Journal of International Economics 87 (2012) 262–276
Contents lists available at SciVerse ScienceDirect
Journal of International Economics
j ourna l homepage: www.e lsev ie r .com/ locate / j i e
Equilibrium parallel import policies and international market structure☆
Santanu Roy a,1, Kamal Saggi b,⁎a Southern Methodist University, Dallas, TX, USAb Vanderbilt University, Nashville, TN, USA
☆ For helpful comments and discussions, we thank twoStaiger, Kyle Bagwell, Rick Bond, Petros Mavroidis, HodakSengupta, seminar audiences at Princeton, Syracuse, St.Cruz, the University of Sydney, the University of New Sou2010 Midwest International Economics Meeting, and thethe Applications of Game Theory to Trade andDevelopmenten during Kamal Saggi's visits to the Stanford Center(SCID) and the World Bank's Development Economics Regration (DECTI); he is grateful to the affiliated researcherSCID and DECTI for their hospitality and support.⁎ Corresponding author at: Department of Economi
1819-Station B, Nashville, TN 37235-1819, USA. Tel.: +E-mail addresses: [email protected] (S. Roy), k.saggi@V
1 Department of Economics, Southern Methodist Unilas, TX 75275-0496, USA. Tel.: +1 214 768 2714.
In a North–South vertically differentiated duopoly we analyze (i) the effects of parallel import (PI) policies onprice competition and (ii) the interdependence of national PI policies. Prices can be higher in the North if bothcountries permit PIs relative to when only the South does. If governments maximize national welfare and de-mand asymmetry across countries is sufficiently large, the North forbids PIs to ensure its firm sells in theSouth and international price discrimination — the South's most preferred market outcome — obtains.When demand structures are relatively similar across countries, the North permits PIs and uniform pricing —
Parallel trade is said to occur when a product protected by someform of intellectual property right (IPR) offered for sale by the rightsholder in one country is re-sold in another country without the rightholder's consent. As is clear, the incentive to engage in such trade nat-urally arises in the presence of significant international price differ-ences, which in turn often reflect the underlying market power ofsellers (Scherer and Watal, 2002).
th Wales, Vanderbilt, the SpringStony Brook 2011 Workshop ont. Parts of this paper werewrit-for International Developmentsearch Group in Trade and Inte-s and the administrative staff of
The possibility of parallel trade affects firm behavior and pricing inmany markets, perhaps the most important of which is the market forpharmaceuticals.2 A recent article published in the Financial Timesnoted that several billion dollars of parallel trade in pharmaceuticalsoccurs within the European Union (EU) annually and that suchtrade accounts for roughly 10% of Europe's medicine trade.3 The big-gest destination markets tend to be Germany, UK, Netherlands, Den-mark, Sweden, Ireland, and Norway— some of the richest countries inEurope where prices generally tend to be the highest. As one mightexpect, the important parallel exporters are Greece and Spain —
countries where prices of medicines are lower than the EU average.Kanavos et al. (2004) document the increased importance of PIs inthe EU pharmaceutical market. They find that from 1997 to 2002,the share of PIs as a percentage of the total pharmaceutical market in-creased from under 2% to 10.1% in Sweden and from 1.7% to about 7%in Germany. On the export side, Greece's share of parallel exports in-creased from under 1% to 21.6% over the same time period. Impres-sive as these figures are, it is worth emphasizing that the observedflows of parallel trade need not be large for PI policies to matter
2 Parallel trade occurs in footwear and leather goods, musical recordings, cars, con-sumer electronics, domestic appliances, cosmetics, clothing, soft drinks, and severalother consumer products (NERA, 1999).
3 See “European drug groups fear parallel trade” Financial Times, June 7, 2010.
263S. Roy, K. Saggi / Journal of International Economics 87 (2012) 262–276
because firms will tend to make different pricing decisions when suchtrade is permitted relative to when it is not.4
Discussions regarding PI policies tend to be quite charged in thecontext of pharmaceuticals and perhaps for a good reason. The issuehas often been heavily politicized in most countries, including theUnited States where it has been debated repeatedly over the yearsin Congress. For example, an article published in the Wall Street Jour-nal on Dec 16, 2009 reported that a measure to allow importation ofprescription drugs from abroad fell short in the US Senate by just 9votes. The bill was sponsored by Senator Byron Dorgan of North Da-kota who argued that his motivation was to protect consumer inter-ests since “…the American people are charged the highest prices intheWorld”. The pharmaceutical industry opposed the bill questioningthe safety of imported drugs. While safety maybe a legitimate con-cern, there is little doubt that the primary issue for firms is the abilityto maintain high prices in the United States.
Goldberg (2010) has argued that the practice of “global referencepricing” on the part of some rich countries and the possibility of PIscan induce pharmaceutical multinationals to not serve low incomecountries and/or raise their prices (even above their optimal mo-nopoly prices) in such markets — outcomes that emerge quitesharply in our model. For example, multinational firms frequentlyrefrain from introducing new drugs in India because the foregoneprofits in the Indian market are trivial relative to the profits thatwould be lost in Canada and many European countries if Indianprices were used as a reference point by these countries while de-termining local prices (Goldberg, 2010). More generally, using dataregarding drug launches in 68 countries between 1982 and 2002,Lanjouw (2005) shows that the presence of price regulations andglobal reference pricing in the industrialized world contributes tolaunch delay in developing countries. In a similar vein, Danzonand Epstein (2008) find that the delay effect of a prior launch in ahigh-price EU country on a subsequent launch in a low price EUcountry is substantially stronger than the corresponding effect of aprior launch in a low price EU country.
Whether or not PIs can flow into a country is a matter of nationalpolicy. A country can choose to permit PIs by adopting the legal doc-trine of international exhaustion of IPRs under which such rights aredeemed to expire globally with the first sale of the relevant product,regardless of the geographical incidence of the sale. On the otherhand, a country can effectively ban PIs by adopting national exhaus-tion of IPRs wherein rights are held to expire only in the market offirst sale thereby leaving the right holder free to prevent its resalein other markets. While national laws pertaining to parallel tradeare complex and multi-faceted, the following characterization broad-ly captures the global policy spectrum: the two largest markets in theworld — i.e. United States and the EU — forbid PIs of patented andcopyrighted goods from most other countries whereas developingcountries tend to vary widely in their restraints on such imports(Maskus, 2000).5 This variation in national PI policies reflects unilat-eral policy decisions since presently there is no multilateral coopera-tion or consensus over policies pertaining to parallel trade. Indeed,the key multilateral agreement on IPRs — i.e. the WTO's Agreementon Trade Related Aspects of Intellectual Property Rights (TRIPS) —
leaves member countries free to implement PI policies of their choice.Given the lack of any multilateral consensus regarding the desir-
ability of parallel trade, two important questions arise. First, how donational PI policies affect oligopolistic competition in global markets?Second, what is the nature of strategic interdependence between PI
4 In this regard, it is noteworthy that Gansland and Maskus (2004) found that afterSweden joined the EU and opened its pharmaceutical market to PIs, prices of drugssubject to competition from PI declined 12–19%.
5 The US policy with respect to PIs of trademarked goods is relatively more open: itallows PIs of trademarked goods (such as cars) when the entities holding the US andthe foreign trademark are the same or are in a parent–subsidiary relationship.
policies of individual countries? We address these questions in aNorth–South model in which the two regions differ with respect totheir domestic demand structure and the quality of goods producedby their respective firms. In particular, the Northern firm's productis of high quality whereas that of the Southern firm is of low qualityand market size as well as the relative preference for high quality islarger in the North. Not only do these stylized asymmetries captureempirically relevant differences between Northern and Southernmarkets, we show that they shed new light on the causes and conse-quence of parallel trade. Indeed, without properly accounting for suchasymmetries, it is difficult to explain the observed variation in PI pol-icies across countries.
The timing of decisions in our model is as follows. First, govern-ments simultaneously decide whether or not to permit PIs. Next,each firm chooses whether or not to offer its product for sale in theforeign market. Finally, given policies and market structure, firmscompete in prices and international trade and consumption occur.To the best of our knowledge, ours is the first paper to provide ananalysis of PI policies in a model that incorporates strategic interac-tion not only in the product market but also at the policy-settingstage.
The existing literature on PIs has extensively explored uniformglobal pricing and international price discrimination by firms withmarket power. In addition to these symmetric market outcomes,an asymmetric scenario where the low quality sells in both marketswhile the high quality firm sells only in the North plays a crucialrole in our analysis. Such an asymmetric market structure canarise in our model because the two firms have uneven export incen-tives: the lure of the lucrative Northern market is stronger than thatof the Southern market. We find that the strategic price competitionunder such a market structure tends to be rather subtle. To gain fur-ther insight, suppose the North permits PIs while the South doesnot. Under such a policy configuration, if demand is relatively simi-lar across countries the low quality firm charges its optimal monop-oly price in the South while both firms charge their optimaldiscriminatory prices in the Northern market. However, if demandstructure is sufficiently asymmetric across countries, the low qualityfirm's optimal monopoly price in the South is lower than its optimaldiscriminatory price for the Northern market. Under such a scenario,the North's openness to PIs induces the low quality firm to set acommon international price that actually exceeds its optimalmonopoly price for the Southern market: i.e. it tolerates a sub-optimally high price in the Southern market to charge a moreattractive price in the Northern market (Lemma 2). The resultingsoftening of price competition in the North, in turn, makes forsakingthe Southern market more attractive for the Northern firm, becauselocal demand for its product is relatively large. Indeed, we show thatsuch an asymmetric market structure can arise not only when onlyone country permits PIs but also when both countries do so(Propositions 2 and 3).
Our policy analysis sheds new light on how heterogeneity in de-mand structure across countries determines national preferences forPI policies. We show that if governments maximize national welfarethe North is more likely to permit PIs (i.e. it prefers to permit PIsover a larger parameter space) when the South does not do so.With its smaller market, the Southern government's influence onmarket structure tends to be weaker, something that is reflectedin the nature of the policy equilibrium: if the North is open to PIs,the South also (weakly) prefers to be open to PIs whereas a North-ern ban on PIs makes the South indifferent between its two policyoptions since it renders the Southern policy inconsequential formarket structure.
The subgame perfect equilibrium of our model (stated inProposition 6) is as follows: when the degree of asymmetry betweenthe two markets is high and each government maximizes its nationalwelfare, the North forbids PIs and international price discrimination
264 S. Roy, K. Saggi / Journal of International Economics 87 (2012) 262–276
prevails; otherwise, it permits PIs and uniform pricing obtains.6 Thispolicy result is noteworthy for several reasons. First, it is surprisingsince North's welfare under uniform pricing is strictly higher thanthat under price discrimination. Therefore, only when the degree ofasymmetry across markets is small can the North implement a policythat yields its most preferred market outcome.Why doesn't the Northsimply permit PIs? As was noted earlier, if the North permits PIs andmarkets are sufficiently asymmetric, uniform pricing does not emergeas an equilibrium outcome. Rather, under such circumstances, thehigh quality firm abstains from serving the Southern market inorder to charge a high price in the Northern market, an outcomethat is detrimental for Northern consumers and overall Northern wel-fare. To avoid this outcome, the North is better off prohibiting PIs:while international price discrimination is not as desirable to theNorth as uniform pricing, it is preferable to an asymmetric marketstructure under which its firm does not sell in the South. This policyresult accords quite well with the type of PI policies that are observedin the world: recall that the two largest markets in the world— the EUand the US — prohibit PIs from most of the rest of the world.7 Our ex-planation for these observed policy outcomes is that by inducing in-ternational market segmentation and shielding their respectivefirms from the threat of arbitrage-induced PIs from rest of theworld, the prohibition of PIs by the EU and the US ensures that theirfirms choose to serve markets in other parts of the world. Further-more, our model suggests that the adoption of these policies on thepart of the EU and the US makes smaller developing countries indif-ferent between their policy options since what they do does not affectmarket outcomes. Such indifference on their part is consistent withthe fact that we do not observe a common exhaustion regime acrossthe developing world.8
The EU's stance on exhaustion of IPRs has been clarified over theyears in a series of cases decided by the European Court of Justice(ECJ). A prominent recent example is Silhouette International SchmiedGesellschaft mbH & Co. v. Hartlauer Handelsgesellschaft mbH, a case in-volving the parallel imports of some spectacle frames into Austriafrom Bulgaria and Soviet Union against the wishes of the trademarkowner (Silhoutette). In its 1998 ruling over this case, the ECJ heldthat national rules allowing for international exhaustion of trademarkrights were incompatible with the functioning of the common inter-nal market in the EU. The court ruled clearly in favor of communityor regional exhaustion — i.e. parallel imports could flow freely withinthe EU but not from outside. This directive of the ECJ was in contrastto the historical policies of several major EU members: Austria, Ger-many, Netherlands, Finland, and the UK all followed international ex-haustion provided parallel imports were essentially identical inquality to locally sold goods with the standard for what constituted“material difference” between the two sets of goods differing some-what across countries.9 One interpretation of this change in the ex-haustion policy of these European nations is that with the formationof the EU, the combined market size of the region came to dictate
6 A noteworthy aspect of this result is that a unilateral prohibition on PIs by theNorth generates a substantial positive spillover for the South: not only do Southern con-sumers enjoy lower prices for both goods under international price discrimination, thelow quality firm also benefits from being able to charge a higher price in the Northernmarket.
7 Furthermore, in several recent bilateral trade agreements that have been dubbed“TRIPS-Plus” — such as the one with Jordan — the US has insisted that the partnercountry not allow PIs from abroad, a policy that goes beyond TRIPS since it takes awaythe partner country's freedom to pick the exhaustion regime of its choosing but is con-sistent with safeguarding the profits of US industries in its market.
8 Indeed, even within Africa, there is a significant variation in exhaustion policies:while Ghana, Namibia, South Africa, and Zimbabwe follow international exhaustion,Botswana, Madagascar, Mozambique, and Nigeria have opted for national exhaustion(Biadgleng, 2009).
9 To be sure, not every EU member followed international exhaustion of trademarks:for example, Italy, France, and Greece did not follow this doctrine. See Baudenbacher(1998).
the exhaustion policy of the region as opposed to the individual mar-ket size of each country. If so, the observed outcome is quite in linewith what is predicted by our model: all else equal, a sufficientlylarge increase in the market size of the North makes it optimal for itto switch from allowing PIs from the rest of the world to forbiddingthem.
Our analysis contributes to, and to some extent unifies, twostrands of the literature on PIs: one that studies interaction betweenfirms taking government policies as given and another that analyzesthe impact of alternative government policies but abstracts from stra-tegic interaction between firms.10 In the latter tradition, the seminalpaper is by Malueg and Schwartz (1994) who show that the possibil-ity of PIs can induce a monopolist to not serve markets with higherelasticities of demand and thereby lower world welfare.11 The centralquestion addressed by Malueg and Schwartz is a normative one:should firms be allowed to establish exclusive sales territories inter-nationally? In our view, it is important to also identify the incentivesthat individual governments have to allow or restrict PIs from a na-tional welfare perspective.
One of the few papers that analyzes the choice of PI policies in amulti-country setting is Richardson (2002). However, our analysisdiffers from his along several important dimensions. First, in ourmodel each firm decides whether or not to sell its product in the for-eign market, while Richardson (2002) considers a scenario where allcountries import a common good from a foreign monopolist who nec-essarily sells in all markets. Second, by incorporating oligopolisticcompetition, our model captures strategic considerations absentfrom his analysis. Third, because each country is an importer as wellas an exporter in our model, government policies must considerboth consumer and producer interests, as opposed to only consumerinterests. Indeed, firm profitability turns out to be an important deter-minant of PI policies in our model.
A commonly advanced argument against parallel trade is that itreduces innovation incentives by undermining the ability of IPRholders to profit from their investments in research and development(R&D) — see, for instance, Li and Maskus (2006).12 In a North–Southmodel of endogenous innovation, Grossman and Lai (2008) analyzestrategic policy choice when the South determines its price controlpolicy in response to the PI policy of the North and show that the in-centives for product innovation in the North (as well as its aggregatewelfare) can be higher when the North permits PIs relative to when itdoes not. While we focus on different questions, some of the interna-tional policy externalities identified in Grossman and Lai (2008) alsoappear in our analysis; in particular, Northern openness to PIs may in-duce the Northern firm to eschew the Southern market in order toavoid indirect competition, and this, in turn, can hurt the South.
2. Model
We consider a vertically differentiated industry in a world com-prised of two countries: North (N) and South (S). The industry pro-duces good x that comes in two quality levels where sh denotes thehigh quality and sl the low quality (sh>sl=1). Assume that theNorthern firm produces the high quality and the Southern firm thelow quality and that the cost of production for both qualities equals
10 It should be noted here that the literature on economic integration contains ana-lyses of international oligopoly where integration or segmentation is exogenously giv-en. See, among others, Smith and Venables (1988) and Venables (1990). Markusen andVenables (1988) examine optimal trade and industrial policy in this context. In our pa-per, national policies endogenously determine whether markets are segmented orintegrated.11 Valletti and Szymanski (2006) build on Malueg and Schwartz (1994) by endogen-izing product quality and show that international exhaustion yields lower welfare rel-ative to national exhaustion.12 However, Valleti (2006) shows that parallel trade can actually encourage cost re-ducing R&D when differential pricing is cost based.
265S. Roy, K. Saggi / Journal of International Economics 87 (2012) 262–276
zero. Each consumer buys at most one unit of good x. If a consumer incountry i buys quality j at price pji, its utility is given by
Ui ¼ θsj−pji where j ¼ h; l: ð1Þ
Utility under no purchase is normalized to zero and θ≥0 is a tasteparameter that captures the willingness to pay for higher quality. Allconsumers prefer high quality for a given price but those with ahigher θ are willing to pay more for both qualities and, in addition,value high quality relatively more.
The high quality product produced by the Northern firm as well asthe low quality product produced by the Southern firm are both pro-tected by an IPR such as a patent or a trade-mark. In particular, it isperfectly legal for the Southern firm to sell its low quality productin both countries; the low quality product is not per se a counterfeitor illegal version of the high quality product. One can think of thetwo products as belonging to different generations — an existingdrug and a more effective drug that is recently introduced after newscientific advances (with non-overlapping patent protection betweenthe products); alternatively, one can think of the quality difference asreflecting country bias or perceived differences in regulatory condi-tions (such as monitoring of product safety), technology and inputquality between the North and the South. The role of PI policy ofeach country is to determine whether or not the IPR enjoyed by afirm over its product is exhausted once it is sold abroad which, inturn, determines whether or not the firm can legally prevent PIs ofunits (of its own product) that it sells abroad.13
To capture demand asymmetry between the North and the South,we assume that market size is larger in the North than in the South; inparticular, we set the number of consumers in the South equal to 1and in the North to μ≥1. Further, we assume that the preference pa-rameter θ is uniformly distributed over the interval [0,μi] in countryi=N,S where μN=μ≥μS=1. This formulation allows us to captureasymmetry in size as well as in the distribution of preferences by asingle parameter μ. In what follows, we refer to μ as the extent of de-mand heterogeneity or asymmetry between the two markets.14 Sinceμ≥1, not only is the market demand for both qualities higher in theNorth, but in fact Northern consumers exhibit higher relative prefer-ence for high quality over low quality in the sense that the distribu-tion of θ, the marginal willingness to pay for better quality, in thepopulation of consumers in the North dominates that in the South(in a first order stochastic sense). As a result, the Northern marketis more lucrative than the South for both products and relativelymore so for the high quality product. Furthermore, when both prod-ucts are offered for sale, demand for high quality is less price elasticin the North than in the South.
When trade is possible, the interaction between firms and govern-ments occurs as follows. The PI policy of each government is eitherone of allowing (denoted by P) or forbidding PIs (denoted by N).Thus, there exist four possible global policy regimes: (P,P), (P,N), (N,P), and (N,N), where the policy of the North is listed first. In thenext four sections, we treat the policy regimes as being exogenouslygiven and focus on the resulting trade and market outcomes. Later,we analyze the problem of endogenous determination of PI policiesthrough strategic interaction between governments.
13 Note that in our framework, if PIs are permitted, consumers do not differentiate be-tween units of the product sold directly by the manufacturing firm and those sold byan importer. This kind of differentiation may be important when the product comeswith warranties and other services that are only provided by the manufacturer or itsauthorized dealers. See, for instance, Ahmadi and Yang (2000).14 It should be mentioned here that the assumption that the support of θ in each mar-ket has zero as lower bound ensures that if both firms set prices without botheringabout the effect of their pricing on their profit in other markets, then both sell in equi-librium. In other words, if firms choose not to serve a market in our model it is not be-cause of the “natural monopoly” effect that can arise in models of price competition ina vertically differentiated duopoly (see, Shaked and Sutton, 1983).
Given national PI policies, each firm decides whether or not tooffer its product for sale in the foreign market. Our implicit assump-tion is that each firm has the option of offering its product for saleabroad via a retail sector that is perfectly competitive in each coun-try.15 Firms' decisions regarding the authorization of sales territoriesdetermine global market structure. In the final stage, given marketstructure and government policies, firms compete in prices and con-sumption (and trade) occur.
In our model, each firm decides whether or not to allow the sale ofits product in the foreign market prior to setting prices. An importantimplication of this formulation is that if the high quality (Northern)firm decides not to serve the Southern market, then in the nextstage, its pricing strategy in no way affects the demand for the lowquality (Southern) firm's product in the South since there is noprice competition between firms in the South. An alternative specifi-cation would be one where both products are always offered for salein both markets and each firm simply chooses a pair of prices — onefor each market. Under such a formulation, the high quality firm caneffectively eliminate sales in the South by charging a price that is suf-ficiently higher than the price charged by the low quality firm. Whileequilibrium policy outcomes under this alternative approach are like-ly to be similar to ours, the price competition stage is more tractableunder our formulation. The two approaches differ at the price compe-tition stage because under the alternative specification an outcomewhere the high quality firm finds it profitable to abandon the South-ern market — for instance, when PI policies prevent price discrimina-tion and the Southern market is too small or the degree of marketcompetition is too severe or both— could be consistent with a contin-uum of pricing equilibria where the high quality firm's foreign price(at which it sells zero in the South) still affects the demand curve fac-ing the low quality firm and places a ceiling on its market power. Fur-thermore, these equilibria will differ with respect to the price atwhich Southern consumers buy the low quality good and thereforein terms of the welfare that they generate. By allowing firms to aban-don foreign markets prior to price competition, our approach sim-plifies the price competition stage and avoids this kind ofindeterminacy.
Under trade, if both qualities are available for purchase at pricesphi and pli, country i's consumers can be partitioned into three groupson the basis of two threshold parameters θli and θhi: those in the rangeof [0,θli) buy neither high nor low quality; those in [θli,θhi) buy lowquality; and those in [θhi,μi] buy high quality where
θli ¼plisl
and θhi ¼phi−pli
Δsð2Þ
where Δs≡sh−sl > 0. Using these threshold parameters, demandfunctions in country i for the two qualities are as follows:
xji pli;phið Þ ¼θhi−θli ¼
phi−pliΔs
− plisl
if j ¼ l
μ i−θhi ¼ μ i−phi−pli
Δsif j ¼ h
:
8><>: ð3Þ
The demand functions in Eq. (3) can be used to calculate consum-er surplus in country i over the two qualities:
csi pli; phið Þ ¼ ∑jcsji pli;phið Þ ¼ ∫
θhi
θli
slθ−plið Þdθþ ∫μ i
θhi
shθ−phið Þdθ ð4Þ
15 Thus, firms do not have to share rents with retailers and the vertical pricing issuesthat are central to the analysis of Maskus and Chen (2002) and Maskus and Chen(2004) do not arise in our model. In a related context, Raff and Schmitt (2007) haveshown that when competitive retailers order inventories before observing market de-mand, a manufacturer can actually benefit from parallel trade.
266 S. Roy, K. Saggi / Journal of International Economics 87 (2012) 262–276
which simplifies to
csli pli;phið Þ ¼ θhi−θlið Þ sl θhi þ θlið Þ2
−pli
� �
and cshi ¼ μ i−θhið Þ sh μ i þ θhið Þ2
−phi
� �:
ð5Þ
In what follows, let r≡ shsl≥1 denote the quality gap between goods
and normalize sl=1.
3. Alternative market outcomes
In our model, PI policies influence global market outcomesthrough two channels. First, they determine whether a firm engagedin international trade can charge differential prices at home andabroad. Second, they affect a firm's incentive to authorize or not au-thorize sales of its product in the foreign market i.e., the decision ofa firm to export or not. In this section, we briefly discuss the variousmarket outcomes that can arise in our model. As we show later, thedegree of demand asymmetry across countries (μ), the quality gapbetween goods (r), and the PI policies of the two governments jointlydetermine which of these outcomes emerges in equilibrium in anygiven situation.
The various market outcomes can be classified as follows:
(i) Autarky {A}: Neither firm exports so that each charges its opti-mal monopoly price in its home market.
(ii) International price discrimination {D}: Both firms export andcharge discriminatory prices across markets.
(iii) Uniform pricing {U}: Both firms export and charge uniformprices at home and abroad.
(iv) Asymmetric market coverage Λf g: only the low quality firm ex-ports and it charges the same price in both countries.
(v) Asymmetric market coverage Λm� �: only the low quality firm
exports but it price discriminates across countries. The super-script m indicates that the low quality firm exercises full mo-nopoly power at home (South).
(vi) Asymmetric market coverage H: only the high quality firm ex-ports and it charges the same price in both markets.
(vii) Asymmetric market coverage {Hm}: only the high quality firmexports but it charges different prices at home and abroad.The superscriptm indicates that the high quality firm exercisesfull monopoly power at home (North).
For ease of reference, the classification of market outcomes (giventhat at least one firm exports) is given in Table 1 below:
As we will show below, market outcomes {H} and {Hm} do notarise in equilibrium. Therefore, we do not discuss these outcomesany further and refer the reader to Roy and Saggi (2011) for the rele-vant details. Under autarky, the local firm in each country acts as amonopolist and the autarkic equilibrium price in the North equalspmh ¼ μsh
2 while that in the South equals pml ¼ 12.
Under price discrimination {D}, in country i the low quality firmchooses pli to solve
Maxpli
πli pli; phið Þ ¼ plixli pli; phið Þ ¼ pliphi−pli
Δs− pli
sl
� �ð6Þ
Table 1Alternate market outcomes and pricing behavior.
Differential internationalprices
Common internationalprices
Both firms export {D} {U}Only low quality exports Λmf g Λf gOnly high quality exports {Hm} {H}
The reaction functions in market i under price discrimination aregiven by
pli ¼phi2r
and phi ¼μ i r−1ð Þ
2þ pli
2:
Under uniform pricing {U}, the low quality firm chooses pl to solve
Maxpl
∑iπli pl; phð Þ ¼ 2plxl pl;phð Þ ¼ 2pl
ph−plΔs
− plsl
� �ð8Þ
whereas the high quality firm chooses ph to solve:
Maxph
∑iπhi pl;phð Þ ¼ ∑
iphxhi pl; phð Þ ¼ ∑
iph μ i−
ph−plΔs
� : ð9Þ
The reaction functions under uniform pricing are as follows
pl ¼ph2r
and ph ¼ μ þ 1ð Þ r−1ð Þ4
þ pl2:
The reaction functions for the low quality firm are the same underdiscrimination and uniform pricing because the demand asymmetryparameter μ directly affects demand for only the high quality goodand it does not appear in the low quality firm's first order conditionfor profit maximization. In other words, an increase in μ leads to anincrease in the low quality firm's price only because the high qualityfirm finds it optimal to raise its price due to an expansion in the setof Northern consumers that value quality relatively more. A compar-ison of the solutions to the pricing problems under {D} and {U} yields:
Lemma 1. Under price discrimination, each firm charges a higher pricein the North: pjN(D)>pjS(D). Furthermore, each firm's price underuniform pricing is the average of its optimal discriminatory prices inthe two markets: pj Uð Þ ¼ ∑i pji Dð Þ=2.
Lemma 1 highlights an important aspect of price discriminationand uniform pricing from the viewpoint of consumer welfare. Whileprices are strictly lower in the North under uniform pricing relativeto price discrimination, the opposite is true in the South. As we willshow later, this clash between consumer welfare in the two countriesover these market structures plays an important role in determiningthe welfare implications of different policy regimes.
When both products are offered for sale in both markets and firmsare constrained to charge uniform prices, if there is too much asym-metry in demand across markets then the equilibrium outcomecould be one where there are no sales of the high quality good inthe South. To ensure that positive quantities are sold in both marketsunder uniform pricing, we need μbμ≡ 6r−1
2r−1. Furthermore, as well shallshow below, to avoid a scenario where price competition is so stiffthat the low quality firm refrains from selling in the North when thehigh quality firm serves both markets, we need r≥r� ¼ 1þ 3
ffiffi2
p8 . For
convenience, we collect these parameter restrictions in Assumption1, which is assumed to hold through-out the paper:
Assumption 1. (i) μbμ≡ 6r−12r−1 and (ii) r≥r� ¼ 1þ 3
ffiffi2
p8 .
In the asymmetric market outcome Λm� �, the low quality firm
charges its optimal monopoly price plm=1/2 in the South and the
two firms charge their optimal discriminatory prices plN(D) andphN(D) in the North so that the outcome in the Northern market isidentical to that under {D}.
267S. Roy, K. Saggi / Journal of International Economics 87 (2012) 262–276
Under Λf g, the low quality firm chooses its common internationalprice pl to solve
Maxpl
plph−plΔs
−plsl
� �þ pl 1− pl
sl
� �ð10Þ
where the first term denotes its profits in the North and the second inthe South, where it is the sole seller. The high quality firm serves onlythe North and solves
Maxph
ph μ− ph−plΔs
� : ð11Þ
The first order conditions for these problems yield the followingreaction functions under Λf g:
pl ¼r−1
2 2r−1ð Þ þph
2 2r−1ð Þ and ph ¼ μ r−1ð Þ þ pl2
:
Using these reaction functions it is easy to show that the pricescharged by both firms lie between their corresponding prices under{U} and {D}; further, the low quality firm's price is higher than its mo-nopoly price in the South.
Lemma 2. (i) Under the asymmetric market outcome Λf g where(only) the low quality firm serves both markets at thecommon international price pl Λð Þ, the price pj Λð Þcharged by firm of quality j, j=h, l, lies in between itsprices under {U} and {D}:pj Uð Þbpj Λð ÞbpjN Dð Þ; j ¼ h; l:Furthermore, the low quality firm's price pl Λð Þ exceedsits optimal monopoly price in the South.
(ii) In the asymmetric market outcome Λm� �where (only) the low
quality firm serves both markets, it charges its optimal monopolyprice pl
m=1/2 in the South while both firms charge their optimaldiscriminatory prices plN(D) and phN(D) in the North.
Having discussed the candidate market outcomes, we next consid-er how PI policies of individual countries influence equilibrium mar-ket outcomes. Since PIs are induced by the possibility of arbitragebetween national markets, it is useful to begin with the case wherePIs are permitted by the North but not by the South.
4. If only the North permits PIs
In this section, we derive the equilibrium market outcome underthe mixed policy regime (P,N) where the North permits parallel im-ports but the South does not. Under this policy configuration, thelow quality (Southern) firm is free to compete in the Northern marketat a price lower than its domestic price; however, the same is not truefor the high quality (Northern) firm.We will show that this creates anincentive for the low quality firm to export i.e., serve both markets.Furthermore, if the asymmetry in demand structure between Northand South is high so that the demand for high quality in the Southis significantly lower than in the North, the high quality firm prefersto forsake the South and simply not export; in that case the asymmet-ric outcome Λf g or Λm� �
obtains. On the other hand, if the demandstructures are not too different, the high quality firm serves both mar-kets and we show that in that case, the North's openness to PIs is suf-ficient to ensure that both firms charge uniform prices i.e., marketoutcome {U} obtains. In what follows, we develop the main argu-ments leading to these results (summarized in Proposition 2 towardthe end of this section).
First suppose that the high quality firm chooses to not serve theSouthern market while the low quality firm serves both markets.Under such a scenario, the low quality firm's pricing behavior de-pends upon the extent of disparity in demand for high quality be-tween the two countries. While the North's openness toward PIsundoes any attempt on its part to charge a lower price in the South,
it is free to charge a higher price there since PIs are forbidden by it.Furthermore, such pricing can indeed arise when the low qualityfirm enjoys monopoly status in the South. To see this, suppose thatthe low quality firm charges its optimal monopoly price pl
m=1/2 inthe South and the two firms charge their optimal discriminatoryprices plN(D) and phN(D) in the North. Given that only the North per-mits PIs, such a configuration of prices can be sustained iff
pmlS≥plN Dð Þ⇔12≥ μ r−1ð Þ
4r−1⇔μ≤μm
l ≡4r−12 r−1ð Þ : ð12Þ
In other words, if μ≤μlm the two markets in effect become per-fectly segmented and despite the North's openness to PIs, the lowquality firm is free to act as an unconstrained monopolist in theSouth. Note also that, under such a scenario, the market equilibriumin the North coincides with international price discrimination; inother words, we obtain the market outcome Λm� �
. On the otherhand, when μ>μlm the low quality firm must charge a common in-ternational price if it chooses to sell in both markets under (P,N)and therefore, the asymmetric market outcome Λf g obtains. Asnoted in Lemma 2, under the outcome Λf g, the uniform pricecharged by the low quality firm actually exceeds its optimal monop-oly price pl
m=1/2 in the South while it falls short of its optimal dis-criminatory price for the North. The inequality pml bpl Λð Þ holdsbecause Northern openness to PIs induces the low quality firm totolerate a reduction in its Southern profit in order to get closer toits preferred Northern price pjN(D).
Whenever the optimal monopoly price in the South plm=1/2 can-
not be sustained by the low quality firm (which happens whenμ>μlm) its reaction function Rl Λð Þ under Λf g lies strictly above its re-action function Rl(D) under {D} — i.e. when μ>μlm, relative to pricediscrimination, the low quality is relatively more aggressive in pricecompetition. This is because pl Λð Þ > pml and the low quality firm isquite eager to reduce its price in response to a price cut by its rival.As a result, the equilibrium pair of prices under Λf g are lower relativeto {D} whereas they are higher relative to {U}.
It is straightforward to show that there exists μl* where μl*bμlm
such that over the parameter range μl*bμbμlm the low quality firmwould be better off charging the common price pl Λð Þ even thoughover this parameter range it can sustain its optimal monopolyprice pl
m in the South while charging its optimal discriminatoryprice plN(D) in the North. This is because pl Λð Þ > plN Dð Þ wheneverμbμlm: while the low quality firm would lose profit in its domesticmarket by charging the common international price pl Λð Þ, whenμ>μl* this loss is more than compensated by the increase in profitthat results from the softening of price competition in the Northernmarket. Of course, the high quality firm would necessarily benefit ifthe low quality firm were to charge a higher price. However, sincethe low quality firm cannot commit to charging a common pricein both markets, when the policy regime is (P,N) and μ≤μlm, inNash equilibrium it charges different prices in the two markets:plN(D) in the North and pl
m in the South.Let πi(m) denote firm i's equilibrium profit under the market out-
come m and define
Δπl≡πl Λ
m� �−πl Að Þfor μ≤μm
lπl Λð Þ−πl Að Þfor μ > μm
l
�
as the low quality firm's unilateral incentive to serve the North — i.e.Δπl is the incremental profit earned by the low quality firm from serv-ing the North given that the high quality firm does not serve theSouthern market.
Our first result is as follows:
Proposition 1. If the North permits PIs whereas the South does not, theautarkic market outcome {A} cannot arise in equilibrium since the low
r
µlm
µ*
µ
r*
µuRegion B: {U}
Region A: {U}
Region C: { m }
Region D: { }
Fig. 1. Equilibrium market structure under (P, N).
268 S. Roy, K. Saggi / Journal of International Economics 87 (2012) 262–276
quality firm's unilateral incentive to serve the Northern market is strictlypositive: i.e. Δπl > 0 for all feasible μ and r.
To see why this is true, suppose the policy regime is (P,N). Whenμ≤μlm, if the low quality firm serves the North the market outcomeΛm� �
obtains i.e., it earns optimal monopoly profit at home and addi-tional profit πlN(D) abroad. Even though pl
m≥plS(D), PIs cannot flowto the South due to its policy stance. Thus, if μ≤μlm thenΔπl ¼ πlN Dð Þ > 0.
Now suppose μ>μlm. Under this scenario, the pricing behavior de-scribed in part (i) of Lemma 2 applies and in Appendix A we showthat Δπl ¼ πl Λð Þ−πl Að Þ > 0. The intuition is as follows: when μ>μlm,preserving its monopoly status in the much smaller Southern marketis not particularly attractive to the low quality firm. Indeed, as notedearlier, for μ>μlm the low quality firm is willing to charge a priceabove its optimal monopoly price in the South so as to serve theNorth at a more desirable price.
Suppose now that the high quality firm chooses to serve the Southand consider the low quality firm's best response. The low qualityfirm's reciprocal incentive for serving the North when it must chargea common price in both markets (due to the North's openness toPIs) is defined by
Δπl Uð Þ≡πl Uð Þ−πl Hð Þ:
It is straightforward to show that Δπl Uð Þ≥0 iff r≥r� ¼ 1þ 3ffiffi2
p8 ,
which is guaranteed by part (ii) of Assumption 1.Proposition 1 and part (ii) of Assumption 1 imply that to derive
equilibrium outcomes under (P,N), we need to only consider thehigh quality firm's best response to the low quality firm serving theNorthern market. Given that the low quality good is sold in both mar-kets, if the high quality firm chooses to serve both markets uniformpricing obtains under (P,N). On the other hand, if the high qualityfirm decides to not serve the Southern market then the market out-come depends upon the degree of demand asymmetry: when μ≤μlm
we obtain Λm� �whereas for μ>μlm, we get Λf g.
Given this, the high quality firm's reciprocal incentive is defined asfollows:
Δπh Uð Þ≡ πh Uð Þ−πhN Dð Þ for μ≤μml
πh Uð Þ−πh Λð Þ for μ > μml
�:
It is straightforward to show that for μ≤μlm
Δπh Uð Þ≥0⇔μ≤μ�≡1þffiffiffi2
p
whereas for μ>μlm we have
Δπh Uð Þ≥0⇔μ≤μu
where μu ≤ μ* iff μ≤μlm and limr→∞
μu=μ*. The fact that the high qualityfirm's reciprocal incentive is positive only when the Northern demandfor high quality is not too large relative to the South is quite intuitive:given that the North permits PIs, the larger the Northern demand forhigh quality relative to the South, the more constrained is the highquality firm's pricing behavior in the North.
We can now derive market outcomes under the policy pair (P,N).These outcomes are illustrated in Fig. 1 drawn in the (r,μ) space.
The downward sloping curve μlm in Fig. 1 defines the boundarybelowwhich the low quality firm is able to charge its optimal monop-oly price pl
m in the South so that the market outcome Λm� �is relevant
whereas above μlm, the low quality firm charges the price pl Λð Þ in bothmarkets and the market outcome Λf g is relevant.
The horizontal line plots μ=μ*: below this curve the high qualityfirm has a reciprocal incentive to serve the South when the lowquality firm is able to sustain its optimal monopoly price (i.e. it
plots Δπh Uð Þ≥0 for μ≤μlm). Above μ*, the high quality firm lackssuch an incentive and prefers the market outcome Λm� �
to uniformpricing {U}. The upward sloping curve μu in Fig. 1 plots the locus ofΔπh Uð Þ ¼ 0 below which the high quality firm has a reciprocal incen-tive to serve the South when the low quality firm charges the com-mon international price pl Λð Þ (i.e. for μ>μlm).
When the demand asymmetry between the two countries exceedsthe outer boundary defined by μu and μ* — i.e. in region C whereμ*bμ≤μlm and in region D where μ>max{μlm,μu} — the high qualityfirm prefers to not serve the South and the equilibrium market out-come is determined by the low quality firm's pricing behavior: inregion C the equilibrium outcome is Λm� �
whereas in region D it isΛf g. It is worth emphasizing that the decision to not serve theSouth on the part of the high quality firm reflects considerationsthat come into play solely due to the North's policy of permittingPIs since, by assumption, selling abroad imposes no additional costson firms. On the other hand, below the outer boundary defined byμu and μ* (i.e. over region A where μ≤μu and region B whereμu≤μ≤ μ*), markets are fairly similar in demand structure and themarket outcome is uniform pricing.
We close this section by summarizing the main results inProposition 2:
Proposition 2. If the North permits PIs and the South does not, the equi-librium market outcomes are as follows:
(i) uniform pricing obtains when μ≤max{μu, μ*} (regions A and B inFig. 1);
(ii) the asymmetric outcome Λm� �obtains when μ*bμ≤μlm (region C
in Fig. 1); and(iii) the asymmetric outcome Λf g obtains when μ>max{μlm,μu} (re-
gion D in Fig. 1).
5. If both countries permit
In this section, we derive the equilibrium market outcome underthe policy pair (P,P) i.e. when both countries permit PIs. We beginby observing that under (P,P), regardless of the degree of market
µu
µh
{U}
{U}
µl
r*
µ
r
{ }
{U}
Fig. 2. Equilibrium market structure under (P, P).
269S. Roy, K. Saggi / Journal of International Economics 87 (2012) 262–276
asymmetry, if a firm serves both markets it must do so at a commoninternational price. More specifically, this implies that market out-comes Λm� �
and {D} cannot arise.Next, we argue that Proposition 1 does not hold under (P,P): i.e.,
when both countries permit PIs, the low quality firm does not neces-sarily have a unilateral incentive to serve the North. Intuitively, whenproducts are not highly differentiated, the decision to serve the Northis not attractive to the low quality firm because price competition inthe North is fierce. And since the low quality firm must charge a com-mon price in both markets under (P,P), stringent competition in theNorth also undermines its profit in the Southern market.16 Under(P,P), direct calculations show that
Δπl≥0⇔μ≥μΛl :
Uniform pricing is an equilibrium under (P,P) iff each firm has areciprocal incentive to serve the foreign market: i.e. Δπj Uð Þ≥0 forj=h, l. Using the incentive functions Δπj Uð Þ along with Δπh and Δπl
allows us to fully describe equilibrium market outcomes under (P,P).Fig. 2 illustrates equilibrium market structures under (P,P).Above the downward sloping curve Δπl ¼ 0 or (μ ¼ μΛ
l ) the lowquality firm has a unilateral incentive to serve the foreign market.The negative slope of the curve is intuitive: as the intensity of productmarket competition decreases (i.e. r increases), the critical level ofNorthern demand required to induce the low quality firm to sell inthe North declines. Below the upward sloping curve μh, the high qual-ity firm has a unilateral incentive to serve the South.
It is useful to compare Figs. 1 and 2. The first point to note is that inregion D (i.e. when μ>max{μlm,μu}), the equilibrium outcome underboth (P,P) and (P,N) is Λf g. When the low quality firm cannot sustainits optimal monopoly price in the South under (P,N), the North's per-missive policy toward PIs is the main determinant of market outcomesince the high quality firm chooses not to serve the South in order tostay close to its preferred price for the Northern market.
Second, in region C (where μ* bμ≤μlm) while Λf g obtains whenboth countries permit PIs, Λm� �
obtains when only the North doesso. Recall from Lemma 2 that under Λm� �
prices in the North equalpjN(D) while in the South the low quality firm charges its optimal mo-nopoly price pl
m=1/2. Thus, given that the North permits PIs and theSouth does not, when μ≤μlm the Southern firm is less aggressive dur-ing price competition under the asymmetric outcome Λf g relative tothat under Λm� �
: pl Λð Þ > pml and pjN(D)> pj Λð Þ. Thus, as we empha-size in Proposition 3 below, over region C prices are higher in theNorth when both countries permit PIs relative to when only theNorth does so while the opposite is true of prices in the South. As aresult, given that the North permits PIs and the Northern firm doesserve the South, the firm's profit is higher in region C if the South per-mits PIs relative to when it does not. Thus, the presence of strategiccompetition implies that, holding the Northern PI policy constant, aunilateral reversal of Southern policy (from banning PIs to allowingthem) can increase the Northern firm's profit by softening price com-petition in the Northern market.
Third, while rough intuition suggests that uniform pricing mightbe more likely to obtain when both countries permit PIs relative towhen only the North does, a comparison of Figs. 1 and 2 shows thatthis is not the case. More specifically, note from these figures thatover region A uniform pricing obtains under both (P,P) and (P,N)whereas over region B uniform pricing obtains only under (P,N).Over region B, the high quality firm's preference between alternative
16 By contrast, under (P,N) the low quality firm's profit in the Southern market is rel-atively better protected due to the Southern prohibition on PIs and it therefore neces-sarily has a unilateral incentive to serve the North. Recall that when μ≤μlm, the lowquality firm actually earns monopoly profit in its market under (P,N) if the high qualityfirm chooses to not sell its goods there.
markets outcomes is as follows: Λf g≻ Uf g≻ Λm� �. Over this region,
when only the North permit PIs, the high quality firm ends up servingthe South since it prefers uniform pricing {U} to Λm� �
. However,when both countries permit PIs Λm� �
is not feasible since the lowquality firm must charge a common international price that exceedsits optimal discriminatory price for the North. The softening of pricecompetition in the Northern market over region B under Λf g makesit worthwhile for the high quality firm to not serve the South under(P,P). It is noteworthy that it is the inability of its rival to price dis-criminate internationally under the regime (P,P) relative to (P,N)that makes the high quality firm opt for the asymmetric outcomeΛf g over uniform pricing.
We collect the main results of this section below:
Proposition 3. Suppose both countries permit PIs. Then, uniform pricingobtains when μ≤μu (region A in Fig. 1) and the asymmetric market out-come Λf g obtains otherwise.17 For a subset of the parameter space wherethe degree of asymmetry between markets is in an intermediate range(i.e. over region C in Fig. 1 where μ* bμ≤μlm), prices are actually higherin the North when both countries permit PIs compared to the policyregime (P,N) where only the North permits PIs.
6. If North forbids
In this section, we discuss the equilibrium market outcomes whenthe North forbids parallel imports. We begin by deriving the equilib-rium market outcome under the policy regime (N,P) where the Southpermits PIs.
We first argue that the autarkic outcome cannot be an equilibriumwhen the North prohibits PIs since the high quality firm has a unilateralincentive to serve the South. To see why, suppose the low quality firmdoes not serve the North. Then, the high quality firm charges its opti-mal monopoly price in the North so long as the South's permissivepolicy toward PIs does not prevent it from doing so. But since μ≥1,it follows that the high quality can always sustain its optimal monop-oly price in the North when the Northern government forbids PIs and
17 For completeness, we should note that there is a tiny area over which both autarkyand uniform pricing are equilibria. This area is defined by μh ≤ μ≤μΛ
l . In this area, eachfirm has a reciprocal incentive to serve the foreign market but no unilateral incentiveto do so. For the remainder of the paper, we will take uniform pricing to be the equi-librium over this tiny region.
π lD= π l
A
πhD= πh
A
Region α: both lose
Region δ : both gain
Region γ : firm l gains
Region β: firm h gains
µ
rr*
Fig. 3. Autarky versus price discrimination.
270 S. Roy, K. Saggi / Journal of International Economics 87 (2012) 262–276
firms compete (only) in the South. This implies that beginning at au-tarky, under (N,P) the high quality firm will necessarily choose toserve the South. Doing so brings an incremental gain of πhS(D)while protecting its monopoly profit in the North: PIs are prohibitedby the North and no PIs occur to the South since the price of thehigh quality goods is lower there (phm≥phS(D)).
We now argue that the low quality firm necessarily has a reciprocalincentive to serve the North when it forbids PIs. To see this simply notethat, given that it does not serve the North, the low quality firm se-cures an incremental gain of πlN(D) by choosing to sell abroad with-out having any detrimental effect on its monopoly profit in the South.
Next, observe that when the North forbids PIs, the Northern policymakes it possible for the high quality firm to price discriminate inter-nationally. This observation rules out uniform pricing as an equilibri-um outcome. Thus, there remain only three candidates forequilibrium under (N,P): Λf g, Λm� �
, and {D}.As before, the choice between two of three remaining candidates
for equilibrium outcomes — Λf g and Λm� �— is determined by the
degree of demand asymmetry. When the South is open to PIs andthe North is not, the low quality firm can charge its optimal monop-oly price in the South only when that price is lower than its discrim-inatory price in the North: i.e. plS
m≤plN(D)⇔μ≥μlm. Thus, overμ≥μlm, the equilibrium has to be either Λm� �
or {D}. However,Λm� �
fails to be an equilibrium because the high quality firm neces-sarily has a reciprocal incentive to serve the South when μ≥μlm: byserving the South it secures an incremental gain of πhS(D) in theSouth without lowering its profit πhN(D) in the North. Thus, wehave shown that when μ≥μlm, both firms have a reciprocal incentiveto serve the foreign market and international price discrimination{D} is the equilibrium outcome.
Now consider the case μbμlm. Consider Λf g as a candidate for equi-librium over this parameter range. Starting at Λf g if the high qualityfirm chooses to serve the South, we move to market outcome {D}whereas if the low quality firm chooses to withdraw from the Northwe revert to autarky {A}. This implies that Λf g is an equilibrium iff(i) πh Dð Þbπh Λð Þ ⇔μ> μhd and (ii) πl Λð Þ > πl Að Þ ⇔ μ> μΛ
l . It is easyto show that the curve μhd lies strictly to the left of r* so that part(ii) of Assumption 1 rules out the parameter range μlΛ≤μbμhd. Inother words, since r> r* it must be that Δπh Dð Þ > 0.
Thus, we have argued that both types of incentives — unilateral aswell as reciprocal — are positive for both firms under the policy pair(N,P). This necessarily implies that international price discriminationis the unique equilibrium outcome under (N,P).
Finally, it is transparent that if the policy pair is (N,N) and PIs can-not flow in either direction, it is a dominant strategy for each firm toserve the foreign market. Furthermore, absent the threat of PIs, firmswill charge their optimal discriminatory prices in each market.
We have:
Proposition 4. If the North forbids PIs, the Southern policy isinconsequential and international price discrimination obtains as theequilibrium outcome.
It is worth noting that Proposition 4 does not imply that both firmsare better off under international price discrimination relative to au-tarky. In fact, it is easy to see that both can be worse off relative to au-tarky when the degree of product differentiation (r) is relatively low:under such circumstances severe price competition lowers their re-spective profits below autarkic levels. This is shown in Fig. 3 whichplots the zero-profit contours forΔπj Dð Þ≡πj Dð Þ−πj Að Þ. The downwardsloping contour is that of the low quality firm while the upward slop-ing one is for the high quality firm.
Fig. 3 can be divided into four regions. In region δ, the degree ofdemand asymmetry (μ) is moderate and products are highly differ-entiated (r is large) and both firms are better off relative to autarky:each firm gets access to another market that is comparable in
demand to its local market where such access is accompanied byprice competition that is relatively weak. By contrast, in region α,the severity of price competition under international price discrimi-nation tips the balance in favor of autarky for both firms. In regionβ, only the high quality firm is better off under international pricediscrimination while in region γ only the low quality firm is betteroff. The intuition is as follows. In region γ, the North–South demandasymmetry is large and the low quality firm benefits substantiallyfrom being able to sell its goods in the North whereas the high qual-ity firm has to share its large domestic market with a competitorand therefore loses relative to autarky. Finally, in region β, demandasymmetry is small and product differentiation is moderately large:under such a scenario, sharing its local market in return for accessto the comparably sized Southern market is not as costly for thehigh quality firm since its competitor is at a substantial quality dis-advantage. For analogous reasons, in region β the low qualityfirm is better off under autarky relative to international pricediscrimination.
7. Equilibrium government policies
We are now ready to derive equilibrium policies. Each country'sobjective is to maximize its welfare. Country i's welfare under mar-ket outcome {M} is a weighted sum of consumer surplus and firmprofits:
where M=D, Λ, Λm or U and 0≤λ≤1. In the above welfare function,πdi(M) denotes profit of country i's firm in its domestic marketwhereas πei(M) denotes its export profit. Also, let world welfareunder market outcome {M} be given by ww(M)=wN(M)+wS(M).
In what follows, we focus primarily on the case where govern-ment's maximize aggregate welfare (i.e. λ=1/2) and then commentbriefly on the two polar cases where governments care only aboutfirms or consumers.
18 If the inequality is strict — i.e. μbμu — then it is a strictly dominant strategy for theNorth to permit PIs.
271S. Roy, K. Saggi / Journal of International Economics 87 (2012) 262–276
7.1. Welfare maximizing governments (λ=1/2)
Our first welfare result reports a comparison of the different mar-ket outcomes from the viewpoint of each country:
Proposition 5. Suppose governments seek to maximize national wel-fare (i.e. λ=1/2). Then, each country's welfare ranking of the variousmarket outcomes that can arise in equilibrium is as follows:
(i) For the North: wN Uð Þ > wN Dð Þ > wN Λð Þ > wN Λm� �whereas
(ii) for the South: wS Dð Þ > max wS Uð Þ;wS Λð Þ;wS Λm� �� �.
Note in particular that the welfare of the North under uniformpricing is strictly higher than that under international price discrimi-nation whereas the welfare of the South is strictly lower. From theSouth's perspective, price discrimination is preferred to uniform pric-ing due to two reasons. First, its firm enjoys strictly higher exportprofits under discrimination since price competition in the North issofter relative to uniform pricing. Second, recall from Lemma 2 thatrelative to uniform pricing, prices are lower in the South underprice discrimination. As a result, both firm profitability and consumerwelfare considerations work in the same direction for the South.However, as Proposition 4 notes, whether or not price discriminationobtains in equilibrium depends on North's PI policy and not on that ofthe South.
For the North, consumer welfare and firm profitability workagainst each other: while consumers are better off under uniformpricing, the high quality firm prefers discrimination. Since higherprices under discrimination transfer part of the Northern consumersurplus over to the low quality firm in terms of profits, the North's ag-gregate welfare is higher under uniform pricing relative to interna-tional price discrimination.
We are now in a position to consider each country's optimal PIpolicy in response to the other. Suppose South permits PIs. What isNorth's optimal PI policy? We can answer this question using Fig. 1and Proposition 5. First note from Proposition 5 that the North willpermit PIs so long as parameters are such that its firm exports tothe South when both markets allow PIs. Using Fig. 1, we concludethat, given that the South permits PI, the North adopts the same PIpolicy iff μ≤μu i.e. over region A where the Northern firm's reciprocalincentive is positive. Now suppose the South bans PIs. Then, Fig. 1 im-plies that the North will permit PIs over both regions A and B (i.e. iffμ≤max{μ*,μu}) since the high quality firm's reciprocal incentive toexport is positive over these regions under policy pair (P,N). Thus,over region B the North permits PIs only when the South forbidsthem implying that Southern openness to PIs reduces North's willing-ness to permit PIs.
Now consider the South's best response to the North's policychoice. Recall that a ban on PIs by the North makes the South indiffer-ent between its policy options since the ban is sufficient to induce in-ternational price discrimination. But what if the North permits PIs?Then, Figs. 1 and 2 indicate that Southern policy matters only over re-gion B (μu≤μ≤μ*) and region C (μ*bμ∗≤μlm). Over the rest of the pa-rameter space, Northern openness to PIs determines the marketoutcome and the South is indifferent between its two policy options.
Over region B, given that North permits PIs, South prefers to per-mit PIs in order to obtain the asymmetric market outcome Λf g as op-posed to uniform pricing while over region C, it prefers to permit PIsto obtain Λf g as opposed to {Λm} sincewS Λð Þ≥wS Λm� �
iff μ≤μlm. Thus,given that the North allows PI, the South strictly prefers to allow PIsover regions B and C whereas it is indifferent between its two policyoptions otherwise.
To derive equilibrium policies, suppose we are in region A (i.e.μ≤μu) so that the high quality firm's reciprocal incentive is positivewhen the low quality firm charges a common international price inboth markets. It is easy to see that both (P,N) and (P,P) are Nash equi-libria over region A: the North has no incentive to deviate since
uniform pricing is its most preferred regime whereas the South's PIpolicy is inconsequential for the market outcome.
Now consider region B (i.e. when μu≤μ≤μ*). Here the marketequilibrium under (P,P) is Λf g whereas under (N,P) it is internationalprice discrimination. SincewN Dð Þ≥wN Λð Þ the North bans PIs in regionB to ensure that international price discrimination obtains therebymaking Southern policy inconsequential. Thus, in region B, both (N,P) and (N,N) are Nash equilibria. Similarly, in region C (i.e. whenμ*bμ∗≤μlm) and region D, i.e. for μ>max{μu, μlm}, it is optimal forthe North to forbid PIs to induce international price discriminationand avoid the asymmetric outcome Λf g while the Southern policy isinconsequential.
We can now state:
Proposition 6. When governments maximize national welfare (i.e.λ=1/2) the equilibrium market outcome is determined by the North'sPI policy:
(i) For μ≤μu (region A in Fig. 1) i.e., when the degree of asymmetrybetween demand structures of the two countries is not too large,permitting PIs is a dominant policy choice for the North and uni-form pricing obtains independent of the South's PI policy.18 Inparticular, (P,P) and (P,N) are both Nash equilibria.
(ii) For μ>μu (regions B, C, and D in Fig. 1) i.e., when the degree ofasymmetry between demand structures of the two markets islarge, prohibiting PIs is a strictly dominant policy choice for theNorth and international price discrimination obtains, indepen-dent of the PI policy of the South. In particular, policy pairs (N,P) and (N,N) are both Nash equilibria.
(iii) The PI policy of the South is always inconsequential inequilibrium.
When markets are sufficiently asymmetric in their demand struc-ture, the North forbids PIs to rule out asymmetric market outcomesΛm� �
and Λf g under which its own firm chooses to not serve theSouth so as to charge a high price in the North, which is detrimentalfor Northern consumers and overall Northern welfare. Note alsothat the nature of the North's equilibrium policy is such that theSouthern policy has no effect on market outcomes, and therefore,welfare. This policy outcome is quite consistent with the observedvariation of PI policies across the world. As we noted earlier, thetwo largest markets in the world — EU and the USA — restrict PIsfrom the rest of the world while there is substantial variationamong developing countries with respect to their PI policies, an out-come that might be indicative of the fact that no one type of PI policyis strictly preferable from their viewpoint.
To gain further insight into the welfare calculus underlyingNorth's decision to ban PIs over all regions except region A, supposethe policy pair is (P,N) and the Northern firm chooses to not export.Now consider a reversal in North's policy from permitting PIs to ban-ning them. The first point to note is that in region C, this unilateralchange in Northern policy has no effect on prices in the Northern mar-ket since under the asymmetric outcome Λm� �
, market prices in theNorth coincides with price discrimination (see Lemma 2). Thus,over region C, forbidding PIs increases Northern welfare because ityields additional export profits without having any adverse effect onlocal consumer surplus.
Over region D, if the North chooses to ban PIs in order to induce itsfirm to export, there are two conflicting effects on Northern welfare.On the positive side, the export profit earned by the high qualityfirm contributes to Northern welfare. On the negative side, prices inthe North are higher under {D} relative to Λf g. However, since pricesof both firms increase and it is the change in the reaction function ofthe Southern firm that causes equilibrium prices to change, it turns
272 S. Roy, K. Saggi / Journal of International Economics 87 (2012) 262–276
out that the share of Northern consumers buying the high quality ac-tually increases. To see this, note that under international price dis-crimination we have
In other words, since μ>μlm in region Dwhile market coverage (i.e.the total number of consumers buying either good) is lower in theNorth under price discrimination relative to the asymmetric outcomeΛf g, a higher proportion of them buy the high quality goods. Thisswitching by consumers from low to high quality dampens the ad-verse effect of the price increases that result when the North changesits policy from allowing PIs to banning them thereby altering the mar-ket outcome from Λf g to {D}.19
Finally, note that in region B, the North has no unilateral incentivedeviate from (P,N) to (N,N) since uniform pricing obtains under (P,N)whereas price discrimination obtains under (N,N). However, in regionB, if the North were to permit PIs, the South also prefers to permit PIsto induce the outcome Λf g. But since wN Dð Þ > wN Λð Þ and a Northernban on PIs is sufficient to yield international price discrimination, inequilibrium, the North ends up banning PIs to avoid Λf g.
It is also noteworthy that when the North does ban PIs, its PI policygenerates a substantial positive spillover for the South: not only doSouthern consumers enjoy low prices under discrimination, the lowquality firm also benefits from being able to charge a more attractiveprice in the North.
It is easy to show that aggregate world welfare is strictlyhigher under uniform pricing relative to price discrimination:ww Uð Þ > ww Dð Þ > max ww Λð Þ;ww Λm� �� �
.20 Intuitively, by yieldingprice differentials across countries, international price discriminationcreates an inefficiency relative to uniform pricing. The two symmetricmarket outcomes dominate the asymmetric ones because the latterinvolve less competition in the Southern market. Proposition 6shows that when countries are not too different in demand structure(as is the case over region A), even though each is guided purely by itsown interest, equilibrium policies are efficient in that they maximizeaggregate welfare.
What if government policies were chosen not to maximize aggre-gate welfare? We turn to this next.
7.2. If λ≠1/2
Consider the case where λ=0 i.e. governments care only aboutfirm profits. To derive equilibrium policies, simply recall that a unilat-eral prohibition of PIs by the North is sufficient to ensure price dis-crimination, the most preferred market structure of its firm. As a
19 An analogous logic explains why the North finds it optimal to ban PIs over all re-gions other than A when the South permits PIs and its firm decides not to export. Asis clear, Southern policy is irrelevant for explaining why the North forbids PIs over re-gion D since the outcome Λf g obtains regardless. However, over regions B and C the PIpolicy of the South does matter since the outcome {Λm} cannot arise when the South isopen to PIs. To understand why the North deviates from (P,P) to (N,P) over regions Band C where μ≤μlm, note that this change in Northern policy causes local consumersto switch from high to low quality but this switching is offset by the fact that total mar-ket coverage expands — i.e. fewer consumers abstain from buying either good.20 Indeed, we can show that ww Λð Þ≥ww Λmð Þ iff μ≤μlm.
result, when λ=0 the policy outcome is as described by part (ii) ofProposition 6.
Now consider the situation where governments care only aboutconsumers (i.e. λ=1). First consider South's best response to alterna-tive Northern policies. As before, a Northern ban on PIs deliversSouth's most preferred outcome and its policy becomes irrelevant. Ifthe North is open to PIs, Southern policy matters only when thehigh quality firm's reciprocal incentive is negative (i.e. it matters inall regions other than region A where μ∗≤μu). Over region B, giventhat the North permits PI, it is optimal for South to ban PIs becausedoing so leads to uniform pricing under which prices are lower inthe South relative to the market outcome Λf g. Over region C, theSouth prefers to allow PIs because doing so yields the market out-come Λf gwhich is preferable to Λm� �
since CSS Λð Þ≥CSS Λm� �whenev-
er μ≤μlm. Finally, for μ>max{μlm,μu}, the Southern policy is irrelevantsince the equilibrium outcome Λf g is invariant to its policy. Thus, ifthe North permits PIs, the South prefers to ban PIs over regions B, per-mit them over region C, and it is indifferent otherwise whereas if theNorth forbids PI, the South is indifferent between its two policyoptions.
Recall that the prices in the North under Λm� �is the same as that
international price discrimination so that we have CSN Dð Þ ¼ CSN Λm� �.
Part (i) of Lemma 2 implies that CSN Uð Þ > max CSN Dð Þ;CSN Λð Þf g. Fur-thermore, CSN Dð Þ≥CSN Λð Þ iff μ≤μlm since the low quality firm's com-mon international pricepj Λð Þ is higher than its optimal discriminatoryprice pjN(D) in the Northern market iff μ≤μlm.
Suppose the South permits PI and consider the North's best re-sponse. It is clear that in region A (i.e. for μ≤μu) it is optimal for theNorth to permit PIs in order to induce uniform pricing. However,over other regions uniform pricing is not an equilibrium under (P,P)and the best the North can do is to induce the market outcome it pre-fers between {D} and Λf g. Since CSN Dð Þ≥CSN Λð Þ iff μ≤μlm, if the Southpermits PIs, the North forbids them in regions B and C to induce inter-national price discrimination whereas it permits them in region D toinduce the outcome Λf g.
Consider now the scenario where South forbids PI. What is North'sbest response? As before, in region A it is optimal for the North to per-mit PIs to induce uniform pricing. In addition, the North permits PIsalso over region B (i.e. when μu≤μ≤μ*) since doing so results in uni-form pricing (see Fig. 1). In region C (i.e. when μ*≤μ∗≤μlm) the Northis indifferent between permitting and not permitting PIs sinceCSN Dð Þ ¼ CSN Λm� �
. Finally, in region D i.e. when μ>max{μlm,μu}Northern consumer welfare is higher if it permits PIs since doing soyields the market outcome Λf g and CSN Λð Þ≥CSN Dð Þ when μ≥μlm.Thus, when λ=1, given that the South forbids PIs, the North (weakly)prefers to allow PIs: over region C it is indifferent between its policyoptions whereas everywhere else it strictly prefers to allow PIs.
We can now state the following result:
Proposition 7. If governments care only about consumer surplus (i.e.λ=1), the following hold in equilibrium:
(i) Over region A and D i.e., when demand asymmetry is relativelysmall or very large, permitting PIs is a dominant strategy for theNorth and the policy choice of the South is inconsequential; both(P,N) and (P,P) are Nash equilibria. Uniform pricing is the result-ing market outcome in region A while the asymmetric market out-come Λf g obtains in region D.
(ii) Over region B, the policy Nash equilibrium is (P,N) and uniformpricing obtains.
(iii) Over region C, prohibiting PIs is a dominant strategy for the Northand the policy choice of the South is inconsequential; both (N,P)and (N,N) are Nash equilibria with international price discrimi-nation as the market outcome.
Two things are worth noting about Proposition 7. First, when gov-ernments care only about consumer welfare, equilibrium PI policies
273S. Roy, K. Saggi / Journal of International Economics 87 (2012) 262–276
are such that international price discrimination is less likely to arise asan equilibrium outcome since the North has a strong incentive tokeep local prices low by keeping its market open to PI. Second, in re-gion D, North chooses to open its market to PIs to induce the asym-metric outcome Λf g under which prices are lower in the Northrelative to international price discrimination. By contrast, recallfrom Proposition 6 that only symmetric market outcomes obtainwhen governments weigh consumer and firm interests equally.
8. Discussion of the model
Since the existing literature on PIs has tended to focus almost ex-clusively on monopoly, in what follows we highlight the conceptualvalue-added of allowing for oligopolistic competition in the productmarket. Furthermore, in order to make the study of strategic interac-tion at two different stages (policy setting and the product market)tractable, we made two key simplifying assumptions — i.e. exportinginvolves no additional costs and quality is exogenously given. In thissection, we also briefly discuss the robustness of our results tochanges in these assumptions.
8.1. Role of competition
Broadly speaking, incorporating strategic interaction in the prod-uct market provides two main types of new insights. First, we findthat the effects of PI policies on prices and firm profitability under ol-igopoly differ substantially from those under monopoly.21 Second,the equilibrium policy choices of the North also differ across thetwo types of market structures. Below, we discuss each set of insightsin turn.
As was noted in Section 5, in our oligopoly model prices can behigher in the North when both countries permit PIs relative to whenonly the North does so (see the discussion below Fig. 2). This happensover region C in Fig. 1. As a result, given that the North permits PIsand its firm does not export, in region C the Northern firm's profit ishigher if the South permits PIs relative to when it does not. By con-trast, if there were no Southern firm, the pricing behavior of theNorthern firm (as well as its profits) would be independent of South-ern PI policy.22 This result points to a new channel via which South-ern policies affect Northern welfare.
Our oligopoly analysis also uncovers the interesting result thatuniform pricing is actually more likely to obtain when only theNorth permits PIs relative to when both countries permit PIs — thishappens over region B in Fig. 1. This implies that, given that theNorth permits PIs, the Northern firm's decision to serve the Southernmarket can also depend upon the Southern PI policy due to its effecton the pricing behavior of the Southern firm. By contrast, if the North-ern firm were a monopolist, whether or not the Northern firmchooses to export as well as whether uniform pricing obtains or notdepends only on the North's PI policy.
Consider now how the presence of the Southern firm affects stra-tegic interaction at the policy setting stage as well as the nature ofequilibrium policies. There are three key points here. First, a modelwithout the Southern firm would be incapable of shedding any lighton the interdependence of PI policies across countries since Northernpolicy would be totally independent of Southern policy. By contrast,in our oligopoly model if governments maximize aggregate welfarethe (i) North is more likely to permit PIs when the South does notand (ii) if the North is open to PIs, the South (weakly) prefers to be
21 In two-country Hotelling type duopoly model, Roy and Saggi (forthcoming) showthat PI policy can act as an instrument of strategic trade policy regardless of whetherfirms compete in prices or quantities.22 Incidentally, if the degree of product differentiation (r) becomes arbitrarily large,our oligopoly model essentially converges to a monopoly model since product marketcompetition disappears.
open to PIs whereas a Northern ban on PIs makes the South indiffer-ent between its two policy options.
Second, it is straightforward to show that if there were no South-ern firm, in equilibrium, the North permits PIs in regions A and Bwhereas the South is indifferent between its policy options. By con-trast, under oligopoly the North permits PIs in only region A (seeProposition 6). Thus, competition from the Southern firm makes itless likely that the North permits PIs. This result not only differentiatesequilibrium policies across the two types of market structures, it alsohas an important empirical implication: it suggests that we shouldobserve more restrictions on PIs in markets where foreign competi-tion is more potent.
Third, the presence of oligopolistic competition has an even stron-ger effect on equilibrium policies when governments care only aboutconsumer surplus (i.e. λ=1). It is easy to see that absent the South-ern firm, if the North cared only about consumer surplus it would al-ways permit PIs: if its firm were to export, the North would enjoy alower price by virtue of uniform pricing; if not, the firm's local pricewould be unaffected by its PI policy. By contrast, as we show inProposition 7, under oligopolistic competition the North can actuallygenerate greater consumer surplus by forbidding PIs (this happensover region C). The critical point is that this happens entirely due tothe effect of the Northern PI policy on the Southern firm's reactionfunction: Northern openness to PIs makes the Southern firm less ag-gressive in price competition which in turn lowers prices of bothfirms in the North. It is noteworthy that in this scenario the Northernfirm's price in its own market depends upon Northern PI policy eventhough it does not sell in the South. By contrast, if the Northern firmwere a global monopolist, Northern PI policy affects its pricing behav-ior only if it sells in the South. Proposition 7 also shows that whenλ=1, over region B, the unique policy equilibrium is (P,N), i.e., South-ern policy is consequential over region B since, over this region, it isoptimal for the North to permit PIs only if the South forbids them.
8.2. Positive costs
For simplicity, like the existing literature on PI, we assume that au-thorizing products for sale in foreign markets does not impose anyadditional costs (marginal or fixed) on firms. An important advantageof this approach is that it allows us to highlight the interaction be-tween PI policies, pricing behavior, and the strategic incentivesfirms have for selling or not selling in each other's markets evenwhen such sales do not involve additional costs relative to domesticsales. In particular, in our model, whenever the Northern firm choosesto not serve the South it does so not to economize on costs but ratherto increase profits by being able to charge a high price in the North.
We expect the qualitative nature of our results to continue to holdif firms face additional fixed costs for accessing foreign markets solong as these costs are small relative to product market profits. Tosee why, suppose firms incurred a fixed cost for selling abroad. If so,each of incentive functions plotted in Figs. 1 and 2 would shift so asto reduce the parameter space over which the two types of incentives(unilateral and reciprocal) are positive. For example, in Fig. 1 both theμh and μu curves shift downward when firms incur a fixed cost forselling abroad. While these shifts in the two curves would alter theparameter space over which each of the market structures is an equi-librium, it would not change the range of outcomes described inFigs. 1 and 2 provided that the costs of selling abroad are not solarge so as to completely eliminate the incentive to do so undersome (or all) of the policy regimes. As is clear, the key welfare rank-ings from the perspective of the two regions also would not be affect-ed by the presence of such costs. For example, the North would stillprefer uniform pricing to price discrimination while the Southwould have the opposite preferences. Of course, the existence ofthese costs would reduce each firm's export profit which in turnwould imply that the Northern government would be less concerned
274 S. Roy, K. Saggi / Journal of International Economics 87 (2012) 262–276
about inducing its firm to export. Note, however, that in our modelthe firm's incentive to export is always weaker than that what is so-cially optimal for its home economy. Thus, it would still be the casethat the firm would choose not to export even when it is better forits home economy that it does so. This implies that the nature of thepolicy equilibrium would be similar to that in our model.23
8.3. Endogenous quality
Our model takes product quality to be exogenously given. Whileendogenizing quality is beyond the scope of this paper, it is worth dis-cussing how we expect our analysis to be modified when quality isendogenously determined. Since what matters in the model is the rel-ative quality level of the two firms, fix the Southern firm's quality at 1and suppose the Northern firm's quality is determined by its invest-ment in quality improvement. Following Valleti (2006), one wouldexpect that the firm's incentive to improve quality would be strongerwhen it can price discriminate internationally relative to when it can-not. This implies that the Northern government's preference for uni-form pricing could be reduced if the Northern firm's incentive toimprove quality is substantially higher under international price dis-crimination. If so, our key policy result (i.e. Proposition 6) wouldneed to be modified in the sense that uniform pricing would likelybe preferred by the North over a smaller parameter space in orderto increase its firm's incentive to improve quality. In our view, furtherresearch is necessary to formally verify this intuitive conjecture, par-ticularly if both firms can invest in quality improvement as opposedto just the Northern firm. Indeed, given that the existing literatureon the impact of PI policies on R&D has tended to focus almost exclu-sively on monopoly, our model could serve as a foundation for furtherresearch in the area.
9. Concluding remarks
A sizeable literature analyzes the pros and cons of parallel trade(see Maskus, 2000 for a comprehensive overview). However, this lit-erature has shed only limited light on factors that determine nationalPI policies. In this paper, we endogenize PI policies in a North–Southduopoly model where the Northern firm produces the high qualityand the Southern firm the low quality. A crucial feature of themodel is that, given government policies, each firm decides whetheror not to offer its product for the sale in the foreign market. Incorpo-rating this feature into the model allows us to endogenously deriveasymmetric market structures of the type where both qualities aresold in the North while only the low quality is sold in the South.Not only are such market structures interesting with respect to thepricing behavior of firms, the possibility that they can arise under cer-tain North–South policy configurations plays a crucial role in deter-mining equilibrium policies.
Intuition suggests that the Northern policy stance ought to play akey role in determining international market structure. This intui-tion finds support in our model, but we show that heterogeneityin demand structure across countries can matter in rather unexpect-ed ways. In this regard, our key result — and one that matches quitewell with the observed nature of real world national PI policies — isthat if the Northern demand and, more particularly, preference forhigh quality is sufficiently higher than that of the South, the Northforbids PIs and international price discrimination obtains as theequilibrium outcome. An especially noteworthy aspect of this resultis that international price discrimination is the South's most
23 Note also that a similar argument applies to the case where firms incur higher mar-ginal costs for exporting, say due to the existence of tariffs or trade costs: under such ascenario each firm's export profit would shrink, but the Northern government wouldstill be interested in inducing its firm to export.
preferred market structure; the North's welfare is actually higherunder uniform pricing. Of course, in choosing to forbid PIs, theNorth is motivated not by altruism but rather its own interests: aban on PIs by the North prevents a scenario where its own (highquality) firm abstains from serving the Southern market in orderto shore up its profit at home. Thus, when demand heterogeneityacross markets is high, by preventing indirect competition fromarbitrage-induced PIs, the Northern prohibition on PIs induces directcompetition in both markets. Only when markets are relatively sim-ilar in demand structure does the North choose to permit PIs andobtain its most preferred market outcome — i.e. uniform pricing —
as an equilibrium outcome.Our analysis of PI policies is novel in that it allows for oligopolistic
competition in the product market. In our view, this is important inthe context of parallel trade: while market power is pervasive whenfirms are protected by patents or other IPRs, true monopolies arerather rare. For example, even in the context of pharmaceuticals sev-eral competing firms often supply drugs andmedicines that help treatany given illness or disease. Secondly, in our model, government pol-icy takes into account both consumer and firm interests. As notedabove, while setting its PI policy, the North must account for the pos-sibility that its own firm might forsake the Southern market in orderto sustain a more attractive price in its local market. By contrast, inthe existing literature, PI policies have been studied primarily fromthe viewpoint of importing countries.
While the model provides some new insights, it abstracts fromseveral important aspects of parallel trade that deserve further re-search. For example, it remains to be seen what additional consider-ations arise under oligopoly when one explicitly takes into accountthe role of intermediaries in parallel trade and the problems of verti-cal control or contracting as analyzed by Maskus and Chen (2002 and2004). It would also be worthwhile to study the two-way relationshipbetween parallel trade and strategic R&D competition, particularly interms of investments in quality improvement. Finally, our analysisconsiders PI policies in isolation, ignoring conventional instrumentsof trade policy such as tariffs and quotas. It would be useful to analyzea model in which PI policies are determined jointly with such tradepolicy instruments in order to obtain a better understanding of anypotential linkages between these types of policies. We hope future re-search will address some of these topics.
Appendix A
Proof of Lemma 1. Under international price discrimination, equilib-rium prices in country i are:
with associated profits πj Λð Þ. Since r≥1 it is straightforward that thelow quality firm's common price in both markets under Λf g is higherthan its price under uniform pricing:
pl Λð Þ−pl Uð Þ ¼ r−1ð Þ2
8r þ 3μ þ 14r−1ð Þ 8r−5ð Þ > 0: ð20Þ
Proof of Proposition 1. The proof proceeds in a straightforward way.Directly calculations show that Δl Λð Þ≡πl Λð Þ−πl Að Þ is increasing in μand that Δl Λð Þ > 0 at μ=μlm. This implies that Δl Λð Þ > 0 for allμ>μlm. As argued in the paper, when μ≤μlm, the low quality firmfaces no trade-off in its local market and serving the North yields astrictly positive gain.
Other supporting calculationsEquilibrium firm profits under uniform pricing equal
The inequality wN Dð Þ > wN Λð Þ can be shown as follows. First, wehave
d wN Dð Þ−wN Λð Þð Þdμ
¼ −2 r−1ð Þ3 μ−μml
� �4r−1ð Þ 8r−5ð Þ2 > 0 iffμ≤μm
l :
Furthermore, direct calculations show that at μ=1 we havewN Dð Þ > wN Λð Þ. Thus, it must be that wN Dð Þ > wN Λð Þ wheneverμ≤μlm. Now consider the case when μ>μlm so that the welfare differ-encewN Dð Þ−wN Λð Þ is decreasing in North–South demand asymmetryμ. Direct calculations show that at the maximum permissible value ofμ, i.e. at μ= μ , we havewN Dð Þ > wN Λð Þ. Thus, it must be thatwN Dð Þ >wN Λð Þ for all μ.
The inequality wS Dð Þ > wS Λð Þ can be shown as follows. We have
∂ wS Dð Þ−wS Λð Þð Þ∂μ μ¼μm
l¼ 4r þ 1ð Þ r−1ð Þ
4 4r−1ð Þ 8r−5ð Þ > 0����
i.e. at the lowest value of μ that is relevant for comparing wS(D) andwS Λð Þ, the welfare differencewS Dð Þ−wS Λð Þ is increasing in μ. Further-more, we have
∂2 wS Dð Þ−wS Λð Þð Þ∂2μ
¼3 r−1ð Þ2 16r2−8r−1
� 2 4r−1ð Þ2 8r−5ð Þ2 > 0
which implies that ∂ wS Dð Þ−wS Λð Þð Þ∂μ > 0 for all μ≥μlm. Since we know that
Ahmadi, R., Yang, B.R., 2000. Parallel imports: challenges from unauthorized distribu-tion channels. Marketing Science 19, 279–294.
Associates National Economic Research, 1999. The economic consequences of thechoice of regime of exhaustion in the area of trademarks. Final Report for DG XVof the European Commission.
Baudenbacher, C., 1998. Trademark law and parallel imports in a globalized world —recent developments in Europe with special regard to the legal situation in theUnited States. Fordham International Law Journal 22, 645–695.
Biadgleng, E.T., 2009. TRIPS Post-grant Flexibilities. Presentation at the UNCTAD Work-shop on Flexibilities in International Intellectual Property Rules and Local Produc-tion of Pharmaceuticals for the Southern Central and West African Region 7–9December 2009, Cape Town, South Africa.
Danzon, P., Epstein, A., 2008. Effects of regulation on drug launch and pricing in inter-dependent markets. National Bureau of Economic Research Working Paper No.14041.
Gansland, Mattias, Maskus, Keith E., 2004. Parallel imports and the pricing of pharma-ceutical products: evidence from the European Union. Journal of Health Economics23, 1035–1057.
276 S. Roy, K. Saggi / Journal of International Economics 87 (2012) 262–276
Goldberg, P.K., 2010. Intellectual property rights protection in developing countries:the case of pharmaceuticals. Journal of the European Economic Association 8,326–353.
Grossman, G.M., Lai, E., 2008. Parallel imports and price controls. The Rand Journal ofEconomics 39, 378–402.
Kanavos, P., Costa-i-Font, J., Merkur, S., Gemmill, M., 2004. The economic impact ofpharmaceutical parallel trade in European member states: a stakeholder analysis.Special Research Paper. LSE Health and Social Care, London School of Economicsand Political Science.
Lanjouw, J. O., 2005. Patents, price controls and access to new drugs: how policy affectsglobal market entry. National Bureau of Economic Research Working Paper No.11321.
Li, C., Maskus, K.E., 2006. The impact of parallel imports on investment in cost-reducingresearch and development. Journal of International Economics 68, 443–455.
Malueg, D.A., Schwartz, M., 1994. Parallel imports, demand dispersion, and interna-tional price discrimination. Journal of International Economics 37, 167–195.
Markusen, J.R., Venables, A.J., 1988. Trade policy with increasing returns and imperfectcompetition. Journal of International Economics 24, 299–316.
Maskus, K.E., 2000. Parallel imports. World Economy 23, 1269–1284.Maskus, K.E., Chen, Y., 2002. Parallel imports in a model of vertical distribution: theory,
evidence, and policy. Pacific Economic Review 7, 319–334.Maskus, K.E., Chen, Y., 2004. Vertical price control and parallel imports: theory and ev-
idence. Review of International Economics 12, 551–570.
Richardson, M., 2002. An elementary proposition concerning parallel imports. Journalof International Economics 56, 233–245.
Roy, S., Saggi, K., 2011. Equilibrium parallel import policies and international marketstructure. Vanderbilt University Economics Department Working Paper 11-W13and World Bank Policy Research Working Paper No. 5802.
Roy, S., Saggi, K., forthcoming. Strategic competition and optimal parallel import policy.Canadian Journal of Economics.
Scherer, F., Watal, J., 2002. Post-TRIPS options for access to patented medicines in de-veloping nations. Journal of International Economic Law 5, 913–939.
Shaked, A., Sutton, J., 1983. Natural oligopolies. Econometrica 51, 1469–1484.Smith, A., Venables, A.J., 1988. Completing the internal market in the European Com-
munity: some industry simulations. European Economic Review 32, 1501–1525.Valleti, T.M., 2006. Differential pricing, parallel trade, and the incentive to invest. Jour-
nal of International Economics 70, 314–324.Valletti, T.M., Szymanski, S., 2006. Parallel trade, international exhaustion and intellec-
tual property rights: a welfare analysis. The Journal of Industrial Economics 54,499–526.
Venables, A.J., 1990. The economic integration of oligopolistic markets. European Eco-nomic Review 34, 753–773.
