Discussion Paper No.232
PRICE SQUEEZE AND CASE OF DEUTSCHE TELEKOM:ECONOMIC PERSPECTIVE
SHUMEI HIRAI
Department of Economics, Seinan Gakuin University
YASUO KAWASHIMA
Faculty of Economics, Chuo University
NOBUFUMI NISHIMURA
Faculty of Law, Chuo University
September

2014

INSTITUTE OF ECONOMIC RESEARCH
Chuo University
Tokyo, JapanPRICE SQUEEZE AND CASE OF DEUTSCHE TELEKOM:ECONOMIC PERSPECTIVE
SHUMEI HIRAI
Department of Economics, Seinan Gakuin University
6-2-92 Nishijin, Sawara-ku, Fukuoka 814-8511, Japanhirai@seinan-gu.ac.jp
YASUO KAWASHIMA
Faculty of Economics, Chuo University742-1 Higashinakano, Hachioji-shi, Tokyo 192-0393, Japanyasuokaw@tamacc.chuo-u.ac.jp
andNOBUFUMI NISHIMURA
Faculty of Law, Chuo University742-1 Higashinakano, Hachioji-shi, Tokyo 192-0393, Japan
1974non@gmail.com

Abstract
We explore the price squeeze test proposed by the European Commission in a partial and a no
relation environments in network industries, which assumes that a new entrant is an equally
efficient competitor to the incumbent firm. Under this assumption, the test in a partial regulation
environment can show precisely what strategies the incumbent employs in a market, and canalso show that differences in costs between the incumbent and the entrant generate either a false
negative or a false positive when the one is superior in costs to the other. Moreover, theincumbent in a no regulation environment has no incentives to employ a price squeeze and thetest generates a false positive in Subgame Perfect Equilibrium. Thus, the test is not a reliablemeasure to judge strategies of the incumbent if a firm can not enjoy costs advantage. As theCommission decision is based on the test, there is a legal flaw in the procedures for judging true
reasons why the entrant exists from a market. It then follows these that the Commission
decision fining Deutsche Telekom should be declined.

JEL classification: K23, L13, L43, L51
Keywords: price squeeze test; equally efficient competitor; difference in costs; false positive;
false negative; legal flaw

1

1

Introduction

Deregulation of a network industry, for example, Telecommunications and a water industry, hascaused new firms to enter into a market. Some firms may succeed in supplying outputs
profitably, while others may exit from a market. Thus, price squeeze cases have arisen. When
new entrants are forced out of a market, deregulation does not enhance market efficiency. There
are several ways to explore whether the entrant is driven out of a market by market competition
or exclusionary strategies by the incumbent. 1 Typical examples are given in the U.S. andEurope. In the U.S., a new act is introduced to deal with these issues. In fact, the 1996
Telecommunications Act requires the regulation authority to examine only whether access rates
for essential inputs are cost based.2
To judge whether the incumbent firm employs such a strategy, the European Commission(henceforth, EC) proposed two definitions of Price Squeeze tests (henceforth, PS test). 3
Bouckaert and Verboven (2004) introduce regulatory environments to analyze price squeeze
tests. We follow their definition of regulatory environments. Bruno, Rey and Saavedra (2013)
give an excellent survey on the economics of a price squeeze.
When we consider the German telecommunication industry, we have to pay attention toparagraph 5 in the European Commission decision of 21 May 2003, which states:“ Charges for access to local networks are partially regulated by the regulatory authority, but
this decision is concerned with unfair prices which have been set by DT itself in the exercise of
its own commercial freedom, and for which it is directly responsible."
It follows that it can be modeled as a partial regulatory environment (or game) or a noregulation environment (or game). The characteristics of the PS test can be examined in theseenvironments: The partial regulatory environment is modeled as a one shot Cournot game,while the other is modeled as a two stage game. Our model is the same as one of important
types of market structure in vertically related markets which Rey and Tirole (2007) explores.
Basic framework and a notation are close to Armstrong (2002) and Bouckaert and Verboven(2004). The PS test is based upon the assumption that a new entrant is an equally efficientcompetitor to the incumbent. 4 This assumption will be called the PS assumption. If this1

Weisman (2003) points out two types of exclusionary behavior that the incumbent canadopt: a price squeeze and sabotage.
2
Bork (1978) and Carlton (2008) insist that the incumbent firm has no incentives to
employ a price squeeze.
3
See the 1998 Notice of the European Commission (1998).
4This is called equally efficient competitor test by Bruno, Rey and Saavedra (2013).
2

assumption holds true, the test can show what strategy the incumbent firm adopts. On the other
hand, we introduce a new test to examine the PS test in these games where the PS assumption is
not valid: Costs of the incumbent and the entrant are not the same. It will be shown in the partial
regulation game that the PS test generates a false negative or a false positive depending upon therelative values of costs of two competitors. 5 It then follows from these and costs of the realfirms that the PS test is not necessarily a reliable measure to judge whether the incumbent has
employed such an exclusionary strategy as a price squeeze.
If we turn our attention to the no regulation game, it will be shown that the incumbent has no
incentives to drive the competitor out of a market, and that the exit of the entrant is solely due toinefficiency of the entrant, not by a price squeeze by the incumbent. These observations of two
regulatory environments reveal that the PS test is not necessarily a reliable measures to judge
behavior of the incumbent. The EC decision, which is based upon the PS test, is not wellfounded in that its decision should be declined. In particular, our analysis of the PS test in the no
regulation game strongly shows that the EC oversteps the mark in the decision of the case of
Deutsche Telekom.
Such concerns about the reliability of the PS test proposed by the EC have been noticed by
Weisman (2003) and Bouckaert and Verboven (2004). Salop (2010) proposes a new test to
judge whether the incumbent practices such an exclusionary strategy. However, the European
Commission has not noticed the possibility that the PS test fails to show precisely what strategy
the incumbent adopts. 6 It follows from these that there is a legal flaw in the procedures for
judging the case of DT. Moreover, it follows from Mathematical Logic that inferences driven
from a false assumption are logically true, but is meaningless. Our analysis of the PS test in two
regulatory environments reveals that the EC decision of 21 May 2003 is not well founded in thatit should be declined.
Our paper is organized as follows: Section 2 sets forth our model and the PS test that is
proposed by the European Commission together with our new test. In Section 3, we set forth apartial regulation game and explore the PS test proposed by the European Commission. It will
be show that a false negative or false positive can arise depending upon the relative values offirms’ average costs. In Section 4, we examine the case of DT in the partial regulatory game. It
will be shown that there is a legal flaw in the EC decision on the case of DT. Section 5
examines the PS test in the no regulatory game. It will be shown that the incumbent has no
incentives to drive a rival out of a market, and that the test generates a false negative. The EC
5Petulowa and Saavedra (2013) pointed out that the test generates a false negative or afalse positive.
6
See, European Commission (2003).
3

decision is not well founded in the no regulatory games. Thus, the decision should be declined.
Section 5 summarizes our observations.

2

The Model and Price Squeeze Tests

Consider a network industry where there are the incumbent firm (firm 1) and a new entrant(firm 2). The incumbent produces an essential input and sells it to the entrant. Thus, foreclosure
is assumed away. 7 Both firms produce outputs in one-to-one proportion. The average costs ofan essential input are given by 𝑐0 , which is assumed equal to zero for simplicity of ouranalysis. 8 The average costs of outputs of firms 1 and 2 are fixed constants 𝑐1 , 𝑐2 + 𝛼,

respectively, where 𝑐𝑖 stands for average costs of firm 𝑖 net of an access rate, and 𝛼 for anaccess rate for inputs.

A demand function is given by
𝑃 = 𝐴 − (𝑥1 + 𝑥2 ) = 𝐴 − 𝑋,(1)where 𝑃 stands for price for outputs, 𝑥𝑖 for outputs of firm i, and 𝐴 for a constant parameter.

To make our analysis tractable, assume that firms are viable in a partial regulation game inwhich access rates are determined by the regulatory authority. This assumption is given by
𝐴 > 2 × 𝑚𝑎𝑥{𝑐1 , 𝑐2 }.

(2)These assumptions guarantee that outputs supplied by firms are positive.
A price squeeze (henceforth, PS) tests proposed by the European Commission, which Bruno,
Rey and Saavedra (2013) calls it the Equally Efficient Competitors (EEC) test, has been used to
examine whether the incumbent is responsible for price squeeze cases in the partial regulation
game. In what follows, the features of the PS tests will be examined concerning whether a new
entrant can reap positive profits. 9 The PS test which we will take up amounts to examining
whether the following inequality is satisfied:𝑃 − 𝛼 ≥ 𝑐1 .

(3)

However, if the assumption that a new entrant is not as efficient as the incumbent firm, the PS
test will not work well, and some serious problems may occur. To examine the features of the
PS test, we introduce the new test using costs of the entrant. Our new test directly considers
7

Yang and Kawashima (2011) shows that the incumbent firm does not have incentives
to employ a price squeeze in no regulation games.
8
We follow Armstrong (2002) in the sense that upstream costs for producing inputs andadditional upstream costs to the entrants are both equal to 0.
9
For an excellent explanation of price squeeze tests, see Bouckaert and Verboven(2004).
4

whether the entrant can make positive profits. This is called the profitability (henceforth, PR)
test, which is
𝑃 − 𝛼 − 𝑐2 > 0,(4)where 𝛼 + 𝑐2 is average costs of outputs by the entrant. This test examines if per-unit profits ofthe entrant are positive. If they are positive, the entrant can supply outputs profitably and can be
viable. Otherwise, the entrant has to exit form a market. Then, this is a direct test of viability ofthe entrant.

3

Partial Regulation Game

Now, consider a partial regulation game where price for inputs is regulated by the authority. It isa fixed constant and given by 𝛼̄ . Although Bouckaert and Verboven (2004) have notconsidered the price squeeze tests in a partial regulation game, we will consider the partial
regulation game by a one shot Cournot game.
The timing of our game is as follows:
1. The authority chooses an access rate 𝛼̄ for inputs from the closed interval 𝑆𝑠𝑞 = [0, 2𝐴 −𝑐1 − 𝑐2 ).

2. The incumbent and a new entrant compete downstream in supplying outputs.
3. The entrant decides whether it can stay at or exit from a market.
4. The authority examines whether the set of access rates and downstream prices can pass the
PS test.
Note that it does not matter whether there is the difference in productivities between two firms.
A less efficient entrant can enter into a market. It will be shown in Section 5 that less efficiententrant can not be viable in no regulation games. In this game, if outputs and/or profits of a firm
is not larger than zero, that firm cannot reap positive profits and then it has to exit from a market.
Note also that total outputs are positive for 𝛼̄ ∈ 𝑆𝑠𝑞 . It will be shown in what follows.
In view of (1), profits of two firms are given respectively by

𝜋1 = (𝑃 − 𝑐0 − 𝑐1 )𝑥1 + (𝛼̄ − 𝑐0 )𝑥2 = ((𝑃 − 𝑐1 )𝑥1 + 𝛼̄ 𝑥2 = (𝐴 − 𝑋 − 𝑐1 )𝑥1 + 𝛼̄ 𝑥2 ,

𝜋2 = (𝑃 − 𝛼̄ − 𝑐2 )𝑥2 = (𝐴 − 𝑋 − 𝛼̄ − 𝑐2 )𝑥2 ,where upstream costs 𝑐0 of producing inputs is equal to 0.
Then, we can now establish:

Lemma 1. If the authority sets access price 𝛼̄ < 𝛼𝑠𝑞 =𝐴+𝑐1 −2𝑐2, outputs of the incumbent and2the entrant, and price of outputs under a partial regulation game are given by5

𝐴 − 2𝑐1 + 𝑐2 + 𝛼̄,
3
𝐴 + 𝑐1 − 2𝑐2 − 2𝛼̄𝑥̄ 2 =,
3
2𝐴 − 𝑐1 − 𝑐2 − 𝛼̄,𝑋̄ = 𝑥̄ 1 + 𝑥̄ 2 =3
𝐴 + 𝑐1 + 𝑐2 + 𝛼̄𝑃̄ = 𝐴 − 𝑋̄ =.
3
𝑥̄ 1 =

However, the entrant can not enter into a market for 𝛼𝑠𝑞 ≤ 𝛼̄ < (2𝐴 − 𝑐1 − 𝑐2 ).

Proof. Differentiating profits 𝜋𝑖 with respect to 𝑥𝑖 yields the best response functions of two

firms. The first order condition of the incumbent is given by𝜕𝜋1= −𝑥1 + (𝐴 − 𝑋 − 𝑐1 ) = 0.
𝜕𝑥1

Solving 𝑥1 yields the best response function of the incumbent (firm 1), which can be expressedas𝑥1 = 𝑅1 (𝑋) = 𝐴 − 𝑋 − 𝑐1 .

Similarly, differentiating profits of the entrant with respect to 𝑥2 yields
𝜕𝜋2= −𝑥2 + (𝐴 − 𝑋 − 𝛼̄ − 𝑐2 ) = 0,
𝜕𝑥2

which enables us to have the best response function of firm 2. It is given by

Noting these functions, we have𝑥2 = 𝑅2 (𝑋) = 𝐴 − 𝑋 − 𝛼̄ − 𝑐2 .

which gives us total outputs 𝑋̄ as𝑋̄ =𝑅1 (𝑋) + 𝑅2 (𝑋) − 𝑋 = 0,

2𝐴 − 𝑐1 − 𝛼̄ − 𝑐2
> 0 𝑓𝑜𝑟 𝛼̄ ∈ 𝑆𝑠𝑞 .
3

Solving these equations for 𝑥𝑖 yields competitive outputs of the incumbent and the entrant. For

example, output 𝑥̄ 𝑖 of firm 𝑖 is given respectively by

𝐴 − 2𝑐1 + 𝑐2 + 𝛼̄,
3
𝐴 + 𝑐1 − 2𝑐2 − 2𝛼̄𝑥̄ 2 = 𝑅2 (𝑋̄) = 𝐴 − 𝑋̄ − 𝑐2 =.
3𝑥̄ 1 = 𝑅1 (𝑋̄) = 𝐴 − 𝑋̄ − 𝑐1 =If access rate 𝛼̄ is less than 𝛼𝑠𝑞 , outputs 𝑥̄ 2 is positive. Outputs of two firms are given by 𝑥̄ 𝑖above. Thus, substituting 𝑋̄𝑖 into a demand function (1) yields downstream price of outputs. It
is given by𝑃̄ = 𝐴 − 𝑋̄ =𝐴 + 𝑐1 + 𝑐2 + 𝛼̄
.
3

6

(5)

Positivity of outputs depends crucially upon access rates set by the authority.
However, if access rate 𝛼̄ is not less than 𝛼𝑠𝑞 , the entrant can not make positive profits andthen it can not stay at a market. Outputs of the incumbent can be positive only if access rate isless than (2𝐴 − 𝑐1 − 𝑐2 ).

�It then follows from Lemma 1 that downstream price is determined by an access rate and that it

increases with the access rates.
When we apply the PS test (3) to the partial regulation game, it is easy to show that𝐴 − 2𝑐1 + 𝑐2 − 2𝛼̄
≥03
The result of the PR test (4) is given by𝑃̄ − 𝛼̄ − 𝑐1 =𝑃̄ − 𝛼̄ − 𝑐2 =𝐴 + 𝑐1 − 2𝑐2 − 2𝛼̄
>0
3

iff

iff

𝛼̄ ≤ 𝛼� =𝛼̄ < 𝛼𝑠𝑞 =Note that 𝛼� and 𝛼𝑠𝑞 are both less than 𝐴 in view of (2).

𝐴 − 2𝑐1 + 𝑐2.
2

𝐴 + 𝑐1 − 2𝑐2
.
2

(6)

The entrant can not make positive profits and exits from a market if the authority sets accessrates equal to 𝛼𝑠𝑞 .

It would be easy to show the arguments above by the use of the PS and the PR lines, which are

given respectively by
𝑃 − 𝛼 − 𝑐1 = 0,

𝑃 − 𝛼 − 𝑐2 = 0.

Both of them are depicted in Figures 1 and 2 together with the Downstream Price line (or DP),which is given by𝑃=

𝐴 + 𝑐1 + 𝑐2 + 𝛼.
3*****Fig.1**********Fig.2*****In what follows, let first take up a game where the entrant is less efficient: i.e., 𝑐1 < 𝑐2 . Then,the PS line (or PS) is below the PR line (or PR). Thus, Fig. 1 shows that 𝛼𝑠𝑞 < 𝛼�. However, if

𝑐1 ≥ 𝑐2 , the PS is above the PR. Thus, it follows from Fig. 2 that the intersection point of the PS

with the DP is left to that of the PR with the DP. Then, Fig. 2 shows that 𝛼𝑠𝑞 ≥ 𝛼�.
Comparing Fig. 1 with Fig. 2, it is straightforward to show that𝛼𝑠𝑞 ⋛ 𝛼�iff𝑐1 ⋛ 𝑐2 .

Note that if outputs and/or profits of a firm is not larger than zero, then the firm has to exitfrom a market. Then, we can now summarize our results as:

7

Lemma 2. When we apply the Price Squeeze test proposed by the European Commission to
the partial regulation game, the results are shown in the following cases:
Case 1: The incumbent can enjoy efficiency advantage: i.e., 𝑐1 < 𝑐2 .

If access price 𝛼̄ set by the authority is in the set [0, 𝛼𝑠𝑞 ), both tests can be passed. The

entrant can be viable. If it is in the closed [𝛼𝑠𝑞 , 𝛼�], it leads to a false negative: The entrant can
not supply outputs profitably even if the PS test is passed. Finally, if it is larger than 𝛼�, bothtests are failed. The entrant can not be viable.

Case 2: The entrant can not enjoy efficiency advantage: i.e., 𝑐1 ≥ 𝑐2 .

If access price 𝛼̄ set by the authority is in the closed set [0, 𝛼�], both tests can be passed. The
entrant can stay at a market. If it is in the open set (𝛼�, 𝛼𝑠𝑞 ), it leads to a false positive:

Although the PS test is failed, the entrant can be viable. Finally, if it is equal to or more than𝛼𝑠𝑞 , both tests are failed and the entrant can not stay at a market.
Proof. Case 1: This game is shown in Fig. 1, where the PR is above the PS . First, if 𝛼̄ ∈[0, 𝛼𝑠𝑞 ), the PS and the PR tests can be passed. Second, if 𝛼̄ ∈ [𝛼𝑠𝑞 , 𝛼�], it follows from thedefinitions of 𝛼𝑠𝑞 and 𝛼� that the PR test is not passed, but that the PS test can be passed.

Thus, the entrant can not be viable in a market even if the PS test indicates that the incumbent
does not practice a price squeeze. Thus, a falsenegative occurs. The typical example of a false
negative is shown in point B in Fig. 1. For 𝛼� ≥ 𝛼𝑠𝑞 , both tests are violated.

Case 2: This is a game which is shown in Fig. 2, where the PS is above the PR. First, for𝛼̄ ∈ [0, 𝛼�], both tests can be passed. If 𝛼̄ is in ( 𝛼�, 𝛼𝑠𝑞 ), it follows from the definitions of 𝛼𝑠𝑞

and 𝛼� that the PR test is passed, but the other can not be passed. Although the entrant can reap
positive profits, the PS test indicates that access price set by the authority can not pass the PS
test. Thus, we can say that the access rate leads to a false negative. One of examples of a false
positive is shown in point C in Fig. 2. It is easy to show that access price 𝛼̄ , which is larger than𝛼𝑠𝑞 , violates both tests. �

Note that it does not matter whether the entrant is more efficient than the incumbent in a partial
regulation game. This is because an access price is set by the authority and then the entrant isless squeezed its profits in an upstream market than in no regulation game. Note that lessefficient entrants can not be viable in no regulation game. 10
10For example, see Bork (1978) and Carlton (2008) in which a downstream market is8We can summarize our results of the exit of a new entrant as:

Proposition 1.

Depending upon the relative values of average costs of firms, we willencounter two distinct types of games, where new entrants are excluded from a market:
1. If a new entrant is less efficient than the incumbent firm, there are two basic games whichcause the entrant to exit from a market:(a). The set(𝛼̄ , 𝑃̄) is below the PS test line: The regulatory authority sets too high access rates
for the entrant to be viable.

(b). The set (𝛼̄ , 𝑃̄) is above the PS test line, but below the PR test line: The inefficiency of theentrant causes the entrant not to make positive profits if the access rate is not so high.

2. If a new entrant is not less efficient than the incumbent firm, then the entrant exits from amarket when the set (𝛼̄ , 𝑃̄) is below the PR test line.
Proof. The first game is shown in Fig. 1, where the entrant is less efficient than the incumbent.
It is easy that the entrant can not reap positive profits only if the access rate is larger that 𝛼𝑠𝑞 .

Moreover, it follows from Fig. 1 that the entrant can not reap positive profits if either 𝛼̄ > 𝛼� or
𝛼𝑠𝑞 ≤ 𝛼̄ ≤ 𝛼.

If the entrant is not less efficient, this game is shown in Fig. 2. It can not make positive profits

only if access rate is below the PR line. �

In short, we find that there are two basic factors which cause the entrant not to stay at a market:
One is a higher access rate set by regulatory authority and the other is inefficiency of the entrant.
Note that new entrants cannot stay at a market even if the PS test is passed. The exit from amarket is due to its inefficiency in that market competition causes an inefficient firm to be
excluded from a market. Thus, the PS test, which assumes that the entrant is equally efficientcompetitor to the incumbent, is not always a reliable measure to judge whether the authority
approves the incumbent to employ a price squeeze.

4

Price Squeeze Test and Case of Deutsche Telekom

So far, it has not been paid attention to the assumption of the PS test: A new entrant is anequally efficient competitor to the incumbent firm: 𝑖. 𝑒. , 𝑐1 = 𝑐2 . This is called the PS

competitive, and Yang and Kawashima(2011) in which a downstream market is aduopoly. Moreover, this will be shown in Section 5.
9assumption. To explore the characteristics of the PS test, our new test, which is called the PR
test, was introduced and expressed as (4). If the PS assumption holds true, the PS test coincides
with the PR test. However, one point should be noted. For 𝑐1 = 𝑐2 , the intersection point of thePS with the DP coincides with that of the PR and the DP. If the intersection is given by a set(𝛼̄ , 𝑃̄), it turns out that𝑃̄ − 𝛼̄ − 𝑐1 = 0,𝑃̄ − 𝛼̄ − 𝑐2 = 0.

It follows from (3) and (4) that a false negative occurs when costs of both firms are equal. In
fact, the PS test can be passed, but the entrant can not make positive profits. However, the set ofan access rate which satisfies equations above does not play an important role in what follows.
Thus, we will ignore it in what follows. 11 Noting these, our arguments are summarized in what
follows:

Lemma 3. If average costs of a new entrant are equal to those of the incumbent firm, then we
have:a). If a set of upstream ( or access rates) and downstream prices can pass the PS test, theentrant can profitably supply outputs.
b). If the set can not pass the test, the entrant can not be viable.

This is what the European Commission would have supposed. Under the PS assumption, if the
PS test is passed, the entrant can be viable. If it is not, it turns out that the incumbent has
employed a price squeeze and then the entrant can not stay at a market. Thus, the PS test is a
precise signal of whether the incumbent has practiced such an exclusionary strategy. If theentrant exit from a market, it turns out that the incumbent has adopted a price squeeze. Under
the PS assumption, the decision of the European Commission on the case of DT holds true.
The German markets in telephone services has been liberalized since 1996, and the Deutsche
Telecom has been subject to regulation at both the wholesale and the retail levels. Although the
DT has been subject to a price cap for baskets of services, it was given discretion to the pricing
strategy of individual component services within the basket. Thus, we consider the German
telecommunications market from the view point of the partial regulation game where the PS
assumption holds true. Although pricing strategy of DT was approved by the German regulatory
authority, the entrant was not able to make positive profits and then exited from the market. It
11

We can be more precise than this: Access rate at which the PS intersects the DP
defines a zero-measure set in the 𝑆𝑠𝑞 . Then, we can ignore such an access rate.
10

then follows from these that a pair of access rates set by the authority and decreases indownstream price by DT were judged that DT practiced a price squeeze and then it was finedfor an abusive price squeeze.
When costs of firms are taken into account, we will encounter quite different scenarios. If theentrant is less efficient than the incumbent, it follows from Proposition 1 that there is apossibility that the entrant are excluded by market competition. Thus, an exclusionary strategy
such as a price squeeze is not a sole reason why the entrant can not stay at a market. We should
not ignore a possibility that an inefficient entrant is excluded from a market by market
competition.
As Rey and Tirole (2007) pointed out, it is well known that costs of firms are difficult toestimate. The EC and the regulatory authority can more easily get access to costs information offirms than private firms. They are publicly financed for their social duties. Moreover, theCommission hires many experts and staffs such as lawyers, accountants and economists, who
can analyze data. It is evident that the EC is more qualified to estimate precisely costs of firms
than the incumbent firm. Moreover, the EC holds the position to judge and fine firms which
employ such an exclusionary strategy.
Ignoring costs of firms causes a serious problem to the Commission, which is summarized in
the following proposition:
We can now establish:

Proposition 2. There is a legal flaw in the procedures of the European Commission forjudgments on case of Deutsche Telekom unless the Commission can give evidence that new
entrants are as efficient as the incumbent firm.

Proof. It follows from Lemma 3 that if the PS assumption is valid a new entrant exits from amarket only when a price squeeze is practiced. However, if the PS assumption does not holdtrue, Lemma 3 does not hold and it follows from Proposition 1 that a false negative or a false
positive can arise. This means that the PS test is not a reliable measure to judge whether a pricesqueeze has been adopted.
To justify to fine DT for an abusive price squeeze, the EC has to examine whether the PS
assumption holds true in the case of DT. However, the Commission decision does not refer tocosts of the entrant. It is indispensable for the EC to show clear evidence that the test can show
precisely strategies of the incumbent. As it has not made such efforts until now, there is a legal
flaw in the procedures for its decision making and the decision by the Commission on the case11

of DT is not well founded. �As the EC keeps closed the data of costs of the incumbent and the entrant to the public in its
decision, there will be serious concerns that the EC can manipulate figures and the definitions ofcosts to justify its decision. In these situations, no one can review the details of its decision.
Instead of estimating costs of firms, the PS assumption is made. As shown in Proposition 1,
difference in productivities of firms plays a key role in our arguments of the case of DT: The PS
test proposed by the EC is not always a reliable means to judge whether a price squeeze has
been practiced. Depending upon the relative values of costs of two competitors, cause and effectdiffer.
The EC may have strong incentives not to disclose the data concerning the case of DT. If data
are open to the public, there will be a lot of criticisms on the EC decision. For example, it isdifficult to define the definition and figures of costs which many people agree with. Thus, thedisclosure of the data opens Pandora‘s box and incurs huge amounts of money and time to EC
in order to justify the decision. Depending upon the definition of costs, it may or may notconclude from Proposition 1 and Lemma 3 that DT does not employ a price squeeze. It follows
from these arguments that the strategy of not opening data to the public enabled the EC to saveefforts and costs, and enables it to succeed in persuading the European Court of Justice toapprove its decision. Thus, it was the dominant strategy for EC.
Moreover, real firms differ in management, production facilities and so on. This means that it
is almost impossible for costs of the entrant to equal those of the incumbent. The assumptionthat the entrant is as efficient as the incumbent does not generally hold true. Even if costs can be
estimated precisely, the assumption is not valid for real firms. 12
Noting these arguments, we can conclude:

Proposition 3. The European Commission decision fining Deutshe Telekom should be declined
unless the Commission has made sure that the entrant is as efficient as the incumbent.

Proof. As pointed out above, the PS assumption that the entrant is as efficient as the incumbent
does not generally hold true. In fact, the Commission has paid no attention to this assumption.
Then, the decision of the EC on the case of DT is derived from false assumptions.

We can be more precise than this. Let 𝐶 be a set of possible costs of firms, which isthe closed interval. It follows from Measure theory in Mathematics that for 𝑐𝑖 ∈ 𝐶, a set(𝑐1 , 𝑐2 ) such that 𝑐1 = 𝑐2 defines a zero-measure set in 𝐶 × 𝐶. Thus, we can ignore
the possibility that the entrant is an equally efficient competitor.
1212

It follows from Mathematical Logic that the conclusions from false assumptions are logicallytrue, but are meaningless. Thus, it follows from Proposition 2 and arguments above that theCommission decision is meaningless and then it is unfounded. Thus, the European Commission
decision should be declined. �

5 Price Squeeze and No regulation Game

Now, consider a no regulation game in which upstream market is not regulated. To proceed with
our analysis, let assume thatand𝑐1 > 𝑐2 ,(7)

𝐴 ≥ 2𝑐1 ,(8)which is due to (2) and (7). It takes the place of (2) in what follows. In fact, this is a more usefuland direct expression than (2). A demand function is given by (1).
No regulation game is modeled as a two-stage game with complete and perfect information.
The timing of this game is as follows:
1. The incumbent chooses access rate 𝛼̄ from the colsed interval 𝑆𝑠𝑞 = [0, 2𝐴 − 𝑐1 − 𝑐2 ).

2. Two firms compete in supplying outputs in a downstream market.
In the second stage, profits of them are expressed as
𝜋1 = (𝑃 − 𝑐1 )𝑥1 + 𝛼̄ 𝑥2 ,

𝜋2 = (𝑃 − 𝛼̄ )𝑥2 .

The best response functions are given respectively by𝜕𝜋𝑖
= 0, 𝑓𝑜𝑟 𝑖 = 1, 2.
𝜕𝑥𝑖

It follows from (6) that if access rate 𝛼̄ set by the incumbent is less than 𝛼𝑠𝑞 , outputs of firms

and price are shown in Lemma 1. However, if 𝛼̄ is not less than 𝛼𝑠𝑞 , the entrant can not enter
into a market. In what follows, our focus is mainly on the former game where 𝛼̄ is less that
𝛼𝑠𝑞 . We will take up the latter if necessary.

In the first stage, the incumbent maximizes its profits given demand for inputs. Noting that one

unit of outputs is produced with one unit of inputs, demand for inputs is given by outputs of theentrant, which is given In Lemma 1: 𝑥̄ 2 =𝐴+𝑐1 −2𝑐2 −2𝛼̄3

if 𝛼̄ is less than 𝛼𝑠𝑞 . 13

Substituting outputs 𝑥̄ 𝑖 and price 𝑃̄ into profits of the incumbent yields

13

If it is not less than 𝛼𝑠𝑞 , 𝑥̄ 2 = 0.

13

𝐴 − 2𝑐1 + 𝑐2 + 𝛼̄ 2 𝛼̄ (𝐴 + 𝑐1 − 2𝑐2 − 2𝛼̄ )𝜋1 (𝛼̄ ) = (𝑃̄ − 𝑐1 )𝑥̄ 1 + 𝛼̄ 𝑥2 = (
) +
.
3
3
The first order condition yields

𝜕𝜋1 (𝛼̄ ) 2(𝐴 − 2𝑐1 + 𝑐2 + 𝛼̄ ) (3𝐴 + 3𝑐1 − 2𝑐2 − 12𝛼̄ ) (5𝐴 − 𝑐1 − 4𝑐2 − 10𝛼̄ )
=
+
=
= 0.
𝜕𝛼̄
9
9
9

The optimal access rate is given by𝛼 ∗ = 𝑎𝑟𝑔𝑚𝑎𝑥𝜋(𝛼̄ ) =where the inequality is due to (7) and (8).

5𝐴 − 𝑐1 − 4𝑐2
> 0,
10

(9)

We can now establish:

Lemma 4. The incumbent does not have incentives to monopolize a downstream market.

Proof. Noting that the profits function of the incumbent is concave,𝜋(𝛼 ∗ ) ≥ 𝜋(𝛼̄ ), 𝑓𝑜𝑟 𝛼̄ ∈ 𝑆𝑠𝑞 ,where the quality holds at 𝛼̄ = 𝛼 ∗ . Note also that 𝛼 ∗ is less than 𝛼𝑠𝑞 . In fact,𝛼 ∗ − 𝛼𝑠𝑞 =5𝐴 − 𝑐1 − 4𝑐2 𝐴 + 𝑐1 − 2𝑐2 3(𝑐2 − 𝑐1 )
−
=
< 0,
10
2
5

where the inequality is due to (7). Thus, the maximum profits can be achieved by supplying
inputs to its competitor. �
Although the incumbent can exclude the entrant by setting access rate equal to 𝛼𝑠𝑞 , theincumbent does not employ such an exclusionary strategy. The monopolization of a downstream
market provides additional profits with the incumbent and at the same time the incumbent loses
a customer in an upstream market. This causes loss of profits to the incumbent. It is notstraightforward that additional profits overcome loss in the upstream. Our Lemma above showsthat the loss is larger than additional profits so that the monopolization of both markets does notenable the incumbent to reap the maximum profits. This is one of the important features invertically related markets. From now on, we can ignore the games in which access rate is larger
than 𝛼𝑠𝑞 .

Next, we can show subgame perfect equilibrium in no regulation game. Substituting 𝛼 ∗ into𝑥̄ 𝑖 , and 𝑃̄ in Lemma 1 yeilds equilibrium outputs and prices in no regulation game.

We can summarize them:

Lemma 5.

If access rate 𝛼̄ set by the incumbent is less than 𝛼𝑠𝑞 , equilbrium outputs and14

prices are expressed respectively as,(𝐴 − 2𝑐1 + 𝑐2 + 𝛼 ∗ ) 5𝐴 − 7𝑐1 + 2𝑐2
=
> 0,
10
3
(𝐴 + 𝑐1 − 2𝑐2 − 2𝛼 ∗ ) 2(𝑐1 − 𝑐2 )
=
> 0,
𝑥2∗ =
3
5
(5𝐴 − 3𝑐1 − 2𝑐2 )> 0,
𝑋 ∗ = 𝑥1∗ + 𝑥2∗ =10
5𝐴 + 3𝑐1 + 2𝑐2> 0.
𝑃∗ = 𝐴 − 𝑋 ∗ =
10
𝑥1∗ =

However, if access rate by the incumbent is not less than 𝛼𝑠𝑞 , the entrant can not enter into amarket and then a market is monopolized by the incumbent.

It is easy to show that subgame perfect equilibrium in the no regulation game generates a false
positive. In fact, substituting 𝑃∗ and 𝛼 ∗ into (3) and (4) yields

5𝐴 + 3𝑐1 + 2𝑐2 5𝐴 − 𝑐1 − 4𝑐2
3−− 𝑐1 = (𝑐2 − 𝑐1 ) < 0,
10
10
5
5𝐴 + 3𝑐1 + 2𝑐2 5𝐴 − 𝑐1 − 4𝑐22−− 𝑐2 = (𝑐1 − 𝑐2 ) > 0,𝑃∗ − 𝛼 ∗ − 𝑐2 =10105𝑃∗ − 𝛼 ∗ − 𝑐1 =where these inequalities are due to (7).

Note that outputs of the entrant depends solely on the difference in costs between two firms. If
the entrant can enjoy advantage in costs, it can reap positive profits and can stay at a market.
However, if it can not, the entrant can not stay at a market. The intuition behind this is simple:
the entrant has disadvantage in costs, which can be overcome by efficiency of production.
However, it is assumed that efficiency is the same to both firms. Then, the entrant can not cope
effectively with the incumbent. Disadvantages in costs play a crucial role in market competition.
This argument can be summarize as follows:

Lemma 6. A necessary and sufficient condition that the new entrant can be viable at a market isthat the entrant is more efficient than the incumbent: 𝑖. 𝑒. , 𝑐1 > 𝑐2 .

Proof. It is easy to show that when we notice outputs 𝑥2∗ of the entrant it can stay at a market if
and only if 𝑐1 > 𝑐2 .

�It is interesting to note that the exit of the entrant can arise not by exclusionary strategy such asa price squeeze by the incumbent, but by inefficiency of the entrant. As the EC assumes away
differences in costs, a possibility that the entrant can not cope effectively with the incumbent
may be ignored.

15

When we apply Lemma 6 to the case of DT, fining DT for abusive price squeeze is not wellfounded. Moreover, it also follows from Lemma 4 that the monopolization of two markets does
not provide the maximum profits with DT. If a new entrant exits from a market, it is due todisadvantages in costs of the entrant, not by exclusionary strategies by the incumbent. Without
examining costs of firms, there can be a legal flaw in the procedures for the case of DT. Thesearguments show that the EC decision is not reasonable judgment of the case of DT.
Thus, we can conclude:

Proposition 4. The EC decision that DT should be fined for abusive price squeeze should be
declined.
It was shown in Proposition 3 that the EC decision is not founded when we apply a partial
regulation game. Following the fact which is expressed in the Commission decision of 21 May
2003, the decision is examined by the use of the no regulation game and then it is concluded
that the decision is not well founded. Our results above still show that there is a possibility that
the EC oversteps the mark. To justify its decision, it is required that the EC should construct amodel which supports its decision.

6

Conclusions

This paper has analyzed the nature of the Price Squeeze test in two distinct types of regulatoryenvironments, which assumes that new entrants are as efficient as the incumbent firm. When we
consider that costs differ between firms, it turns out that there are several reasons why a new
entrant can not be viable at a market. Our model showed that the PS test arises a false negative
or a false positive depending upon the relative values of firms’ costs. Thus, the entrant exits
from a market not only bya price squeeze by the incumbent, but also by inefficiency of theentrant: Less efficient entrants can not cope effectively with the incumbent. This is a game inwhich the incumbent is not responsible for the exit and should not be fined.
If new entrants are equally efficient competitors to the incumbent, the test proposed by the EC
is reliable means to judge whether the incumbent has adopted a price squeeze. However, if theentrants are not equally efficient we have shown that we encounter quite different scenario: It is
not reliable measures to judge whether the incumbent has adopted a price squeeze. This meansthat there is a legal flaw in the procedures for making decision of the case of DT. In fact, the EC
has not demonstrated by its model that DT might not have employed such an exclusionary
strategy. Thus, the present model has shown that there is a legal flaw in the decision of the EC

16

on the case of DT not only in the partial regulation environment, but also in a no regulation
environment. Thus, the EC decision fining DT for abusive price squeeze should be declined.
It is true that precise estimation of firms’ costs is a very difficult and complicated job. Afterthe estimation of costs of the entrant, it will be found that the entrant is not equally efficient.
Thus, the EC decision depends upon a false assumption. It follows from Mathematical Logic
that the decision on the case of DT is logically true, but is meaningless. To answer our criticism,
the EC has to construct its own model which supports its decision.

Acknowledgments

Hirai thanks Seinan Gakuin University for financial support. We also would like to thankProfessor Toichiro Asada, Akio Matsumoto, and Masahiro Yabuta of Chuo University for theiradvices and suggestions.

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[3] Bouckaert, J., & Verboven, F. (2004), “Price Squeezes in a Regulatory Environment,"
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[4] Bruno, J., Rey, P., & Saavedra, C. (2014), “The Economics of Margin Squeeze," IDIE
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[5] Carlton, D. W. (2008), “Should “Price Squeeze" Be a Recognized Form of Anticompetitive
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[6] European Commission (1998), “Notice on the Application of the Competition Rules toAccess Agreements in the Telecommunications Sector," 98/C: 265/02. (also in Official Journalof the European Union C 265, 22/08/1998: 2-28.)[7] European Commission (2003), “Commission Decision of 21 May 2003 relating a proceedingunder Article 82 of the EC Treaty ," Official Journal of the European Union L 263, pp.9-41.
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17[9] Rey, P., & Tirole, J. (2007), “A Primer on Foreclosure," in Handbook of Industrial
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[10] Salop, S. (2010), “Refusals to Deal and Price Squeeze By an Unregulated, VerticallyIntegrated Monopolist," Antitrust Law Journal, 76(3), pp.709-740.
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Discussion Paper No. 171, Institute of Economic Research, Chuo University.

18

Fig. 1 False Negative
𝑐1 < 𝑐2𝑃

𝑃𝑅: 𝑃 − 𝛼 − 𝑐2 = 0
𝑃𝑆: 𝑃 − 𝛼 − 𝑐1 = 0
𝐷𝑃: 𝑃 =B𝑃�

𝐴 + 𝑐1 + 𝑐2 + 𝛼
3

𝑐2
𝑐1
0

𝛼𝑠𝑞

𝛼�

𝛼�

𝛼

Fig. 2 False Positive𝑐1 ≥ 𝑐2

𝑃

𝑃𝑆: 𝑃 − 𝛼 − 𝑐1 = 0
𝑃𝑅: 𝑃 − 𝛼 − 𝑐2 = 0
𝐷𝑃: 𝑃 =C𝑃�

𝐴 + 𝑐1 + 𝑐2 + 𝛼
3

𝑐1
𝑐2
0

𝛼�

𝛼�

𝛼𝑠𝑞

19

𝛼