Economc non wth equal subsdes: In the economc unon case, we assume that the planner chooses the same level of subsdes for both frms, ndependently of the cost levels for each frm wth the obectve of maxmzng the total socal welfare of both the producers and the consumers net of subsdes. Ths way, the welfare functon depen on the two frms' profts and on consumpton n the unon, where V px s the utlty functon of consumers country ). Therefore, the total socal welfare of the unon can be defned as: s ) x, x, s ) + x, x, s ) + x, s ) s x 6) Substtutng, the problem to be maxmzed s: max s ) V cx c x { s s }, 7) subect to s s s ; x, x 0. Takng the dervatve of 7) yel: 8) x d V c c Settng the frst-order condton equal to zero we obtan: p c ) + p c ) 0 9) From expresson 5) and 6) we obtan that the change n output s: 5 Ths assumpton s based on the fact that t s dffcult to ustfy dfferent output subsdes for each country n the context of an economc unon.

8 8 + + α R p + + α R α [ + R] p [ + R] p [ + R] α ) R The frst term, whch s postve, measures the effect of the subsdy on the output of the frm; the output subsdy shfts out the best-response functon of the frm lowerng ts effectve cost and ncreasng producton. By contrast, the second term s negatve, whch ndcates the loss n output caused by the output subsdy receved by the rval frm as also ts best-response functon shfts out. Note that the change n output depen on the market share of each frm n the case of non-lnear demand functons. In the case of convex demand R<0), output of the lower cost frm frm ) ncreases, whereas output of the hgher cost frm frm ) decreases f R α α ). For 0) > concave demand R>0) output of the hgher cost frm frm ) ncreases whereas output of the lower cot frm frm ) decreases f R α α ). Fnally, n the case of lnear demand R0), gven that p x)-, we have: > that s, the output of the two frms ncreases by the same amount. On the other hand, the change n total output n the economc unon s always postve, ndependently on the exstence of cost asymmetry: yel: [ + R] ) > 0 p ) Substtutng expresson 0) n the frst-order condtons of the frms' proft maxmzaton, α α ) R α α ) R p x s ) + p x s ) 0 p [ + R] p [ + R] From ths we obtan the followng expresson for the optmal level of the unform subsdy: ) s α εp x) α ) R where x s the total output n the unon. 6 From that, we obtan we followng result: 4) Proposton : The unform output subsdy n the economc unon s postve f R α α ). Otherwse, t s negatve a tax). < 6 Only when t s necessary to tngush between the non-cooperatve case and the economc unon case we wll use the superscrpt to denote the output n the economc unon stuaton.

9 9 As can be observed, the unform output subsdy n the economc unon, expresson 4), s postve for convex and lnear deman -<R 0). However, f the demand s concave enough and frms have dfferent costs, expresson 4) can be negatve, ndcatng the optmal polcy s to set up a tax. Ths s found to be unon s: R α α ) >. For the lnear case, the optmal subsdy n the economc εpx) s 5) Note also that the general expresson for the optmal subsdy s the same n the case of symmetry n costs, gven that α. Therefore, the expresson for the optmal subsdy n the economc unon s always postve provded that there s symmetry n producton costs. As asymmetres n costs ncrease, the optmal subsdy becomes negatve for concave nverse demand functons. Note that f only the two producng countres on the economc unon, then ths s n fact an nternatonal monopoly regardng the mperfectly compettve product, so the planner's optmal polcy s to set up a tax. result: 7 α From the optmal subsdy level n the economc unon we obtan the followng well-known Proposton : If c ones for all R. If c c c, then the prce and the output n the economc unon are the compettve, then the prce s the average of the costs. Proof: In the case of symmetrc costs the market share of both frms s equal and then the optmal subsdy n the economc unon s: ε ) x 6) s p x p where from the frst-order condton of the proft maxmzaton: p x) x p x) c + s By substtuton, we obtan that p x) c. Ths result mples that, n spte of the fact that we are consderng an mperfectly compettve market a duopoly), the optmal subsdy settng n the economc unon motvates the frm to produce the output of a perfectly compettve market, ndependently of the demand functon curvature. 7) 7 In fact, as s ponted out by Neary [994], f markets are compettve, export subsdes should be zero n a small open economy and should be negatve a tax) f the economy has monopoly power n trade.

10 0 Also, f we consder the exstence of asymmetrc costs, n the case of a lnear demand, we obtan the result that the prce n the economc unon s the average of the costs. The sum of the frst-order condtons for the two frms s: p x) x p x) c c s + From expresson 5) the unform output subsdy n the economc unon can be defned as: p x s 9) Substtutng 9) n 8) we obtan that: c ) + c p x 0) 8) Economc non versus Pre-unon export subsdes: In ths secton, we turn to compare the economc unon stuaton wth respect to the tradtonal soluton of two exportng countres settng subsdes n a non-cooperatve game. As we have showed above, n the pre-unon case, the frm wth lower costs obtans the hghest subsdy. However, n the economc unon, the subsdy level s the same for both frms, ndependently of costs. If we compare both stuatons for the cost symmetrc case, we obtan the followng result. Proposton : In the symmetrc case c ), the optmal subsdy n the economc unon s larger c than the optmal subsdy n the non-cooperatve game for all R. Proof: By proposton we know that the prce n the economc unon s the perfectly compettve prce, so p x ) c. In the non-cooperatve game, gven symmetry n costs, the subsdy level for both frms s: s + R p x 4 + R ) and substtutng n the frm's frst-order condton, we obtan: p x p c + s ) sng equatons ) and ) we fnd that the prce n the non-cooperatve game s: p c + + R s Gven that the last term of ths expresson s postve for R>-, we obtan: )

11 p x ) < p x) 4) As the prce n the economc unon s lower than the prce of the product n the noncooperatve game, the total output n the economc unon s greater. Ths s only possble f the optmal subsdy level n the economc unon s larger than n the pre-unon case. Therefore, we obtan that, wth equal producton costs, the level of subsdy n the economc unon s larger than n the prevous stuaton for all demand functons. Ths means that producton wll be larger n the economc unon wth respect to the prevous stuaton as t s shown by proposton. Ths large level of subsdy s, n fact, caused by the exstence of consumers n the socal welfare of the unon. Ths way the subsdes are not ncreasng the consumpton and thus, the socal welfare) n a foregn market, but n the domestc market. A specal case n whch we can compare the level of subsdes n both stuatons wth asymmetrc costs s that n whch the demand s lnear. Proposton 4: If R0, the subsdy level n the economc unon s greater than n the pre-unon case, that s, s > s > s. Proof: sng the frst-order condton of the proft maxmzaton problem of frm n the pre-unon case, we fnd that the prce s: p s + c 5) and smlarly for frm. Then, n the pre-unon case c c s s. On the other hand, the prce n the economc unon s: c ) + c p x 6) Therefore, we fnd that p x ) < p x), gven that c + c ) / < c + s. Ths mples that, at the subsdes level, x > x. Ths s only possble f s > s >. s In the lnear demand case, and n spte of asymmetres n producton costs, the level of subsdy n the unon s larger than n the prevous stuaton. Then, both frms get a hgher level of subsdes. However, the ncrease n the subsdy that each frm receves s dfferent compared to the prevous non-cooperatve stuaton. The less effcent frm receves proportonally more subsdy n the economc unon than the most effcent frm. Ths means that the new polcy subsdy shfts out the reacton functon of frm by more than the reacton functon of frm. Ths mples an allocatve change n effcency regardng the prevous stuaton of non-cooperatve export subsdes

12 avodng the effect that a non-cooperatve export subsdy helps the wnners, gven that the level of subsdy of the most effcent frm s larger than the subsdy of the less effcent frm. 8 nfortunately, the above proposton cannot be generalzed to the case of a non-lnear demand. However, gven contnuty n the level of subsdy respectng the curvature of the demand functon, we can approxmate the relatonshp between the subsdes n both stuatons. From expresson ) we know that the subsdy for the less effcent frm n the pre-unon case can be negatve f R < / α, that s, for values of the curvature of the demand functon between and, dependng on the dfferences n cost. On the other hand, the subsdy for the more effcent frm n the pre-unon case s always postve, and followng Neary [994] we know that the mnmum dfference between both subsdes takes place when the demand s lnear. Wth respect to the subsdy n the economc unon, we obtan that t can be negatve a tax) f the demand s concave when there are dfferences n cost. Fnally, the unform subsdy level s larger than the subsdes n the non-unon case when the demand s lnear. Therefore, the optmal subsdy n the economc unon s a decreasng functon n R. In fact, ths s due to the presence of the consumer n the government's welfare functon. In mperfectly compettve markets, convex deman tend to gve hgh values of the optmal subsdy because the gans n consumer surplus from the lower prces are large relatve to the subsdy cost. However, n the case of concave deman, the gans n consumer surplus from lower prces are small relatve to the subsdy cost. That s why n the economc unon, f the demand s concave enough, the optmal subsdy wll be negatve. The same argument can be used n the export subsdes pre-unon case. As n ths case the consumer surplus s not a component of the socal welfare of each producng country all producton s for export), they only take nto account the proft-shftng effect of the subsdy on the frms. Such effect wll be larger n the case of concave demand and smaller n the case of convex demand. From the prevous analyss, we can compare the two stuatons for some specal cases. Frst, we study the stuaton n whch the optmal level of subsdy n the economc unon s equal to the level of subsdy of the most effcent frm n the non-cooperatve game. In ths case, the unform subsdy level n the economc unon equals the subsdy of frm n the pre-unon case and therefore greater than the subsdy of frm, s s and s > s. That s, the new subsdy lowers margnal costs to frm, but does not change margnal costs to frm. Thus, the new subsdy polcy only shfts out the reacton functon of frm wth respect to the prevous stuaton. Ths mples that the 8 In the appen, we present the lnear verson of the model.

13 producton of ths frm wll ncrease and the producton of frm wll decrease. However, the total producton wll be ncreased. Proposton 5: A level of subsdes n the economc unon equals the pre-unon subsdy of the lower-cost frm: ) Increases the producton of the frm wth hgher costs. ) Decreases the producton of the frm wth lower costs. ) Increases the total producton. v) Increases the profts of the frm wth hgher costs. v) Decreases the profts of the frm wth lower costs. Proof: ) Increases the producton of the frm wth hgher costs: The frst-order condton of the maxmzaton problem of frm s: p x) + p x c + s 0 7) Dfferentatng 7) wth respect to and s : [ + R] x + αr > 0 8) p ) Decreases the producton of the frm wth lower costs: The frst-order condton of the maxmzaton problem of frm s: p x) + p x c + s 0 9) Dfferentatng 9) wth respect to and x : + αr < 0 + α R x ) Increases the total producton: + + > 0 p [ + R 4) ] gven that < < 0. v) Increases the proft of the frm wth hgher costs: d + α R x x + > 0 4) x x s x + R v) Decreases the proft of the frm wth lower costs: 40)

14 4 d x[ + αr] + < 0 4) x x x + R Ths way we obtan the result that profts n country the cost-effcent country) decrease, whereas profts n country the hghest cost country) ncrease. Second, we study the stuaton n whch the unform output subsdy n the economc unon s equal to the level of subsdy of the less effcent frm n the non-cooperatve game pre-unon). In ths case, the unform subsdy level s equal to the subsdy of frm n the pre-unon case and therefore lower than the subsdy of frm. That s, the new subsdy does not affect the margnal costs of frm, but t ncreases the margnal costs of frm, gven that the level of subsdy n ths stuaton s lower. So, s < s and s s. Thus, the new subsdy polcy only shfts to the left the reacton functon of frm wth respect to the prevous stuaton. Ths mples that the producton of ths frm wll decrease whle the producton of frm wll ncrease. However, n ths case we expect a reducton n the total producton. Proposton 6: A level of subsdes n the economc unon equals the pre-unon subsdy level of the hgher-cost frm: ) Decreases the producton of the frm wth lower costs. ) Increases the producton of the frm wth hgher costs. ) Decreases the total producton. v) Increases the profts of the frm wth hgher costs. v) Decreases the profts of the frm wth lower costs. Proof: ) Decreases the producton of the frm wth lower costs: Dfferentatng the frst order condton of frm wth respect to and s : + α R > 0 44) p [ + R] snce the dervatve s postve, a reducton n the subsdy to frm wll reduce ts producton. ) Increases the producton of the frm wth hgher costs: Dfferentatng the frst order condton of frm wth respect to and x : x x + α + α R < 0 R gven the negatve relatonshp between outputs, the reducton n the output 45)

15 5 of frm causes an ncrease n the output of frm. ) Decreases the total producton: + + > 0 p [ + R 46) ] as the above expresson s postve, a reducton n the subsdy to frm wll reduce the total producton. v) Increases the proft of the frm wth hgher costs: d [ + α R] x + < x x x + R 0 47) as the above expresson s negatve, a reducton n the subsdy to frm, ncreases profts of frm. v) Decreases the proft of the frm wth lower costs d + αr x x + > 0 48) x x s x + R as the above expresson s postve, a reducton n the subsdy to frm decreases profts of frm. Therefore, we obtan the result that profts n country the cost-effcent country) decrease, whereas profts n country the less effcent country) ncrease. IV. Conclusons In ths paper we show the mportance of cost asymmetry and demand elastcty for subsdy polcy n the case of an economc unon n the context of the ''thrd-market'' model proposed by Brander and Spencer [985]. We compute the optmal subsdy level n an economc unon of the two producng countres and the mportng country under the assumpton of unform subsdes for both frms, ndependently of the exstence of asymmetres n costs. We fnd that the optmal subsdy n the economc unon can be negatve a tax) f frms have dfferent costs and the demand s concave. Of course, we obtan ths result neglectng cost asymmetry between prvate and socal costs, that s, assumng that the socal cost of publc fun s unty. Another mportant queston s the amount of the total subsdy that each country has to pay. In ths paper we assume that the subsdy s pad by the common economc authorty, regardless of the proporton correspondng to each of the three countres. Part of our current research agenda s the ntroducton of asymmetry between prvate and socal costs n an economc unon plus takng nto consderaton the proporton of the amount of subsdy that each country n the unon s able to pay.

16 6 As a result, we fnd that the output and hence the prce) n the economc unon wth the optmal subsdy s the perfectly compettve one, ndependently of the demand curvature. When comparng the economc unon case wth the non-cooperatve strategc polcy game, we fnd that, when costs are symmetrc, the optmal unform output subsdy level n the unon s greater than n the non-cooperatve case for any curvature of the demand functon. We also show that, wth asymmetres n costs and a lnear demand, the optmal subsdy n the unon s larger than the optmal subsdes of the frms n the prevous stuaton. We study two partcular cases, when the unform output subsdy s equal to the subsdes receved by each frm n the pre-unon proft-shftng export subsdy stuaton. We obtan the new subsdy polcy n the economc unon unform output subsdy) favours the less effcent frm compared to the pre-unon non-cooperatve export subsdy stuaton. Appen In ths appen we present a lnear verson of the model. Let x x + x be the total output and p a x be the nverse demand functon, wth a 0. Let s be the subsdy per unt of output receved by frm and M be the total amount of money to be pad by country. The proft functon of frm s > x, x, s ) a c x) x + s x A.) and gven that there s no consumpton n the producng countres, the socal welfare of country, for,, only depen on frm's profts and the value of subsdy payments, and t s defned as: x, x, s ) x, x, s ) M A.) whereas the socal welfare of country s: x ax a x) x M A.) Wthout loss of generalty, we assume that the frm n country s more effcent than the frm n country,. e., c. Let A a c and ta a c. We assume that A > 0 and t, ), where < c t can be nterpreted as a measure of the cost dfferences between the frms. 9 Let x, s, s ) be the total socal welfare obtaned as the sum of the welfare of the three countres. 9 Ths assumpton s necessary n order to ensure that, n the case of the countres competng n subsdes, the output of the less effcent frm s postve.

17 7 We now focus on the relatonshp between a stuaton n whch countres compete n subsdes wth a stuaton n whch the three countres decde to form an economc unon wth a common economc authorty that decdes a common level of subsdes for both frms n order to maxmze the ont socal welfare of the three countres. Non-cooperatve subsdes: We denote the Nash equlbrum varables n ths stuaton wth the superscrpt nu non-unon). The Nash equlbrum subsdes, output and profts subsdes for each frm are s nu x nu At ), s 5 nu A t) 5 At ) nu A t), x A.4) nu [ At ) ], [ A t ] nu ) The noncooperatve Nash subsdy equlbrum s characterzed by postve producton subsdes n both producng countres. However, the more cost compettve frm gets the hgher level of subsdy and the subsdy dfferental equals the producton cost dfferental see Neary, 994). In ths stuaton, each of the producng countres pays the total amount of subsdes to ts nu nu nu nu frm and country pays nothng. Therefore, M s x for, and M 0. Operatng, the total socal welfare at the Nash equlbrum for the three countres s nu 4 A 7t t + 7) 5 A.5) As t s shown by Colle [99], the socal welfare of the producng countres wll usually be lower at the Nash equlbrum n producton subsdes than under free trade. Thus, both countres wll usually lose f there s a trade war as Bhagwat [988] clamed. Only wth sgnfcant cost dfferences t s possble that the most effcent country wll be better off at the Nash equlbrum n export subsdes than under free trade. Fnally, country ncreases ts socal welfare gven that the subsdes decrease the prce and ncrease the total output. Economc non: In the stuaton n whch the three countres decde to form an economc unon, we assume the exstence of a common economc authorty. Ths common authorty decdes a common level of subsdes for both frms such that the socal welfare of the economc unon s maxmzed. As before, we assume that the decson on the level of subsdy s rreversble and pror

18 8 to the decson of frms on output. We denote the equlbrum varables n ths stuaton wth the superscrpt the three countres n the economc unon). We assume that there s a ont fnancal responsblty by the countres n the unon. The socal welfare functon n ths case s defned as: s) x, x, s) + x, x, s) + x, s) M A.6) where M M, gven the fnancal responsblty n the unon. The Nash equlbrum common subsdy, output and profts of each frm n the economc unon are: s x A t ) 4 + A t ) A t), x A.7) [ At ) ], [ A t ] ) As we can observe, the optmal subsdy, output and profts of both frms n the economc unon of the three countres are larger than the equlbrum values n the non-cooperatve export nu subsdy game s > s > s countres s [ ] t, 9 nu ). Operatng, the Nash equlbrum total socal welfare for the three A 5t 6t + 5) A.8) 8 Comparng the total socal welfare n both stuatons, we obtan that there are values of t ) for whch the total socal welfare n the economc unon s greater than the total socal welfare n the pre-unon stuaton. Moreover, the total socal welfare n the economc unon s always larger than that n the free trade no subsdes) stuaton. References Balassa, B. [96], The Theory of Economc Integraton, Homewook, Irwn. Bandyopadhyay, S. [997], Demand elastctes, asymmetry and strategc trade polcy, Journal of Internatonal Economcs 4; pp Bhagwat, J. [988], Protectonsm, MIT Press, Cambrdge. Brander, J. [995], Strategc trade polcy, Handbook of Internatonal Economcs, vol. III, edted by G. Grossman and K. Rogoff, Elsever Scence BV.

19 9 Brander, J. and Spencer B. [985]: Export subsdes and nternatonal market share rvalry, Journal of Internatonal Economcs 8; pp Colle, D. [99], Proft-shftng export subsdes and the sustanablty of free trade, Scottsh Journal of Poltcal Economy, 40; pp De Meza, D. [986], Export subsdes and hgh productvty: Cause or Effect? Canadan Journal of Economcs 9; pp Gruenspecht, H. [988], Export subsdes for dfferentated products, Journal of Internatonal Economcs 4; pp Hne, R. [994], Internatonal economc ntegraton, n Surveys n Internatonal Trade, edted by D. Greenaway y L., Wnters, Blackwell. Neary, J. [994], Cost asymmetres n nternatonal subsdy games: Should governments help wnners or losers?, Journal of Internatonal Economcs 7; pp