Boone, J.

Potters, J.J.M.

English

Research Papers in Economics

Transparency and prices with imperfect substitutes
Jan Boone
1, Jan Pottersz ⁎
Tilburg University, The Netherlands
Received 24 August 2005; received in revised form 23 May 2006; accepted 27 June 2006
Available online 27 October 2006
Abstract
We show that an increase in consumer transparency may increase prices if goods are imperfect substitutes. If the
consumers have more information about the goods that are available and about corresponding prices they will
increase their demand. The effect of this on prices may override the competition enhancing effect of transparency.
© 2006 Elsevier B.V. All rights reserved.
Keywords: Transparency; Demand effect; Competition effect
JEL classification: D40; L10
1. Introduction
It is often suggested that transparency will increase competition, reduce prices, and increase consumer
surplus. In this paper we illustrate a potential caveat to this argument. A rise in transparency increases
consumer awareness about the different products available and about their prices. If goods are imperfect
substitutes this may increase total demand and lead to higher prices.
2 Of course, this demand effect
Economics Letters 93 (2006) 398–404
www.elsevier.com/locate/econbase
⁎ Corresponding author. Department of Economics, Tilburg University, P.O. Box 90153, 5000 LE, Tilburg, The Netherlands. Tel.: +31 13 466
8204; fax: +31 13 466 3042.
E-mail address: j.j.m.potters@uvt.nl (J. Pottersz).
1 CentER, TILEC, Tilburg University, ENCORE, UvA, IZA and CEPR.
2 Others have studied the potential impact of transparency on tacit collusion (e.g., Schultz, 2005, Møllgaard and Overgaard, 2000, Nilsson,
1999). Our analysis is purely based on a static analysis, a feature it shares with Janssen and Moraga (2000) and Schultz (2004). In the latter paper
transparency covers not only awareness about prices but also about the exact product characteristics.
0165-1765/$ - see front matter © 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.econlet.2006.06.003disappears if goods are perfect substitutes. In this case we are left with the competition effect of
transparency: competition intensifies and prices decrease when buyers become better informed.
We employ a static model in which there are two types of buyers. One type of buyer is perfectly
informed about all products and prices offered by different sellers; the other type is only informed about
the product and price of one seller and is restricted to buy from this particular seller.
3 The fraction of
buyers that is perfectly informed is an exogenous parameter which we take as a measure for the level of
transparency in the market.
2. Model
Consider a market with n producers and continuum of consumers of size 1. Consumers' utility
functions are of the form
uðx1; N ;xn;MÞ¼
X n
i¼1
xi−x2
i −2r
X
j>i
xixj
()
þ M ð1Þ
where xi is the amount of good i (=1,…, n), M is a composite good of all the other products in the
economy, and σ indicates the degree to which goods from different producers are substitutes. Let a
fraction τ of consumers be aware of all the n products in this market. They maximize the utility function
above subject to a budget constraint. It is routine to verify that the inverse demand functions of these
informed customers are of the form
pI
kðxk;x−kÞ¼1−2xk−2r
X
lpk
xl
Of the (1−τ) other consumers, a fraction 1
n knows only of product i and is not aware of any other
product. Their utility function is u(xi, M)=xi−xi
2+M. The inverse demand function of an uninformed
consumer equals
pU
i ðxiÞ¼1−2xi
We say that transparency increases in this market as the fraction of people τ who are aware of all
products increases.
Now we analyze the equilibrium, that is, the prices that clear the market. Let xj denote total output of
firm j. Further, let xj
U(xj
I) denote firm j's output per head of uninformed (informed) customer. Although
there are asymmetric equilibria in which some firms only produce for their “own” captive consumers,
4 we
focus here on equilibria in which all firms produce for both informed and uninformed consumers, i.e.,
xj
U>0 and xj
I>0. Since there are τ informed customers and 1−s
n uninformed customers who only know
3 This is similar to, though not the same as Varian's (1980) assumption that the uninformed are randomly allocated to one of
the sellers.
4 See the working paper version of this paper (at http://greywww.kub.nl:2080/grey.les/ center/2002/7.html)f o ra
characterization of these equilibria.
399 J. Boone, J. Pottersz / Economics Letters 93 (2006) 398–404firm j's product, the following relationship holds between these output levels: sxI
j þ 1−s
n xU
j ¼ xj. Next, we
assume that sellers cannot distinguish an informed from an uninformed customer. Hence, we assume that
sellers cannot price discriminate, implying that pj
I(x1
I,…, xn
I, M)=pj
U (xj
U, M). Together these two
conditions determine market demand.
Proposition 1. Given the total output vector (x1,…,x n), the market equilibrium price for product j equals
pjðx1; N ;xnÞ¼1−bxj−g
X
kpj
xk
where
g ¼ gðr;s;nÞ¼
2n2rs
½ð1−sÞð1−rÞþns ½n−ð1−sÞð1−rÞðn−1Þ 
ð2Þ
b ¼ bðr;s;nÞ¼g þ
2nð1−rÞ
ð1−sÞð1−rÞþns
ð3Þ
Note that for τ=1 we are back again in the usual case where β=2 and γ=2σ. That is, if the market is
perfectly transparent we get the demand function which corresponds to the case where every consumer
has utility function (1). Also note that for the case where τ<1 and goods are perfect substitutes (σ=1), we
get β=γ=2. So in that case β and γ do not depend on τ. The reason why β and γ for the case σ<1
depend on τ is that the firm faces two markets: one where decreasing marginal utility is strong (the
uninformed market where consumers only buy the firm's own product) and one where it is weaker
(because with σ<1 the informed consumers like variety and hence are willing to consume more).
5 The
parameters τ and n determine the size of the uninformed market, which equals 1−s
n .I fσ=1, goods are
perfect substitutes and marginal utility decreases at the same speed in both markets. Hence the relative
sizes of these markets are irrelevant.
Finally, note that
dpj
dx ¼ −ðb þð n−1ÞgÞ < 0. If all firms raise their output simultaneously by an amount
dx, all prices will fall. Furthermore, it can be shown that
Aðbþðn−1ÞgÞ
As < 0, implying that the fall in pj is
bigger the smaller is τ. The intuition for this is that as τ decreases, more is sold on the uninformed market
where marginal utility decreases faster than on the informed market. Hence, a given rise dx leads to a
bigger fall in prices. From this we see immediately that, for given output levels, it is possible that a rise in
transparency increases all prices pj. If firms choose symmetric output levels, x=x1=…=xn then we have
pj=1−(β+(n−1)γ)x. For given x, a rise in transparency τ increases prices pj. The intuition for this effect
is that if consumers become better informed about the availability of goods which are imperfect
substitutes then total demand will increase.
6 But if total supply is taken as given, the market equilibrium
price must increase in order to restore the equality of demand and supply. This we call the demand effect
of transparency, because supply is fixed in this analysis.
5 The observation that marginal utility goes down faster on the uninformed market suggests that the firm would prefer to have
informed consumers only. At first sight, this seems to contradict the idea that the firm is a monopolist on the uninformed market
which makes this uninformed market more profitable than the informed one. The point is that we are taking output levels x1,…,
xn fixed at this moment. The next section introduces the idea that output levels are determined in Nash equilibrium. This
introduces the competition effect of transparency τ.
6 The effect is even stronger when goods are complements (σ<0).
400 J. Boone, J. Pottersz / Economics Letters 93 (2006) 398–4043. Cournot–Nash equilibrium
In this section, we analyze the equilibrium in case that firms compete in quantities. As the next
proposition shows an increase in transparency will lead to increase in quantities. We focus on the case that
firms have identical quadratic cost functions cðxiÞ¼c1xi þ 1
2c2x2
i .
Proposition 2. The unique symmetric Cournot–Nash equilibrium (x
C,…,x
C) is characterized by
1−c1
2bþðn−1Þgþc2. Furthermore, when σ<1 we have dxC
ds > 0.
Firms increase their output levels if more consumers become informed about available products and
prices. This effect and its intuition are in line with the conventional wisdom regarding competition on
transparent markets. The competition between firms becomes fiercer if the group of informed consumers
becomes larger. This effect of transparency can be labeled the competition effect of transparency. The
effect is not restricted to quadratic or convex cost functions. Moreover, it can be shown to hold also when
firms compete in prices rather than quantities.
The competition effect does not necessarily imply, though, that prices will decrease as transparency
increases. This is due to the demand effect that we have seen in the previous section.
Proposition 3. With σ<1 it holds for the price p
C=1−(β+(n−1)γ)x
C in the symmetric Cournot–Nash
equilibrium that
dpC
ds
> 0 ijf c2 > c ¯2u
2n2r
ð1−r þð n−1 þ rÞsÞ
2
If products are imperfect substitutes, total demand increases if more consumers become aware of more
products. Hence, if the competition effect is “small” the demand effect may dominate. In particular, when
supply is very inelastic, output will only marginally increase with transparency. Furthermore, it can be
shown that dc ¯2
dr > 0, and dc ¯2
dn > 0. As goods become closer substitutes and as the number of firms
increases, the cost function needs to be more convex to get that a rise in τ raises prices. The intuition is
that for higher σ consumers have a weaker taste for variety and hence the demand effect is smaller. If there
are more firms, each firm is smaller and hence an increase in demand can be spread over more firms with
relatively lower marginal costs.
Finally, we have a look at welfare effects. Since the equilibrium level of quantities x
C is increasing in τ,
social welfare (defined as the sum of consumer and producer surplus) is also increasing in τ. This can be
seen as follows. Social welfare is here defined as consumer surplus minus production costs as a function
of output levels. The first derivative of welfare with respect to output of product i then equals the marginal
utility of good i minus the marginal cost of good i. In this case, consumers' marginal utility of good i
equals the price of good i. So the sign of the derivative of welfare with respect to the output level of good
i, equals the sign of pi−c1−c2xi
N which is positive. Furthermore, in those cases in which prices are
decreasing in τ, profits are decreasing and consumer surplus is increasing in τ. However, it is not
necessarily the case that consumers benefit from a rise in transparency. If supply is rather inelastic,
consumers may loose, despite the fact that total output increases. The intuition for this result is as follows.
A rise in τ has the two positive effects. First, it raises total output. Second, it increases the number of
informed agents who have higher utility than the uninformed agents. The first positive effect can be
reduced to zero by increasing c2. The second positive effect is outweighed by the loss in utility of both
informed and uninformed agents. These agents lose utility, because the increase in the number of
401 J. Boone, J. Pottersz / Economics Letters 93 (2006) 398–404informed agents raises demand for all goods and hence raises prices. Hence, if costs are very convex the
competition effect of transparency is limited and consumer welfare can fall as τ rises.
4. Conclusion
The impact of transparency on prices and consumer surplus is more subtle than conventional wisdom
seems to suggest. In our model an increase in transparency under some circumstances leads to an increase
in prices and a decrease in consumer surplus. These effects are due to, what we have called, the demand
effect of transparency. If goods are imperfect substitutes and consumers have a taste for variety, more
widespread information about the availability of goods wets consumers appetite and shifts demand
outward. This demand effect may counterbalance the downward pressure on prices due the competition
effect of transparency. This is more likely to happen if supply is relatively inelastic. Goods for which this
may be relevant include antiques, art, collectibles (such as, coins, stamps, toys, and sports cards),
memorabilia, and land. For example, for someone collecting ancient coins one coin is not a perfect
substitute for another coin. Compared to trading coins at fairs and local shops, we can expect that the
possibility to trade over the Internet makes more people aware of a wide supply of coins. Our model
suggests that this will lead to an increase in the demand for coins. Since the supply of ancient coins is
more or less fixed, this will lead to an increase in prices. We believe that this is an interesting hypothesis
that could, at least in principle, be tested empirically.
Acknowledgement
We acknowledge the helpful comments by a referee of this journal, by seminar participants at the
University of Virginia and by participants of the Encore workshop on Market Transparency and by
Tjalling de Vries in particular. We thank the Netherlands Organisation for Scientific Research (NWO) and
the Royal Netherlands Academy of Arts and Sciences (KNAW) for financial support (grant numbers
016.025.024, 453.03.606).
Appendix A. Proofs
Proof of Proposition 1. From pj
I(x1
I,…, xn
I, M)=pj
U(xj
U, M) it follows that xj
I+σ ∑k≠jxk
I=xj
U. Substitution
into sxI
j þ 1−s
n xU
j ¼ xj and rewriting yields
xI
j ¼
n
ns þð 1−sÞð1−rÞ
xj−
rð1−sÞ
ns þð 1−sÞð1−rÞ
X n
k¼1
xI
k ð4Þ
Substituting into the expression for the price yields
pj ¼ 1−2ð1−rÞxI
j−2r
X m
k¼1
xI
k ¼ 1−
2ð1−rÞn
ns þð 1−rÞð1−sÞ
xj− 2r−
2ð1−rÞrð1−sÞ
ns þð 1−rÞð1−sÞ
   X n
k¼1
xI
k
¼ 1−
2ð1−rÞn
ns þð 1−rÞð1−sÞ
xj−
2nrs
ns þð 1−rÞð1−sÞ
   X n
k¼1
xI
k
402 J. Boone, J. Pottersz / Economics Letters 93 (2006) 398–404Summation of Eq. (4) over j and rewriting gives
Pm
j¼1 xI
j ¼
n
ns þð 1−sÞð1−r þ rnÞ
Xn
j¼1 xj. Inserting
in the expression for pj gives
pj ¼ 1−
2ð1−rÞn
ns þð 1−rÞð1−sÞ
xj−
2n2rs
½ns þð 1−rÞð1−sÞ ½ns þð 1−sÞð1−r þ rnÞ 
X n
k¼1
xk
which corresponds to the expression in the Proposition. □
Proof of Proposition 2. The first order condition for xj is: 1−2βxj−γ∑i≠j xi−c2xj−c1=0. Hence in the
symmetric equilibrium we find that
xC ¼
1−c1
2b þ gðn−1Þþc2
To prove that dxC
ds > 0, we write the denominator of x
C as β+(β+γ(n−1)). From
Aðb þð n−1ÞgÞ
As
< 0
and
Ab
As < 0 it follows that dxC
ds > 0. □
Proof of Proposition 3. For the Cournot–Nash price we have
pC ¼ 1−ðb þð n−1ÞgÞxC ¼ 1−ð1−c1Þ
b þð n−1Þg
b þ gðn−1Þþb þ c2
¼ 1−ð1−c1Þ
1
1 þ
b þ c2
b þð n−1Þg
Hence
dpC
ds
> 0f
d
b þ c2
b þð n−1Þg
  
ds
> 0
The last inequality can be written as
db
ds
ðb þð n−1ÞgÞ−ðb þ c2Þ
dðb þð n−1ÞgÞ
ds
ðb þð n−1ÞgÞ
2 > 0
or equivalently
c2 > −b þð b þð n−1ÞgÞ
db
ds
  
dðb þð n−1ÞgÞ
ds
  
It is tedious but straightforward to verify that this can be written as
c2 > c ¯2 ¼
2rn2
ð1−r þð n−1 þ rÞsÞ
2 □
403 J. Boone, J. Pottersz / Economics Letters 93 (2006) 398–404References
Janssen, Maarten, Moraga, Jose, 2000. Consumer Search and the Size of Internet Markets, Tinbergen Institute Discussion Paper
2000–0042/1.
Møllgaard, Peter,Overgaard,Per, 2000.Market Transparency: AMixed Blessing? Working paper,Copenhagen Business School.
Nilsson, Arvid, 1999. Transparency and Competition, working paper, Stockholm School of Economics.
Schultz, Christian, 2004. Market transparency and product differentiation. Economics Letters 83, 173–178.
Schultz, Christian, 2005. Transparency on the consumer side and tacit collusion. European Economic Review 49, 279–297.
Varian, Hal R., 1980. A model of sales. American Economic Review 70 (4), 651–659.
404 J. Boone, J. Pottersz / Economics Letters 93 (2006) 398–404

Transparency, prices and welfare with imperfect substitutes.

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