Market Size, Cannibalization and Policy Competition for a. Multiproduct Multinational Firm

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1 Market ze, Cannbalzaton and Polcy Competton for a Multproduct Multnatonal Frm Q Duan *, Je Ma ** and Yang Yue *** (Pekng Unversty) July 1, 011 Abstract Ths paper studes polcy competton for a foregn-owned multproduct monopolst frm producng two products that are horzontally dfferentated between two countres of dfferent sze. We show that the equlbrum outcome of FDI competton s determned by the nteracton between the market sze effect and the cannbalzaton effect, and countres subsdy polces. Welfare effects of competton for FDI are derved; n partcular, we show that the competng countres may Pareto strctly gan from or Pareto strctly lose from FDI competton. Key Words: Foregn drect nvestment (FDI); Polcy competton; Market sze; Cannbalzaton; Welfare JEL Classfcaton: F; F3; H5; H73; L * Department of Appled Economcs, Guanghua chool of Management, Pekng Unversty, ejng , Chna. ** Correspondng author. Department of Appled Economcs, Guanghua chool of Management, Pekng Unversty, ejng , Chna; E-mal: jema@gsm.pku.edu.cn; Phone: +86 (0) ; Fax: +86 (0) *** Department of Appled Economcs, Guanghua chool of Management, Pekng Unversty, ejng , Chna. 1

2 1. Introducton Foregn drect nvestment (FDI) has joned nternatonal trade as a prmary drvng force of globalzaton and t grows much faster than ether trade or ncome n recent decades. 1 As key players n globalzed economes, multnatonal frms typcally produce a vast range of consumer goods. For nstance, Volkswagen Group, va ts Volkswagen Group Chna dvson, has 14 subsdares n Chna, wth hangha Automotve Industry Corporaton (AIC), and Frst Automoble Works (FAW) beng the two major Chnese partner companes. Volkswagen Group Chna enjoys sales of about 1.9m cars n the Chnese market n 010 and s the largest foregn carmaker. The products of AIC nclude VW brands: Tguan LW, Touran, Passat ew Lngyu, Lavda, Polo (hatchback and notchback), Cross Polo, antana and antana Vsta; and Škoda brands: Octava, Faba and uperb. The products of FAW consst of VW brands: Jetta A, ew ora, Golf, agtar, Magotan and Volkswagen CC; and Aud brands: A6L, A4L and Q5. On the other hand, durng the past twenty years, polcy competton for attractng FDI has become commonplace. 3 For nstance, Changchun and hangha fercely competed for the locaton of Toyota s nnth jont venture plant n Chna n 009. hangha won the plant and t wll produce economy famly cars, possbly Aygo and Q, for Chna and Thaland from 0. 4 Regons or countres have an economc ncentve to attract foregn nvestors snce possble benefts of FDI nclude job creaton, technologcal spllover and mport substtuton effects. In addton, when a regon or country succeeds n attractng FDI n one sector, t can 1 ee arba avarett and Venables et al. (004), Chapter 1. ee oth AIC and FAW are stated-owned enterprses. The head offce for AIC s n hangha, whle that for the FAW s n Changchun, the captal cty of Jln Provnce, Chna. 3 For an overvew of polcy competton for foregn drect nvestment, see UCTAD (1996), Oman (000), Charlton (003) and arba avarett and Venables et al. (004). 4 Although Changchun lost the plant, as a state-owned enterprse FAW exerted hgh pressure on Toyota. As a result, Toyota decded to expand the capacty of Fengyue plant, ts jont venture plant wth FAW n Changchun. Fengyue wll be opened up n 013 and ts product lnes wll nclude Rez, Prus, etc.

3 help encourage other manufacturng ndustres to follow and unleash a flow of new nvestments to that regon or country. Thus, the benefcal effects of FDI wll be renforced. At the same tme, there are also a number of reasons why multnatonal frms wsh to launch new overseas plants. The nvestments may be drven by the market seekng motve. The access to cheap nputs and resources, such as labor, both unsklled and sklled, land, raw materals and parts and components for assemblng nto fnal goods s also relevant. When evaluatng possble nvestment locatons, multnatonal frms may also have a logstcal concern. 5 The outcome of FDI competton s determned by the nteracton between these factors. In ths paper, we study polcy competton for a foregn-owned multproduct monopolst frm producng two products that are horzontally dfferentated between two countres of dfferent sze. 6 We ask the followng questons. On the postve sde, () under what condton wll a country wn part or all of producton of the multnatonal frm? () how s the equlbrum subsdy for attractng FDI determned? On the normatve sde, () s allocatve effcency acheved? () what s the dstrbuton effect of competton for FDI? () compared to the case when countres do not provde any fnancal ncentve to attract FDI, whether does FDI competton Pareto mprove or Pareto deterorate natonal welfare of the competng countres? We show that whether a country wll wn part or all of producton of the multnatonal frm s determned by the nteracton between the market sze effect, the cannbalzaton effect and mport substtuton effects. The frst two effects determne the multnatonal frm s nvestment premum of a partcular locaton of producton; whle mport substtuton effects determne two countres wllngness to pay to attract part or all of producton of the multnatonal frm. We also characterze the condton under whch the wnnng country wll 5 For nstance, see the case of Intel s nvestment n Chna, Wall treet Journal Asa, March 3-5, ote that we may renterpret the two horzontally dfferentated goods as two product lnes, whch consst of one good respectvely. In addton, countres can be easly renterpreted as regons / jursdctons n our paper. 3

4 subsdze/tax the multnatonal frm. On the welfare effects of FDI competton, we frst show that allocatve effcency s acheved when countres engage n competton to attract the multnatonal frm. After analyzng ts dstrbuton effect, we show that the competng countres may Pareto strctly gan from or Pareto strctly lose from competton for FDI. Our analyss has mportant mplcatons for nternatonal nvestment polcy. There s a polcy debate about the possble effects of bddng war for frms on the competng countres. The advocates of FDI competton argue that tax competton s better than tax harmonzaton snce the latter s a governmental tax and spendng cartel, whch s as objectonable as a prvate cartel. On the other hand, the opponents argue that competton for FDI results n a pure waste of resources of the competng countres. In addton, t may weaken publc fnances and dstort the locaton of nvestment. Our analyss suggests that FDI competton may strctly Pareto mprove natonal welfare of the competng countres when they compete for multproduct multnatonal frms and at the same tme the cannbalzaton effects are suffcently great. If ths s the case, there s no need for callng for tax harmonzaton. On the other hand, competton for FDI wll strctly do harm to the competng countres when they do not dffer that much n sze and the cannbalzaton effects are suffcently small. As a result, Multnatonal frms wll receve a transfer from host countres. Ths calls for nternatonal cooperaton to contan excesses of polcy competton for FDI. Related Lterature Ths paper s among the frst papers studyng polcy competton for multproduct multnatonal frms and relates to several strands of lterature. 7 There have been nterestng contrbutons whch consder two asymmetrc countres competng for a proft-maxmzng sngle product multnatonal frm from the rest of the world, and have trade costs and 7 ased on recent emprcal evdence that has hghlghted how the export patterns of multproduct frms domnate world trade flows, and how they respond to dfferent economc condtons across export markets by varyng the number of products they export, Mayer et al. (011) study the effects of export market condtons on the relatve export sales of products: they refer to ths as the frm s product mx choce. Also see references they cte. 4

5 mperfect competton as the basc buldng blocks for the partal equlbrum analyss. Haufler and Wooton (1999) consder the case where two countres dffer n sze. In arros and Cabral (000), besdes dfference n sze, a new asymmetry s ntroduced nto the analyss,.e., the small country suffers from problems of unemployment, whle the large country does not. jorvatn and Eckel (006) consder the stuaton where two countres not only dffer n sze, but also dffer n market structure,.e., there s a domestc frm located n the large country, whch produces the same good as the foregn frm does, whle ths s not the case n the small country. Fumagall (003) examnes the case where two countres of dfferent levels of technology compete for the locaton of a foregn-owned frm. 8 Raff (004) extends the above two-country framework to consder how free-trade agreements and customs unons affect the locaton of FDI and socal welfare, takng nto account that governments may adjust taxes and external tarffs to compete for FDI. Haufler and Wooton (006) also extend the two-country framework to analyze the effects of a regonally coordnated proft tax or locaton subsdy n a model wth three actve countres, one of whch s not part of the unon, and a globally moble frm. ehrens and Pcard (008), and ucovetsky and Haufler (008) study bddng war for frms n the context of the endogenous presence of horzontal multnatonal frms. 9 ehrens and Pcard (008) develop a two-country model of subsdy competton n whch utltaran governments non-cooperatvely bd for frms by taxng/subsdzng setup costs n order to maxmze ther resdents consumpton surplus and proft clams. Frms choose both the number and the locaton of the plants they operate, and the equlbrum market structure s affected by governments subsdy polces. ucovetsky and Haufler (008) present a model where frms endogenously choose a natonal or a multnatonal form, n response to the tax 8 he assumes that the market sze s equal n both countres, and hence does not consder the market sze effect n the paper. 9 In these papers, natonal frms refer to the frms producng goods only n the domestc countres, whle multnatonal frms refer to the frms producng goods both n the domestc country and n the foregn country. They are sngle product frms rrespectve of ther organzatonal form. 5

6 advantage accord to a multnatonal status. Governments are able to commt to long-term tax dscrmnaton polces before frms decsons are made and before statutory captal tax rates are chosen non-cooperatvely. 10 Our paper dffers from the above contrbutons manly n that we consder polcy competton for a multproduct rather than a sngle product multnatonal frm; and study FDI locaton choce, the equlbrum subsdy polcy and welfare. 11 Ths paper s also related to the lterature of tax competton for moble captal n tradtonal publc fnance, such as ucovetsky (1991), Wlson (1991), Kanbur and Keen (1993), and Trandel (1994). In a perfectly compettve envronment, t ntroduces asymmetres between countres and studes the nteracton of dfferent tax nstruments. However, snce proft-maxmzng frm s dfferent from moble captal, thus, as Fumagall (003) notes, ths approach s more approprate when dealng wth competton for portfolo nvestments rather than for FDI. The remander of the paper proceeds as follows. ecton sets out the model. Follows equlbrum and welfare analyss. ext, we compare our results wth those establshed n prevous contrbutons on polcy competton for FDI. The fnal secton concludes. ome proofs are contaned n the Appendx. 10 Amergh and Peralta (010) consder the stuaton where a frm servng two unequally-szed jursdctons must choose the locaton of ts frst producton plant, and decde whether to open a second plant to serve the other market through local sales rather than exports. As an exporter, t pays taxes only to the regon where t locates ts producton plant. A double-plant mult-regonal frm pays taxes n both regons; however, t may shft taxable profts across two regons at a cost. ote that the frm they consder s a sngle product frm. 11 Haaparanta (1996) uses a common agency approach to studyng competton for FDI between two countres wth unequal wage rate. oth countres face problems of unemployment and wll gan from FDI from ncreased employment (reduced unemployment). He treats FDI as beng perfectly dvsble and consders the mpact of polcy competton on how the foregn frm allocates ts captal between the competng countres. Ths dfferentates hs paper from our paper and other prevous contrbutons cted. ee Wlson (1999) and Wlson and Wldasn (004) for surveys of tax competton lterature. 6

7 . Model A regon conssts of two countres of dfferent sze. The number of households n Country s, whle t s n country, wth. 13 Representatve households of the two countres share the same utlty functon: 1 1,, u q q z q q b q q q b q z (1) where q 1 and q are consumptons of two dfferentated products, and z s the consumpton of a numerare good; b 1 measures the degree of product dfferentaton,,. In each country, each household provdes one unt of labor and receves a wage. Assume that wage rates across two countres are equal and the common wage rate s denoted by w. Households wage ncome may be subject to a lump-sum tax. (If t s negatve, t s a lump-sum subsdy.) Hence, representatve households total expendture cannot exceed ts wage ncome mnus/plus taxes/subsdes. The nverse demands of country s representatve household are gven by p1 1bq1 q, p 1bq q1 whle the drect demands are gven by 1 1, q b1bp p1 b 1 q b bp p b 1 1 where p 1 and p denote the prces of the two dfferentated products n country. Country s aggregate demands for products 1 and are: 1 1, Q b1bp p1 b 1 Q b bp p b 1 1 whle those of country are: 1 1, Q b1bp p1 b 1 Q b bp p b 1 1 A multnatonal frm from the rest of the world ntends to make an nvestment n the regon n order to servce the regonal demand. Ths may be due to that transportaton costs 13 ote that we may normalze the market sze of the small country to be 1, and hence nterpret the market sze of the bg country as the relatve market sze of the two countres. ee later dscusson. 7

8 assocated wth exportng the dfferentated goods to the regon are prohbtvely hgh, so that n order to supply the regonal market the multnatonal frm needs to go for FDI. 14 Denote the multnatonal frm s FDI locaton choce by a vector:, j,, j,, where the frst component means that the multnatonal frm locates the producton of q 1 n country ; whle the second component means that t locates the producton of q n country j. (As noted n the Introducton, two dfferentated goods can be renterpreted as two product lnes. We use product lne and good/product nterchangeably n the followng analyss.) Therefore, the multnatonal frm has four possble locaton choces:,,,,,,, In order to produce any one of the dfferentated products, the multnatonal frm frst needs to establsh a producton lne. After payng the fxed set-up cost, t uses one unt of labor to produce one unt of the dfferentated product. We also assume that the fxed cost of settng up any product lne s F 0 rrespectve of ts locaton. 15 Two markets are segmented and as a result when the multnatonal locatng the producton of good k n one country and sellng t n another country, t needs to pay a transportaton cost per unt, 0. Hence, the generalzed margnal cost for the multnatonal frm to sell good k n country s gve by ck, and j j,,, ; c j w c j w 1 1 c, j w, c, j w. 14 The reasons for makng ths assumpton are as follows. The trade versus FDI choce s well understood from the lterature on trade costs and foregn drect nvestment. ee eary (009) for a recent survey. It s not the focus of our paper. 15 We make ths assumpton n lne wth prevous contrbutons. Allowng for dfferences n fxed nvestment costs would have obvous effects on the FDI locaton choce. All else beng equal, the low cost country becomes a relatvely more attractve locaton. 8

9 Here, / j, f / j ; / j, f / j. We suppose w 1. Ths guarantees that the multnatonal frm s able to servce both countres demand rrespectve of ts locaton choce. The two countres and the multnatonal frm play a two-stage game of complete nformaton. In the frst stage, two countres smultaneously announce lump-sum subsdes s,, to the multnatonal frm (condtonal on t locatng part or all of producton n ther terrtores). 16 nce the budget of a government must be balanced, the subsdy pad to the multnatonal frm s fnanced by a poll tax. 17 In the second stage, the multnatonal frm makes ts locaton choce and then servces the regonal demand. The multnatonal frm receves ts profts plus/mnus subsdes/taxes. The two countres receve natonal welfare, W u, mnus/plus subsdes/taxes. efore gong further, note that both countres may beneft from FDI and have an economc ncentve to attract FDI smply because of mport substtuton effects n our model. Ths s true when b. In order to smplfy analyss, we consder the case where b. 18 In addton, snce the two dfferentated products enter nto the representatve households utlty functon n a symmetrc way, and the technologes for producng the two dfferentated products are the same, FDI locaton choces, and, are equvalent. Hence, we consder three possble locaton choces:,,,, n the followng analyss. ext, we solve the model from backward. and 16 It s a lump-sum tax f s s strctly negatve. 17 When a country collects taxes from the multnatonal frm, t redstrbutes the revenues among ts households as a poll subsdy. 18 We can show that the results obtaned n the paper carry over to the case where b. 9

10 3. Equlbrum Analyss We frst consder the benchmark case where two countres do not engage n FDI competton,.e., s 0,,,. We smply determne what the proft-maxmzng FDI locaton choce s. When the multnatonal frm chooses a locaton to supply the regonal demand, t receves: where p and k p,, k 1, k ck qk F () equlbrum prce, sales and profts wll be: q denote good k s prce and sales n country. The k q k p k 1c k (3) 1 ck1c k (4) 6 1c 1 1 k ck c k,, 1, 6 F (5) k In partcular, w w w 1 w w w,, F 6 6 (6.1) 1w 1w, F (6.) 1w 1w, F (6.3) nce t s straghtforward to show,,,.e., the multnatonal frm wll not locate producton of both goods n the small country, we need to compare the profts recevng when t choosng, wth those recevng when t choosng,. In other words, the multnatonal frm s decson problem s that gven one good, say good 1, s produced n the bg country, whether should the other good, say good, be produced n the bg country or n the small country? Defne 1 w 1,, (7) w

11 s the multnatonal frm s nvestment premum when t locatng the producton of both goods n the bg country. Obvously, t wll choose, demand f and only f the nvestment premum s nonnegatve. 19 to servce the regonal Proposton 1 0 f and only f 1 w (8) 1 w Proof. Condton (7) mples the Proposton mmedately. The forces that drve the nvestment premum are market sze effect and cannbalzaton effect. On the one hand, other thngs beng equal, the multnatonal frm prefers producng both goods n the bg country to producng them n the small country snce shppng goods from one country to another country ncurs transportaton costs. Call ths the market sze effect. On the other hand, when both goods are produced n the bg country, they cannbalze each other sales both n the bg country and n the small country. All else beng equal, the multnatonal frm should allocate the producton of the two goods n dfferent countres n order to allevate the cannbalzaton effect. 0 The multnatonal frm s equlbrum locaton choce s determned by these two effects together. Consder the market sze effect and the cannbalzaton effect of the multnatonal frm shftng the producton of good from the small country to the bg country. efore dong ths, the multnatonal frm s profts recevng from good 1 are: w w w w w 1w , 6 6 When the producton of good has been shfted to the bg country, the multnatonal frm s profts recevng from good 1 are: 19 We prescrbe that when the nvestment premum s zero, the multnatonal frm chooses to locate the producton of both goods n the bg country. 0 ee aldwn and Ottavano (001). 11

12 1w 1w 1, Obvously, the above proft change s due to cannbalzaton effect only, call t CE 1 CE 1w 1w 1 0 When the producton of good s shfted to the bg country, the multnatonal frm s profts recevng from good are drven by both the market sze effect and the cannbalzaton effect. efore movng the producton of good to the bg country, the profts t receves from good are: w w w w 1w 1 1 1w 1 1, 6 6 After shftng producton, t receves from good : 1w 1w, We dvde the proft change nto the market sze effect and the cannbalzaton effect. In order to get the market sze effect, we frst control the cannbalzaton effect. ote that the magntude of the cannbalzaton effect s affected by the generalzed margnal costs of supplyng products 1 and. Assume that after movng the producton of good to the bg country, the low-cost good faces a hgh-cost good 1 n the bg country; whle the hgh-cost good faces a low-cost good 1 n the small country. 1 ow, the profts the multnatonal frm receves from good are: w w w w w 1w , 6 6 Wth the help of ths experment, we get the market sze effect: 1w 1w 6 ME,, 0 1 efore shftng producton, the low-cost good faces the hgh-cost good 1 n the small country, whle the hgh-cost good faces the low-cost good 1 n the bg country. What we have done n the text keeps the generalzed margnal costs of the two products n each market stll beng dfferent and n ths sense, we have controlled the cannbalzaton effect. We may control the market sze effect and get the cannbalzaton effect at the frst place.

13 and the cannbalzaton effect s gven by: 1 w 1 CE,, 0 w In summary, the market sze effect of the multnatonal frm shftng the producton of good from the small country to the bg country, callng t ME, s gven by whle the cannbalzaton effect s gven by 1w 1w 6 0 ME ME, CE CE 1w 1w For convenence, we use the absolute vale of CE1 CE to denote the cannbalzaton effect, callng t CE. It turns out when the condton (8) holds, the market sze effect domnates the cannbalzaton effect, and the multnatonal frm locates the producton of both goods n the bg country. Otherwse, t locates the producton of dfferent goods n dfferent countres. ext, we turn to dscuss the welfare mplcatons of the multnatonal s FDI locaton choce and want to know whether ts choce acheves allocatve effcency. Allocatve effcency requres that the multnatonal frm s FDI locaton choce should maxmze ts profts and two competng countres natonal welfare. From prevous dscusson, two countres natonal welfare correspondng to each of the multnatonal frm s locaton choces s easly calculated: 13 1 w W, w (9.1) w w w w , 4 W w (9.) 1w W, w (9.3) 1 w W, w (10.1) w w w w , 4 W w (10.)

14 1w W, w (10.3) It s easy to show:,,, W W W and,,, W W W We defne,, 1w1w W W 4 (11.1),, 1w1w W W 4 (11.) measures the net benefts of the bg country by hostng the producton of both goods rather than one good, whle measures the net benefts of the small country by hostng the producton of one good rather than mportng both goods from the bg country. 3 Proposton When countres do not engage n competton for FDI, allocatve effcency s acheved. 1 Proof. When w 1w country. Frst of all, t s easy to see, the multnatonal frm chooses to produce both products n the bg,,,,,, W W W W 0 In addton, t s also straghtforward to show W, W,, W, W,, 0 Hence, allocatve effcency s acheved when the multnatonal frm chooses to locate the 1 producton of both goods n the bg country. When w 1w, the multnatonal frm 3 Ths mples that both countres have an economc ncentve to compete for FDI due to the mport substtuton effects. 14

15 chooses to produce one product n one country. Usng smlar arguments, we can establsh that allocatve effcency s acheved. Fgure 1 We use Fgure 1 to brefly summarze dscusson of the above subsecton. The horzontal axs measures the unt transportaton cost, whle the vertcal axs measures the relatve market 1 sze. The upward slopng curve represents the case where w 1w, and t dvdes the plane nto two regons. When parameter confguratons fall nto regon I, the multnatonal frm chooses to produce both products n the bg country, whle when parameter confguratons fall nto regon II, t locates the producton of dfferent goods n dfferent countres. In any case, allocatve effcency s acheved. Polcy competton for FDI Let us turn to dscuss polcy competton for FDI. In the last stage of the game, after observng two countres lump-sum subsdy polces, the multnatonal frm smply makes ts locaton choce to maxmze ts profts plus subsdes. 4 In the frst stage, two countres play a 4 Its equlbrum prce-quantty decson s not affected by two countres lump-sum subsdy polces, and t s the same as that n the benchmark case. 15

16 ash subsdy game. Instead of dervng two countres best responses, then characterzng ash equlbra, we use a smple and ntutve way to approach the soluton. 5 As the frst step, note that the small country s not able to attract the multnatonal to locate the producton of both goods n ts terrtory n an equlbrum outcome. Lemma 3 When two countres engage n FDI competton, FDI locaton choce,, cannot emerge n an equlbrum outcome. Proof. ee Appendx., The small country s net gans when the multnatonal frm changng ts locaton choce from, to, are strctly domnated by those of the bg country when the multnatonal frm changng ts locaton choce from, to, Compared to the locaton,, choosng locaton,,., the multnatonal frm s nvestment premum when, s strctly negatve. Hence, the small country cannot wn two product lnes n an equlbrum outcome. Accordng to Lemma 3, the analyss s much smplfed. nce the possble FDI locaton that wll emerge n an equlbrum outcome s, or,, t seems that two countres compete for one product lne only. ote that the small country s subsdy payment condtonal on the multnatonal frm choosng, s should not exceed ts net gans,, The smlar argument apples to the bg country and,, s s The RH of the above expresson represents the bg country s valuaton for the addtonal product lne, whle LH represents the extra payment should be made n order to attract t. 5 The full characterzaton of ash equlbra of the frst stage of the game s avalable upon request. 16

17 ased on the above arguments, we have the followng result on the equlbrum locaton of FDI. Proposton 4 The bg country wll attract both product lnes f and only f ( ME CE) ( ) 0 () Otherwse, two countres attract one product lne respectvely. Moreover, t s straghtforward to show ( ME CE) ( ) 0 f and only f condton (8) holds. 6 ext, we turn to dscuss two countres equlbrum payments to the multnatonal frm. Proposton 5 (1) In the case where the bg country attracts both product lnes, ts equlbrum payment to the multnatonal frm s: 1 w, 3 1 w s (13) () In the case where two countres attract one product lne respectvely, the bg country s equlbrum payment s: whle that of the small country s: Proof. ee Appendx. 1 w, 3 1 w 3 s (14.1) w, 3 1 w 3 s (14.) Ths s because we consder a monopoly model wth lnear demand functons and the monopolst frm s generalzed margnal producton costs are constants, so that the monopolst frm s profts recevng from the sale of one product n one country and the country s consumpton surplus dervng from the product are proportonate. Consderng other forms of demand may make us have more case to analyze; however, the basc drvng forces that we address are stll there and our results cannot be changed qualtatvely. 17

18 In the frst case, the bg country wll choose a payment as low as possble such that the small country s not able to attract one product lne or two product lnes to ts terrtory. In the second case, note that two countres subsdy polces must prevent both the small country and the bg country from attractng both product lnes to ther terrtores. ased on ths argument, we can pn down two countres equlbrum payments. 7 When the bg country wns two product lnes, note that when 3, ts equlbrum payment s negatve and t collects a lump-sum tax from the multnatonal frm. When 3, ts equlbrum payment s postve and t pays a lump-sum subsdy to the multnatonal frm. It s easy to establsh that other thngs beng equal ts equlbrum payment to the multnatonal frm ncreases wth the small country s sze, whle decreases wth ts own sze. When t collects taxes from the multnatonal frm, the tax revenues ncrease wth the per unt transportaton cost; whle n case where t pays a subsdy to the multnatonal frm, the subsdy ncreases wth the per unt transportaton cost. When two countres attract one product lne respectvely, frst consder the equlbrum 31 payment of the bg country. ote that t s postve when 31 when w 1w w 1w ; whle t s negatve. It s easy to show that agan other thngs beng equal the bg country s equlbrum payment to the multnatonal frm ncreases wth the small country s sze, whle decreases wth ts own sze. Agan, when t collects taxes from the multnatonal frm, the tax revenues ncrease wth the per unt transportaton cost; whle n case where t pays a subsdy to the multnatonal frm, the subsdy ncreases wth the per unt transportaton cost. 1 ext, consder the equlbrum payment of the small country. When 1 negatve; whle when w 31w w 31w, t s, t s postve. It s straghtforward to show that other thngs beng equal the small country s equlbrum payment to the multnatonal frm ncreases wth the bg country s sze, whle decreases wth ts own sze. When t collects taxes 7 ote that the equlbrum subsdy payments are affected by the absolute measure rather than the relatve measure of the two countres sze. Also see Footnote

19 from the multnatonal frm, the tax revenues ncrease wth the per unt transportaton cost; whle n case where t pays a subsdy to the multnatonal frm, the subsdy ncreases wth the per unt transportaton cost. 4. Welfare Analyss In ths secton, we consder the welfare mplcatons of FDI competton and want to ask the followng questons. Frst, s allocatve effcency acheved? econd, what are the dstrbuton effects of FDI competton for the competng countres as a whole? Thrd, compared to the benchmark case, does FDI competton Pareto mprove/deterorate natonal welfare of the competng countres as a whole? The frst queston s answered n Proposton 6. Proposton 6 When countres engage n FDI competton, allocatve effcency s acheved. Proof. ote that the equlbrum payments made by countres to the multnatonal frm are lump-sum transfer payments. Hence, smlar arguments to those used n the proof of Proposton establsh the result stated n the proposton. That FDI competton wll acheve allocatve effcency s a well known result obtaned n the contrbutons consderng polcy competton for a sngle product frm. 8 We show that ths result carres over to the case when countres compete for multproduct multnatonal frms. ext, we turn to the dstrbuton effect of FDI competton. 1 Proposton 7 Consder the case when w 1w,.e., the multnatonal frm produces both products n the bg country. Compared to the benchmark case, (1) the small country s natonal welfare s unchanged; () whle the bg country benefts from FDI competton f and only f 3; when 3, t loses from t. 8 For nstance, see jorvatn and Eckel (006). 19

20 Proof. Part (1) s establshed by the fact that regardless of whether countres engage n FDI competton, the multnatonal frm chooses to produce both goods n the bg country when 1w 1w. Part (). In the case consdered, the bg country wns two product lnes and when 3, t collects a lump-sum tax from the multnatonal frm, hence, ts natonal welfare s strctly hgher than that n the benchmark case. When 3, t pays a lump-sum subsdy to the multnatonal frm, hence, ts natonal welfare s strctly lower than that n the benchmark case. 1 Proposton 8 Consder the case where w 1w,.e., the multnatonal frm chooses to produce dfferent goods n dfferent countres. Compared to the benchmark case, (1) natonal 1w welfare of the small country wll be mproved by FDI competton f and only f ; 1 when w 31w 31w, t loses from t. () natonal welfare of the bg country wll be mproved 31w 31 by FDI competton f and only f ; when 1w w 1w, ts natonal welfare wll be deterorated. Proof. Frst of all note that regardless of whether countres engage n FDI competton, the multnatonal frm chooses to produce one good n one country. Hence, compared to the benchmark case, a country s natonal welfare s mproved when t collects a lump-sum tax from the multnatonal frm; whle ts natonal welfare s deterorated when t pays a lump-sum tax to the multnatonal frm. For the small country, ts equlbrum payment s 1w negatve/postve when / ; whle that of the bg country s negatve/postve 31w when /. 1w 31w An nterestng result mpled by Proposton 7 and Proposton 8 s regardng when competng countres as a whole strctly gan or lose from FDI competton. 0

21 1 Corollary 9 When w 1w,.e., the multnatonal frm chooses to produce dfferent goods n dfferent countres, FDI competton Pareto strctly mprove natonal welfare of the two competng countres, f and only f 31 w 1 w ; t wll Pareto strctly deterorate 1w 3 1w 1w 3 1w natonal welfare of them f and only f. 31w 1w Fgure We brefly summarze our dscusson on polcy competton for FDI wth the help of Fgure. The horzontal axs measures the unt transportaton cost; whle the vertcal axs 1 measures the relatve market sze. Curve F1 represents the case where 1 w 1w. When parameter confguratons are on the left sde of t, fallng nto regon I, the bg country wns 3 both product lnes. The horzontal lne segment F represents the case where and t

22 splts regon I nto two parts. Regon I.1 represents the case where the bg country taxes the multnatonal frm, hence FDI competton weakly Pareto mproves natonal welfare of the competng countres. When parameter confguratons fall nto regon I., the bg country pays a subsdy to the multnatonal frm and competton for FDI weakly Pareto deterorates natonal welfare of the competng countres. Regon II represents the case where two countres attract one product lne respectvely. Here, the downward slopng lne segment F3 31 represents the case when w 1w ; whle curve F4 represents the case where 1w 31w. They together splt Regon II nto three parts. When parameter confguratons fall nto regon II.1, snce two countres pay a subsdy to the multnatonal frm respectvely, FDI competton strctly Pareto deterorates natonal welfare of the competng countres. In regon II., the bg country taxes whle the small country subsdzes the multnatonal frm. Hence, compared to the benchmark case, the bg country s natonal welfare s mproved; whle that of the small country s deterorated. Regon II.3 represents the case where both the small country and the bg country are able to tax FDI, hence competton for FDI strctly Pareto mprove natonal welfare of the competng countres. 5. Dscusson As we have seen n the prevous analyss, ntroducng multproduct multnatonal frms nto the analyss of FDI competton affects the FDI locaton choce, nvestment polcy and welfare n nterestng ways. Our paper both contrbutes and complements the lterature of polcy competton for FDI n a number of respects. When countres do not provde any fnancal nventve to attract FDI, whch country s the attractve locaton for FDI? Our paper shows that when allocatng ts producton among the competng countres, the multproduct multnatonal frm faces a trade-off between the market sze effect and the cannbalzaton effect. If the former domnates the latter, the multnatonal frm chooses to produce both goods n the relatvely large country. If ths s not the case, t allocates the producton of dfferent goods n dfferent countres. Consder papers

23 studyng polcy competton for sngle product multnatonal frms. In jorvatn and Eckel (006), the attractve locaton for FDI s determned by the nteracton between the market sze effect and the competton effect. When the former domnates the latter, the foregn frm wll nvest n the large country, and vce versa. Whle absent polcy competton for FDI, both Haufler and Wooton (1999) and arros and Cabral (000) show that the foregn frm wll establsh a plant n the large country due to market sze effect. In Fumagall (003), the foregn frm wll defntely nvest n the techncally advanced country. In case when countres engage n FDI competton, we show that the relatvely large country has a chance to attract at least one product lne, whle the relatvely small country may attract at most one product lne. When consderng tax competton for a sngle product frm, arros and Cabral (000), jorvatn and Eckel (006) and Fumagall (003) show that both countres has a chance to wn the frm; whle n Haufler and Wooton (1999), the small country wll never wn FDI competton snce the two competng countres only dffer n market sze. 9 Let us turn to dscuss welfare ssues. arros and Cabral (000), Fumagall (003) and jorvatn and Eckel (006) show that allocatve effcency s acheved when countres compete for FDI,.e., from an aggregate perspectve, polcy competton leads to an effcent outcome. Though Haufler and Wooton (1999) do not explore the welfare mplcatons of FDI competton, ther analyss mply ths result as well. We show that ths result carres over to the case where countres compete for a multproduct multnatonal frm. Moreover, an nterestng result that we obtan s that polcy competton for FDI may Pareto strctly mprove or Pareto strctly deterorate natonal welfare of the competng countres. When consderng polcy competton for a sngle product frm, jorvatn and Eckel (006) obtan the result that tax competton for FDI may Pareto weakly mprove the welfare 9 ome papers show that FDI competton ncreases the attractveness of the small country (arros and Cabral (000) and jorvatn and Eckel (006)), or the less technologcally advanced country (Fumagall (003)) as locaton for the nvestment snce ts valuaton of FDI s hgher than that of the other country. As a result, polcy competton may change the FDI locaton choce n these papers. 3

24 of the competng countres. 30 That happens n the case where one of the competng countres does not beneft from the entry of the multnatonal frm; hence, ts valuaton of FDI s strctly negatve. Ths ncreases the barganng power of the other country and may lead to taxaton of FDI rather than subsdes. Our result s derved n the stuaton where both countres have an economc ncentve to attract FDI. ehrens and Pcard (008) show that compared to a world n whch multnatonal frms are dsregarded, the presence of multnatonal frms relaxes the problem of tax competton, hence allevatng the race to the bottom. However, smlar result cannot be obtaned when countres compete for multproduct multnatonal frms snce compared to the case where countres compete for a sngle product frm, they may strctly lose from FDI competton Concludng Remarks We have studed polcy competton for a foregn-owned multproduct monopolst frm between two countres of dfferent sze. We show that the equlbrum outcome of FDI competton s determned by the nteracton between the market sze effect and the cannbalzaton effect, and countres subsdy polces. Welfare effects of competton for FDI are derved; n partcular, we show that the competng countres may Pareto strctly gan from or Pareto strctly lose from competton for FDI. Our model naturally has some lmtatons. We capture the dea that countres beneft from FDI due to mport substtuton effects. In addton, the stuaton that we focus on s relevant for market seekng FDI. We do not consder other possble benefcal effects of FDI, such as job creaton and technologcal spllovers; and do not take nputs or resources seekng FDI nto account. However, to the best of our knowledge, our paper s among the frst 30 Though Haufler and Wooton (1999) do not consder welfare mplcatons of FDI competton, ther analyss mples a smlar result to that of jorvatn and Eckel (006), whle the drvng force s dfferent. 31 ote that ehrens and Pcard (008) do not consder the case where two countres dffer n sze. ucovetsky and Haufler (008) use a tradtonal publc fnance model to study captal tax competton when frms can endogenously choose ther organzatonal form, whch s dfferent from our approach. 4

25 contrbutons ntroducng multproduct multnatonal frms nto polcy competton for FDI models. We want to further explore other mplcatons of ths nterestng dea n our future research. Appendx Proof of Lemma 3 We prove Lemma 3 by contradcton. uppose that the multnatonal frm chooses to produce both goods n the small country n an equlbrum outcome, and the small country s subsdy payment to the multnatonal s s, small country s gross natonal welfare s: the bg country s gross natonal welfare s:. Accordng to Expressons (9.3) and (10.1), the 1 w W, w; 1w W, w. Accordng to Expresson (6.3), the multnatonal frm s profts are: 1w 1w, F. From the prevous dscusson, we know that f the multnatonal frm produces both goods n the bg country, the small country acheves gross natonal welfare: whle that of the bg country s: 1w W, w; 1 w W, w Accordng to Expresson (6.), the multnatonal frm s profts are: 1w 1w, F 5

26 Hence, the subsdy offered by the small country to the multnatonal frm condtonal on t producng both goods n ts terrtory wll not be bgger than ts net gans from the change of FDI locaton,.e., from, to,,,,, 1w 1w s W W. However, note that the bg country s able to choose a subsdy payment, whch satsfes such that,,, s W W,,, 1w 1w 1w 1w s (A1) and attracts both product lnes. In an equlbrum outcome, the equalty holds n the above nequalty, and the bg country s mnmal payment can be solved 1 w 1 w, w 1 w s. Hence, that the small country attracts both product lnes cannot emerge n an equlbrum outcome. Proof of Proposton 5 Part (1). From the proof of Lemma 3, we know that 1 w 1 w, w 1 w s s the mnmal subsdy offered by the bg country, whch can successfully prevent the small country from attractng both product lnes to ts terrtory. Here, we also need to check whether the small country s able to ncrease s,, wth s,, such that to attract one product lne. The bg country may choose a s, to prevent the small country from dong ths, whch satsfes ( ME CE) s, s, 6

27 wth s, s,. Ths s, exsts snce n the case we consder, the followng nequalty ( ME CE) always holds..e. Part (). Frst of all, two countres subsdy polces must satsfy, s,, s, s, 1 w 1 w,,,,, s s s (A) n order to prevent the small country from attractng both product lnes. Here, the bg country s subsdy payment should not exceed ts net gans from the change of FDI locaton,.e., from, to,,,,, 1w1w 4 s W W. mlarly, the small country s subsdy payments must satsfy,,,, 1w1w 4 * * s s W W, (A3) ts net subsdy payment should not exceed ts net gans. Condtons (A) and (A3) together mply 1, 3 w 1 w 3 1 w 1 w 3 s In an equlbrum outcome, the equalty holds n the above nequalty, gvng the mnmal s, that preventng the small country from attractng both product lnes. ext, two countres subsdy polces must satsfy * * * ( ),,, MECE s s s (A4) n order to prevent the bg country from attractng both product lnes. mlar to the above arguments, here 7

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