Discussion Paper No. 1026

A MANUFACTURER’S INCENTIVE
TO OPEN ITS DIRECT CHANNEL
AND ITS IMPACT ON WELFARE

Noriaki Matsushima
Tomomichi Mizuno
Cong Pan

March 2018

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, JapanA manufacturer’s incentive to open its directchannel and its impact on welfare∗
Noriaki Matsushima†, Tomomichi Mizuno‡, Cong Pan§
March 27, 2018

Abstract
We consider a bilateral monopoly in which a manufacturer can open its direct channel that is less eﬃcient than the existing retailer. We find the following results. The
manufacturer opens its direct channel if its bargaining power over the existing retailer
is weak. Opening the direct channel is detrimental to social welfare if this channel is
eﬃcient. Under a linear demand specification, if the equilibrium unit price under suchopening is higher than that under no opening, the opening reduces social welfare undermost of the parameter range of the eﬃciency of the manufacturer’s direct channel.

Keywords: distribution channels, supplier encroachment, two-part tariﬀ contract, welfare
JEL Classification Numbers: L14, L22, M11, D43∗

We thank the seminar participants at Shinshu University for their valuable discussions and comments.
We gratefully acknowledge the financial support from the Japan Society for the Promotion of Science (JSPS),
KAKENHI Grant Numbers JP15H03349, JP15H05728, JP17H00984, and JP16K17116. The usual disclaimer
applies.
†
Institute of Social and Economic Research, Osaka University, Mihogaoka 6-1, Ibaraki, Osaka, 567-0047,
Japan. Phone: (81)-6-6879-8571. Fax: (81)-6-6879-8583. E-mail: nmatsush@iser.osaka-u.ac.jp‡
Graduate School of Economics, Kobe University, 2-1 Rokkodai, Nada, Kobe, Hyogo, 657-8501, Japan.
Phone: (81)-78-803-6802. Fax: (81)-78-803-7289. E-mail: mizuno@econ.kobe-u.ac.jp§
Faulty of Economics, Nagoya University of Commerce & Business (NUCB), 4-4 Sagamine Komenokicho Nisshin-shi, Aichi, 470-0193, Japan. Phone: (81)-561-73-2111. Fax: (81)-561-73-1202.
E-mail: pancongecon@gmail.com

11 Introduction
Manufacturers often open their own direct channels to expand accessibility to consumers
even when they indirectly sell products through traditional retail channels. Owing to thetougher downstream competition in those markets, such introductions of direct channels,
known as “encroachment,” intuitively seem welfare-improving, although existing retailers
that trade with those manufacturers fall into diﬃculties to maintain profits as large as before.
Such a positive eﬀect of encroachment on welfare seems more likely to hold if a manufacturer is eﬃcient. This fact has put policymakers in a dilemma of whether encroachment
should be given policy support from the perspective of social welfare or legally restrained toprotect existing retailers’ benefits (Kalnins, 2004).1
Because of the common expectation of a positive impact of encroachment on welfare(Dutta et al., 1999; Blair and Lafontaine, 2005), the welfare magnitude of this important
issue has not been theoretically considered in the economics literature, except for the recent
study by Pan (2018), who considers an ex ante downstream duopoly wherein two retailers are oﬀered take-it-or-leave-it contracts secretly from a monopoly manufacturer.2 The
main focus of Pan (2018) is to show that encroachment may result in higher price and lower
consumer surplus although the negative impact of encroachment on social welfare is also
discussed in his concluding remarks. A manufacturer using encroachment to solve its commitment problem plays a key role in Pan (2018), meaning that the counterintuitive result
is driven by two important elements: (i) the ex ante downstream duopoly of existing retailchannels and (ii) contract secrecy. Specifically, in Pan (2018), encroachment may reduce1Some theoretical studies even show that such an introduction of a direct channel does not always harm
existing retailers (see Arya et al., 2007; Matsushima and Mizuno, 2018). These studies provide theoreticalsupport for the positive eﬀect of encroachment on existing retailers.
2This market structure is extensively discussed in the literature on supplier opportunism. The main findingis that under such a structure, the upstream monopolist faces a commitment problem in that it fails to achieve amonopoly outcome (e.g., Hart and Tirole, 1990; McAfee and Schwartz, 1994; Reisinger and Tarantino, 2015).

2social welfare because it changes the market outcomes from an ex ante duopoly to an ex postquasi-monopoly.3 Moreover, he does not discuss the impact of encroachment on existingretailers because their ex ante and ex post profits are always zero owing to take-it-or-leave-it
oﬀers.
In the current study, we consider a manufacturer–retailer (bilateral monopoly) relation
so that the manufacturer’s commitment problem is no longer a concern. A bargaining problem is also considered so that the pros and cons of encroachment can be tracked from theperspectives of the players. Further, the ex ante market status is a bilateral monopoly in ourstudy, implying that our result is motivated by a diﬀerent and new mechanism than in Pan(2018).
We consider a bilateral monopoly in which a manufacturer can open its direct channel,
which is less eﬃcient than the existing retailer. We need to compare two cases: (i) the
manufacturer does not open its direct channel and (ii) it opens its direct channel, inducing
a downstream duopoly. In the first case, the manufacturer and retailer determine a two-parttariﬀ contract through Nash bargaining, inducing them to set the unit price at the marginal
production cost of the manufacturer in equilibrium. In the second case, they also determine
a two-part tariﬀ contract through Nash bargaining by considering the joint profits including
the profit of the manufacturer’s direct channel. This consideration distorts the unit price inequilibrium because the trading pair needs to balance the quantities in the direct and indirectchannels by controlling the unit price that directly influences the quantity of the existingretailer.
We first show that the manufacturer opens its direct channel if its bargaining power overthe existing retailer is weak. We then show that the distortion through opening the manufacturer’s direct channel is detrimental to social welfare even if the direct channel is eﬃcient.
3

We call the ex post status a quasi-monopoly because it is exactly a monopoly only when selling directly
is as eﬃcient as selling via existing retailers.

3This is because the trading pair would then overly depend on the production of the manufacturer’s direct channel, which is still less eﬃcient than the existing retailer. The welfare
property is a novelty of our study. In addition, under a linear demand setting, if the equilibrium unit price under encroachment is higher than that under no encroachment, opening
a direct channel reduces social welfare and the existing retailer’s profit under most of theparameter range of the eﬃciency of the manufacturer’s direct channel. This outcome has
an important policy implication that the competition authority should consider a claim by
an existing retailer that trades with an encroaching manufacturer if the claim is based on an
increase in its unit price, which is another novelty of our study.
Another closely related study is Reisinger and Tarantino (2015) whose ex ante market
structure is close to that in Pan (2018). A monopoly manufacturer that secretly supplies twocompeting retailers with asymmetric marginal costs in a take-it-or-leave-it manner (downstream duopoly) faces a commitment problem. The authors study the manufacturer’s incentive for vertical integration in solving this problem. The main finding is that when the
manufacturer chooses to integrate with the ineﬃcient retailer, it will subsidize the other efficient retailer to optimally reallocate the channel distribution.4 This finding implies thatvertical integration is welfare-improving (welfare-reducing) if and only if the degree of subsidization is high (low). This setting is similar to ours in that encroachment can also becomprehended as downward integration with an inactive retailer. However, in Reisinger andTarantino (2015), integration with the ineﬃcient retailer rather than the eﬃcient one is always suboptimal for the manufacturer, implying that the welfare-reducing impact of vertical
integration can only happen oﬀ the equilibrium path.5 Conversely, our study oﬀers a new
insight that the welfare-reducing downward entry may actually happen in equilibrium.
The remainder of the paper is as follows. Section 2 provides the model setting. Section
4

The Nash bargaining setting is also considered in the web appendix of Reisinger and Tarantino (2015).

5

As an extension of their model, by incorporating marginal cost uncertainty, they show that both downstream retailers can be chosen by the manufacturer as a partner for vertical integration.

4

3 shows the analytical outcome of the model. Section 4 presents the welfare property of theoutcome in Section 3. Section 5 concludes.

2 ModelLet us first consider a monopoly supply chain that comprises one upstream manufacturer
U and one downstream retailer D. U supplies final products to D that then resells themto consumers. U can also choose whether to directly supply to consumers through a directchannel, which is known as “supplier encroachment.” We assume that D incurs no cost in
the reselling process. On the contrary, when U encroaches, it incurs a positive marginal costfor retailing c.6 For simplicity, U’s production cost is normalized to zero.
The trading term between U and D is determined through a negotiation over a two-parttariﬀ contract comprising a unit price w and a fixed fee f . The negotiation outcome isdecided by the Nash bargaining solution. The bargaining power of U over D is β ∈ (0, 1).
We assume that U’s direct channel and D supply homogeneous final products in the retailmarket.7 Denote D’s quantity by qD and U’s by qU (if it encroaches). We assume that theinverse demand function P(Q) for final products is nonnegative, strictly decreasing, and twice
diﬀerentiable, where P is the price and Q is the total quantity sold in the retail market. To
guarantee that profit functions are strictly quasi-concave and that resale competition involves
strategic substitutability, we assume P′ (Q) + QP′′ (Q) < 0 (Vives, 1999).
The game proceeds as follows. In stage 1, U chooses whether to encroach. In stage 2, U
6

The assumption that retailers are more eﬃcient than manufacturers is common in the literature. Such aneﬃciency gap occurs for various reasons. For example, in competition between bricks-and-mortar retailers andmanufacturers’ online stores, the latter are less familiar with consumers’ preferences than the former, which
benefit from direct contact (Arya et al., 2007). Moreover, the latter incur higher transportation costs by shipping
directly to consumers, whereas the former benefit from bulk shipping (Li et al., 2015). Further, the latter mustrisk returns and redress because consumers cannot physically inspect products before ordering (Pan, 2016).
7

If they compete in heterogeneous products, U would have a stronger incentive to encroach because it
would enjoy an market expansion eﬀect by doing so.

5and D negotiate over the two-part tariﬀ contract. In stage 3, if U encroached in stage 1, D
and U simultaneously set their own quantities; otherwise, only D sets its own quantity.
The timeline in which U’s encroaching decision comes before the contracting process
follows the idea that starting a direct channel is relatively irreversible and thus must be taken
prudently. For example, to conduct direct sales, whether through an online store or a physicaldirect store, U has to deal with resale issues such as inventory and siting locations, which
are always regarded as long-term decisions.

3 Analysis
The game is solved by backward induction. Based on U’s decision in stage 1, there are two
types of subgame: U encroaches or not. We use the superscripts e and n to denote eachsubgame. Note that the Nash bargaining process naturally guarantees that the negotiation
between U and D succeeds in equilibrium and that U does not foreclose D because D ismore eﬃcient than U’s direct channel.

3.1

U does not encroach

First, we discuss the subgame wherein U does not encroach. In stage 3, given the unit priceassigned in stage 2, D sets quantity q to maximize its profit:
q(w) ≡ arg max (P(q) − w) q.
q

To simplify the notation, I define the industry profit as Π M (w) ≡ P(q(w))q(w), where thesuperscript M represents the integrated monopoly.8 Anticipating the outcome in stage 3, U
8

In this case, U and D act as if they are integrated as one agent. They jointly solve their maximization
problem and then divide the aggregate profit based on their bargaining powers. The payments via the unit pricebecome internal transfers and thus do not aﬀect the industry profit.

6

and D know that if the negotiation succeeds, they can obtain
πnU = wq(w) + f, πnD = (P(q(w)) − w) q(w) − f.

On the contrary, if the negotiation breaks down, both of them obtain zero profits. The negotiation in stage 2 specifies the contract as follows:
max {πnU }β {πnD }1−β .
w, f

The first-order condition can be denoted as follows:
∂q
w=0
∂w

(1)

⇒ wn = 0; f n = βΠ M (0).

The corresponding profits of U and D are
πnU = βΠ M (0); πnD = (1 − β)Π M (0).

This result is standard. With a two-part tariﬀ contract, U always sets the unit price to its
production cost (zero) and abstracts D’s surplus through the fixed fee based on its bargaining
power.

3.2

U encroaches

Next, let us consider the subgame wherein U encroaches. In this case, it sells through both
D and its direct channel. The following maximization problems in stage 3 aremax (P(qD , qU ) − w) qD − f, max (P(qD , qU ) − c) qU + qD w + f,
qD

qU

7

leading to the subgame quantities: qD (w, c) and qU (w, c). We define the industry profit asfollows (we use the superscript I to represent it):ΠI (w, c) ≡ P(qD (w, c), qU (w, c))qD (w, c) + [P(qD (w, c), qU (w, c)) − c]qU (w, c).

If the negotiation succeeds, they can obtain
πeU (w, c, f ) = [P(qD (w, c), qU (w, c)) − c]qU (w, c) + wqD (w, c) + f,
πeD (w, c, f ) = [P(qD (w, c), qU (w, c)) − w]qD (w, c) − f.

On the contrary, if the negotiation breaks down, U has a disagreement payoﬀ in which it
directly sells and monopolizes the retail market with marginal cost c, although D gains zeroprofit. The profits of U and D in the negotiation breakdown are given asMe′πe′
U = Π (c), πD = 0.

The bargaining problem in stage 2 is given as{}β { e}max πeU (w, c, f ) − πe′πD (w, c, f ) 1−β ,Uw, fleading to
we ≡ arg max ΠI (w, c) − Π M (c),w[]
f e = (1 − β) Π M (c) − (P(qD (we , c) + qU (we , c)) − c)qU (we , c)[]+β P(qD (we , c) + qU (we , c))qD (we , c) − we qD (we , c) .

8

Owing to the bargaining procedure, they set w as if they maximize their joint profit throughthe control of w and split the maximized joint profit through fixed fee f . By using the envelop
theorem, we derive the first-order condition of w:
∂qD
∂qU
∂qD
w + P′ (·)
qU + P′ (·)
qD = 0.
∂w∂w }| ∂w {z(2)commitment of encroachment

In addition to the first term of Eq. (1) in the case without encroachment, the second and thirdterms are included. Those terms reflect the control of the downstream quantities through w.
Specifically, the second term of Eq. (2) denotes a positive eﬀect on w, while the third term
denotes a negative one. Intuitively, as marginal cost c increases, the relative eﬃciency ofD improves, inducing the bargaining pair to increase qD through a decrease in w. In otherwords, we expect that the positive correlation between c and qD is monotonic. Here, weshow that the statement actually holds true.
We remark on the equilibrium property in the second- and third-stage outcomes. D’squantity qD is ultimately controlled by unit price w, which implies that the two-part tariﬀ
contract can be regarded as a quantity-based one, (qD , f ). We can convert the procedure in
the second and third stages as follows: the bargaining in stage 2 is that U chooses qD to
maximize the joint profit of the bargaining pair, anticipating qU (qD ), which will be chosen
by U’s direct channel in stage 3. In stage 3, because U has already levied the fees on D instage 2, it ignores the impact on D’s profit. In other words, U solves the following:max [P(qD , qU ) − c]qU ,qU

from which we have U’s best-response function qU (qD , c). In stage 2, U solves the following:max [P(qD , qU (qD , c)) − c]qU (qD , c) + P(qD , qU (qD , c))qD − Π M (c).
qD

9

(3)

Lemma 1 The optimal qD is given by
qeD = −c ×(P′′ qU + 2P′ )(> 0).
(P′ )2(4)

Proof. The first-order condition of U’s direct channel in stage 3 is given by
P′ qU + P − c = 0.

(5)

Totally diﬀerentiating Eq. (5) gives rise todqU
P′′ qU + P′
= − ′′.
dqD
P qU + 2P′(6)

By using Eq. (6), the maximization problem in Eq. (3) can be derived as[P′ qU + P − c]dqU
dqU
+ P′ q D+ P′ qU + P′ qD + P = 0
dqD
dqD

dqU
+ c + P′ qD = 0dqD−c⇒ qD = ′.
P × (1 + dqU /dqD )⇒ P′ q D

Substituting Eq. (6) into the last equation gives rise to the expression in Lemma 1. Becauseof strategic substitutability, qD is positive.
Lemma 1 implies that as long as D has a cost advantage, it is always assigned a positive
share proportional to c by U. Because of continuity, it is straightforward that when c isalmost zero, qeD will be close to zero. Owing to strategic substitutability, qeU will be close
to the monopoly quantity under which its marginal cost is zero. Then, the positive eﬀect in
Eq. (2) becomes a dominant one so that we > 0. This fact is summarized by the following
lemma.

10

Lemma 2 ∃ c̄ > 0 such that ∀ c < c̄, we > 0.
D is possibly oﬀered a tax in a bilateral monopoly with a two-part tariﬀ contract. Given
that U has committed to encroachment, when its direct channel is eﬃcient, it would rather
restrain D’s sales and shift some share back to U’s direct channel.
In Reisinger and Tarantino (2015), when a manufacturer supplies duopoly retailers withasymmetric marginal costs and the manufacturer integrates with the less eﬃcient retailer, themore eﬃcient one will be oﬀered a subsidy. This result is similar but essentially diﬀerent
to ours because we consider the case wherein the manufacturer creates a new retailer (i.e.,
encroachment) instead of integrating with an incumbent one. In other words, the baseline
situation in Reisinger and Tarantino (2015) is an asymmetric downstream duopoly with amonopoly manufacturer, whereas that in our study is a bilateral monopoly with the possibilityof supplier encroachment. In our study, the manufacturer’s decision on whether to encroachis explicitly considered and the subsidy can exist in the subgame perfect equilibrium. Thispart is discussed after we derive Proposition 1.

3.3

U’s incentive to encroach

Note that with a general demand function, we cannot explicitly derive the equilibrium unit
price we . Despite this, given a certain we that satisfies Eq. (2), the corresponding profits inthis subgame can be denoted as
πeU = βΠI (we , c) + (1 − β)Π M (c); πeD = (1 − β)[ΠI (we , c) − Π M (c)].

To restrict our attention to the parameter range wherein encroachment happens in equilibrium, we need to confirm U’s incentive to encroach within the parameter range whereinits direct channel is active. Let ĉ such that qeU > 0 for any c < ĉ. By comparing πnU with πeU ,11

we derive the following equation:
πeU − πnU = β[ΠI (we , c) − Π M (0)] + (1 − β)Π M (c).

(7)

Compared with the monopoly case with zero marginal cost, the industry profit of the duopoly
case with one agent having a positive marginal cost (i.e., c > 0) is strictly lower, no matterhow U chooses we . In other words, an eﬃciency loss at the industry level is inevitable.
Hence, the first term of Eq. (7) is always negative. On the contrary, when c < ĉ, the second
term must be positive.9 Therefore, whether U encroaches is decided by U’s bargaining
power, which is summarized in Proposition 1.
Proposition 1 Given that c < ĉ, U encroaches when its bargaining power is relatively small.
Formally,β<Π M (c).
Π M (c) + Π M (0) − ΠI (we , c)

When U’s bargaining power is weak, the transfer from D in the bilateral monopoly is small.
Encroachment enhances U’s bargaining position through an increase in its disagreement
payoﬀ, whereas it diminishes the total industry profit.
The threshold value of β in Proposition 1 is always located in the interval (0, 1). Then,by comparing it with the case of no encroachment, U encroaching may either raise or reduce
the unit price contingent on the value of c, which contrasts with most of the literature on
supplier encroachment.10
Π M (c) is positive if the monopoly price is higher than c. The condition c < ĉ guarantees that qeU is positivein duopoly competition and thus that the duopoly price is higher than c. Because the monopoly price is always
higher than the duopoly price, Π M (c) must be positive if c < ĉ is satisfied.
910

In all studies modeling a linear contract, the unit price must reduce after encroachment (e.g., Arya etal., 2007); by contrast, in all research that models a two-part tariﬀ contract, the unit price must increase after
encroachment (e.g., Matsushima and Mizuno, 2018; Pan, 2018).

12

4 Welfare
We check the impact of U’s encroachment on the total surplus and consumer surplus. First,
we consider it under the general demand function. Second, by employing a linear demand
function, we explicitly solve the problem in the previous section.
The social surplus is denoted byW=∫ qU (qeD (c),c)+qeD (c)P(x)dx − cqU (qeD (c), c).

0

By diﬀerentiating W with respect to c, we have(
) d(qU (qeD (c), c) + qeD (c))
dW
= P qU (qeD (c), c) + qeD (c)− qU (qeD (c), c) − c × (qU (qeD (c), c))′ .
dc
dc
At c = 0, the diﬀerential isd(qU (qeD (c), c) + qeD (c))
dW
M
= P(q )
− qM ,
dc c=0dc
c=0(8)

where q M is the monopoly quantity in which its marginal cost is zero. From Eqs. (4), (5),and (6), we have the following relation:11d(qU (qeD (c), c) + qeD (c))
dqe (c)∂qU= (dqU /dqD + 1) D+dc
dc c=0∂c c=0c=0P′(P′′ q M + 2P′ )1
×+ ′′ M= − ′′ M′′
2
P q + 2P(P )P q + 2P′
P′′ q M + P′
= − ′ ′′ M
> 0.
P (P q + 2P′ )11(9)

By substituting Eq. (6) into the first line of Eq. (9), we obtain the first fraction in the second line of Eq.
(9). By simply diﬀerentiating qeD in Eq. (4) with respect to c, we obtain the second fraction in the second lineof Eq. (9). Finally, from the partial derivative of qU in Eq. (5) with respect to c, we obtain ∂qU /∂c at c = 0.

13

By using the above outcomes in Eqs. (8) and (9) and Eq. (5) at c = 0, we obtaindW
P′′ q M + P′
P= −P ′ ′′ M
− q M = ′′ M
< 0.
′
dc c=0P (P q + 2P )P q + 2P′

(10)Note that the social surplus under no encroachment is the same as that under encroachment
when c = 0. In addition, the consumer surplus under no encroachment is the same as that
under encroachment when c = 0. From the facts and results in Eqs. (9) and (10), we have
Proposition 2.
Proposition 2 For small c, U’s encroachment is detrimental to the social surplus, but beneficial to the consumer surplus.
When c is small, the market share of U’s direct channel is large, implying that the relatively
ineﬃcient channel handles most retailing. This ineﬃcient allocation of production worsens
the social surplus.

Linear demand caseSecond, we set a linear inverse demand function, p = a − bQ, tofurther investigate the welfare property of the model. The other settings are the same asin the main model: the profits are πU = [a − b(qU + qD ) − c]qU + wqD + f and πD =[a − b(qU + qD ) − w]qD − f , while the Nash product is NP = [πU − OP]β [πD ]1−β , where
OP = (a − c)2 /(4b) if U encroaches and OP = 0 otherwise.
We first consider the case without encroachment. In the third stage, from the first-orderconditions ∂πD /∂qD = 0 and qU = 0, we have qLn
D (w) = (a − w)/(2b), where the superscript
Ln denotes the case with no encroachment under linear demand. By substituting this result
into NP and solving the first-order conditions ∂NP/∂w = 0 and ∂NP/∂ f = 0 for w and f ,we have wLn = 0 and f Ln = a2 β/(4b). From the above results, we obtain the outcomes as

14

follows:aa2 β, wLn = 0, f Ln =,2b4ba2 (1 − β)
a2
3a2
a2 β
Ln
Ln
πULn =
, πLn
=
,
CS
=
,
W
=
.
D
4b
4b
8b
8b
qULn = 0, qLn
D =

(11)

Next, we consider the case with encroachment. In the third stage, from the first-orderconditions ∂πD /∂qD = 0 and ∂πU /∂qU = 0, we have qULe (w) = (a − 2c + w)/(3b) andqLe
D (w) = (a − 2w + c)/(3b), where the superscript Le denotes the case with encroachment
under linear demand. By substituting this result into each firm’s profit, we have πULe (w) andπLe
D (w). In the second stage, we derive the optimal two-part tariﬀ. Since the outside option
with encroachment does not depend on w and f , we can calculate the optimal contract asfollows. The first step is to maximize the net joint profit, πULe (w) − (a − c)2 /(4b) + πLe
D (w), withrespect to w. Then, we have wLe = (a − 5c)/2. The second step is to divide the maximized
Le
Le
Le
2
Le
Le
net joint profit by f . Then, by solving πLe
D (w ) = (1 − β)[πU (w ) − (a − c) /(4b) + πD (w )]for f , we have f Le = c2 (3 + β)/b. From the above results, we obtain the outcomes as follows:a − 3c2c
a − 5cc2 (3 + β)
, qLe
, wLe =
, f Le =
,
D =
2b
b
2
b
(12)
(a − c)2 + 4c2 β
c2 (1 − β)(a + c)2
3a2 − 2ac + 11c2
Le
Le
Le
Le
πU =
, πD =, CS =
, W =
.
4b
b
8b
8b
qULe =

From these outcomes, we can show that Lemmas 1 and 2 are satisfied. In other words, forLe
any c > 0, qLe> 0.
D > 0; and for any c < a/5, w

In the first stage, U decides to encroach if πULe > πULn . By solving this for β, we haveβ<(a − c)2.
(a − 2c)(a + 2c)

This condition corresponds to Proposition 1.
Finally, we compare the social surplus with the consumer surplus in the two cases. From

15

CS Ln and W Ln in Eq. (11) and CS Le and W Le in Eq. (12), we have Proposition 3.
Proposition 3 Under linear demand, the social surplus under encroachment is lower thanthat under no encroachment if and only if 0 < c < 2a/11. In addition, the consumer surplus
under encroachment is always larger than that under no encroachment.
The former argument in Proposition 3 confirms that a welfare reduction caused by encroachment is more likely to occur when the direct channel is suﬃciently eﬃcient. The latterargument follows from the fact that CS Le is increasing in c. This is similar to that in Pan
and Yoshida (2018), who consider an international oligopoly wherein foreign manufacturers carrying out FDI sell products through local retailers and foreign-made products directly
through e-commerce sites.12
We also check how encroachment aﬀects the profit of D and the unit price, namely we
LnLe
check πLe
− wLn . The calculations lead to the following proposition, whichD − πD and w

confirms Lemma 2.
Proposition 4 Encroachment always decreases the profit of D. It increases the unit price if
and only if c < a/5.
The latter argument in Proposition 4 is almost consistent with the condition in Proposition 3that encroachment is detrimental to the social surplus. This finding implies that an increase
in w can be a signal that encroachment is welfare-reducing and that the competition authority
should consider a claim by an existing retailer that trades with an encroaching manufacturer
if the claim is based on an increase in its unit price.
12

In their model, local bilateral supply chains also supply local products. The model structure is similar toours in that the cost disadvantage in direct selling is captured by a specific tariﬀ in Pan and Yoshida (2018).
The main purpose of Pan and Yoshida (2018) is to show that a tariﬀ reduction may result in a higher local price,which thus reduces the local consumer surplus. Although the model setting in Pan and Yoshida (2018) partiallyoverlaps that in our study, we focus on comparing welfare with encroachment with that without encroachment.
Such a comparison is outside the scope of Pan and Yoshida (2018).

16

5 Conclusion
We consider a bilateral monopoly model in which an upstream manufacturer that trades witha downstream retailer can open its direct channel (so-called supplier encroachment). We
show that encroachment by the manufacturer may harm social welfare, although it changes
the downstream market from a monopoly to a duopoly. This finding complements the recent
study by Pan (2018), who also shows that supplier encroachment may harm social welfare in an ex ante downstream duopoly. Under a linear demand specification, we show thatwelfare-decreasing encroachment occurs almost along with an increase in the unit price forthe downstream retailer, which implies that the competition authority should consider a claim
by an existing retailer that trades with an encroaching manufacturer if the claim is based on
an increase in its unit price.
Matsushima and Mizuno (2018) extend the linear demand setting by incorporating thecost-reducing eﬀorts of an existing retailer. The main concern of Matsushima and Mizuno(2018), however, is how the threat of supplier encroachment influences the retailer’s eﬀort
level and economic welfare. Our study and Matsushima and Mizuno (2018) thus complement each other.

References[1] Arya, A.; Mittendorf, B. and Sappington, D. E. M., 2007, The bright side of supplierencroachment. Marketing Science 26(5), 651-659.
[2] Blair, R. D. and Lafontaine, F., 2005, The Economics of Franchising. Cambridge, UK:
Cambridge University Press.
[3] Dutta, S.; Heide, J. and Bergen, M., 1999, Vertical territory restrictions and public
policy: Theories and industry evidence. Journal of Marketing 63(4), 121-134.
17

[4] Hart, O. and Tirole, J., 1990, Vertical integration and market foreclosure. Brookings
Papers on Economic Activity: Microeconomics 1990, 205-276.
[5] Kalnins, A., 2004, An empirical analysis of territorial encroachment within franchised
and company-owned branded chains. Management Science 23(4), 1-20.
[6] Li, Z.; Gilbert, S. M. and Lai, G., 2015, Supplier encroachment as an enhancement or ahindrance to nonlinear pricing. Production and Operations Management 24(1), 89-109.
[7] Matsushima, N. and Mizuno, T., 2018, Supplier encroachment and retailer eﬀort. ISER
Discussion Paper No. 1027. Osaka University.
[8] McAfee, R. P. and Schwartz, M., 1994, Opportunism in multilateral vertical contracting: Nondiscrimination, exclusivity and uniformity. American Economic Review 84(1),210-230.
[9] Pan, C., 2016, Retailer’s product line choice with manufacturer’s multichannel marketing. ISER Discussion Paper No. 938. Osaka University.
Available at SSRN: http://ssrn.com/abstract=2808837.
[10] Pan, C., 2018, Supplier encroachment and consumer welfare: Upstream firm’s opportunism and multichannel distribution. ISER Discussion Paper No. 1020. Osaka University.
Available at SSRN: https://ssrn.com/abstract=3124026.
[11] Pan C. and Yoshida, S., 2018, Multichannel distribution under international oligopoly.
Mimeo.
[12] Reisinger, M. and Tarantino, E., 2015, Vertical integration, foreclosure, and productive
eﬃciency. RAND Journal of Economics 46(3), 461-479.

18

[13] Vives, X. 1999. Oligopoly Pricing. Cambridge, Massachusetts: MIT Press.

19