Strategic Competition and Optimal Parallel Import Policy.

Transcription

1 Strategic Competition and Optimal Parallel Import Policy. Santanu Roy y Soutern Metodist University, Dallas, TX. Kamal Saggi z Vanderbilt University, Nasville, TN. Abstract Tis paper sows tat parallel import policy can act as an instrument of strategic trade policy. We demonstrate tis result in two-country international duopoly were a domestic monopolist competes wit a rival rm in te foreign market if it cooses to incur te xed investment cost of exporting. Te two rms sell orizontally di erentiated goods and compete in prices. Wen te foreign market is signi cantly larger tan te domestic one, te ome rm gains if it is unable to price discriminate; its desire to not deviate too far from its optimal monopoly price in te domestic market makes it (credibly) less aggressive in price competition abroad wic softens price competition and raises pro ts. On te oter and, wen te foreign market is not signi cantly larger, it is optimal for te ome country to forbid parallel imports since international price discrimination yields iger pro ts to te ome rm. We draw out te implications of te two types of parallel import policies for global welfare. Keywords: Parallel Imports, Exports, Trade Policy, Oligopoly, Product Di erentiation, Market Structure, Welfare. JEL Classi cations: F13, F10, F15. We tank co-editor Beverly Lapam and two anonymous referees for teir useful suggestions and insigtful comments. y Department of Economics, Soutern Metodist University, 3300 Dyer Street, Dallas, TX , USA. sroy@smu.edu; Tel: (+1) z Department of Economics, Vanderbilt University, Box 1819-Station B, Nasville, TN , USA. k.saggi@vanderbilt.edu; pone: (+1)

2 1 Introduction Tis paper sows tat a country s policy stance towards parallel imports (PIs) can serve as an instrument of strategic trade policy by altering te beavior of its rm during price competition abroad. 1 It is well recognized tat restrictions on PIs a ect te ability of a monopolist to engage in price discrimination across markets wit consequent welfare implications. Wat is somewat less understood, owever, is te e ect PI policies ave on strategic conduct and rent acquisition by rms engaged in competition in international markets, and ow, in turn, tese considerations in uence te welfare calculus determining optimal PI policies. In particular, wen tere are substantial di erences in market structure and competitiveness across markets, permissive PI policies tat tie te exercise of market power in one country to tat in anoter may signi cantly modify te outcomes of strategic competition. Suc asymmetries across markets often arise due to international di erences in te degree of IPR protection, competition policy, and oter suc policies tat determine market access. In our two-country duopoly model, te products of te two rms are assumed to be di erentiated orizontally on a Hotelling product space. To be able to export successfully, te ome rm must rst incur a xed investment cost tat is irreversible in nature. Te endogeneity of te ome rm s export decision allows us to examines ow te ome country s PI policy a ects te rm s incentive to export. Te timing of decisions is as follows. First, te two governments (ome and foreign) coose teir PI policies: eac government faces a discrete coice to permit or forbid PIs. Next, te ome rm decides weter or not to bear te xed investment cost necessary to export. Finally, rms coose prices if te ome rm exports, rms compete in prices; oterwise eac rm operates as a monopolist in its local market. An important insigt of our analysis is tat, wen PIs are proibited by te ome country, te domestic rm can reduce its price in te foreign market witout a commensurate reduction in its domestic price, and as a result, it becomes a more aggressive price competitor in te foreign market relative to wen PIs are permitted. Wile te freedom to reduce price abroad witout lowering domestic pro ts tends to increase te domestic rm s foreign market sare, it also tends to increase te intensity of price competition and terefore, reduces equilibrium market power in te foreign market. If su ciently strong, tis reduction in market power reduces te export pro tability of te domestic rm and terefore creates a rationale for permitting PIs as opposed to restricting tem. 3 It sould be observed tat tis insigt is 1 Parallel imports arise wen a product protected by some form of intellectual property rigts sold by te rigts older in one country is re-sold in anoter country witout te rigt older s permission. Te incentive to engage in suc trade arises in te presence of signi cant price di erences across countries. Wile muc of te literature on parallel imports assumes a monopoly supplier, tere do exist several analyses of international oligopoly wit integrated and segmented markets were te underlying pricing regime is taken as exogenous: see, among oters, Markusen and Venables (1988), Smit and Venables (1988) and Venables (1990). By contrast, in our model, national parallel import policies endogenously determine weter markets are segmented or integrated. 3 In teir seminal contribution to optimal strategic trade policy under oligopolistic competition, Grossman and Eaton (1986) sowed tat it may be optimal to impose an export tax on te ome rm in order to soften international price competition; our paper indicates tat parallel import policy can play a similar role.

3 novel to te existing literature on PIs tat as tended to focus largely on te monopoly case. 4 To see wy tis matters, note tat if te domestic rm were a global monopolist, ten ceteris paribus, a restriction on PIs sould (at least weakly) increase its incentive to serve te foreign market after all, a monopolist is always free to carge a common price in bot markets if it is pro t maximizing to do so. Tus, by creating te possibility of international price discrimination, a proibition of PIs by a country can only make its monopoly rm better o. We nd tat wen price competition abroad is intense, te ome country is decisive in te sense tat only its PI policy a ects te market outcome. Similarly, wen competition abroad is weak, only te foreign country s policy is consequential. An important result of our analysis is tat, despite te presence of strategic considerations, a country s nationally optimal policy can sometimes be globally optimal, making te need for international coordination over PI policies unnecessary. Tis congruence between national and global welfare obtains wen te ome country is decisive and te xed costs of exporting are not too large so tat inducing exports is nationally as well as globally optimal. Interestingly, we sow tat suc a protrade (i.e. export inducing) PI policy is not unique; rater, underlying parameters determine weter permitting or proibiting PIs induces exports. On te oter and, wen te foreign country is decisive, it always cooses to permit PIs. Suc openness to PIs on its part can not only deter te ome rm from exporting, but can also lower overall world welfare wen te xed cost of exporting is not too large. By sowing tat openness to PIs is not necessarily pro-trade and tat suc openness can create a signi cant international externality, te model elps gain some insigt into te issue of wen and wy coordination over PI policies migt be useful. As is clear from above, an important aspect of our approac is tat te ome rm s decision to export is endogenous. Tis formulation is motivated by a ost of empirical evidence wic indicates tat pricing regulations (wic are anoter type of policy tat a ect te ability of rms to price discriminate internationally) ave a strong in uence on te entry of rms into foreign markets see Danzon and Epstein (008), Danzon et. al. (005), Lanjouw (005), and te recent overview article by Goldberg (009). Furtermore, prior teoretical work on PIs as explicitly argued tat price regulations and PI policies can lead rms to serve (or not serve) certain markets see, for example, Malueg and Scwartz (1994). In te current literature on PIs, te incentive for individual nations to impose restrictions on PIs primarily takes into account tree sets of factors tat result from te increased ability of rms to engage in international price discrimination. First, te cange in domestic consumer welfare resulting from iger domestic retail prices in markets wit more inelastic demand including te possibility tat certain markets wit very elastic demands may be served only wen rms can price discriminate su ciently see Malueg and Scwarz (1994). Second, te increased ability of manufacturers to engage in vertical controls suc as resale price maintenance and exclusive territories to protect retailers from competitive rent dissipation and free riding by foreign sellers wic on te one and, reduces retail competition tus increasing retail price, and on te oter and, increases te incentive of retailers to invest in 4 For example, Malueg and Scwartz (1994), Ricardson (00), Valletti (006), all assume tat te product market is monopolistic. Roy and Saggi (010) do consider an oligopolistic product market but, as we note below, teir model di ers from ours in important ways.

4 marketing, advertising and retail infrastructure in te domestic market tat eventually bene ts domestic consumers and expands demand see Maskus and Cen (00 and 004) and Ra and Scmitt (007). Tird, te increased ability of governments to regulate domestic market power for various purposes and to preserve rent for private investment in R&D and production of intellectual property witout aving to contend wit te dissipation of tis rent troug international arbitrage see Li and Maskus (006), Valletti (006), Valletti and Szymanski (006), and Grossman and Lai (008). Te structure of our model igligts a novel consequence of a restrictive PI policy viz., te cange in te competitiveness of te domestic rm in te foreign market arising from its ability to carge a low price abroad witout su ering any erosion in its domestic market power, te consequent cange in te rent earned by te rm abroad and, in te nal analysis, its very incentive to export. Finally, Roy and Saggi (010) analyze PI policies in a vertically di erentiated international oligopoly were, unlike tis paper, tere is no asymmetry in potential market access for rms, and te focus is on relating equilibrium government policies to di erences in te structure of demand between countries. Te literature on industrial organization contains extensive analysis of entry and oligopolistic competition wen rms ave captive market segments and may or may not be able to price discriminate across market segments (see, Stole 007). In particular, various autors ave examined te consequence of regulations suc as "universal service obligations" tat prevent price discrimination across market segments (see, among oters, Armstrong and Vickers 1993, Valletti et al 00, Anton et al 00). Te comparison of market outcomes and regulations in tis literature is often based on aggregate welfare of all market segments. In our framework, te ability to price discriminate across national boundaries is determined by independent policy decisions of various nations, and eac nation cares only about its own national surplus ignoring te surplus acquired by foreign rms and consumers. Tis divergence of national interests is exactly wy PI policies can end up acting as a type of strategic trade policy. Te paper is organized as follows. Section describes te model wile sections 3 and 4 derive equilibrium PI policies under strong and weak competition respectively. Section 5 discusses to wat degree our results are robust to te mode of competition by considering a model were rms compete in quantities as opposed to prices. Section 6 concludes. Model Tere are two countries: ome (H) and foreign (F ). Firm, te ome country s domestic rm, as an intellectual property rigt (IPR) over its product. For te sake of concreteness, we will suppose tat tis IPR is a product patent. We will assume tat te ome rm faces no competition in te domestic market and can export its product to te foreign market after incurring a xed cost. Te foreign country as its own domestic rm, called te foreign rm (denoted by f), wose product is orizontally di erentiated from te product of te ome rm. Firm f s product can be sold legally witin te foreign country but is not exported. Tus, tere is asymmetry in potential market access between te two rms. One way to tink about tis asymmetry in potential market access is in terms of di erences in IPR protection across countries. Te ome country o ers strong protection and a broad interpretation of te 3

5 product patent eld by te ome rm tat, in particular, precludes any closely related product from being sold witin its borders. Te foreign country, on te oter and, o ers relatively weak protection and narrow interpretation of te product patent eld by te ome rm tat, in particular, allows a substitute product to be sold witin its borders. Te foreign rm cannot export to te ome country because of te strong and broad enforcement of te ome rm s product patent in te ome country. However, te asymmetry in potential market access can also arise from many oter sources suc as di erences in te cost of marketing products abroad. We adopt te Hotelling linear city model of orizontal product di erentiation were te product space is te unit interval [0,1]; te ome rm s product is located at 0 and te foreign rm s product is located at 1. Note tat ere location does not refer to geograpical location but rater a pysical caracteristic (or type) of te product. We assume tat production cost is zero for bot rms. Te market in eac country consists of a continuum of consumers wose most desired product types are distributed uniformly on te unit interval. Eac consumer buys one or zero unit of a product and earns gross surplus V from consuming te product. If a consumer consumes a product wose actual product type is located at a distance d from er "most desired" product type, se incurs a (psycological) transport cost t:d, t > 0, in addition to paying te price carged. Te total mass of consumers in country i is given by n i 0, i = H, F. Witout loss of generality, we set n H = 1; n F = : (1) To be able to export to te foreign market, te ome rm must rst incur te xed cost 0. Te motivation beind tis assumption is simple: selling its good in te foreign market may require te ome rm to make certain kinds of investment in dissemination of product information, creation of consumer awareness and establising access to te retail infrastructure etc. Furter, te rm may need to autorize sales of its product in te foreign market. Tese export related decisions ave to be made prior to actual selling of goods in te foreign market, and are terefore assumed to be observable by its competitor before market competition occurs. In particular, if te ome rm makes no investment and does not autorize sales of its product abroad, te foreign rm will know tat it as unrestrained monopoly power in its domestic market. In order to abstract from issues related to vertical relationsips, we will assume tat rms sell teir products directly to consumers or, equivalently, te retailing sector in eac market is perfectly competitive wit zero marginal retailing cost (so consumers buy at te price set by te manufacturing rm). Eac country cooses between one of two options - to allow PIs wit no restrictions (P) or to not allow tem at all (N). Wile one can imagine various intermediate options, tese are te two types of policies tat are most commonly observed and, in fact, correspond exactly to te binary decision on weter to ave national or international exaustion of intellectual property rigts. It is generally recognized tat te possibility of PIs reduces te ability of a rm to sell its product at signi cantly lower prices in oter countries. In order to focus on te strategic interaction between rms and governments, we assume perfect arbitrage; in particular, if PIs are allowed and a rm sells abroad at even sligtly lower price, te competitive retailing 4

6 sector in te country can acquire te same product from abroad and sell it domestically at zero transaction cost. 5 In tat case, if a rm wises to serve bot markets, it cannot sell abroad at lower price. If bot countries permit PIs, ten te rm must in fact carge equal prices in bot markets. We will see tat suc uniformity in pricing may actually old even if only one of te two countries permits PIs. Formally, te game proceeds in tree stages. First, te two governments decide weter or not to allow PIs. Next, te ome rm decides weter or not to enter te foreign market. Finally, rms set prices in every market tey serve. We determine te subgame perfect Nas equilibrium outcome of tis game. We assume tat: > 3 : () 3 t V 4t (3) Restriction () and te second inequality in (3) togeter ensure tat wen te ome rm does not pre-commit to exclude te foreign market, tere exists a pure strategy equilibrium were it sells a strictly positive quantity in tat market; in particular, te equilibrium pro t of te ome rm wen it serves bot markets exceeds te pro t from serving only te ome market even if te xed cost is zero. Te rst inequality in (3) ensures tat wen bot rms serve te foreign market, all consumers buy in equilibrium (complete market coverage); it also implies tat V > t so tat it is socially optimal for all consumers to buy. We begin wit some general observations. For i =, f, we denote te price, te quantity sold and te pro t earned by rm i in its domestic and foreign markets by (p i,q i, i ) and (p i,q i, i ), respectively. If rm i is te only rm serving its domestic market, ten te domestic demand it faces is given by: D i (p i ) = n i, p i V t (4) V p i = n i, p i V t: (5) t Te domestic monopoly price p m i and monopoly quantity q m i of rm i tat maximize its domestic pro t are given by: and p m i = V t, q m i = 1, if V t (6) p m i = V, qm i = V, if V t: (7) t If te ome rm decides to export to te foreign country, ten assuming tat all buyers buy, 5 Tis is obviously a simplifying assumption. In general, under an oligopolistic setting, te ome rm can price discriminate internationally even if its country is open to parallel trade, provided tat te number of rms is di erent in te two markets (see, among oters, Ganslandt and Maskus, 007). 5

7 te demand in te foreign country for te ome rm s product is given by: 1 d (p ; p f ) = + p f p ; if (p f p ) [ t; t] (8) t = 0; if (p f p ) t wile = ; if (p f p ) t; d f (p ; p f ) = d (p ; p f ): (9) If te ome rm can price discriminate across te two markets, it s reaction function in te foreign market is given by: p = t + p f : (10) Te reaction function of te foreign rm is given by: p f = t + p : (11) Tese reaction functions assume tat te prices are not too large so tat te market is fully covered. If bot rms ave te reaction function as indicated above, ten te it is easy to ceck tat tere is a unique Nas equilibrium outcome of price competition in country j s market given by: p = p f = t; (1) wit eac rm selling to alf te market. Eac rm s pro ts (gross of any xed cost of serving te market) in te foreign country are given by: f = f = t : (13) Observe tat in te above equilibrium, competitive price (t) is lower tan te monopoly price (maxfv t, V g) if, and only if, V t. In particular, if V < t, ten te competitive outcome generates prices in te foreign country tat are iger tan te monopoly price. Te intuition ere is tat wit competition, rms split te market and terefore te marginal buyer s taste or desired product is closer to te product eac rm sells wic, in turn, induces te rms to carge iger prices relative to a monopoly situation (te marginal buyer s taste is furter away from te actual product type). We sall call tis te nice e ect. In wat follows, we refer to te situation were V t as strong competition and te situation were V < t as weak competition; tis also accords wit te standard interpretation of iger values of t implying greater product di erentiation and ence, softer price competition. As it turns out, tere are major di erences between te policy and market outcomes between tese two cases. In particular, since only te ome rm as te ability to export, only one country s PI policy ends up mattering. Under strong competition, if te ome country is open to PIs ten te ome rm cannot price discriminate internationally since te price under competition is lower tan its monopoly price and te foreign country s PI policy is irrelevant. 6

8 Similarly, wen competition is weak, only te PI policy of te foreign country matters wereas te PI policy of te ome country is not consequential. We begin wit te strong competition case. 3 PI policy under strong competition In tis section, we analyze te policy and market outcomes were V t and competition in te foreign country is strong. Recall tat under assumption (3), V 4t so tat we e ectively con ne attention to V [t; 4t]: 3.1 Market outcome In tis subsection, we caracterize te market outcome (in stage 3) following eac pair of PI policy coices, and te ome rm s decision regarding weter or not to export. Independent of te policy coices, if te ome rm decides not to export to te foreign country, ten te market outcome in eac country is te autarkic monopoly outcome. In te rest of tis subsection, we focus on te situation were te ome rm cooses to export. To begin, consider te situation were bot countries proibit parallel trade. Tis implies tat te pricing decisions in te two markets are independent and, in particular, te ome rm faces no constraint on its ability to price discriminate across te two markets. It follows ten tat in te ome country, te ome rm sets its domestic price at te monopoly level and sells te monopoly quantity as given by (6); in particular, all consumers buy in te ome country. In te foreign country, te equilibrium prices are as indicated in (1) and rms split te market in te foreign country evenly. In particular, te pro ts (gross of te xed cost of exporting) are given by: Observe tat V t implies N = V t, N = N f = t : (14) p N = V t pb i.e., te domestic price of te ome rm exceeds its foreign price, so tat, as long as te ome country proibits parallel trade, te equilibrium market outcome remains uncanged even if te foreign country allows PIs (prevents te ome rm from carging a lower price in its domestic market). Indeed, tis is te unique equilibrium market outcome wen te ome country proibits PIs, independent of te PI policy of te foreign country. Next, consider te market outcome wen bot countries allow parallel trade so tat te ome rm is constrained to carge identical prices in bot markets, i.e., p = p. In tis case, te gross total pro t of te ome rm if it exports to te foreign country is given by: = t p [1 + d (p ; p f )], for p V t and p V t p + d (p ; p f ), for p [V t; V ] 7

9 were d is given by (8). Note tat te pro t function as a kink at p = V t. Maximizing te two parts of te pro t function wit respect to p taking into account te boundary constraints, we obtain te reaction function of te ome rm. Let p f and p f be de ned as follows: p f = V t 3 + and p f = V t : It is easy to ceck tat p f < p f and tat p f and p f are strictly positive if V is large relative to t, and less tan zero if V is close to t. Te reaction function of te ome rm is given by: + t p = + p i f, if p f > 0 and p f 0; p f (15) i = V t, if p f > 0 and p f maxf0; p f g; p f = 1 ( + ) [(V + t) + p f ], if p f maxf0; p f g: Observe tat te above reaction function is at for a certain range of te rival s price; tis at range corresponds to a discontinuity in te marginal revenue of te ome rm at te kink point of its gross revenue function. Te rst part of te reaction function corresponds to te situation were te rival s price is su ciently low so tat te ome rm also carges a low price (below its ome monopoly price) to be competitive abroad; at suc price, te ome rm sells to all buyers at ome. Te second part of te reaction function re ects a situation were te price carged by te foreign rm is moderately ig so tat te ome rm can carge its optimal monopoly price in te ome market witout losing muc market sare in te foreign market. In tis range, even wen te rival raises its price, te jump discontinuity in te marginal revenue of te ome rm (at te ome monopoly price were it sells to all ome consumers) prevents te ome rm from altering its best response. Te last part of te reaction function corresponds to te situation were te foreign rm s price is so ig tat te ome rm is induced to expropriate more revenue out of foreign buyers tat ave a closer taste for its product by raising its ome rice above te optimal monopoly price under suc a situation, te ome rm forsakes some pro t in te domestic market to increase its pro t in te foreign market. Te foreign rm s reaction function is identical to tat in (11). It can be cecked tat te (unique) Nas equilibrium outcome is given by: 4 p P = t and p P f = t if V > t (16) and p P = V t and pp f = V if t V t : (17) 8

10 Note tat if V > t ten 4 t < V t so tat te equilibrium described in (16) corresponds to a situation were te foreign rm s reaction intersects te ome rm s reaction in te rst of its tree parts described in (15); te equilibrium described in (17) corresponds to an intersection in te second part of te ome rm s reaction. In bot cases, te ome rm carges a price less tan or equal to V t, its optimal monopoly price at ome. Te Nas equilibrium outcome described above remains unperturbed even if te foreign country does not allow PIs so tat te ome rm is free to carge a lower price in its domestic market in te ome country. Indeed, for V t, tis is te unique Nas equilibrium outcome wen te ome country allows PIs, independent of te PI policy of te foreign country. Te quantities sold in tis equilibrium are given by: q P = 1, qp = 1 3, qp f = + 1, if V > t (18) and q P = 1, qp = 1 V, qf P 4t = V, if t V t 4t : (19) Assumption () ensures tat tat all quantities are strictly positive. Observe tat, p P > pp f wic re ects te fact tat te ome rm is less aggressive in price competition tan te foreign rm because it loses pro t in its ome market if it reduces price (below its monopoly price); tis is re ected in te lower market sare of te ome rm. Since p P V t, all consumers buy in te ome country and terefore, te quantity sold in te ome country is identical to tat wen te ome rm is free to price discriminate between te two countries. Also observe tat te prices are iger tan wat te two rms carge in te foreign market wen te ome rm can price discriminate: in oter words, non-discrimination softens price competition. Te literature on PIs as empasized tat allowing PIs reduces domestic price and increase domestic consumers surplus. Tis e ect can be seen ere as long te ome rm serves te foreign market: Weter or not PIs are permitted, all consumers buy in te ome market. If V > t ; ten te ome price falls from (V t) to t wen te ome country moves from a policy of proibiting PIs to allowing it, wic raises te domestic consumer surplus at ome (total transport cost remains uncanged). If V t 3 + 1, te ome price and ome consumers surplus remain una ected by PI policy. In te range of parameter values were te equilibrium price of te ome rm is strictly below (V t), te prices carged by bot rms decline wit, te relative size of te market in te foreign country. If V > t rm pro ts (gross of te xed cost of exporting) 9

11 are as follows: P = t , P = t , and P f 3 = t (0) wereas if t V t we ave P = V t; P 1 = (V t) V ; and P f 4t = V 8t (1) It can be cecked tat P N () 4 3 max 1; V t t : () i.e., if te ome rm exports, it earns iger pro t under non-discriminatory pricing (tan under price discrimination) if, and only if, te size of te foreign market () exceeds te critical tresold. Using () and te second inequality in (3), we ave P + P V t; so tat te ome rm is always better o serving bot markets tan simply serving te ome market, if te xed cost = 0: To sum up, wen V t (strong competition) and te ome country allows PIs, te following old: (i) If te ome rm cooses to export, it carges a common price in bot markets tat does not exceed te monopoly price in its domestic market and lies strictly below te latter if competition is very strong (in wic case it sacri ces domestic pro t wen it serves te foreign market). (ii) All consumers buy in te ome country. (iii) Bot rms carge prices tat are iger tan wat tey would if te ome rm could price discriminate between te two markets. (iv) Te ome rm carges a iger price and as lower market sare in te foreign country tan te foreign rm and te gross foreign pro t of te ome rm is iger tan wat it earns if it is free to price discriminate between te two markets if, and only, if i.e., te foreign market is relatively large. 3. Policy outcome From our discussion in te previous section, it follows tat under strong competition, te market outcome is independent of te PI policy of te foreign country. All tat matters is weter or not te ome country allows PIs. Te next proposition describes te optimal policy of te ome country: Proposition 1 Suppose V t (strong competition). Ten, te following old: (i) If ten it is optimal for te te ome country to proibit PIs. Tis is te unique optimal policy if < and < N (oterwise te ome country is indi erent between te 10

12 two policies). Furter, for < and [ P,N ], te ome country s proibition of PIs is pro-trade i.e. it induces te ome rm to export. (ii) If ten it is optimal for te ome country to allow PIs. Tis is te unique optimal policy if > and < P (oterwise te ome country is indi erent between te two policies). Furter, for > and [ N,P ], te ome country s openness to PIs is pro-trade i.e. it induces te ome rm to export. Te proof of te proposition is straigtforward. Regardless of te ome country s policy, te ome rm sells to all consumers in te ome market so tat total domestic surplus generated in te ome country is independent of its PI policy. Tus, te only way in wic PI policy of te ome country a ects domestic welfare is via its impact on te net foreign rent acquired by te ome rm in te foreign country. From our discussion in te previous section (and particularly, using ()), we know tat te ome country can increase te rent acquired by te ome rm in te foreign market by allowing PIs if, and only if, : Te rest of te proposition follows immediately. Tus, wen competition in te foreign market is strong, te ome country s PI policy (wic is all tat matters for te market outcome) is based exclusively on te pro tability of its rm. Wen te foreign market is not signi cantly larger a ome proibition on PIs allows te domestic rm to price discriminate internationally and tereby creates te most pro table conditions for it in te foreign market (and terefore provides te most inducement to export). On te oter and, if te foreign market is signi cantly larger, allowing PIs and preventing te domestic rm from price discrimination creates te best opportunity for it to pro t from te foreign market. Tis is because suc a policy softens price competition abroad by making te domestic rm less willing to lower its price and te pro t gain from being able to carge iger prices outweigs te competitive disadvantage tat te domestic rm su ers by being constrained to carge te same price in bot markets. Te nationally optimal PI policy under strong competition is always pro-trade; in particular, wen te foreign market is not signi cantly larger in size and te xed cost of exporting is moderately large, it is te proibition of PIs tat induces te ome rm to export. 3.3 Global welfare analysis under strong competition In tis section, we analyze te implications of te optimal policy coice by te decisive country (te ome country in te case of strong competition) for global welfare (wic in our model, reduces to te total net surplus of te two countries). To begin, observe tat as bot markets are fully covered in equilibrium, as long as te ome rm serves te foreign market, te only di erence in global surplus across market outcomes induced by PI policies is in te total transport cost incurred by consumers in te foreign market. If PIs are not allowed and te ome rm exports, ten te market outcome in te foreign country is one were eac rm as equal market sare; tis is te " rst best" outcome as it minimizes total transport cost. If PIs are not allowed and te ome rm exports, te ome rm sells to less tan alf te foreign market wic adds to te transport cost in te foreign market and terefore leads to loss of welfare. However, tis does not mean tat proibiting PIs is always globally e cient as te ome rm may ten coose to not serve te 11

13 foreign market. If te ome rm cooses to abandon te foreign market as a consequence of cange in PI policy, ten te global welfare implication is based on a comparison of te increase in transport cost wen only one (instead of two) products are sold in te foreign market and te xed cost of serving te foreign market. Te next proposition outlines te welfare implications of optimal policy: Proposition Suppose V t (strong competition).ten, te following old: (i) Suppose minf P,N g. If ten te ome country s policy decision to proibit PIs is globally e cient. On te oter and, if > ten te ome country s policy decision to permit PIs is globally ine cient. (ii) Suppose minf P,N g maxfp,n g. Ten, te following old: (ii.a) Wen te ome country s policy decision to proibit PIs is globally e cient if t 4 ; oterwise, it is ine cient. (ii.b) Wen > te ome country s policy decision to permit PIs is globally e cient if t( ); oterwise it is ine cient. 9 A formal proof of tis proposition is contained in Roy and Saggi (011a), te working paper version of tis paper. Part (i) of Proposition describes a situation were te xed costs of exporting are small and te ome rm exports to te foreign country regardless of te PI policy of te ome country. As indicated above, in tat case, te equilibrium policy outcome is e cient ( rst best) if, and only if, te ome country proibits PIs and using Proposition 1, tis occurs if, and only if, : Parts (ii:a) and (ii:b) refer to a situation were te PI policy of te ome country does a ect te ome rm s incentive to export. Under suc a scenario, te ome country s optimal policy is one tat induces its rm to export to te foreign country. However, tis product market outcome is globally e cient only wen te xed cost of exporting is not larger tan te reduction in total transport cost in te foreign market wen te ome rm exports (at uniform or discriminatory pricing depending on te nature of te optimal PI policy of te ome government wic, as we ave seen in Proposition 1 depends on weter is above or below ). Proposition generally indicates tat unless te xed cost of exporting is large, te ome country s policy coice is globally optimal. Tis implies tat in markets were xed costs of exporting are minor, tere may be little reason for international intervention or coordination over PI policies. Note tat tis conclusion also applies to nations tat coose to proibit PIs from relatively similar sized countries. 4 Weak competition and PI policy In tis section, we analyze te policy and market outcomes were V < t i.e., competition in te foreign country is weak. Recall tat under assumption (3), V 3 t so tat we e ectively con ne attention to V ( 3 t; t): In order to ensure tat te duopoly outcome in te foreign market is always one wit complete market coverage (all consumers buy), we need te following 1

14 additional restriction: Note tat (3) is always satis ed if t < 1: t < (3) 4.1 Market outcome wit weak competition In tis subsection, we caracterize te market outcome following eac pair of PI policy coices and te decision of te ome rm on weter or not to serve te foreign market. As before, independent of te policy coices, if te ome rm decides not to serve te foreign market (in te foreign country), ten te market outcome in eac country is te autarkic monopoly outcome as indicated in (7). Note tat V < t implies tat (unlike te case of strong competition) te monopoly outcome now is one were some consumers do not buy and monopoly power causes domestic distortion. In te rest of tis subsection, we focus on te situation were te ome rm does serve its foreign market. To begin, consider te situation were bot countries proibit parallel trade. Tis implies tat te ome rm faces no constraint on its ability to price discriminate between its domestic and foreign markets. It follows ten tat in te ome country, te ome rm sets its domestic price at te monopoly level and sells te monopoly quantity as given by (7). In te foreign country, te equilibrium prices are as indicated in (1) and te rms split te market in te foreign country evenly. In particular, te pro ts (gross of te xed cost of serving te foreign market) are given by: N = V 4t, N = N f = t : (4) Observe tat V < t implies p N = V < pn i.e., te domestic price of te ome rm is below its competitive foreign price. Tis equilibrium market outcome remains uncanged even if te ome country allows parallel trade as long as te foreign country proibits parallel trade. Indeed, tis is te unique equilibrium market outcome wen te foreign country proibits parallel trade, independent of te PI policy of te ome country. Note tat tat te net welfare generated in te foreign country in te above market outcome if te ome rm serves bot markets is given by: Z qn WF N = V = V 0 3t 4 = t Z qn f 0 txdx txdx : (5) Next, suppose tat bot countries allow PIs so tat te ome rm cannot price discriminate between ome and foreign markets. Recall tat in tis case te domestic monopoly price of te ome rm is V > V t. Suppose te ome rm serves its foreign market in te foreign country. Te reaction functions of te two rms continue to be as given by (15) and (??) tat N 13

15 were derived in te previous section. However, it can be cecked tat te (unique) Nas equilibrium outcome is one were te foreign rm s reaction function intersects te ome rm s reaction in te tird part of te tree parts described in (15). In particular, te equilibrium prices are: 4V + 3t p P = Te quantities sold in tis equilibrium are given by: q P = 1 4V + 3(V t) 1 ; q P = t t V t V + (3 + 4)t and p P f = : (6) ; and q P f = 1 1 t t V : (7) It is easy to ceck tat under (3), all consumers earn positive net surplus. Te equilibrium common price p P carged by te ome rm satis es: p P > V > V t and furter p P < pp f and qp > qf P : In oter words, in trying to compete wit te foreign rm in te foreign market using a non-discriminatory pricing, te ome rm actually ends up raising bot its own price (as well as its rival s price) above its domestic monopoly price. As te ome rm incurs a loss of domestic pro t wenever it raises its price above te domestic monopoly price, it is actually more reluctant to raise its price tan te foreign rm, and ence more aggressive in price competition (over tis range of prices) tan te foreign rm, despite te fact tat te foreign rm as no captive market to reckon wit. Tis re ects te nice e ect tat we discussed earlier; as competition is weak and consumers care strongly about taste, rms ave an incentive to raise teir price sarply wen tey serve smaller number of consumers wose tastes are closer to teir product type. Te fact tat p P exceeds te ome monopoly price ( V ) tat te ome rm would like to carge in its domestic market if it was allowed to price discriminate, also implies tat te above Nas equilibrium outcome remains unperturbed if te ome country proibits parallel trade i.e., if te ome rm is allowed to carge a iger price in its domestic market. Indeed, for V < t, tis is te unique Nas equilibrium outcome wen te foreign country allows parallel trade, independent of te PI policy of te ome country. Te gross foreign pro t earned by te ome rm wen it carges a common price in bot markets is given by: P (4V + 3t) 1 = t V : (8) t It sould be noted tat even toug te price carged by te ome rm is iger tan its domestic monopoly price (i.e. p P f > V ), it is lower tan wat it would carge in te foreign country if it could price discriminate (werein it carges t abroad) since V < t implies p P < t. It is straigtforward to ceck tat even toug te ome rm earns iger market sare in 14

16 te foreign country tan it would if it could price discriminate (were rms split te market evenly), te pro t it earns under non-discriminatory pricing in te foreign country is lower: P < N = t : (9) Using te fact tat V ( 3 t; t); it is easy to ceck tat te equilibrium total pro t of te ome rm exceeds its optimal monopoly pro t at ome and te ome rm always serves te foreign market if te xed cost = 0: Te total welfare generated in te foreign country (wen V < t and te ome rm exports) is given by te gross surplus net of total transport cost and te pro t lost to te ome rm: It can be cecked tat: Z qp WF P = V = q P 0 t qp f p P txdx Z qp f 0 txdx + (V t): (30) P W P F > W N F (31) i.e., te ome rm generates iger net welfare in te foreign country wen it serves tat market wit nondiscriminatory pricing rater tan wit discrimination. Even toug te ome rm olds iger market sare under non-discrimination and, in particular, causes loss of welfare by increasing te taste related "psycological cost" incurred by buyers, it also expropriates less rent and te latter e ect dominates. 4. Policy outcome wit weak competition In tis subsection, we outline te implications for PI policy tat follow from our analysis of te e ect of PI policy on market outcomes for te case of weak competition. From our discussion in te previous subsection, it follows tat te market outcome is independent of te PI policy of te ome country, te exporting nation. All tat matters is weter or not te foreign country, te importing nation, allows PIs. Te next proposition outlines te optimal policy of te foreign country: Proposition 3 Suppose V < t. If N, ten it is optimal for te foreign country to permit PIs, wile for > N te PI policy of te foreign country as no impact on te market outcome. In particular, if P, if te foreign country allows PIs ten te ome rm exports to its market carging a non-discriminatory price in bot countries wereas if [ P,N ], ten te foreign country s openness to PIs deters te ome rm from exporting and preserves te foreign rm s local monopoly. Te proof of te proposition follows directly from our discussion in te previous subsection. Wen te foreign country permits PIs it generates te nondiscriminatory pricing outcome, 15

17 wile proibiting PIs allows te ome rm to price discriminate in equilibrium. As sown in te previous we ave tat te ome rm generates iger net welfare in te foreign country wen it serves tat market wit nondiscriminatory pricing rater tan wit discrimination i.e., WF P > W F N : However, we ave also seen tat te gross foreign pro t of te ome rm under te two PI policy options of te foreign country satisfy: P < N : It follows terefore tat if P, te ome rm serves te foreign market independent of te PI policy of te foreign country and in tat case, it is optimal for te foreign country to allow PIs. On te oter and, if [ P,N ], ten te ome rm serves te foreign market only if te foreign country proibits PIs, in wic case te welfare of te foreign country is given by WF N ; if te foreign country allows PIs, te market in te foreign country is monopolized by te foreign rm wic ten carges te monopoly price V, sells to V t buyers and leads to welfare: cw F = V Z! V t txdx t It can be sown tat WF N < W c F for V (t,t) so tat it is optimal for te foreign country to permit PIs to prevent te ome rm from entering its market. 6 Proposition 3 indicates tat unlike te case of strong competition, for te range of parameters for wic te coice of PI policy matters for te market outcome, te decisive country under weak competition as a unique nationally optimal policy coice and it is one of allowing PIs. By allowing PIs, te foreign country prevents price discrimination by te ome rm tat, in turn, actually reduces te rent tat te ome rm can extract via exporting (toug it increases te rm s market sare in te foreign country). Wit weak competition, reducing rent transfer abroad becomes te driving motive of te foreign country s policy. In fact, if te xed cost of exporting exceeds a certain level, te optimal policy of allowing PIs by te foreign country deters entry by te ome rm and leads to autarky. 4.3 Global welfare under weak competition We now analyze te global welfare implication wen competition is weak. Since te foreign country is decisive ere, it is su cient to focus on its policy. Proposition 4 Suppose V < t (Weak Competition).Ten, te following old: (i) If P ten te foreign country s decision to permit PIs is globally ine cient. (ii) If P < N ten te foreign country s policy to permit PIs is globally suboptimal if is small wereas it is globally optimal if is large enoug i.e. it lies witin te interval ( P,N ]. A formal proof of tis proposition is contained in Roy and Saggi (011a), te working paper version of tis paper. 6 It is straigtforward to establis tat W N < W c if 3V +6t 8tV > 0. Furtermore, we ave 3V +6t 8tV = (t V ) + t( V t) wic is positive for V 3 t and 3V + 6t 8tV = (V t) + t(t V ) wic is 3 3 positive for V 3 t: 0 16

18 Tus, under weak competition, not only is te market outcome dependent only on te PI policy of te importing nation (te foreign country), but te nationally optimal policy coice of te foreign country generates an outcome tat is globally ine cient unless te xed cost of serving te foreign market is very large. In particular, wit weak competition te foreign country s optimal policy of allowing PIs to prevent price discrimination is geared towards reducing te rent expropriated by te foreign rm, and tis is wat leads to global ine ciency. Tis suggests tat wit weak competition (tat may be closely related to weak protection of IPRs available to foreign rms in importing nations), tere is a case for reversing te apparently open PI policies of suc nations since suc policies can simply driven by te desire to preserve te rents of local rms and may, in fact, restrict trade if te xed cost of exporting is moderately large. 5 Discussion: Robustness to Alternative Modeling. It is well known tat results in te literature on strategic trade policy are often sensitive to weter te underlying strategic interaction between rms takes place in a game of strategic complementarity or substitutability. Our results on te nature of strategic PI policy ave been derived in a framework were rms engage in price competition in te foreign market (i.e., te market game is one of strategic complementarity). It is natural to wonder weter te qualitative results would be overturned if rms engaged in Cournot quantity competition instead (game of strategic substitutability). Roy and Saggi (011b) contains a simple treatment of a Cournot version of our model assuming tat rms produce omogenous goods and tat market demand is linear in bot countries. For simplicity, te xed cost of exporting is ignored. In suc a framework, weter te ome monopoly price exceeds te foreign competitive price (wit segmented markets) depends on te relative size of ome demand and tis, in turn, determines weter te ome or te foreign government s PI policy is consequential; if te relative size of ome demand exceeds a tresold, only te ome government s PI policy matters, wile te foreign government s policy is decisive below te tresold. As one would expect, relative to price competition, Cournot competition generates very di erent strategic incentives for te rms and te governments. Noneteless, several key qualitative results developed in te model wit price competition continue to old. First, a permissive PI policy regime tat forces te ome rm to engage in uniform pricing at ome and abroad can increase its total pro t, and terefore its incentive to serve te foreign market. Tis is one of te key e ects underlying our results in Section 3. Under price competition, te captive market at ome makes te ome rm unwilling to price low in te foreign market under uniform pricing, and due to strategic complementarity it also induces to te foreign rm to carge a iger price; te net result is tat bot rms may end up carging iger prices in equilibrium and earning iger pro ts tan under discriminatory pricing. In te Cournot competition case, te mecanism troug wic uniform pricing bene ts te ome rm is somewat di erent and can be decomposed into two opposing forces. Wen ome demand is relatively smaller tan foreign demand, te captive market at ome induces te ome rm to maintain low uniform price across te two markets wic, in turn, induces 17

19 it to produce large quantity in te foreign markets; te no discrimination constraint in e ect elps te ome rm to credibly commit to sell large quantities and sifts its reaction function out. Because of strategic substitutability, tis tends to reduce te market sare of te foreign rm tus creating an advantage for te ome rm (and does not necessarily aggravate te intensity of competition as would be true under strategic complementarity). But tere is an opposing e ect of te no discrimination constraint: te ome rm is muc more willing to contract its output in response to any expansion of te rival s output (i.e. it makes te ome rm s reaction function steeper). Tis is because te ome rm may to sell more at ome to equalize prices su ering loss in its ome pro t and, to reduce tis loss, it is willing to cut back its foreign output more aggressively. Tis "more accommodating" stance of te ome rm in response to expansion of output by te foreign rm works against te rst e ect; te foreign rm is likely to take advantage of tis and pus its own sales more aggressively. Weter te rst e ect dominates te second depends on te relative size of ome demand. Wen ome demand is relatively low, te uniform pricing constraint induced by a permissive PI policy raises te ome rm s pro t and in fact, increases its market sare in te foreign market as well as te volume of trade. Second, in te Cournot case wen ome demand is signi cantly large relative to foreign demand, te ome government proibits PIs in order to induce te ome rm to serve te foreign market; if tere were a positive xed cost of serving te foreign market tis e ect would be furter enanced. Tis is very similar to te result obtained wit price competition. Tird, in te Cournot case, if ome demand is not signi cantly larger tan foreign demand and te ome government s PI policy is decisive, it prefers to allow PIs; tis is comparable to our result tat wit price competition, te ome government permits PIs under price competition wen te foreign market is signi cantly larger and te ome government is decisive (wic appens wen competition is strong). Finally, werever te foreign government s PIs policy is decisive, it allows PIs (as in te weak competition case under price competition). As one would expect, not all results under quantity competition are qualitatively similar to tat under price competition. Te main di erences between quantity and price competition are regarding te e ect of policy on quantity exported and weter te optimal policy is pro-trade. Furter, unlike te case of price competition, te e ects of PI policy on pro ts of te two rms may go in opposite directions; tis is also true about te e ect on ome welfare and te pro t of ome rm. An important feature of our model is tat te ome rm enjoys monopoly power at ome but faces competition in te foreign market. As noted in Section, tis asymmetry can be seen as a way to capture te di erences in IPR protection across countries; te ome government ensures broad and strong protection of te IPR of te ome rm tat in e ect creates monopoly power at ome, but te same is not true in te foreign market. Suc asymmetries often exist between developed and developing country markets for many products. Wile te existence of asymmetry in market power is important for our results, te precise nature of tis asymmetry is less so. We expect tat our qualitative results sould old even if te ome rm faces some competition in te ome market (from, say, a local rm) as long as te intensity of competition is signi cantly lower in te ome market tan in te foreign market. 18