Parallel Trade with an Endogenous Market Structure
Pei-Cyuan Shih
Department of International Business, Ming Chuan University, Taiwan
Hong Hwang
Department of Economics, National Taiwan University, and RCHSS, Academia Sinica, Taiwan
and
Cheng-Hau Peng[†]
Department of Economics, Fu Jen Catholic University, Taiwan
(This version, 2017/10/23)
Abstract
This paper sets up a two-country model in which there is one domestic manufacturer authorizing its product to a distributor in the foreign country. The distributor can sell the product not only to its own market (i.e., the foreign market) but also back to the domestic market. The latter is called parallel trade. The paper investigates the effects of parallel trade on the profit of the manufacturer and social welfareif the domestic market structure is endogenously determined.It is found thatparallel tradeshould be encouraged rather than banned as itincreasesnot onlythe profit of the manufacturer but also the welfare of both the domestic and the foreigncountries.
JEL classification: F12, F13, L11, L13
Keywords: Parallel trade, Endogenous market structures, Social welfare
1
Parallel Trade with an Endogenous Market Structure
1. Introduction
In the past decade, parallel trade (PT) has become more visible and of greater relevance in global trade, and drawn considerable debate in the literature (see Ganslandt and Maskus, 2004; Ganslandt and Maskus, 2008;Grossman and Lai, 2008; Kao and Peng,2009; Hwang, Huang and Peng, 2014; Maskus and Stähler, 2014; Matteucci and Reverberi, 2014; and Hwang, Peng and Shih, 2014, among others).
PT of a product involves selling the product outside the distribution network authorized by the manufacturer. Therightsoforiginalproducers tocontrolinternationaldistribution arise fromtheexerciseofintellectualpropertyrights(IPR).The scope of IPR depends however ona country’s exhaustion policy. Under international exhaustion, a manufacturer’s IPR on a good endsonce it is sold. It has hence no right to regulate its resaleto any market including the manufacturer’s own market.
According to the First Sale Doctrine of the United States copyright law, PT was illegal. Not until recently, however,the Supreme Court of the United States passed legislation toallow textbooks andother goods made and sold abroad can be re-sold online and in discount stores without violating the United States copyright law.[a]Namely,the First Sale Doctrine is not applicable to PT and United States-made items such as textbooks, CDs, and computer software purchased from foreignmarkets can now be re-sold back to the United States. Besides, Ford sells numerouscarsback from Canada and Mexicoevery yearwithout its authorizationinhigher-priced United States,whetherbythe authorized retailers or other tradingcompanies (Roy and Saggi, 2011).PT is also prevalent in countries such as China, Japan, and Taiwan. For example, people there can buy products such as cameras, automobiles, electronics, cosmetics, pharmaceuticals, motorcycles, clothes, etc. which via the channel of parallel trade. Nowadays,PT is a lawful form of tradein the European Union (EU) based on the principle of free movement of goods. By contrast, a foreign authorized distributor is not allowed to resell the product back to the manufacturer’s home country under national exhaustion rule.
Whether PT should be permitted or banned is an open question, having receivedgrowing attention in policy debates and academicliteratures. This policy issue is particularly relevant inindustries, such as pharmaceuticals.Itwasfound that EU lost approximate $3 billion sales per yearin the pharmaceutical sector alone owing to the occurrence of PT(Ganslandt and Maskus,2004).
As the role of PT becomes increasingly important in global trade, a growing literature has begun to explore the effects of PT on global welfare.The main focus along this strand of research is on optimal PT policies (see, for example, Maskus and Chen, 2004; Chen and Maskus, 2005; Grossman and Lai, 2008; Matsushima and Matsumura, 2010; Mueller‐Langer, 2012; Mukherjee and Zhao, 2012; Hwang, Huang and Peng, 2014; Maskus and Stähler, 2014, among others). In their pioneer papers, Maskus and Chen (2004) utilize a two-country and two-firm Cournot model with a linear demand to investigate the optimal quantitative control of PT for an import country. They show that restricting parallel trade has an ambiguous welfare effect, depending on the trade cost of PT. Chen and Maskus (2005) reach a similar result with a general demand function. Matsushima and Matsumura (2010) find that allowing PT can be beneficial for both domestic and foreign manufacturers, because PT serves as a commitment to soften the competition.Mueller‐Langer (2012) extends Maskus and Chen (2004) by assuming that products are heterogeneous andthe manufacturer adopts one-part tariff pricing. He shows thatPThas a positive effect on global welfare if the difference inmarket size between the two countries is large and trade costs are low. Furthermore,Mukherjee and Zhao (2012) find thatPTmightbe profitable for the manufacturerif there is a labor union in the domestic country. Grossman and Lai(2008) show that the pace of innovation is faster in a world adopting international exhaustion than nationalexhaustion.Hwang, Huang and Peng (2014) investigate the welfare of tariffication on parallel import. They show that tariffication is socially undesirable for the importcountry no matter the manufacturer adopts one-part or two-part tariff pricing. However, the aforementioned papers all ignore an important fact: the market structure could be different with and with no PT. To the best of our knowledge, there is no research examining how anendogenous market structure (EMS) affects the optimal PT policies and their welfare implications. In this paper, we shall fill the gap. In addition, we shall also investigate the effects of PT on the wholesale price and the profit of the manufacturer.
This paper is closely relevant to theEMS literature.There isa new theoretical research waveby applying EMS to different issues,such as, Horstmannand Markusen (1986), Melitz (2003),De Santis and Stähler (2004), Etro (2004)and Markusen and Stähler (2011).
Most papers onPTemploy a simplified modelwith one manufacturer dealing withone distributor.[b]In this paper, we assume there are multiple local rivals and foreign distributors and their numbers are endogenously determined i.e., EMS. Withan EMS we shall show that PTcan increase not only the profitof the manufacturer but also the welfare of the involved countries and hence should be encouraged. These resultsare in sharp contrast to those derived in the literature; they also bear important policy implications.
The remainder of this paper is organized as follows. Section 2 investigates the equilibrium ofPTunder endogenous market structure. Section 3 analyzesthe profitabilityof the manufacturer and welfare implications under endogenous market structures. Section 4 concludes the paper.
2. The model
Assume there are two countries, country A and country B. There is an incumbent manufacturer, located in country A, sells units of its product to its own market which we call it market A. To produce the product, the manufacturer incurs a constant marginal cost,c. The manufactureralso authorizesa foreign distributor to sell theproductin country B. The foreign distributor may engage in parallel trade by selling the product back to country A. By doing so, it incurs a per-unit trade cost which is assumed to be .[c] Let us denoteand as the amounts of the product the distributor sells tomarket A (i.e., PT) and market B. We further assume that the manufacturercharges a two-part tariff, i.e., a fixed fee T and a wholesale pricingwwhen sellingthe product to the distributor.In addition, there are potential and symmetric rivals (hereafter, the domestic rivals) in market A, all producing the homogenous product, ,with a marginal cost and a fixed cost.[d]The inverse demand functions ofmarkets A and B are respectively and , where , and with the property , .
The game in question comprises two stages. In the first stage, the manufacturer chooses its optimal pricing contract (and T) and offers it to the foreign distributor. In the second stage, the domestic rivals determine whether to enter the market, and the manufacturerand the domestic rivals determine their optimal outputs in market A whereas the foreign distributor determinesits optimal sales in the two markets.The sub-game perfect Nash equilibrium will be solved via backward induction.
In the finalstage,the profit functions ofthe manufacturer, the domestic rivalsandthe foreign distributorcan be respectively expressed as follows:
(1)
. (2)
(3)
The first-order conditions for profit maximization of the firms and the zero-profit condition for entry are respectively as follows:
(4)
, (5)
,(6)
,(7)
(8)
The equilibrium ofthe domestic market is solvedby (4) to(7) whereas that of the foreign market is solved by(8).
In the domestic market, there are n+2 players including n symmetric local potential rivals, the manufacturer, and the foreign distributor. In order to illustrate the equilibrium in a two-dimension reaction function diagram, we merge the n+2 equations into two equations as follows. First, by summing(4) and (6), we can derive
, (9)
where . We shall call this as the joint reaction function of the manufacturer and the foreign distributor. In addition, by symmetry,equation (5) can be rewritten as follows:
,(10)
where x is the output of the representative local rival. This is the reaction function of the representative local rival. Finally, we derive from(7),and substitute it into (9) and(10). The latter helps us remove (7) from the equation system in the domestic market. It is straightforward to show that has the following properties:
, .(11)
By totally differentiating(9) and(10), and then making use of (11), we derive the slope of the jointreaction function of the manufacturer and the foreign distributor and that of the representative domestic rival respectively as follows:
,.
We can use Figure1 to illustrate the two reaction functions. In Figure 1, denotes the joint reaction function of the manufacturer and the foreign distributor while represents the reaction of the representative domestic rival.As depicted in the figure, thecurve is horizontal, i.e., the slope of is equal to zero, due to the free entry assumption.It implies that the equilibrium output of each rival firm is fixed andnot affected by. This result is in sharp contrast to the exogenous market structure case in which the equilibrium output is determined by two negatively slopedreaction functions. The intuition is as follows. Given the zero-profit condition, the equilibrium output of each rival firm is at the tangency of its perceived demand and the average cost.An increase in shifts the perceived demand inwards and makes it below theaverage cost,resulting in a profit loss for each rival firm. The equilibrium will be restored only if some firms exit from the market which shifts the perceived demand back to its tangency position. It means that a change in Z can only affect the number of the rival firms but not its output level.This result is in line with those in the EMS literature, such asEtro(2006, 2007), Davidsonand Mukherjee (2007), Ino and Matsumura (2012), and Cato and Oki (2012).Given the above discussions, we can construct the following lemma.
Lemma1. The optimal output of the representativedomestic rival isindependent ofthe joint output of the manufacturer and the foreign distributorifthe market structure is endogenously determined.
Hwang et al. (2014) assume that the number of the domestic rival firms is exogenously determined and find that the optimal output of the representative domestic rival decreases with that of the manufacturer or the foreign distributor. But by Lemma 1, we find that this negative relationship breaks downif themarket structure is endogenously determined.
Figure 1. The reaction functions under endogenous market structure
After completingLemma 1, we now get back to the first-order condition for profit maximization of the domestic market. By utilizing(4)to(7) and the symmetry of the domestic rivals, we canderive the comparative static effects as follows:
,
.
The above results follow that an increase in decreases the volume of PT, increases the number of the domestic rivals, but has no effect onthe outputs of the manufacturer and the domestic rivals. The intuition is as follows. An increase in raises the effective marginal cost of the foreign distributor,making it less competitive in the domestic market. This would also raise the profit of the domestic rivals to a positive level, attracting more domestic rivalsto enter the market till the zero profit condition is restored. It implies thatan increase inchanges only the number of the local rivals, but has no effect on, and .[e]We use Figure 1 to illustrate this result. In Figure 1, anincrease in shifts inwards. If the number of firms is fixed, the equilibrium price in the domestic market will be higher than each rival firm’s average cost. In this context,each incumbent firm makes positive profit, and then entry occurs. Given the above discussions, we build the proposition as follows.
Proposition 1.If the market structure is endogenously determined, an increase inthe wholesale price increases the number ofdomesticrivals buthas no effect on the equilibrium output and price of the domesticmarket.
According to Proposition 1, we find that if the market structure is endogenously determined, a decrease in the wholesale price increasesPT, which in turn decreases the number of the local rivals. However, it does not affect the domestic price and the total sales . Thus, we can further construct the lemma as follows.
Lemma2. The equilibrium domestic market price and total sales are not affected by parallel tradeif the market structure is endogenously determined.
This intuition is as follows. An increase in PTmakes the profit of the domestic rivals turnnegative, causingsome rival firms to exit from the market,and the perceived demand beingshiftedback to its tangency position.
We now move to the first-stage game. By substituting the equilibriumoutputs from the second-stage game into(1), we can rewrite the profit function of the manufacturer as follows:
By substituting the constraint into the profit function,differentiating itwith respect to , and then applying the envelope theorem,we derive the first-order condition for profit maximization of the manufacturer as follows:
.(12)
The second-order condition is satisfied as . By totally differentiating(12) with respect to and , we canderive that:, where .Moreover, by evaluating (12) at ,we have
.(13)
Itshows that the optimal wholesale price is equal to or less than its marginal cost,depending on the volume of PT. If PT is prohibited (i.e., x*=0), the manufacturer should set the wholesale price equal to its marginal cost.By contrast, the wholesale priceshould be set lower than the marginal cost if PT is allowed (i.e.,).The intuition behind this result is quite straightforward. If PT is prohibited, the manufacturer uses the wholesale price to maximize its profit from the foreign market only. Clearly, it should set the price equal to the marginal cost and use fixed fee to extract the monopoly rent acquired by the foreign distributor. By contrast, if PT is allowed, the manufacturerhas an incentive to set its wholesale price lower than its marginal cost for two reasons. First, adecrease in the wholesale price increasesPT, which reduces the number of thelocal rivals, but has no effect on its profit from directly serving the domestic market as the price and the sales remain unchanged(by Proposition 1).Second, by setting the wholesale price below the marginal cost, the manufacturer can raise its profit via PT. Thus, we can establish the following proposition.
Proposition 2. If the market structure is endogenously determined and parallel trade is allowed, the wholesale price charged by the manufacturer is necessarily lower than its marginal cost.
The above result differs sharply from those in Maskus and Chen (2004) and Li and Maskus (2006). They assume that the manufacturer faces no local rivals and adopts two-part tariff pricing under an exogenous market structure. They find that when the trade cost is high, the manufacturer would definitely set the wholesale price above its marginal cost to save on the trade cost. Contrarily, the manufacturerin our model,always set the wholesale pricelower than the marginal cost to increase its market share in and profit from the domestic market via PT.
3. Profitand welfare analysis
In this section, we shall make profit and welfare analysis of PT under an EMS.Note that the manufacturer will set if PT is banned. Given, the occurrence of PT increases the manufacturer’s profit asits profit from the foreign market remains the same but that from the domestic market via PT increases. This explains again why the manufacturer would set the wholesale price below its marginal cost and also implies that PT is profitablefor the manufacturer under an EMS.Therefore, we establish the following proposition.
Proposition 3. If the market structure is endogenously determined, PT increases the profit of the manufacturer.
The above result is of interest and in sharp contrast to the findings inMaskus and Chen (2004) and Li and Maskus (2006). Under an exogenously given market structure,they bothconclude that PT definitely reduces the profit of the manufacturer.But their result is reversed when the market structure is endogenously determined. It is also worth mentioning that ourresult is in parallel to the findings of Matsushima and Matsumura (2010) andMukherjee and Zhao (2012). The formershows thatallowing PT can be beneficial for both domestic and foreign firms because PT serves as a commitment to soften the price competition,while the latter assumes that there is a labor union in the domestic market and concludes that the openness of PT might be profitable for the manufacturer.
We theninvestigate thewelfare effects of PT. The social welfare levelsof the domestic and foreign countries are expressedrespectively as follows: