Vertical Pricing and Parallel Imports

Vertical Pricing and Parallel Imports Yongmin Chen Keith E. Maskus Department of Economics, University of Colorado at Boulder July 2000 Abstract: When a manufacturer (or trademark owner) sells its product through an independent agent in one country, the agent may nd it pro table to engage in parallel trade, selling the product to another country without the authorization of the manufacturer. Although parallel imports can be deterred when the manufacturer s wholesale price is su ciently high, there is a trade-o between improving vertical pricing e ciency and reducing parallel imports. In equilibrium, parallel imports can come from a country with higher retail prices. Restricting parallel imports tends to increase welfare when trade cost is high, but may reduce welfare when trade cost is low. JEL Classi cation Number: F12, L1, K11. Key Words: Parallelimports,paralleltrade,verticalpriceformation. Correspondence to: Yongmin Chen, Department of Economics, University of Colorado at Boulder, Boulder, CO 80309, USA. (303)492-8736; yongmin.chen@colorado.edu We thank Jonathan Eaton, Damien Neven, Marius Schwartz, and participants at numerous seminars for helpful comments. An earlier and substantially di erent version of this paper was prepared for and presented at the International Seminar on International Trade, NBER, June 4-5, 1999. Chen acknowledges research support from the National Science Foundation under grant # SES 9911229. 1

1. Introduction Parallel imports are goods brought into a country without the authorization of the original trademark or copyright owner, after those goods have been placed into circulation legitimately in another market. For example, certain compact disks produced under license to Sony may be authorized for sale only in Indonesia. If the Indonesian dealer or an independent agent ship some of these disks to Australia for sale without the authorization of Sony, these disks shipped to Australia will be called parallel imports. Although there are no o cial statistics on the volume and nature of parallel imports, parallel trading is considered a signi cant phenomenon. According to some recent estimates, parallel imports account for somewhere between 5-20% of trade within the European Union for goods such as musical recordings, consumer electronics, cosmetics and perfumes, and soft drinks (NERA, 1999). Policies towards parallel imports have been a much discussed issue in international trade negotiations (Maskus and Chen, 1999). A country s policy regarding parallel imports stems from its speci cation of the territorial exhaustion of intellectual property rights (IPRS). Under the doctrine of national exhaustion, rights are exhausted upon rst sale within a nation but the ability of IPRS owners to prevent parallel trade between countries remains intact. Under the doctrine of international exhaustion, rights are ended upon rst sale anywhere and parallel imports are permitted. An intermediate policy is to adopt regional exhaustion, in which rights are exhausted within a group of countries, thereby permitting parallel trade among them, but are not exhausted outside the region. Despite attempts by the American negotiators in the Uruguay Round to incorporate a global standard of national exhaustion into the Agreement on Trade-Related Aspects of Intellectual Property Rights (TRIPS), no such consensus could be developed. Thus, presently countries are allowed to sustain their di erent policies concerning parallel imports. However, TRIPS itself is subject 2

to reform in the year 2000 (Maskus, 1998), raising the possibility of this issue being re-visited. Moreover, in laying the grounork for the new Millennium Round of trade negotiations, U.S. trade authorities have advanced the notion of a global rule of national exhaustion, or elimination of parallel trade. Despite signi cant policy interests in parallel imports, there has been very limited economic analysis on this issue. Malueg and Schwartz (1994) present an interesting model of parallel trade, in which parallel imports occur due to international thirddegree price discrimination by a manufacturer (or copyright owner), but this is the only formal analysis in the literature. Less formal literature discusses the problems that emerge when parallel traders free ride on the marketing and service investments of authorized distributors (Chard and Mellor, 1989; Bar eld and Groombridge, 1998). Basically, the existing explanations view parallel trade as arising from international price di erences and the resulting international price arbitrage by parallel traders. While the existing studies have provided important insight on the issue of parallel imports, we believe that they are not adequate, for two important reasons: First, typically a parallel trader either is an authorized wholesaler himself or obtains the good directly from an authorized wholesaler. 1 Thus, it is the wholesale price, not the retail price, that determines the pro tability of parallel trade. From a theoretical perspective, it is therefore important to depart from the existing theories focus on retail prices and to develop a theory of parallel imports that takes into account the vertical formation of prices. Second, there are important empirical regularities that are troublesome for the existing theories. In particular, it has been noticed that parallel imports sometimes ow from a high-price country to a low-price country (see, for instance, NERA, 1999; Palia and Keown, 1991). This is inconsistent with 1 For instance, it is estimated that up to 20% of the market for Coca-Cola in the United Kingdom is served by parallel imports coming from wholesalers in other European nations. See Coke s Public-Relations Trouble Was Worsened by Gray Trade, The Wall Street Journal, July 6, 1999. 3

parallel trade based on price arbitrage. In this paper, we develop a model of parallel imports that incorporates the formation of prices in a vertical relationship. When a manufacturer sells its product through an independent agent (distributor) in a certain country, it has the incentive to set its wholesale below what it would be if the manufacturer could directly set the retail price, in order to reduce the double-markup distortion. This may enable the agent to sell the product pro tably in another country, without the authorization of the manufacturer, even when the retail price in the other country is lower. In a simple two-country model, we explore the manufacturer s trade-o between improving vertical pricing e ciency and preventing parallel importing, 2 and show that parallel imports can ow from a high-price country to a low-price country. Without legal restriction on parallel importing, the combined social surplus in two countries can increase in the cost of parallel trade. Restricting parallel imports by governments always bene ts the manufacturer, but it can either raise or reduce the combined social surplus in two countries. Our paper is closely related to Brander and Krugman (1983), who develop the seminal theory of reciprocal dumping. They show that trade can occur between two countries with identical demands, by two rms with identical costs. This is because the two markets are segmented and each rm chooses its outputs in the two countries separately. Our model shares similar intuition as Brander and Krugman in that in our model, the distributor chooses its output in two countries separately because the markets are segmented. However, in our model the production cost for the distributor is endogenous, depending on the wholesale price of the manufacturer. This introduces additional interesting trade-o s that are the focus of our analysis. The prevention of parallel imports is essentially the enforcement of an exclusive 2 We shall allow the manufacturer to use two-part tari contracts, so that the double-markup problem can be avoided if not for the concerns of parallel imports. 4

territory for a manufacturer or rights holder in the international context. As such, our study of parallel imports is also closely related to the literature on vertical restraints. 3 While our analysis of parallel trade (or exclusive national territories) is rather di erent from existing models in this literature, it shares some similar intuition with a recent paper by Chen (1999), which shows how oligopoly price discrimination by competing retailers may make it desirable for a manufacturer to impose resale price maintenance. The paper proceeds as follows. In the next section we set up the model. In the third section we characterize the equilibrium of the model and study its properties. In the fourth section we consider the e ects of a government policy that legally prevents parallel imports. The nal section concludes. 2. The Model A manufacturer, M; sells its product in two countries, A and B: In country A; M sells directly to the consumers, or sells through a wholly-owned subsidiary whose output is set by M: In country B, M sells its product through an independent exclusive distributor, L: The inverse demand in A is p = p A (q); and that in B is p = p B (q); both of which are continuously di erentiable functions: Manufacturer M has a constant marginal cost of production c 0: The retailing cost in both countries is normalized to zero. 4 Suppose that M can o er L any contract in the form of (w; T); where w is the wholesale price at which L purchases from M and T is a transfer payment (franchise fee) from L to M: 5 However, M cannot prevent L from selling the product back to A; either directly or through intermediaries. That is, either M cannot legally limit L 0 s 3 See, for instance, the survey by Katz (1989). 4 The model can be easily extended to include positive retailing costs in both countries. 5 Equivalently, we can think of L being a licensee of M in country B: In this case T will then be the license fee and w the royalty payment per unit of output. Contracts with a xed fee and per-unit royalty are common in international licensing (Contractor, 1981). 5

territory of sales, or it is too costly for M to enforce any such constraint. 6 Suppose that L incurs an additional constant marginal cost t 0 in selling the good back to A: For instance, t could be the additional transportation cost or transaction cost. Assume that if L sells in Country A, it will compete with M in a Cournot fashion in A: Let the quantities sold in A by M and L be q AM and q AL ; respectively, and the quantity sold in B by L be q B. The timing of the game is as follows: M rst o ers contract (w; T) to L; which is either accepted or rejected. If the contract is rejected, no product is sold in B and M chooses its output in A: Otherwise, L chooses its outputs in both A and B; and simultaneously M chooses its output in A: A subgame-perfect Nash equilibrium is, for any (w; T) accepted by L; apair(q AM ;q AL ) that constitutes a Nash equilibrium in A; together with an optimal choice of q B by L; and a contract (w; T) that is chosen optimally by M: As usual, we solve the model by backward induction. For preliminaries, we rst consider equilibrium in Country A; taking as given any (w; T) that is accepted by L: The pro ts of M and L through sales in A are: ¼ AM = q AM [p A (q AM + q AL ) c]+(w c)q AL ; (1) ¼ AL = q AL [p A (q AM + q AL ) w t] : (2) Given any (w; T) accepted by L; a Nash equilibrium in A; denoted as (q AM (w);q AL (w)); where q Ai 0; solves the following rst-order conditions: p A (q AM (w)+q AL (w)) c + q AM p 0 A(q AM (w)+q AL (w)) 0; (3) p A (q AM (w)+q AL (w)) w t + q AL p 0 A (q AM(w)+q AL (w)) 0; (4) 6 However, we assume that M or any agents of M other than L will not sell in B: 6

where (3) holds as an equality if q AM (w) > 0 and (4) holds as an equality if q AL (w) > 0: Notice that (q AM (w);q AL (w)) will depend on the parameter values of c and t. The equilibrium price in A will be p A (q AM (w)+q AL (w)): We next consider equilibrium in Country B; again taking as given any (w; T) that is accepted by L: Distributor L chooses q B to maximize (p B (q B ) w)q B : Denote the equilibrium (optimal) choice by q B (w); and let ¼ B (w) =(p B (q B (w)) w)q B (w): The equilibrium price in B is p B (q B (w)): To allow for general results, we do not restrict the demand functions in either country to a particular form. We instead make the following assumptions: A1. Fori = A; B; q[p i (q) c] is a concave function of q; q o i =argmax q 0 fq[p i (q) c]g exists uniquely for any given c; and q B (p o A) > 0; where p o A = p A (q o A): A2. Foranyq AM > 0 and q AL > 0; @ 2 ¼ Ai @p Ai @p Aj < 0: Furthermore, for any given t and for i = M; L; if t<p o A c; q Ai (w) is a continuous function for w 2 [c; p o A t] and is continuously di erentiable for w 2 [c; p o A t): Notice that q o A (or po A) are the pro t-maximizing output (or price) for a monopolist in A: Assumption A1 ensures that pro t in country i is maximized only with output q o i for i = A; B; and quantity demanded in B is positive at price p o A. A2 is the usual assumption that q Ai and q Aj are strategic substitutes, with the addition restriction on q Ai (w) that will facilitate the analysis of optimal w: A1 and A2 canbesatis edfor a variety of demand functions and parameter values. Consider, for instance, Example. p A = a q; p B =1 q; a 2 [ 3 ; 2]; c=0;t 0: 4 Both A1 and A2 are satis ed for this example. We shall use this example to illustrate our results throughout the paper (The detailed calculations for this example can be found in Maskus and Chen, 1999). 7

3. Equilibrium Analysis Lemma 1 For any given t 2 [0;p o A c); there exists a unique ¹w(t) >csuch that q AL (w) > 0 if w < ¹w(t) and q AL (w) = 0 if w ¹w(t); where ¹w(t) p o A t: Furthermore, when w< ¹w(t); q AM (w) increases in w; q AL (w) decreases in w; and [q AM (w)+q AL (w)] decreases in w; and when w ¹w(t); q AM (w) =qa: o Proof. When w 0; since if q AL (w) =0; we would have q AM (w) =q o A and p A (q AM (w)+q AL (w)) w t + q AL (w)p 0 A (q AM(w)+q AL (w)) = p o A w t>0; contradicting equilibrium condition (4). When w p o A t; q AM (w) = qa o and q AL (w) =0solve equilibrium conditions (3) and (4) and thus constitute the equilibrium in market A. For any tc such that q AL (w) > 0 if w< ¹w(t) and q AL (w) =0if w ¹w(t): When w< ¹w(t); both conditions (3) and (4) hold with equality. Then, q AL (w) decreases in w from condition (4); and consequently q AM (w) increases in w since q AM (w) decreases in q AL from (3). Furthermore, adding up the two equalities given by (3) and (4), we have 2p A (q AM (w)+q AL (w)) c w t +(q AM (w)+q AL (w))p 0 A(q AM (w)+q AL (w)) = 0; which implies that (q AM (w)+q AL (w)) decreases in w: Note that when t p o A c; q AL (c) =0: Thisisthecasewheret is so high that parallel imports do not occur even if w = c: We shall say in this case that parallel trade is blocked. Lemma 1 tells us that if tc:we shall say that parallel trade is deterred if w>cand q AL (w) =0: 8

To solve the equilibrium for the entire model, notice that rm L 0 s pro t in B; excluding T; is ¼ B (w): The equilibrium choice of T by M must satisfy T = T (w) ¼ AL (w)+¼ B (w): Any contract (w; T(w)) is accepted by L in equilibrium. The equilibrium choice of w therefore maximizes the joint industry pro ts in two countries, (w); where (w) =¼ AM (w)+¼ AL (w)+¼ B (w)+(w c)q B (w): That is, (w) =(q AM (w)+q AL (w)) (p A (q AM (w)+q AL (w)) c) tq AL (w)+(p B (q B (w)) c) q B (w) We have: (5) Proposition 1 For any given t; the model has a subgame perfect Nash equilibrium. When t p o A c; the equilibrium value of w; w (t); is c: When t<p o A c; w (t) 2 (c; ¹w(t)]; w (t) solves d (w) =0if w (t) < ¹w(t); and w (t) = ¹w(t) if ¹w(t) maximizes (w); where d (w) =0is given by d [(q AM (w)+q AL (w)) (p A (q AM (w)+q AL (w)) c)] t dq AL(w) +d [(p B(q B (w)) c) q B (w)] (6) =0: Proof. First, when t p o A c; w (t) =c since this induces the optimal retail price in B without causing positive parallel imports. Next, suppose that t<p o A c: Notice that if w ¹w(t); q AL (w) =0; and thus further increases in w have no e ect on (q AM (w)+q AL (w)) (p A (q AM (w)+q AL (w)) c) tq AL (w) 9

but reduces (p B (q B (w)) c) q B (w): And if w<c; (w) < (c): Therefore the search for the optimal w can be limited on the compact interval [c; ¹w(t)]; on which (w) is continuous. Thus w (t) exists and w (t) 2 [c; ¹w(t)]: Since 0 (w) exists everywhere on [c; ¹w(t)] except possibly at ¹w(t); we must have that w (t) solves (6) if w (t) < ¹w(t); and w (t) = ¹w(t) if ¹w(t) maximizes (w). The contract (w (t);t(w (t))); together with (q AM (w);q AL (w)) in country A and q B (w) in country B; constitutes a subgame perfect Nash equilibrium. Finally, notice that if t 0 at w = c, and hence w (t) >cfor any t<p o A c: We notice that if w (t) is a single-valued function everywhere, the subgame perfect Nash equilibrium must be unique. Notice that as long as tc: This suggests that parallel trade, when it is not blocked, always causes vertical price ine ciency. We note that by assumption A2, q Ai (w) is di erentiable at ¹w(t) from left. Proposition 2 There exists some ¹t 1 > 0 such that w (t) < ¹w(t) when t<¹t 1 ; and there exists some ¹t 2 2 [¹t 1 ;p o A c) such that w (t) = ¹w(t) when t>¹t 2 : Furthermore, ¹t 1 = ¹t 2 if (t) 1: dt Proof. First, d (w) = d [(q AM(w)+q AL (w)) (p A (q AM (w)+q AL (w)) c)] ¹w(t) t dq AL(w) + d [(p B(q B (w)) c) q B (w)] ; ¹w(t) ¹w(t) ¹w(t) 10

where the rst term is zero due to the envelope theorem, the second term is arbitrarily close to zero when t tends to zero, but the third term is a negative constant. Therefore, when t is su ciently small, < 0; and hence w (t) < ¹w(t): That is, there ¹w(t) d (w) exists some ¹t 1 > 0 such that w (t) < ¹w(t) when t<¹t 1 : Next, we show that there exists some ¹t 2 ; ¹t 1 ¹t 2 ¹t 2 : Suppose that this is not true. Then there exists some t that is arbitrarily close to p o A c; for which w (t) < ¹w(t) and d (w) w =0: But since (t) w (t)! c + when t! (p o A c) ; and the third terms on the left side of (6) tends to zero by the envelope theorem when w! c + ; we have d (w) w (t)! d [(q AM(w)+q AL (w)) (p A (q AM (w)+q AL (w)) c)] w (t) t dq AL(w) when w (t)! c + : This implies that d (w) w > 0 for any t that is lower than but (t) su ciently close to (p o A c), acontradiction. Finally, we show that ¹t 1 = ¹t 2 if (t) 1: It su ces to show that if 1 dt (t) 1; then for any t 0 > 0 such that w (t 0 ) < ¹w(t 0 );w (t) < ¹w(t) for all t<t 0 : dt Since w (t 0 ) < ¹w(t 0 ); w =0: Consider any (t 0 ) t<t0 : Then ¹w(t) =p o A t = d (w) p o A t 0 + t 0 t = ¹w(t 0 )+t 0 t: If 0 (t) ; then w (t) w (t 0 ) < ¹w(t 0 ) < ¹w(t): If dt 1 (t) < 0; then dt (t) < 0; or dt (t): Integrating on both sides, dt we have t 0 t (w (t 0 ) w (t)); or w (t) <w (t 0 )+t 0 t< ¹w(t 0 )+t 0 t =¹w(t): w (t) > 0 Intuitively, when t is small, parallel imports can be deterred only when w is much higher than c: Starting from the w that is just high enough to cause q AL (w) =0; a small decrease in w has second-order negative e ects on the pro t in A andonthe trade cost, but has a rst-order positive e ect on the pro t in B: Thus there will be equilibrium parallel imports when t is small. When t is large, on the other hand, parallel imports may be deterred with a w that is only slightly higher than c. Starting from w = c< ¹w(t) and q AL (w) > 0; a small increase in w has second-order negative 11

e ect on the pro t in B; but has rst-order positive e ects on the pro t in A and on trade cost. Thus when t is su ciently large but still below p o A c; parallel imports will be deterred. The optimal change in w caused by a change in t is likely to be a smaller amount than the change in t itself. Therefore it is likely that (t) 1 and thus ¹t dt 1 = ¹t 2 : For our linear demand example, ¹t 1 = ¹t 2 = 3 a; ¹w(t) = a t; and 14 2 8 2a+8t if t >< 3 a 13 14 w (t) = a t if 3 a<t a : 2 14 2 >: 0 if t a 2 Since q AL (w (t)) > 0 when w (t) < ¹w(t), q AL (w (t)) = 0 when w (t) = ¹w(t); ¹t 2 <p o A c; and w (t) = ¹w(t) =c if t p o A c; we immediately have the following results concerning equilibrium parallel imports: Corollary 1 In equilibrium, there is parallel importing from country B to country A if t<¹t 1, parallel trade is deterred if ¹t 2 <tq o A,and q B (w (t)) <q o B: Thus, if p A (q o A) p B (q o B); which would be true if demand in A is not higher than in B; we must have p A (q AM (w (t)) + q AL (w (t))) p B (q o B): We thus have: Corollary 2 A su cient, but not necessary, condition for parallel imports to occur andtobeoriginatedfromacountrywithhigherpricesist<¹t 1 and p A (q o A) p B (q o B): Thus, parallel imports can ow from a country with a higher retail price to a country with a lower retail price. This can happen for countries with similar demands or 12

for countries with di erent demands. This result is in contrast to the predictions from the existing theories of parallel imports. The key to the unusual result here is the recognition that the cost of acquiring the product to a parallel trader need not be the (retail) market price, but could instead be the wholesale price of the manufacturer. When the manufacturer cannot directly set retail prices of the independent distributor, the retail price will generally be higher than the wholesale price, even though by our assumption no additional retailing costs are involved. To induce the pro tmaximizing retail price, and when a franchise (license) fee can be charged, ideally the manufacturer wants to set the wholesale price at its marginal cost of production. 7 But such a wholesale price would enhance the distributor s pro tability in engaging in parallel trade. The manufacturer can still reduce or even eliminate parallel imports by raising the wholesale price, but this leads to less pro table retail price from the manufacturer s perspective. In equilibrium, the manufacturer balances the needs to improve vertical pricing e ciency and to limit parallel imports. 8 Inserting w (t) into equation (5), we obtain the equilibrium pro ts for M as = (q AM (w (t)) + q AL (w (t))) (p A (q AM (w (t)) + q AL (w (t))) c) tq AL (w (t)) + (p B (q B (w (t))) c) q B (w (t)): Parallel imports reduce the pro ts of the manufacturer (or the joint industry pro ts in two countries), not only because it creates competition in the country receiving 7 Our insight does not necessarily depends on the availability of two-part tari contracts. Even if M can only change w and cannot charge T;parallel imports can still occur and can originate from a country with the higher (retail) price. The availability of two-part tari contracts highlights the e ects of parallel imports on vertical pricing e ciency. 8 Notice, however, that even if M can set the retail price in B directly so that vertical pricing e ciency is not a concern, parallel trade may still occur. But such parallel trade would then only be due to international price di erences. Our theory does not preclude such parallel imports, but suggests an additional important reason. 13

parallel imports and because it incurs additional transaction (transportation) costs, but also because it prevents the manufacturer from achieving e cient vertical pricing (setting the wholesale price to marginal cost). An interesting issue is how may change as trade cost t changes. An increase in t increases the trade cost for a given amount of parallel imports, but it can also cause reductions both in w (t) andinthe amount of parallel imports, with generally ambiguous e ects on : But if ¹t 2 <t< p o A t; or if parallel trade is deterred in equilibrium, then a marginal increase in t clearly increases : This is because in this case an increase in t will a ect only throughareductioninw (t) = ¹w(t) =p o A t; which results in an increase in (p B (q B (w (t))) c) q B (w (t)): We now turn to the joint social surpluses in two countries, which we call global welfare. The global welfare in equilibrium is Z S qam (w (t))+q AL (w (t)) Z = (p A (q) c) dq tq AL (w qb (w (t)) (t))+ (p B (q) c) dq (7) 0 0 Similar to the e ect on pro t, the e ect of a change in t on global welfare tends to be ambiguous in general, but if ¹t 2 <t<p o A t; a marginal increase in t clearly increases S ; since in this case an increase in t will a ect S only through a reduction in w (t) =p o A t; which results in an increase in Z qb (w (t)) 0 (p B (q) c) dq: When t<¹t 2 ; it is less clear how (w (t)) and S will change as t changes. An increase in t is likely to cause a less than proportional decrease in w : If this is the case, an increase in t increases both the rst and the third terms of (w (t)) in equation (5), but can reduce the term tq AL (w (t)) in equation (5); and an increase in t increases the third term of S in equation (7), but reduces the rst term in (7) and may also reduce the term tq AL (w (t)) in (7). The net e ect of an increase in 14

t on (w (t)) is thus ambiguous, and so is the e ect on S : But if an increase in t reduces (w (t)); it must also reduce S ; while if an increase in t increases (w (t)); it may or may not increase S : For our linear demand example, decreases in t when t< 1 but increases in t 9 when 1 <t< a; and 9 2 S decreases in t when t< 3 a = ¹t 14 1 = ¹t 2 but increases in t when 3 a<t< a : Thus, at least in this example, both global pro ts and global welfare 14 2 are U-shaped functions of t: 4. The E ects of Restricting Parallel Imports If L is prevented from selling the product back to A; either because there exists e ective vertical restraint imposed by M or because parallel imports are not legally allowed by governments, then again with a contract (w; T); and denoting equilibrium (optimal) variables by adding superscript v"; it is optimal for M to set: w v = c; and T v = ¼B o = q B (c)[p B (q B (c)) c]: Prices in A and B will then be p v A = p o A; p v B = p o B: (8) When tc;p B = p B (q B (w )) >p o B; and p A = p A(q AM (w )+q AL (w )) p o A parallel imports occur in equilibrium. We thus have with strict inequality if Proposition 3 Assume that t<p o A c: Then, restricting parallel imports reduces prices in the country where parallel imports originate and may or may not raise prices in the country receiving parallel imports. Thus, restricting parallel imports bene ts consumers in the country where parallel imports originate but may or may not hurt consumers in the country receiving parallel imports. imports always bene ts the manufacturer. However, restricting parallel 15

Turning to global welfare, restricting parallel imports increases welfare of the country where parallel imports originate, but has ambiguous e ects on the country receiving parallel imports. When t 2 (¹t 2 ;p o A c); parallel imports will be deterred through some w (t) >cin equilibrium. In this case, government restrictions on parallel imports replace the ine cient vertical-price deterrence with a legal deterrence and thus eliminate the price distortion in B without causing other losses. When t<¹t 2 ; on the other hand, restricting parallel imports eliminates the ine ciency in vertical pricing for B and avoids the wasteful additional transaction costs due to parallel imports, but results in higher prices in A: It thus has ambiguous e ects on global welfare. For our linear demand example, however, we nd that S <0 if t is su ciently small. We thus have Proposition 4 Restricting parallel trade may either increase or reduce global welfare. When t 2 (¹t 2 ;p o A); restricting parallel imports increases global welfare; and when t is su ciently small, restricting parallel imports can reduce global welfare. We also note that if t p o A c; restricting parallel imports has no welfare e ects. In Brander and Krugman (1983), restricting reciprocal dumping avoids resource waste in cross-hauling but results in higher prices in both countries. Restricting parallel trade in our model also avoids resource waste in cross-hauling but results in higher prices in the country receiving parallel imports. However, here restricting parallel trade actually reduces the prices in the country where parallel imports originate. The reason is that there is the additional vertical pricing ine ciency caused by parallel trade in our case. Although in both cases restricting trade is (weakly) welfare improving when trade cost is su ciently high, the mechanisms for these outcomes are rather di erent. In Brander and Krugman, when t is just at the prohibitive level, a small decrease in t reduces welfare due to the loss from the replacement of domestic production with high cost imports; while here when t is high enough to deter parallel 16

trade, a marginal decrease in t reduces welfare since it leads to an even higher w (t) and thus to more ine ciency in vertical pricing. In Brander and Krugman, when t is su ciently small, free trade is welfare improving since resource waste in cross-hauling is small. In our case, however, allowing parallel trade may have ambiguous welfare e ects even when t is small, since the ine ciency in vertical pricing does not go away as t goes to zero. There are situations, though, where allowing parallel trade is welfare improving if t is su ciently small, as is the case in our linear demand example. Whether parallel importing should be established as a global policy is under debate in the WTO. Our analysis can shed light on this issue. Our nding that parallel importing can increase world welfare in some situations but reduce world welfare in other situations suggests that neither a policy that always bans parallel trade nor a policy that always facilitates it is justi ed from the perspective of economic e ciency. Our analysis further suggests that policy choices concerning parallel imports are closely related to choices on other trade policies. For instance, if it is desirable that parallel imports be legally allowed, then it could also be desirable to reduce any trade barrier that increases the cost of parallel trading. On the other hand, if the cost of conducting parallel imports is su ciently high, part of which could be due to the presence of signi cant trade barriers, then it might be desirable not to allow parallel imports legally. 5. Conclusion This paper has studied a model of parallel imports incorporating vertical pricing considerations. We nd that while the possibility of parallel imports can increase retail market competition, it can also a ect a manufacturer or rights owner s incentive in setting the wholesale price (or royalty payment) and reduce vertical pricing e ciency. Although parallel imports can be deterred by the manufacturer through a su ciently high wholesale price, they can nevertheless occur in equilibrium and can 17

even originate from the country with higher prices. We nd that global welfare increases in trade cost under certain conditions, and that for some demand systems the global welfare as a function of trade costs assumes a U-shape curve. The possibility of parallel imports (weakly) decreases global welfare when trade cost is large, but can increase welfare when trade cost is low. To the extent that trade cost is likely to be higher for countries in di erent regions than for countries within a region, parallel trade is more likely to increase welfare within a region than in the entire world trading system. While we believe that vertical pricing considerations o er an explanation of parallel imports, our theory should be considered as complementary to other explanations of parallel imports that have been formally or informally suggested. Interestingly, although for di erent reasons, there are similarities between the policy implications of our analysis and those of Malueg and Schwartz (1994). Both their analysis and ours suggest that some restrictions on parallel imports, especially between countries that have very di erent demands or high trade costs, could be desirable. Our analysis also suggests a need to coordinate international policy towards parallel imports with other trade policies: if trade cost is already high, perhaps due to high trade barriers, then permitting parallel imports alone without other trade policy changes can worsen global welfare. To the extent that parallel imports may allow one distributor to free ride on another distributor s promotional activities and reduce e ciency of promotional activities, a case may be made for the prevention of parallel imports. Our analysis suggests that there need not be externalities of this type in order to have welfare-improving restrictions on parallel imports. The need to improve vertical price e ciency can make it desirable to prevent parallel imports. Recently, concern about parallel trade has surfaced in pharmaceuticals and biotechnology, on the one hand, and the copyright industries including software, recorded music, videos, and book publishing, on the 18

other. These sectors are characterized by high R&D costs but low marginal costs of production and distribution. Thus, the di erences between retail prices and marginal costs for these products are often signi cant. Our theory may prove to be particularly useful in these situations. Even though our model is highly stylized, the basic insights of our analysis can hold in a much more general context. The manufacturer can sell through several distributors, and there can be more than two countries. As long as each distributor has market power, the trade o between vertical pricing e ciency and parallel imports explored in our model will be present, and so will be the type of parallel trade that emerges in our model. Notice, however, that with competition among distributors, manufacturers can possibly set higher wholesale prices to combat parallel imports without worsening vertical pricing distortions. We can also allow rms to compete in prices, if the parallel imports are viewed as di erentiated products from the original product of the manufacturer. Again, the manufacturer would face the trade-o between achieving vertical pricing e ciency and preventing parallel imports, but the analysis would be much less tractable. We could also imagine retailers incurring xed selling costs in each country. In the presence of selling costs, parallel imports may cause a manufacturer to refrain from selling in a particular country at all. Thus, such costs would make restricting parallel imports more likely to increase the combined social surplus in two countries. REFERENCES [1] Bar eld, C.E. and M.A. Groombridge, 1998, The economic case for copyright owner control over parallel imports, The Journal of World Intellectual Property 1, 903-939. [2] Brander, J. and P. Krugman, 1983, A reciprocal dumping model of international 19

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