We examine a two-sector model characterized by monopoly provision in market 1 and perfect competition in market 2. We follow the set up in Martin (1999), but we consider the case where goods 1 and 2 can be either substitutes or complements. With this framework, we analyse the profit sacrifice required if the monopolist offers a bundle consisting of one unit of good 1 and k units of good 2 to foreclose the competitive sector. Our results show that foreclosing rivals via bundling is less costly when products are complements rather than substitutes.

Flavio Menezes

Tina Kao

English

Research Papers in Economics

 
 
 
THE AUSTRALIAN NATIONAL UNIVERSITY 
 
WORKING PAPERS IN ECONOMICS AND ECONOMETRICS 
 
 
Bundling and Foreclosure 
 
 
Tina Kao 
Australian National University 
 
Flavio Menezes 
University of Queensland 
 
 
September 29, 2006 
 
 
Working Papers in Economics and Econometrics No. 478 
Australian National University 
 
ISBN: 086831 478 1 
 
 
JEL Classification: L11, L12, L41. 
Keywords: Bundling, foreclosure. 
 
 
Abstract 
We examine a two-sector model characterized by monopoly provision in market 1 and perfect 
competition in market 2. We follow the set up in Martin (1999), but we consider the case where 
goods 1 and 2 can be either substitutes or complements. With this framework, we analyse the 
profit sacrifice required if the monopolist offers a bundle consisting of one unit of good 1 and k 
units of good 2 to foreclose the competitive sector. Our results show that foreclosing rivals via 
bundling is less costly when products are complements rather than substitutes. Bundling and Foreclosure
Tina Kao
Australian National University
Flavio Menezes
University of Queensland
September 29, 2006
Abstract
We examine a two-sector model characterized by monopoly provision in market 1
and perfect competition in market 2. We follow the set up in Martin (1999), but we
consider the case where goods 1 and 2 can be either substitutes or complements. With
this framework, we analyse the pro￿t sacri￿ce required if the monopolist o⁄ers a bundle
consisting of one unit of good 1 and k units of good 2 to foreclose the competitive sector.
Our results show that foreclosing rivals via bundling is less costly when products are
complements rather than substitutes.
JEL Classi￿cation: L11, L12, L41.
Keywords: Bundling, foreclosure.
1 Introduction
A ￿rm that has market power may undertake a number of actions designed to make it di¢ cult
for rivals to compete pro￿tably. These actions, which include for example the foreclosure of
a market to rivals, can be characterised under the rubric of exclusionary conduct.1
In this paper we examine the relationship between pro￿t sacri￿ce associated with foreclo-
sure via bundling and the degree of substitutability between the products. The conduct that
we examine is similar to what Nalebu⁄ (2005) referred to as ￿ exclusionary bundling￿ : A ￿rm
with market power in good 1 and facing actual (or potential) competition in good 2 prices a
bundle in a way that makes it impossible for equally-e¢ cient one-good rivals in market 2 to
compete. Unlike traditional predatory pricing, the exclusionary behavior need not be costly
1For a survey and literature review of exclusionary conduct, see Fallon and Menezes (2006).
1to the ￿rm. In this spirit, we consider how a monopolist can use bundling to minimise the
pro￿t sacri￿ce, if any, required to foreclose a competitive market.
Our paper is close to Martin (1999). In his two-goods model, there is a monopolist in one
sector and the other sector is characterised by duopolists competing by setting quantities.
Although the demand for the two goods is assumed to be independent, Martin shows that by
o⁄ering a bundle consisting of one unit of good 1 and 1 unit of good 2, the monopolist can
create substitution relationships between the two goods.
We utilise the same set up but instead consider the case where goods 1 and 2 can be
either substitutes or complements. We then analyse the incentives for the monopolist to o⁄er
a bundle consisting of one unit of good 1 (the monopoly good) and k units of good 2 (the
competitive good) to foreclose the competitive sector. We show that the choice of k is crucial
for minimising the pro￿t sacri￿ce required for foreclosure. When foreclosure is accomplished
by o⁄ering (as part of the bundle) a larger quantity of good 2, vis-￿-vis the quantity that is
o⁄ered absent the conduct, without a⁄ecting the supply of good 1 in the market, the conduct
does not require pro￿t sacri￿ce.
Our main result is that foreclosing rivals via bundling is less costly when products are
complements rather than substitutes. When the two goods are substitutes the monopolist
could foreclose the competitive sector by supplying a large quantity of good 1 ￿this would
not require bundling. With bundling, this strategy is even more e⁄ective. By including good
2 in the bundle, the bundle is a closer substitute to good 2 than good 1 alone. Increasing
the supply of the bundle, or decreasing the price of the bundle, puts more pressure on the
demand for good 2 compared with increasing the supply of good 1 only. However, producing
more of good 1 and good 2 results in a reduction in the price of good 1 since the two goods are
substitutes. In this sense, foreclosure by producing more good 2 is costly for the monopolist.
When two goods are complements, it is not possible to foreclose the competitive sector
without bundling. However, by including good 2 in the bundle, the monopolist can choose
k to create a bundled good which is a substitute to good 2. Foreclosure is thus feasible
by increasing the supply of this bundled good. Furthermore, increasing the supply of good
2 for foreclosure purposes helps to maintain the price for good 1 since the two goods are
complements. Therefore, the foreclosure strategy is less costly for the monopolist when the
two goods are complements.
A full analysis of foreclosure would necessitate an analysis of the prospective market struc-
ture to determine whether recoupment is possible when foreclosure requires pro￿t sacri￿ce.
There are two questions one can ask: the ￿rst is what pro￿t sacri￿ce would be required to
2foreclose the second market; the second is what would the motivations be for the monopolist
to foreclose the second market. In this paper, we focus only on the ￿rst question. The second
question will be the subject of future research.
2 The Model
We consider a two-sector model where the market for good 1 is characterised by a monopoly
provider and the market for good 2 is characterised by perfect competition. Firm 1 is the
monopolist in the market for good 1 but also supplies into competitive market for good 2.
We follow Martin (1999) in that the demand for goods 1 and 2 can be derived from a social
welfare function of the form
U = m + a(Q1 + Q2) ￿
1
2
￿
Q2
1 + 2￿Q1Q2 + Q2
2
￿
; (1)
where m represents all other goods in the economy.
The corresponding inverse demand curves for the two goods are
p1 = a ￿ (Q1 + ￿Q2) (2)
and
p2 = a ￿ (￿Q1 + Q2): (3)
The parameter ￿ lies strictly between ￿1 and +1. If ￿ = 0, the demand for the two goods
are independent. If ￿ > 0, the two goods are substitutes, and they are complements if ￿ < 0.
The marginal cost of production in markets 1 and 2 are equal to c1 and c2, respectively,
and there are no ￿xed costs. Under the assumed market structures, we have Q1 = q1
1 and
Q2 =
PN
n=1 qn
2, where all N ￿rms are price takers.
3 The Benchmark Equilibrium
We ￿rst compute equilibrium pro￿ts under the benchmark, de￿ned as the equilibrium in
the absence of exclusionary behaviour. In particular, Firm 1 can choose among two pricing
schemes: independent pricing and pure bundling (selling goods 1 and 2 as a bundle). When
the monopolist prices the two products independently, it acts as a price taker in market 2
and sets p2 = c2. The monopolist then maximises its pro￿t by choosing its supply in market
1. When the monopolist chooses to sell by pure bundling, it sells a bundle consisting of 1
unit of good 1 and k units of good 2. This bundle is represented by (1;k), with k ￿ 0.
3All remaining ￿rms in market 2 sell the bundle consisting of (0;1). The monopolist chooses
both its supply of the bundled good and k to maximise its pro￿ts with the restriction that
the actual price of good 2 ￿that is, the price of the bundle (0,1) ￿is set equal to its marginal
cost.
Proposition 1 Absent exclusionary behaviour, independent pricing and pure bundling gen-
erate the same equilibrium pro￿t level for the monopolist.
Given that the price of good 2 is e⁄ectively set at marginal cost, the quantity of good
2 supplied in the market remains the same under independent pricing and pure bundling.
Therefore, the monopoly rent remains the same under the two schemes. This is analogous to
the reasoning behind the Law of One Monopoly Rent.
We denote by bM the monopolist￿ s supply of the bundled good. Let b be the total supply
from ￿rms 2 to N in market 2. The quantity of the two goods are thus
Q1 = bM (4)
and
Q2 = kbM + b: (5)
With the bundled goods, the social welfare function can be expressed as
U = m + a((1 + k)bM + b) ￿
1
2
￿
b2
M + 2￿bM (kbM + b) + (kbM + b)
2
￿
: (6)
The inverse demand functions for the bundled goods are
pbM = a(1 + k) ￿
￿
2k￿ + k2 + 1
￿
bM ￿ (￿ + k)b (7)
and
pb = a ￿ (￿ + k)bM ￿ b: (8)
Under the price-taking and no predation assumptions, pb = c2: This then de￿nes the quantity
sold by competitors in market 2:
b = a ￿ (￿ + k)bM ￿ c2: (9)
Substituting this quantity into Equation 7 gives:
pbM = (1 ￿ ￿)a + (k + ￿)c2 ￿ (1 ￿ ￿)(1 + ￿)bM: (10)
4Setting marginal revenue for the bundle equal to the marginal cost of the bundle yields:
bM =
(a ￿ c1) ￿ ￿(a ￿ c2)
2
￿
1 ￿ ￿2￿ : (11)
The resulting pro￿t in the benchmark equilibrium is
￿ = (p1 ￿ c1)Q1 =
((a ￿ c1) ￿ ￿(a ￿ c2))
2
4
￿
1 ￿ ￿2￿ : (12)
4 Foreclosure
In this section, we determine what is the optimal pricing structure if Firm 1 is determined
to foreclose the market for good 2. We assume that the monopolist can only foreclose the
market by o⁄ering the bundle. In particular, we rule out the possibility that the monopolist
can o⁄er good 2 by itself below cost and drive out all other competitors. In addition to
possible antitrust implications, doing so may require higher pro￿t sacri￿ce than under pure
bundling.
The inverse demand functions when bM consists of the bundle (1;k) and b consists of the
￿ bundle ￿(0;1) are given in Equations 7 and 8. Price-taking behaviour in market 2 implies
that ￿rms 2 to N set pb = c2. We now compute the quantity of bM required to foreclose the
market for good 2 by solving equations 7 and 8 for the bM that would results in b = 0. This
gives:
bM =
a ￿ c2
(￿ + k)
: (13)
This quantity implies a bundle price equal to:
pbM = a(1 + k) ￿
￿
1 + 2￿k + k2￿
bM
=
a(k ￿ 1)(1 ￿ ￿) +
￿
2k￿ + k2 + 1
￿
c2
k + ￿
; (14)
and the resulting pro￿t level is
￿ = (pbM ￿ c1 ￿ kc2)bM
=
(a(k ￿ 1)(1 ￿ ￿) ￿ (k + ￿)c1 + (1 + k￿)c2)(a ￿ c2)
(k + ￿)
2 : (15)
The monopolist then chooses k to maximise pro￿t:
max
k
￿ =
(a(k ￿ 1)(1 ￿ ￿) ￿ (k + ￿)c1 + (1 + k￿)c2)(a ￿ c2)
(k + ￿)
2 : (16)
5The ￿rst order condition yields
￿
2a ￿ ak ￿ a￿ ￿ 2c2 + ak￿ + kc1 + ￿c1 ￿ k￿c2 ￿ a￿2 + ￿2c2
￿
(a ￿ c2)
(k + ￿)
3 = 0:
For k 6= ￿￿, this holds for
k =
￿￿(a ￿ c1) +
￿
2 ￿ ￿2￿
(a ￿ c2)
(a ￿ c1) ￿ ￿(a ￿ c2)
: (17)
When k = ￿￿, the function attains the minimum as in this case the demand for bM and
b are independent. That is, Firm 1 would not be able to foreclose the competitive sector by
o⁄ering bM. The second order condition con￿rms that the solution in Equation 17 yields the
maximum.
The proposition below establishes the optimal k for both the substitutes and complements
cases.
Proposition 2 The optimal k is that for ￿ > 0, k￿ =
￿￿(a￿c1)+(2￿￿2)(a￿c2)
(a￿c1)￿￿(a￿c2) for
￿a￿(2￿￿2)(a￿c2)
￿ ￿
c1 ￿ a ￿ ￿(a ￿ c2). Otherwise, k￿ = 0. For ￿ < 0, k￿ =
￿￿(a￿c1)+(2￿￿2)(a￿c2)
(a￿c1)￿￿(a￿c2) . The resulting
quantity and pro￿ts are
bMj
k￿=
￿￿(a￿c1)+(2￿￿2)(a￿c2)
(a￿c1)￿￿(a￿c2)
=
a ￿ c2
(￿ + k)
=
(a ￿ c1) ￿ ￿(a ￿ c2)
2
￿
1 ￿ ￿2￿ ; (18)
￿j
k￿=
￿￿(a￿c1)+(2￿￿2)(a￿c2)
(a￿c1)￿￿(a￿c2)
=
((a ￿ c1) ￿ ￿(a ￿ c2))
2
4
￿
1 ￿ ￿2￿ ; (19)
bMjk￿=0 =
a ￿ c2
￿
; (20)
and
￿jk￿=0 =
(￿(a ￿ c1) ￿ (a ￿ c2))(a ￿ c2)
￿2 : (21)
Proof. See the appendix.
When the two goods are substitutes, for small c1 ( c1 ￿
￿a￿(2￿￿2)(a￿c2)
￿ ) and large c1 (
c1 ￿ a ￿ ￿(a ￿ c2)), to foreclose the competitive market, the monopolist only o⁄ers bundles
consisting of (1;0). For intermediate c1, the monopolist chooses k￿ > 0. When the two goods
are complements, the monopolist always o⁄ers the bundle (1;k), with k > 0.
When the monopolist o⁄ers the bundle with k￿ =
￿￿(a￿c1)+(2￿￿2)(a￿c2)
(a￿c1)￿￿(a￿c2) , the quantity of
bM o⁄ered is the same as Q1 in the benchmark case. Since bM consists of (1;k), the supply
of Q1 is the same under foreclosure and in the benchmark. Thus foreclosure does not distort
the monopolist￿ s quantity choice in market 1, and there is no pro￿t sacri￿ce required.
6The lower bound of c1 for k￿ ￿ 0 would be negative if c2 is su¢ ciently small. Or if
c2 ￿
￿
2 ￿ ￿2 ￿ ￿
￿
a
￿
2 ￿ ￿2￿ : (22)
When c2 is large and c1 is small, it is relatively costly to include good 2 in the bundle, and
the monopolist o⁄ers the bundle (1;0) to foreclose market 2. Therefore, foreclosure requires
pro￿t sacri￿ce in this parameter range.
So far in the paper, pro￿t sacri￿ce refers to pro￿t below the benchmark equilibrium pro￿t
level, not necessarily price below the marginal cost. Note that ￿jk￿=0 < 0 if
c2 ￿ a(1 ￿ ￿)
￿
￿ c1: (23)
Since
c2￿a(1￿￿)
￿ < a ￿ ￿(a ￿ c2) for ￿ > 0, when c1 > a ￿ ￿(a ￿ c2), the monopolist has to
price below the marginal cost to foreclose the competitive sector, which would result in the
below-cost pricing behaviour traditionally associated with exclusionary conduct. In fact, for
c1 > a ￿ ￿(a ￿ c2) and c2 < (1 ￿ ￿)a, it is not possible to foreclose the competitive market
unless the monopolist is willing to pay the consumers to take away the bundle. It is also
important to note that unlike the traditional predatory story, in our setting, pro￿t sacri￿ce
occurs in the market for good 1,while foreclosure takes place in the market for good 2.
5 Conclusion
In this paper, we analyse the pro￿tability of an exclusionary bundling strategy. The key result
is that it is less costly for the monopolist to foreclose the market when the two goods are
complements rather than substitutes. A major policy implication is that bundling may raise
more competitive concern when two goods are complements. This is in contrast to traditional
emphasis of competition policy on mergers among ￿rms who o⁄er close substitutes than when
they are complements. Furthermore, as in Nalebu⁄(2005)￿ s analysis of exclusionary bundling,
foreclosure via bundling does not necessarily require pro￿t sacri￿ce. Therefore, absence of
pro￿t sacri￿ce does not necessarily imply absence of exclusionary intention.
References
[1] Fallon, J. and F. M. Menezes (2006), ￿ Exclusionary Conduct: Theory, Tests and some
relevant Australian Cases ￿ , Competition and Consumer Law Journal, vol 13, pp. 197 -
240.
7[2] Nalebu⁄, B. (2005), ￿ Exclusionary Bundling.￿Antitrust Bulletin, vol. 50, no. 3, pp. 321 -
70.
[3] Stephen, M. (1999), ￿ Strategic and Welfare Implications of Bundling. ￿Economic Letters,
vol. 62, no. 3, pp. 371-76.
6 Appendix
Proof. of Proposition 2: The solution is interior (that is, k is non-negative) if
￿￿(a ￿ c1) +
￿
2 ￿ ￿2￿
(a ￿ c2)
(a ￿ c1) ￿ ￿(a ￿ c2)
￿ 0:
Note that (a ￿ c1) ￿ ￿(a ￿ c2) ￿ 0 if c1 ￿ a ￿ ￿(a ￿ c2):
For c1 ￿ a ￿ ￿(a ￿ c2), k ￿ 0 if
￿c1 ￿ ￿a ￿
￿
2 ￿ ￿2￿
(a ￿ c2):
Case (1) For ￿ > 0, k ￿ 0 if
c1 ￿
￿a ￿
￿
2 ￿ ￿2￿
(a ￿ c2)
￿
:
Case (2) For ￿ ￿ 0, in order to create a bundle that is a substitute for good 2, we require
k + ￿ ￿ 0 or
￿￿(a ￿ c1) +
￿
2 ￿ ￿2￿
(a ￿ c2)
(a ￿ c1) ￿ ￿(a ￿ c2)
￿ ￿￿:
This holds if
a ￿ c1
a ￿ c2
￿ ￿:
This is true for ￿ ￿ 0.
8

Bundling and Foreclosure

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