DP2010-09

The Strategic Effects of Parallel Trade~Market s teal ing a nd wage cu tting~*
Arijit MUKHERJEE
Laixun ZH AOMarch 10, 2010

* The Discussion Papers are a series of research papers in their draft form, circulated to encourage
discussion and comment. Citation and use of such a paper should take account of its provisional character.
In some cases, a written consent of the author may be required.

The Strategic Effects of Parallel Trade~Market stealing and wage cutting~Arijit Mukherjee*
University of Nottingham and The Leverhulme Centre for Research in Globalisation andEconomic Policy, UK

andLaixun Zhao**
RIEB, Kobe University, Japan
February 2010

Abstract: Why do producers often accept parallel trade in some markets such as
automobiles, clothing, toys and consumer electronics? This paper identifies two newfactors, viz., market stealing and union-wage cutting, which may make parallel trading
beneficial to a manufacturer. Specifically, (i) under perfectly competitive labour markets inboth the home and foreign countries, parallel trade may help a manufacturer to steal market
shares from competitors, if it is more cost efficient or sells in more markets thancompetitors; and (ii) in a unionized labour market, parallel trade may help by lowering theunionized wage. These benefits of parallel trade disappear when such factors are removed.
Key Words: Firm-asymmetry; Labour Union; Parallel import
JEL Classifications: F21; F23__________________________*

School of Economics, University of Nottingham, University Park, Nottingham, NG7 2RD, UK; E-mail:arijit.mukherjee@nottingham.ac.uk; Fax: +44-115-951 4159.

**

Research Institute for Economics & Business, Kobe University, Kobe 657-8501, Japan; E-mail:zhao@rieb.kobe-u.ac.jp; Fax: +81-78-803-7006.

1. Introduction
A common concern of policy makers is to protect the property rights of innovators fromunauthorized production. While there exist strict measures (e.g., patent protection) to guard
the interest of the innovators, a closely related issue, namely, parallel trade (or grey
markets), which allows unauthorized sale of a product, is often allowed.1 Many countries
such as Australia, New Zealand and Singapore have liberalized restrictions on parallel
trade and the European Union is also very active in reducing restrictions on internal
parallel trade.2 As noted in Scherer (1994), the first major competition policy enforcementin the EC is related to an attempted dealership territoriality within the EC. Malueg and
Schwartz (1994) confirm that policies worldwide generally support parallel trade.3
While the conventional belief is that parallel trade hurts manufacturers by creatingcompetition, anecdotal evidence suggests that parallel trade may benefit them at least insome markets. For example, “ … some manufacturers, while publicly opposed to graymarket sales of their products, privately do little to inhibit their flow and in some instanceseven go so far as to encourage these transactions” (Lipner, 1990, p. 4). A report prepared
for the EU commission (NERA, 1999, p. 11) states that “[s]ome parallel trade, however,seems to be beneficial to the trademark owner.” In the North American automobile market,
retailers selling new automobiles must sign a contract with manufacturers forbidding themto re-sell these cars in other countries. However, over 200,000 vehicles intended for the
Canadian market were resold south of the border in 2001 (increased from 16,000 in 1996
(Automotive News, 2002)), yet the no-parallel-trade clause was not enforced, thus
imposing no penalties on the retailers.
1

As mentioned in Maskus (2000), parallel trade occurs when a good protected by a patent, copyright, or trademark,having been legally purchased in one country, is exported to another country without the authorization of the local ownerof the intellectual property rights in the importing country.
2
Richardson (2002) documents that restrictions on parallel trade originating outside the EU are quite permissible.
3
In the US, parallel trade was US$7-10 billions in the mid-1980s (Cespedes et al., 1988), and rose up to US$20 billion
more recently (Computer Reseller News, 2001). In Europe, the volume of parallel trade varies from 5% of sales (onappliances, motorcars and consumer electronics) to almost 15% (on musical recordings, cosmetics and perfumes)(NERA, 1999). The House of Commons (1999) report shows that the volume of parallel trade in the UK motorcycle
market is around 25% of sales.

1

In the present paper, we provide two strategic reasons for profitable parallel
trading: parallel trade may benefit a manufacturer either by stealing markets from thecompetitors or by reducing the unionized wage faced by the manufacturer. The model
explains why some manufacturers often accept parallel trade in markets where productmarket competition is visible, such as in automobile, cloths, toys and consumer electronics,
and when the factor market is imperfect, such as in some European and U.S. markets, andalso justifies policy markers’ relaxed approach towards parallel trade.
First, section 2 examines the effect of market stealing, leaving the factor (labour)market perfectly competitive. We use a framework of two manufacturers one of whom
serves both domestic and foreign markets and the other serves only the domestic market.
We find that the former firm’s profit is higher under parallel trading of its product.
Moreover, if both firms serve both markets, parallel trading can benefit the firm that ismore cost efficient.
Second, in Section 3 we consider labour market imperfection by assuming aunionized home-country labour market. We demonstrate that parallel trade from a foreigncountry to the home country reduces the unionized wage. Even though parallel trade
increases competition in the home market, this wage-reducing effect can dominate thecompetition effect, making parallel trading beneficial to the manufacturer.
Previous literature has generally argued that parallel trade reduces profits of the
manufacturers (Malueg and Schwartz, 1994, Richardson, 2002, Maskus and Chen, 2004
and Hur and Riyanto, 2006, etc.). There are also works which show that manufacturers cangain from parallel trade under certain conditions, such as if a country chooses both thetariff level and whether or not to allow parallel trade (Knox and Richardson, 2002), or if
the product of the parallel trader and that of the manufacturer are differentiated (Ahmadi
and Yang, 2000). More recently, Raff and Schmitt (2007) explain that, in the presence ofdemand uncertainty, parallel trade may benefit the manufacturers if the following four2

conditions are met: the retailers must order the product before the realization of demand, it
is costly to maintain inventories, the states of demand are different across markets, anddifferent states of demand need to affect the quantity demanded rather than the consumers’
willingness to pay for the products.
In contrast, the present paper provides a new rationale for profitable parallel
trading, even if the government is not an active agent, the products of the manufacturer andthe parallel trader are homogeneous and there is no uncertainty that creates the motives forrisk diversification through parallel trade. Certainly these are important factors that cancause parallel trading to arise. However, our focus is on the importance of market stealing
and union-wage cutting, which has been ignored in the literature.
The remainder of the paper is organized as follows. Section 2 examines the effects
of product market competition with a perfectly competitive labour market. Section 3 looks
into the case of a labour union. Finally, section 4 concludes.

2. The effects of product market competition
Consider a manufacturer, firm 1, which sells its product in two countries, A and B. In
country A, firm 1 sells directly to the consumers. In country B, firm 1 sells through an
independent exclusive distributor, I. We assume that firm 1 offers I a contract in the formof (w, T), where w is the wholesale price and T is a transfer payment (franchise fee) paid
up-front from I to firm 1. So far, the model is in line with the vertical pricing model of
Maskus and Chen (2004).
Now we introduce market competition, by assuming that in country A, the productmarket is a duopoly with firms 1 and 2 competing with homogeneous products. Both firms
have constant marginal costs, which is normalized to zero for simplicity. To demonstrate
our result in the simplest way, we start our analysis with the assumption that firm 1 sells in

3both countries A and B, while firm 2 sells only in country A, which might be caused byresource constraints. This assumption will be relaxed in Subsection 2.3 to see how theanalysis is affected if both firms serve both countries. We assume that the inverse market
demand function in each country is P = 1 – q.
We consider the following sequence of moves. At stage 1, firm 1 gives a take-it-orleave-it contract (w, T) to firm I, which either accepts or rejects it. We assume that I
accepts the offer if it earns at least its reservation payoff, which is normalized to zero. If I
accepts the contract, at stage 2, firms 1, 2 and I choose their outputs simultaneously, andthe respective profits are realized. If I does not accept the contract, at stage 2, there is nosale in country B, and firms 1 and 2 choose their outputs simultaneously and their profits
are realized. We solve the game by backward induction.

2.1. No parallel tradeFirst, consider the case of no parallel trade. If I accepts firm 1’s contract, given w and T,
firms 1, 2 and I maximize the following expressions simultaneously to determine theirrespective outputs:
Max(1  q A1  q A 2 )q A1  wqBI  T ,(1a)

Max(1  q A1  q A 2 )q A 2 ,(1b)Max(1  qBI  w)qBI  T ,

(1c)

q A1

qA 2

qBI

where the first subscript denotes the country and the second one the firm.
Standard calculations show that the equilibrium outputs areq A1  q A 2  1/ 3 and qBI  (1  w) / 2 .
The profits of firms 1, 2 and I are then4(2) 1np   A1   B1  1/ 9  w(1  w) / 2  T , 2np  1/ 9 , Inp  (1  w)2 / 4  T .
Since firm 1 gives a take-it-or-leave-it offer to I, the equilibrium transfer payment is
T np  (1  w) 2 / 4 . Firm 1 then determines the wholesale price w by maximizing
Max 1/9+w(1-w)/2+(1-w) 2 /4 ,(3)wwhich gives the equilibrium wholesale price as wnp  0 . The reason for this result is easy
to understand. Since I sells the product in country B as a monopolist, firm 1 finds no reason
to distort I’s output choice. Hence, firm 1 charges the wholesale price that creates the
maximum profit in I, and it also extracts this profit through the transfer payment.
Therefore, under no parallel trade, the equilibrium offer made by firm 1 to I is
( w, T )  (0, 1/ 4) , and this offer will be accepted by I.
The net equilibrium profits of firms 1, 2 and I are respectively

 1np  13 / 36 ,  2np  1/ 9 , and  Inp  0 .

(4)

2.2. Parallel trade
Next consider the game under parallel trade. As in Maskus and Chen (2004), Li and
Maskus (2006) and many others, in this situation, I not only sells the product in country A,
but also in country B if it is profitable. Hence, while offering the contract to I, firm 1 needs
to internalize this possibility.
If I accepts firm 1’s contract, given w and T, firms 1, 2 and I maximize thefollowing expressions simultaneously to determine their outputs:
Max(1  q A1  q A 2  q AI )q A1  w(qBI  q AI )  T ,(5a)

Max(1  q A1  q A 2  q AI )q A2 ,

(5b)

q A1

qA 2

5

Max (1  qBI  w)qBI  (1  q A1  q A2  q AI  w)  T .

qBI , q AI

(5c)Standard calculations give the equilibrium outputs as
q A1  q A 2  (1  w) / 4 , qBI  (1  w) / 2 and q AI  (1  3w) / 4 .

(6)

The profits of firms 1, 2 and I are 1p   A1   B1  (1  w) 2 /16  w(3  5w) / 4  T , 2p  (1  w) 2 /16 , Ip  (1  w) 2 / 4  (1  3w)2 /16  T .
The equilibrium transfer payment is obtained as T p  (1  w) 2 / 4  (1  3w) 2 /16 . Firm 1then determines the wholesale price w by maximizing
Max (1+w) 2 /16  w(3  5w) / 4  (1  w) 2 / 4  (1  3w) 2 /16 .
w(7)

The equilibrium wholesale price is obtained as w p  0 .
It is interesting to note that even if firm 1 faces competition from I in country A, it
does not charge a positive wholesale price to I. The intuition can be understood as follows.
On one hand, I is a monopolist seller in country B. On the other hand, under parallel trade,not only firm 1 but also firm 2 face competition from I. These combined effects induce
firm 1 to keep I’s marginal cost (which is the wholesale price) low.
The equilibrium offer made by firm 1 to I is then ( w, T )  (0, 5 /16) , which will
be accepted. The net equilibrium profits of firms 1, 2 and I are respectively

 1p  3 / 8 ,  2p  1/16 , and  Ip  0 .

(8)

Now we are in position to state two propositions:

Proposition 1: The equilibrium outputs of firms 1 and 2 are lower with parallel trade than

without.

6

Proof: The outputs of firms 1 and 2 are q Anp1  q Anp2  1/ 3 under no parallel trade, which are

greater than the counterparts under parallel trade, q Ap1  q Ap2  1/ 4 . ■Proposition 1 shows that parallel trade reduces the outputs of both firms 1 and 2.

Proposition 2: Parallel trade increases the profit of firm 1 and reduces that of firm 2.
Proof: The result follows immediately from (4) and (8). ■The reason for Proposition 2 is as follows. Parallel trade enables I to steal businessfrom both firms 1 and 2 in country A. However, since firm 1 can use the transfer payment
to extract profit from firm I while firm 2 cannot, parallel trade in effect helps firm 1 to gainfrom firm 2’s business loss to firm I, making firm 1 better off and firm 2 worse off.
The above analysis is based on homogenous products. However, the implications of
product differentiation are straightforward as follows. If firms 1 and 2 produce imperfect
substitutes, it will reduce the intensity of competition between them. As a result, thebusiness stealing effects under parallel trade will be weakened. At the extreme situation, if
the products of firms 1 and 2 are isolated, parallel trade will not affect the market share andthe profit of firm 2, since the product of the parallel trader (which is actually the product offirm 1) is also isolated from firm 2’s product. Then parallel trade increases competition
only for firm 1. Hence, Proposition 2 holds if the products of firms 1 and 2 are not too
much differentiated.

2.3. Competition in both markets
In this subsection we extend the model to cover competition in both markets. We find thatprofit raising parallel trade can still occur if the firms differ in marginal costs.
7

Consider that both firms 1 and 2 serve both markets A and B. Each firm sells
directly to the consumers in country A, but firms 1 and 2 sell their products throughindependent exclusive distributors I1 and I 2 respectively in country B. 4 However, we
assume that the marginal cost of production is c for firm 2, while it has been normalized tozero for firm 1. Also, c  12 / 53 , which is sufficient to ensure that all equilibrium outputs
are positive. We consider the same timeline as in the previous section.

2.3.1. No parallel trade
If firms 1 and 2 give the offers ( w1 , T1 ) and ( w2 , T2 ) to I1 and I 2 and the offers are
accepted, these firms maximize the following expressions simultaneously to determine
their outputs:
Max(1  q A1  q A 2 )q A1  w1qBI 1  T1 ,(9a)

Max(1  q A1  q A 2  c)q A2  ( w2  c)qBI 2  T2 ,(9b)

Max(1  qBI 1  qBI 2  w1 )qBI 1  T1 ,(9c)

Max(1  qBI 1  qBI 2  w2 )qBI 2  T2 .

(9d)

q A1

qA 2

qBI 1

qBI 2

Standard calculations show that the equilibrium outputs are q A1  (1  c) / 3 ,q A2  (1  2c) / 3 , qBI 1  (1  2w1  w2 ) / 3 and qBI 2  (1  2w2  w1 ) / 3 .
The profits of firms 1, 2, I1 and I 2 are then

 1np   A1   B1  (1  c) 2 / 9  w1 (1  2 w1  w2 ) / 3  T1 ,
 2np   A 2   B 2  (1  2c)2 / 9  ( w2  c)(1  2w2  w1 ) / 3  T2 ,
 Inp1  (1  2w1  w2 )2 / 9  T1 ,
 Inp2  (1  2w2  w1 )2 / 9  T2 .
4

In a different context, Ziss (1997) considers the effects of exporting by the manufacturers through distributors on
strategic trade policies.

8Since firms 1 and 2 give take-it-or-leave-it offers to respectively I1 and I 2 , the equilibriumtransfer payments are T1np  (1  2w1  w2 ) 2 / 9 and T2np  (1  2w2  w1 ) 2 / 9 . Firms 1 and 2
determine the wholesale prices w1 and w2 respectively by maximizing
Max (1+c) 2 /9+w1 (1-2w1 +w 2 )/3+(1-2w1 +w 2 ) 2 /9 ,(10a)Max (1-2c) 2 /9+(w 2 -c)(1-2w 2 +w1 )/3+(1-2w 2 +w1 ) 2 /9 ,

(10b)

w1

w2

which gives the equilibrium wholesale prices as w1np  

1  2c1  8cand w2np  . Hence,55both firms 1 and 2 charge wholesale prices which are lower than their marginal costs ofproduction. It is clear that the business stealing motive in a Cournot oligopoly is the reason
for this type of pricing strategies. Firms 1 and 2 want to reduce the marginal costs of I1
and I 2 respectively to make them more competitive in country B, and then use the transfer
payment to extract the gain from higher competitiveness. This logic is in line with the
incentives for strategic separation as in Vickers (1985) and Ziss (1997).
Since c  12 / 53 , we obtain positive equilibrium outputs, evaluated at theequilibrium wholesale prices. Under no parallel trade, the equilibrium offers made by firms
1 and 2 to I1 and I 2 are respectively ( w1np , T1np )  ((1  2c) / 5, 4(1  2c) 2 /25) and( w2np , T2np )  ((1  8c) / 5, 4(1  3c) 2 /25) , and these offers will be accepted by I1 and I 2 .
The net equilibrium profits of firms 1, 2 I1 and I 2 are respectively

 1np  (43  122c  97c 2 ) / 225 ,  2np  (43  208c  262c 2 ) / 225 and  Inp1   Inp2  0 . (11)9

2.3.2. Parallel trade
Next consider the game under parallel trade. Then I1 and I 2 not only sell in country A, butalso in country B if that is profitable. Hence, when offering the contracts to I1 and I 2 ,firms 1 and 2 need to internalize this possibility.
If I1 and I 2 accept the contracts of firms 1 and 2, the equilibrium outputs are
determined by maximizing the following expressions:
Max(1  q A1  q A 2  q AI 1  q AI 2 )q A1  w1 (qBI 1  q AI 1 )  T1 ,(12a)

Max(1  q A1  q A 2  q AI 1  q AI 2  c)q A 2  ( w2  c)(qBI 2  q AI 2 )  T2 ,(12b)

Max (1  qBI 1  qBI 2  w1 )qBI 1  (1  q A1  q A 2  q AI 1  q AI 2  w1 )q AI 1  T1 ,

(12c)

Max (1  qBI 1  qBI 2  w2 )qBI 2  (1  q A1  q A 2  q AI 1  q AI 2  w2 )q AI 2  T2 .

(12d)

q A1

qA 2

qBI 1 , q AI 1

qBI 2 , q AI 2

Standard calculations yield the equilibrium outputs as q A1  (1  c  w1  w2 ) / 5 ,q A2  (1  4c  w1  w2 ) / 5,

qBI 1  (1  2w1  w2 ) / 3,

qBI 2  (1  2w2  w1 ) / 3,

q AI 1  (1  c  4w1  w2 ) / 5 and q AI 2  (1  c  4w2  w1 ) / 5 .
The profits of firms 1, 2, I1 and I 2 are then

 1p   A1   B1  (1  c  w1  w2 )2 / 25  w1[(1  2w1  w2 ) / 3  (1  c  4w1  w2 ) / 5]  T1 ,

2p   A2  B2  (1  4c  w1  w2 )2 / 25  (w2  c)[(1  2w2  w1 ) / 3  (1  c  4w2  w1 ) / 5]  T2,

 Ip1   BI 1   AI 1  (1  2 w1  w2 ) 2 / 9  (1  c  4w1  w2 )2 / 25  T1 ,
 Ip2   BI 2   AI 2  (1  2w2  w1 ) 2 / 9  (1  c  4w2  w1 )2 / 25  T2 .
The equilibrium transfer payments are T1  (1  2w1  w2 ) / 9  (1  c  4w1  w2 ) / 25p2

2

and T2  (1  2w2  w1 ) / 9  (1  c  4w2  w1 ) / 25 . The equilibrium wholesale prices can bep22

found as w1p  (34  77c ) /188 and w2p  (34  299c ) /188 . It is clear that the wholesale10

prices are higher under parallel trade than under no parallel trade. The total equilibrium
profits of firms 1, 2 I1 and I 2 are respectively

1  (616  3003c  3867c ) / 4418 , 2  (616  10439c  28260c ) / 4418 , I1  I 2  0 . (13)
2

p

2

p

p

p

Proposition 3: Parallel trade reduces the profit of firm 2 but increases that of firm 1 ifc  c*  11/ 50 (approx.) .
Proof: We compare the profits of firm 2 under parallel trade and under no parallel trade.

Specifically, using the expressions in (11) and (13), we have that  ( 1p   1np ) / c  0 forc  [0,12 / 53] . Further,  1p   1np at c  12 / 53 , but  1p   1np at c  0 . Hence, there exists
c*  11/ 50 (approx.) such that the profit of firm 1 is higher under parallel trade than underno parallel trade if c  c* , which proves the result. ■Some explanations are in order. Under parallel trade, wholesale prices affect theintensity of competition in both countries A and B. A lower wholesale price charged by afirm, say firm 1, not only reduces the profits of firm 2 in both countries, it also tends toreduce the profit of firm 1 in country A. This negative impact induces the firm to charge a
relatively higher wholesale price under parallel trade compared with no parallel trade.
Even if the products of both firms 1 and 2 are being traded in a parallel way, therent extracting effect is stronger for the more cost efficient firm. If firm 1 is very much cost
efficient than firm 2, parallel trade makes the former firm better off by extracting asignificant amount of rent from the latter firm. In contrast, if we remove the marginal costdifference between the two firms, their rent shifting effects offset each other, and as aconsequence, the intensity of product market competition will be increased, reducing the
profits of both firms.

11

3. Unionized labour market in the home country

In this section we examine the role of unionized labour markets. To isolate its impacts, we
make some changes to the above analysis by assuming that firm 1 is a monopolist producerof the product. This firm has a plant in both country A (the home country) and country B(the foreign country), and serves both countries from the respective plants. We assume thatthe labour market in country A is unionized, while that in country B is perfectlycompetitive, and the reservation wage rates in both countries are c, which are assume to be
zero for simplicity. There is a transportation cost t for trade between the countries. We
assume that the inverse demand from the consumers’ in country A is PA  1  q A while it isin country B is PB  a  qB , with a < 1. This structure is similar to the “partial FDI” case ofLommerud et al. (2003), who exclude parallel trade.
We adopt the right-to-manage6 model of labour unions,7 where the labour unionchooses the wage rate and firm 1, which requires one unit of labour to produce one unit ofoutput, determines the employment/output level. We consider full bargaining power of thelabour union to demonstrate our results in the simplest way.

3.1. No parallel trade
We analyze the following moves of the game. At stage 1, the labour union sets the wage incountry A. At stage 2, firm 1 hires labour and produces in countries A and B. Then profits
are realized. The game is solved by backward induction.
Given the wage rates in both countries, firm 1 maximizes:

6

We refer to Vannini and Bughin (2000), Lommerud et al. (2003), López and Naylor (2004), Skaksen (2004) and
Mukherjee (2007), to name a few, for works on the right-to-manage model of labour unions.
7
The ‘efficient bargaining’ model, which stipulates that the firms and unions bargain over wages and employment, is analternative to the right-to-manage model. See, Layard et al. (1991) for arguments in favour of right-to-manage models.

12Max (1  q A1  w)q A1  (1  qB1 )qB1 .

(14)

q A1 , qB 1

The equilibrium outputs in countries A and B are respectively
qA1  (1  w) / 2

andqB1  a / 2 .

(15)

Therefore, the labour demand in country A is L  (1  w) / 2 . The labour union
maximizes the following expression to determine the wage rate:Maxw

w(1  w),2

(16)

which gives
w*,np  1/ 2 .

(17)

We assume that t  w*,np , i.e.,t  1/ 2 ,(18)which ensures that firm 1 has no incentive to export its product between the countries,
given that we have assumed away the cost of setting up a business in country B. Even if the
setup cost is positive but small enough, firm 1 prefers to produce in country B.
The total profit of firm 1 is

 1np   A1   B1 

(1  w) 2  a 2 1  4a 2

.
4
16

(19)

3.2. Parallel trade
Assume that there is a firm in country 2, called K, who buys the product of firm 1 incountry B and sells it back to country A. It is assumed that firm 1 does not know theidentity of the parallel trader as in Hur and Riyanto (2006),8 and as in the previous
section the parallel trader derives utility only from profit but not from consumption.

8

If the parallel trader can be identified, firm 1 will not sell the product to the parallel trader if parallel trade makes itworse off. Here we show that parallel trade benefits firm 1, and thus it has less incentive to restrict parallel trading even if
it knows the identity of the parallel trader.

13

Hence, the demand in country B now comes from both consumers and the parallel
trader. While producing its output in country B, firm 1 needs to internalize this effect.
We consider the following game under parallel trade. At stage 1, the labour union
charges wage in country A. Then at stage 2, firm 1 makes its production decisions incountries A and B, and K buys the product of firm 1 in country B and sells it in country A.
Then the profits are realized. The game is still solved by backward induction.
Since K buys the product in country B, it creates demand in that country along withthe demand from the consumers. However, the demand by K depends on its sales incountry A. Hence, while determining the output in country B, firm 1 should correctly
anticipate the demand from K and adjust the demand function in country B accordingly.
Given the wage rate in country A, the transportation cost t and the price PB at
which K buys the product in country B, K determines its output to maximize:
Max(1  q A1  q AK  PB  t )q AK

(20)

q AK

and firm 1 maximizes the following expression to determine output in country A:
Max(1  q A1  q AK  w)q A1 .

(21)

q A1

The equilibrium outputs of K and firm 1 in country A are respectively
q AK 

1  2( PB  t )  w
1  2w  PB  t
and q A1 
. Firm 1 anticipates this demand from K.
3
3

Hence,
PB 

the

total

inversedemandincountry

B

can

be

expressedas1  3a  2t  w  3qB, which firm 1 should correctly anticipate and use in5

determining the output in country B. 9
Therefore, the outputs q AK , q A1 and qB1 are determined by maximizing theexpressions (20), (21) and the following expression:
9

In contrast to the last section, where the demand from the distributors affects the derived demand for firm
1’s product, here the demand from the parallel trader affects the market demand.

14

1  3a  2t  w  3qB1
Max(
)qB1 .
qB 1
5

(22)

The equilibrium outputs and the price in country B at a given w are respectively
q AK 

1  2( PB  t )  w
1  2w  PB  t
1  3a  2t  w
1  3a  2t  w, q A1 , qB1 and PB .
3
3
6
10
The wage in country A is then determined by maximizing the following expression:w(1  2w  PB  t )
.
3

(23)

The equilibrium wage is w 

1  PB  t
1  3a  2t  w, we obtain the. Given PB 
10
4

Max
w

equilibrium wage in country B to be w*, p 

11  3a  8t.
39

Given the equilibrium wage, the equilibrium outputs and the price in country B are
respectively q AK 
PB 

40  21a  56t
22  6a  16t
25  60a  35t
 0 , qB1 , q A1 
117
117
117

25  60a  35t. It can also be found that the demand by the consumers in country B at
195

PB is qBC  a  PB 

135a  25  35t. Note that qBC  q AK  qB1 .
195

We assume that t 

a

and

40  21a, which ensures that q AK  0 and qB1  0 . Further, if
56

3( .06, approx.) , then our assumption (18) implies that qBC  0 . Hence, we assume
54

in the following analysis that140  21at , where the first inequality comes from (18).
256

1 40  21a4
However, the range of t over [ ,] is non-empty if a   .57(approx.) . We
256
7
restrict our attention to .06  a  .57 . Also t  w*, p for .06  a  .57 , i.e., firm 1 has no
incentive to export its product between the countries.

15

Proposition 4: The equilibrium wage in country A is lower and firm 1’s equilibrium output

is higher in country A under parallel trade than under no parallel trade.
Proof: We find that w*,np  w*, p if t 

17  6a1
40  21a, which holds for  t 
.
16
2
56

Firm 1’s output in country A is higher under parallel trade than under no parallel
trade, i.e.,

22  6a  16t 1
29  24a1
40  21a, which holds for  t .■
 if t 
117
4
64
2
56

The intuition for the wage reducing effect of parallel trade is as follows. Parallel
trade increases competition in country A. Hence, ceteris paribus, it reduces the labourdemand faced by the labour union in the country, which in turn forces the union to reduce
its wage hike. On the one hand, the increased competition due to parallel trade tends toreduce the output of firm 1 in country A; on the other hand, the lowered wage tends toincrease firm 1’s output. Our result shows that the wage-reducing effect dominates thecompetition effect, and thus increases firm 1’s output in country A.
The total profit of firm 1 under parallel trade is 1p   A1   B1 

(22  6a  16t ) 2 (25  60a  35t ) 2

.
13689
22815

(24)

Proposition 5: The profit of firm 1 is higher under parallel trade than under no parallel

trade for1
40  21at 
and .06  a  .57 .
2
56

 1p
1
40  21a. The comparison of (19) and (24) at
Proof: We have 0 for  t t2
56
t  1/ 2 shows that  1p   1np for .06  a  .57 . ■16

The reason for the above result is as follows. Parallel trade intensifies competition incountry A, though it creates higher demand in country B. For a given wage, the competition
effect dominates the demand-raising effect, and thus parallel trade tends to reduce firm 1’s
profit. This is clearly true if the labour markets in both countries are perfectly competitive(see Appendix for detailed proof). However, one must take into account another effect. As
shown in Proposition 4, parallel trade reduces the union wage in country 1, and therefore,
helps to reduce firm 1’s marginal cost of production in country A. The beneficial wagereducing effect (along with the demand-raising effect) outweighs the negative competition
effect and hence increases firm 1’s profit under parallel trade. That is, in the presence of alabour union, parallel trade may benefit a manufacturer by reducing the unionized wage.
To show the role of unions in the simplest way, we have given the labour union fullbargaining power. The other extreme case is full bargaining power of the manufacturer. In
this situation, the equilibrium wage is equal to the reservation wage of the worker. The
analysis under this situation is similar to that shown in the Appendix. Hence, it is clear thatthe presence of a labour union may make a manufacturer better off under parallel trade if
the bargaining power of the labour union is not very low.
The market demand function in country A, from which the labour demand isderived, plays an important role in determining the beneficial effects of parallel trade. We
may conjecture the case of a different demand situation. For example, as the elasticity ofthe market demand function in country A increases, it will have a lower adverse impact onfirm 1’s production and labour demand in that country following parallel trade, since a
relatively smaller reduction in the price of the final goods is required to accommodate theoutput of the parallel trader. Hence, as the elasticity of the market demand function
increases, firm 1 needs to reduce its output by a lower amount following parallel trade. In
other words, both the adverse competition effect and the favourable wage-reducing effect17

fall with a more elastic market demand function. However, the demand-raising effect incountry B remains, thus increasing the possibility of a beneficial parallel trade.

4. Conclusion

It is generally believed that parallel trade reduces profits of the manufacturers. However,
empirical evidences do not always support this view. In this paper, we identify two newfactors under parallel trade, viz., market stealing and union-wage cutting, which may be
responsible for generating higher profits to some manufacturers. Market stealing arises insituations when the manufacturer is even slightly more efficient or sells in more markets
than its competitors. In these situations, the manufacturer can strategically take advantageof parallel trading in its competition with rivals. Similarly, it can also use this advantage in
an imperfect factor market, such as when labour is unionized. As long as the union has
some bargaining power for wage hikes, parallel trading can help the manufacturer toweaken the wage demand. For these reasons, many manufacturers often accept parallel
trade in some markets.

18

Appendix
Parallel trade makes the manufacturer worse off without a union

Consider the set up of Section 3 with the exception that the labour markets are perfectlycompetitive in both countries. For simplicity, assume that the reservation wage is zero inboth countries. If there is no parallel trade, standard calculations show that the total profit
of firm 1 is  1np 

1  a2.
4

The equilibrium values under parallel trade follows immediately from Section 3
with w = 0. We have q A1 
qBC 

7a  1  2t
1  3a  2t
and PB . The boundary conditions are as follows: q AK and
10
10

qB1 are positive for t a

11  3a  8t
1  3a  2t
4  3a  8t
 0 , qB1 , q AK ,
30
615

4  3a1
1  7aif, and qBC  0 for t  0 if a  , but qBC  0 for t 
8
7
2

1
.
7
The

total

profit

of

firm

1

under

parallel

trade

is

 1p
(11  3a  8t ) 2  15(1  3a  2t ) 2. The profit of firm 1 is convex in t, and 0 for
 
900
t
p
1

t

 1p
33a  2929
29
if a 
, but.
 0 for t  0 if a 
62
33
33
t
The relevant values of t and a are t  (1  7a 4  3a1
4  3a,) and a  , t  [0,
) and
2
8
7
8

1
29
33a  29 4  3a29
 a  1.
a
, and t  (
,
) and
7
33
62
8
33
Standard calculation shows that  1np   1p .

19

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21