Collusion in markets with imperfect price
information on both sides
Christian Schultzy
March 2016
Abstract
The paper considers tacit collusion in markets which are not fully
transparent on both sides. Consumers only detect prices with some
probability before deciding which …rm to purchase from, and each …rm
only detects the other …rm’s price with some probability. Increasing
transparency on the producer side facilitates collusion, while increasing transparency on the consumer side makes collusion more di¢ cult.
Conditions are given under which increases in a common factor, a¤ecting transparency positively on both sides, are pro-competitive. With
two standard information technologies, this is so, when …rms are easier
to inform than consumers.
Keywords: Transparency, Tacit Collusion, Cartel Theory, Competition Policy, Internet. JEL: L13 ,L40
Department
of
Economics,
University
of
Copenhagen,
cs@econ.ku.dk,
www.econ.ku.dk/CSchultz
y
I have bene…tted from discussions with Joe Harrington, Morten Hviid, Kai-Uwe Kühn,
and Thomas Rønde and with seminar audiences in Copenhagen, Boston and Norwich. I
am grateful to comments and suggestions of two referees and the editor.
1
1
Introduction
The e¤ect of market transparency on competition is much debated; see for
instance OECD (2001). The EU Council …nds that "The transparency of energy prices contributes to the creation and smooth operation of the internal
energy market" and Council Directive 90/377/EEC speci…es a procedure to
improve the transparency of gas and electricity prices charged to industrial
end-users, see O¢ cial Journal (1990). Similarly, it is a general perception
that price comparison sites promote competition since they facilitate price
comparisons for consumers.
On the other hand, many …nd that improved transparency on the producer side facilitates tacit collusion. For example, Albaek et al. (1997) argue that the Danish Competition Authority’s decision to gather and publish
…rm-speci…c transaction prices for ready-mixed concrete made tacit collusion easier and led to increased prices. In general competition authorities are
well aware about the potential anti-competitive e¤ects of price-disclosures,
see e.g. OECD (2012).
It is an interesting and unresolved issue whether and when an increase in
price transparency a¤ecting both sides of the market at the same time is procompetitive. This paper investigates this issue and consider tacit collusion
in a Hotelling market. It assumes that only a fraction of consumers are
informed about prices as in Varian (1980) and that …rms learn each other’s
prices with some probability only.
I …nd that in a homogeneous market, increasing transparency on on
both sides of the market is anti-competitive since here only the producer
side matters. In a di¤erentiated market, however, this is not so. In general,
the result depends on the relative elasticities of transparency with respect
to the common factor a¤ecting transparency on either side.
For two of the most widely used information technologies in the literature - a simple concave technology and the model of Butters (1977) and
Grossman-Shapiro (1984) - the result is unambiguous. In a su¢ ciently differentiated market, an increase in a common factor promoting transparency
on both sides is pro-competitive provided …rms are easier to inform than
consumers are. When …rms are easy to inform, they are well informed from
the outset and changes in price transparency a¤ect the more poorly informed
2
consumer side more.
From a competition policy perspective, the results imply that if tacit
collusion is a relevant and major concern, then in homogeneous markets
competition authorities and consumer agencies should not make e¤orts to
improve price transparency. Price transparency only a¤ects competition
through the producer side, and this e¤ect is anti-competitive.
In (su¢ ciently) di¤ erentiated markets, both producer and consumer side
e¤ects are relevant and they counter each other. Under standard assumptions on information proliferation, the consumer side e¤ects dominate and
measures, which increase transparency on both sides, are likely to be procompetitive.
2
Roadmap and Related literature
Throughout the paper …rms rely on price-monotoring schemes, where a deviation from collusive play is punished if it is detected. As is well known
from Green and Porter (1984) …rms may rely on sales-monotoring schemes
as well. A section investigates the case where …rms also use sales-monotoring
schemes. This complicates the model, but for the cases considered the results
are robust.
In the main part of the paper transparency is exogenous, determined by
forces external to the …rm. A section considers what happens when …rms also
can advertise their own price. Again the model becomes more complicated
and analytical solutions are not avaliable. However, in numerical simulations
the results are robust to …rms own advertising.
Improved transparency on the producer side is mostly viewed as anticompetitive as it facilitates tacit collusion, see for instance, Stigler (1964),
Green-Porter, (1984), Tirole (1988), Kühn and Vives (1995) and Kühn
(2001). Many contributions argue that improvements in transparency on the
consumer side, on the other hand, are pro-competitive. Here the arguments
usually refer to a static setting, building on results of the search literature of
the 70’ies and 80’ies like Salop and Stiglitz (1977), Varian (1980), Burdett
and Judd (1983), Stahl (1989), and many others.
In Schultz (2005), I show that in a di¤erentiated Hotelling market improved transparency on the consumer side makes tacit collusion more di¢ -
3
cult while it has (almost) no e¤ect if the market is almost homogeneous, see
Herre and Rasch (2013) for more general settings.
Nilsson (1999) considers a homogeneous market with costly consumer
search. He shows that lower search costs facilitate collusion since search
intensi…es and lowers pro…ts in the punishment phase but not in the normal
phase. Petrikaite (2015) considers costly consumer search in a di¤erentiated
market. She shows that for most parameter values, collusion becomes more
stable if the search costs increase.
While many papers seek to endogenize transparency in various ways, I
focus on the case, where transparency is exogenous and potentially a¤ected
by an agent or authority outside the market such as a consumer agency. In
the present paper therefore, the fraction of informed consumers does not
di¤er in the collusive and punishment phases. Armstrong (2014) surveys
some of the more recent literature on market-transparency in both a static
and a dynamic setting.
None of these papers considers the e¤ect of changing transparency at
both sides of the market at the same time.
The organization of the rest of the paper is the following. Section 3
introduces the market. Section 4 characterizes the one period equilibrium.
Section 5 introduces tacit collusion and the e¤ects of transparency and discusses how sales monitoring as well as advertisement by the …rms a¤ect the
results of the main model. Section 6 considers the case where transparency
changes on both sides of the market simultaneously. Section 7 o¤ers some
concluding comments.
3
The market
We consider a Hotelling market with a continuum of consumers. Consumer
x is located at x 2 [0,1]. A consumer wishes to buy zero or s units of the
good where s is a stochastic variable distributed according to the cdf.
(s)
with mean equal to one: We assume that [0; 1] is contained in the support
of
; so that any decline in demand below the mean is possible.
The two …rms are located at 0 and 1, respectively, and consumers know
this. A consumer buying s goods at the price p from a …rm she is located y
away from receives utility (u
p
ty) s: The parameter t > 0 is the trans-
4
portation cost, re‡ecting the degree of product di¤erentiation or "pickiness"
of the consumers. All consumers are potential customers at each …rm: u
t:
If a consumer is informed about both …rms’ prices, she is indi¤erent
between buying from either …rm if she is located at
x(p0 ; p1 )
A fraction
1 p1 p0
+
:
2
2t
(1)
of the consumers is informed about both …rms’prices, while
the rest are uninformed as in Varian (1980). An uninformed consumer has
an expectation pei of …rm i0 s price. An uninformed consumer cannot learn
prices by visiting both …rms, she can only visit one …rm in a period. The
variable
is our measure of market transparency at the consumer side. The
distribution of each information type of consumers is uniform on locations.
In a period, the time line is as follows: First s realizes and …rms do
not observe it. Firms set prices and some consumers observe them, the rest
form expectations. Consumers decide on which …rm to visit - if any. If an
uninformed consumer arrives at a …rm and …nds that the price is higher
than expected, she may decline to buy. Finally, transactions take place.
We will assume that the fraction of informed consumers is su¢ ciently
high such that
2
t
<
;
(2)
u
2+
this implies that the market is covered in a one period pure strategy Nash
equilibrium.
We will focus on symmetric equilibria where pe0 = pe1 : As will become
clear, the equilibrium price will be so low (at most u t=2) that all consumers
buy and each …rm faces (1
) =2 uninformed consumers. The number of
consumers visiting …rm 0 can therefore be
8
>
+ 12
>
>
>
p1 p0
<
1
+ 12
2 + 2t
D(p0 ; p1 ; ) =
1
>
>
2
>
>
: 1
u p0
2
t
written as
if
p0 < p1
t
if
p1
t
p0
p1 + t
if
p1 + t
p0
u
if
p1 = u
t
2
p0
t
2
(3)
u:
Firm 00 s demand equals D(p0 ; p1 ; )s and the expected demand equals D (p 0 ; p1 ; ) :
Marginal costs are constant, normalized to zero, so …rm 00 s pro…t in a period
is p0 D(p0 ; p1 )s and the expected pro…t
0
Under (2) the monopoly price is pm = u
5
equals p0 D(p0 ; p1 ):
t=2:
4
One period equilibrium
The one period Nash equilibrium may be in pure or mixed strategies depending on the degree of product di¤erentiation relative to the maximal
willingness to pay, t=u; and the transparency of the market,
. We …rst
consider the pure strategy equilibrium.
In a symmetric equilibrium, the …rms set the same price, serve both
informed and uninformed consumers, and the price, pN ; and expected pro…t,
N;
are
pN =
t
N
;
t
:
2
=
(4)
When …rms choose prices, they take into account that the informed consumers only notice a price decrease. An increase in consumer transparency,
; makes demand more elastic, increases competition, and lowers the equilibrium price and pro…t. In the one shot game, the …rms therefore jointly
have no interest in promoting consumer transparency.
1
When the Nash equilibrium is in pure strategies, then
pm
pN
pN
is a measure of the relative gains to …rms from monopoly pricing relative to
competitive pricing. We can rewrite condition (2) as
> 0:
(2’)
When goods are close substitutes, pN = t= becomes very low and will
not be an equilibrium price. It becomes a better option for a …rm to pursue
the rip-o¤ strategy of Salop and Stiglitz (1977) and raise its price to the
monopoly price and only sell to the (1
visit the
1
…rm2 :
) =2 uninformed consumers who
This is the case when the degree of product di¤erentiation
It is straightforward to check that the second order condition for maximum is ful…lled.
In deriving the equilibrium, we assumed that the market is covered and the second line
of (3) is relevant, hence it should not be advantageous to undercut the other …rm by t
and gain the whole informed market. This takes that
ful…lled for all positive
t
t
+
1
2
<
t
2
; which is
and t: Under assumption (2) the market is covered in the Nash
equilibrium.
2
If the …rm decides to sell only to a fraction of the uninformed consumers arriving, the
best price solves maxp0 (1
the best choice is p0 = u
)
u p0
p0
t
, if it decides to sell to all, p0 = u
t
:
2
6
t
:
2
For small t;
is so low that
t
2 (1
)
<
u
(1 + ) (2
)
,
>
1
:
(5)
When (5) is ful…lled, a symmetric pure strategy equilibrium does not exist.
Varian (1980) shows that in a homogeneous market (i.e. where t = 0) a
symmetric mixed strategy equilibrium exists. The same happens when the
goods are close but not perfect substitutes. Schultz (2005) characterizes the
symmetric mixed strategy equilibrium. The characterization does not allow
closed form solutions, but it is shown (in Lemma 1) that as the transport
cost t tends to zero; the limiting expected pro…t of each …rm is3
lim
N
t!0
=
1
2
u:
(6)
The result is intuitive: It is always an option for a …rm to charge the
reservation price, which equals u when transportation costs vanish, and only
serve the uninformed consumers arriving. In a mixed strategy equilibrium,
each price in the support of the distribution must give same expected pro…t,
and hence the expected pro…t is given by (6). When goods are almost homogeneous, the market works as if …rms extract almost all possible rent from
the uninformed consumers and none from the informed. Varian obtained
this result for a homogeneous market.
5
Tacit Collusion
Now we consider the repeated game. There are in…nitely many periods,
= 0; :::; 1: The size of the market, s; di¤ers over periods, we assume that
s is drawn from the distribution
independently over the periods. Firms
seek to maximize the discounted sum of expected pro…ts and both have the
discount factor ; which ful…lls 0 <
< 1: A consumer’s information type
(as well as her location) is the same in all periods.
It is not important for the one period analysis whether …rms can observe
each other’s prices ex post but it is for the dynamic analysis. We will identify
transparency on the producer side with the probability that a …rm observes
the other …rm’s price. Let this probability be ; where 0 <
1: Tacit
collusion will be a¤ected by the inability to monitor rivals’prices perfectly.
3
We abuse notation slightly by designating the expected pro…t
as in the mixed strategy equilibrium
7
N
in the pure as well
If a …rm observes the other …rm’s price it becomes common knowledge.
It may be, for instance, that the price is featured on a homepage run by an
independent consumer agency known to both …rms, newspapers may cite the
price, or they are both aware that a person has disclosed the information.
A price cut may go unobserved by the other …rm but it will a¤ect its
sales and this may be taken as a sign of under-cutting as noticed by Stigler
(1964). However, in a market with stochastic demand low sales may also be
due to slack demand. At …rst, we focus on trigger strategy equilibria where
…rms use price-monitoring strategies and only initiate punishments when a
price cut is observed. In a special section, we will address sales-monitoring
schemes.
The "Wood Pulp" cartel provides a prominent example of a cartel relying on price-monotoring strategies. The European Commission describes in
detail how the cartel members coordinated and monitored prices. It cites
explicit threats of punishments for price-cuts: “The Finns will respect the
Spanish dominance in Spain if ENCE really increase their prices in other
countries: If Fincell learns about prices below US $ 360 also in the future,
they will reconsider their policy as to sales in Spain!”(O¢ cial Journal, 1985
§ 60).
We focus on a trigger strategy equilibrium. Firms punish observed deviations from collusion by reverting to the one-shot Nash equilibrium for the
rest of the game (Friedman, 1971).
When …rms collude on p; their expected pro…t is (p) = p=2 in all periods. If a …rm deviates to a lower price, only informed consumers learn this
before they visit the …rm. The uninformed expect the …rm to set p and half
of them will visit the …rm and get a nice surprise. The other half visits the
other …rm and will not observe the deviation. The optimal deviation price
is
pd =
8
<
:
1
2
p+
p
t
if
t
p
2t +
if p > 2t +
t
t
(7)
:
The …rst expression in (7) applies when the optimal deviation does not
capture the whole market. The deviation pro…t is
(
2
1 ( p+t)
if p 2t + t
d
8
t
(p) =
(p t) 1+2
if p > 2t + t :
8
(8)
Both expressions are increasing in
when p > t= : Hence, a deviation is
more pro…table when the market is more transparent on the consumer side.
With probability ; the deviation is observed and a punishment commenced.
Collusion on the price p is viable if the present value of collusive pro…ts
exceeds the expected pro…t from a deviation plus the present value of the
expected continuation pro…t after a deviation. The non-deviation constraint
therefore is
1
1
d
(p)
(p) +
N
1
+ (1
)
(p):
1
(9)
We assume that …rms collude on the best possible price, either the
monopoly price, pm = u
t=2 or some lower price. If
2 ;
then
d (pm )
(10)
is given by the …rst expression in (8) otherwise it is given by
the second.
We now consider the case where product di¤erentiation is relatively high
so that (5) is not ful…lled and the one shot Nash equilibrium is in pure
strategies.
Inserting the relevant expressions, we …nd that the non-deviation constraint for full collusion on the monopoly price (9) is ful…lled when …rms are
su¢ ciently patient, namely when
(
^
+4
if
2
(1+ = )
if
>2 :
(11)
7 2 ; the crucial discount factor ^ is increasing
Regardless of whether
in the level of market transparency at the consumer side,
; (since
de-
pends positively on ) and decreasing in the level of market transparency
on the producer side,
4.
More consumer transparency makes collusion more
di¢ cult, while more producer transparency makes it easier.
Increasing transparency on the consumer side has two e¤ects, a deviation
becomes more pro…table, but the ensuing punishment becomes harder as
well. On balance, the …rst e¤ect is the larger one. Increasing transparency
on the producer side makes it more likely that a deviation is detected, and
this makes a deviation less tempting thus, collusion becomes easier.
4
2 for all
if u=t < 5=2 and otherwise for
9
1= (u=t
5=2).
If
< ^, it is not possible for the …rms to sustain full collusion on the
monopoly price and the most pro…table equilibrium involves a collusive price
which exactly makes the non-deviation constraint (9) ful…lled (as originally
noted by Chang (1991) for a fully transparent Hotelling market). This gives
8
<
1+4 1
pN
if
2 +
(12)
pc =
2
(1
)
N
: 1+
:
p
if
>
2
+
( + )
Clearly, pc and the associated pro…t are decreasing in transparency on the
consumer side and increasing in transparency on the producer side.
5.1
Including both Price and Sales Monotoring Schemes
Throughout the main body of the paper, we assume that …rms’ collusive
strategies involve price-monitoring schemes only. However, …rms may employ sales monitoring schemes as well and initiate punishment phases when
they face unexpectedly low sales (Green-Porter, 1984). Suppose therefore
that …rms also initiate punishment phases if their sales fall below some speci…ed level, q > 0:
We now focus on the case where a deviation to pd does not capture the
whole market: Following a deviation to pd ; the probability the other …rms’
sales fall below q is then given by
F pd ; p; q
Thus,
@F (pd ;p;q )
@pd
1 pd p
+
2
2t
Pr s
0
@1
=
2
q
1
2
+
pd p
2t
+
1
2
1
+
2
1
q
A > 0:
> 0; and a deviation to a lower price increases the proba-
bility the other …rm’s sales fall below q:
The non-deviation constraint (9) is modi…ed to
v (p)
d
(p) +
+ (1
N
(13)
1
) F pd ; p; q
N
1
+ 1
F pd ; p; q
v (p) ;
where v (p) is the continuation pro…t in the normal phase. Rewriting gives
v (p)
d (p)
+
1
+ (1
) F pd ; p; q 1
(1
) (1 F (pd ; p; q))
10
N
:
Furthermore, the continuation pro…t in the normal phase is
v (p) =
N
(p) + (q) 1
(p)
<
:
1
(1
(q))
1
The inequality follows since with probability F (p; p; q) =
(14)
(q) the punish-
ment phase is initiated because of slack demand although nobody deviated.
^; so that it is possible for the
It directly follows from (14) that if
…rms to collude on the monopoly pro…t using price monitoring strategies
only, then this is pro…t maximizing for the …rms.
Consider then the case where the discount factor is so low that collusion
on the monopoly price is not possible using price monitoring strategies alone.
Clearly, when
; the probability of observing a deviation, tends to zero,
collusion becomes infeasible using price monitoring strategies only. This is
also clear from the …rst line in (12), as
to
pN :
! 0; the best collusive price tends
In this case, …rms will gain from using sales monitoring strategies
and initiate punishments after a period of low sales.
It is clear that whenever price monitoring is feasible to some extent,
i.e. when
> 0; it is optimal (possibly partly) to rely on price monitoring
strategies. Price monitoring helps deterring deviations and it is costless in
the normal phase, contrary to sales monitoring schemes.
When sales monotoring schemes are employed, an increase in
facilitates
and makes collusion more pro…table. To see this, assume the non-deviation
constraint (13) binds. If
increases with d , q can be lowered so that the
constraint still binds and F =
1
d
1
d
N
1 F
d
(1 (1
))2 1
is lowered with d =
the normal phase continuation pro…t with
: This increases
> 0: As the left
hand side of (13) increases faster in v than the right hand side, this increase
in normal phase continuation pro…t slackens the non-deviation constraint.
As it turns out a full characterization for the case where …rms use both
price and sales monitoring strategies is not available 5 .
Summing up, price monitoring is always optimal if possible. If and are
su¢ ciently high so that > ^; then it is optimal only to rely on price monitoring strategies. Otherwise, …rms may gain by employing sales-monitoring
strategies. In both cases, if transparency on the producer side increases,
5
For the case of a uniform distribution of demand, one can show that the optimal
deviation is the solution to a third degree polynomial.
11
…rms will rely more on price-monotoring and this facilitates collusion. In
the sequel we will only consider price monitoring schemes.
5.2
When the …rms can advertise own price
For the most of the paper, we treat transparency as exogenous, determined
by factors external to the …rms. But, what if each …rm - at least with
respect to its own price - can in‡uence the amount of information available
to consumers? Advertising - e.g. in the form at a posted price outside the
store - is indeed possible.
Assume therefore that each …rm can advertise and increase the fraction
of consumers observing its price with
i
at the cost 21 c
2;
i
where c > 0, so
that the total fraction of consumers observing its price is
expected pro…t is then ~ 0 = p0 D(p0 ; p1 ; +
0)
1
2c
+
i:
Firm 00 s
2:
0
In the symmetric one shot Nash equilibrium, the equilibrium price is
expected by the consumers, so …rms will not spend resources informing about
the price,
0
=
1
= 0; and the equilibrium price is p = t :
Similarly, in the normal phase in the repeated game, prices are as expected and no advertising takes place. However, if a …rm were to make a
deviation it would want to inform consumers about the unexpected pricecut.
We now only consider the case where a deviation does not capture the
whole market. When the …rms collude on the price, p; the optimal deviation,
pd ;
d;
is given by the …rst order conditions
pd =
1
2
p+
t
+
d
and
d
= pd
p
pd
:
2ct
(15)
Comparing with (7) we see that the …rm wishes to inform more consumers about the low price and consequently the deviation is to a lower
price than when this is not possible. It directly follows that the possibility
of informing more consumers makes the deviation pro…t larger. This implies that collusion is harder, the crucial discount factor is larger than ^
as given in (11). It is straightforward to show that a decrease in the cost of
advertising, c; makes deviations more pro…table and destabilizes collusion.
Totally di¤erentiating (15) one …nds that increasing the exogenous transparency
lowers the deviation price, pd ; and increases the …rm’s advertising.
12
Hence, an increase in transparency makes deviations more pro…table. However, it also makes the punishment phase in the repeated game more harsh.
As the solution to (15) is the root of a third degree polynomial a more
general result is not available but in the numerical examples I have investigated an increase in is pro-competitive: it increases the crucial discount
factor ^ as is the case when advertising is not possible. For sure (by continuity) this result is true for high values of c; where the amount of own
advertising is small. In the sequel, we will disregard advertising and focus
on exogenous factors a¤ecting transparency.
6
Changes in Transparency on both Sides
So far we, have considered changes in transparency on each side independently. However, it may well be that measures in‡uencing one side also
in‡uence the other side. Producers may also visit price comparison sites
aimed at consumers and both sides may read news in the press.
Suppose, therefore, that there is some common factor, ; which increases
both the fraction of informed consumers and the likelihood that a …rm observes the other …rm’s price, so that
where 0 ( ) > 0:
An increase in
;
@ ( )
@
.
@b @
@b @
db
=
+
:
d
@ @
@ @
( ) be the elasticity of
e
db
>0,
d
e
;
;
<
(
1 + 1=
1+
An increase in the common factor
wrt
= ( )
a¤ects the lowest discount factor compatible with full
collusion with
Let e.g. e
= ( ) where 0 ( ) > 0 and
(
)
wrt : Then
if
2
if
>2 :
(16)
is pro-competitive if the elasticity of
is su¢ ciently large relative to the elasticity of
wrt : The crucial
cut o¤ value depends on the gains from collusion and the transparency on
the consumer side. When
2 ; an increase in
is pro-competitive if the
consumer side elasticity exceeds the producer side elasticity.
If full collusion on the monopoly price cannot be sustained, then the
13
e¤ect on the best collusive price, pc ; is
dpc
@pc @
@pc @
=
+
;
d
@ @
@ @
so
dpc
d
<0,
e
e
;
<
;
8
<
: 1+
1
4
((1 )
2
(1
1+
if
)2
)
2 +
if
>
2 +
:
(17)
Again, an increase in the common factor is pro-competitive if the consumer
side elasticity is su¢ ciently higher than the producer side elasticity.
When a common factor a¤ects transparency on both sides, the competitive e¤ect hinges on where information spreads more easily, as measured by
the relevant elasticities. Evidently, this depends on how information spreads
- i.e. on the information technology.
Suppose an agency spends resources informing market participants about
prices, let these resources be represented by
. We will now consider how
this a¤ects the market under two well-known information technologies.
First, suppose that the probability the …rms are informed about prices
is given by6
0+
;
(18)
+
+h
0
where h > 0 represents the costliness of increasing the chance the …rms learn
( )=
the prices, and
0
> 0 implies that even if the agency spends no resources,
there will be some chance the …rms learn each other’s prices.
Suppose, similarly that the same kind of function determines the probability a consumer is informed, ; but the costliness, f > 0; of informing a
consumer may be di¤erent.
( )=
0
0+
+
+f
:
Hence,
e
e
;
;
=
h
f
+
0+
0
+f
< 1 i¤ h < f;
+h
i.e. if …rms are less costly to inform. Suppose
2 ; so that an optimal
deviation captures the whole market. From (16) and (17) we then have
that more resources spent by the agency on information is pro-competitive
6
Coate (2004) uses this function.
14
if f > h. If
2 ; then relative elasticity has to be less than a cut o¤ value
below one, and f has to be su¢ ciently much larger than h:
Now consider Grossman and Shapiro’s (1984) information technology
(based on Butters (1977)). Here ads are placed in magazines7 . The probability a consumer reads a given magazine is r; which is independent of the
probability she reads a di¤erent magazine. If a consumer reads a magazine
with an ad, she sees the ad. Then if the agency places ads in
magazines,
the probability that a given consumer will see none of these ads is (1
r) .
To avoid the special case, where the probability a consumer is informed
is zero, we assume that there will be one magazine informing about prices
even if the agency does not. To simplify, assume the agency does not use this
magazine. Hence, the probability a consumer does not learn about prices is
(1
r)
+1 :
Conversely, the probability she does learn about prices is
( )=1
The elasticity of
wrt
e
(1
r)
+1
:
(19)
is
;
=
ln (1
(1 r) +1
:
r)
(1 r) +1 1
(20)
Di¤erentiating, we …nd
@e ;
=
@r
(1
r) (1
r)
+1
1
2
1
As 0 < r < 1; this is negative if ln (1
(1
r)
r)a+1 <
+1
+ ln (1
1
(1
r)
+1
(1
r)
+1
; which
is indeed true as ln 1 = 0; ln 0 (1) = 1; and ln 00 (x) < 0. Hence e
r)
;
is
decreasing in r:
Suppose that the probability a …rm reads a given magazine is z: Then the
probability that the …rm is informed is ( ) = 1 (1 z)
+1
and e
;
is given
by (20) with r replaced by z: If …rms spend more resources than a consumer
on collecting information, i.e. are more likely to read a given magazine than
a consumer, then z > r; and since the elasticities are decreasing in r and z;
we have e
7
;
>e
;
:
In fact, colluding …rms in the vitamins industry used magazines to announce price
changes to the public/competitors (Marshall, Marx and Raif, 2008). I am grateful to a
referee for pointing to this example.
15
+1
:
Hence, if …rms spend more resources than consumers in achieving information, so z > r, they are more likely to be informed and provided
2
then (16) and (17) are ful…lled and an increased e¤ort by the consumer
agency is pro-competitive. Again if
2 ; z has to be su¢ ciently much
larger than r for this to be the case.
Accordingly, for both information technologies, a larger e¤ort in informing the market is pro-competitive if …rms are su¢ ciently easier to inform.
In this case, they are better informed from the outset than consumers. If
the market is su¢ ciently di¤erentiated (such that the …rst lines in (16) and
(17) are relevant) …rms just need to be easier to inform.
These results may appear counter-intuitive at …rst: If …rms are easier to
inform, one could imagine that an increase in information is anti-competitive
as transparency will be higher on the producer side. The crucial feature,
however, is that the elasticities matter. If …rms are easier to inform, they
are better informed from the outset and an increase in information will have
relatively less impact on the producer side of the market.
Schultz (2005) showed that in the almost homogeneous market changes in
transparency on the consumer side do not a¤ect the scope for tacit collusion.
Changes in price transparency therefore only a¤ect competition through the
producer side and since this e¤ect is anti-competitive, the total e¤ect is anticompetitive. In the limit as the market becomes homogenous (as t ! 0) the
optimal deviation is to p
t (see 7): Inserting the limiting pro…t
N
from
(6) into the non-deviation constraint (9) gives the crucial discount factor for
collusion on the monopoly price
lim =
t!0
This is independent of
7
1
1+
and decreasing in :
Concluding remarks
Theoretical predictions of welfare e¤ects can di¤er depending upon whether
the rivalry between …rms is modelled statically or dynamically. Our results
pertain to markets where there is the potential for tacit collusion. They
suggest that homogeneous and di¤erentiated markets di¤er with respect to
16
how one should assess the virtues of measures promoting price transparency
a¤ecting both sides of the market.
In a homogeneous market, only the producer side e¤ect matter and this
e¤ect is anti-competitive. In such markets, competition agencies or consumer agencies should not promote price transparency if tacit collusion is
the major concern.
In di¤erentiated markets, the issue is more complicated. In the simple di¤erentiated Hotelling market, the e¤ects stemming from the two sides
counter each other. Under standard assumptions about information proliferation, and assuming that …rms are better informed than consumers, the
consumer side e¤ect dominates and in such markets measures promoting
price transparency are pro-competitive even if tacit collusion is a concern.
In this paper I assume that the probability of detecting a rival’s price is
exogenous. Firms have a joint incentive to monitor each other since this facilitates collusion. Furthermore, each …rm will have an individual incentive
to monitor its competitors so that it is not cheated upon. If such monitoring is costless we would expect …rms to monitor each other. If they do,
then increased transparency is pro-competitive since then it only a¤ects the
consumer side.
However, monitoring of rivals may not be costless and sometimes even
prohibitively expensive. Clearly, each …rm has an individual incentive to
hide a deviation and o¤er secret rebates. Then, the results of this paper
show that things are intricate and that one needs to assess the competitive
e¤ects of an increase in transparency on a case-by-case basis.
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