DOCUMENTS DE RECHERCHE WORKING PAPERS – N° 01025

CENTRE
DE RECHERCHE
RESEARCH CENTER
DOCUMENTS DE RECHERCHE
WORKING PAPERS
– N° 01025 –
Quality Uncertainty and Welfare in a Search Economy
Damien BESANCENOT
University of Panthéon-Assas (Paris) and ERMES
Radu VRANCEANU
ESSEC, Department of Economics
October 2001
GROUPE ESSEC
CERNTRE DE RECHERCHE / RESEARCH CENTER
AVENUE BERNARD HIRSCH - BP 105
95021 CERGY-PONTOISE CEDEX FRANCE
TÉL. : 33 (0) 1 34 43 30 91
FAX : 33 (0) 1 34 43 30 01
Mail : [email protected]
GROUPE ESSEC,
ÉTABLISSEMENTS PRIVÉS D'ENSEIGNEMENT SUPÉRIEUR,
ASSOCIATION LOI 1901,
ACCRÉDITÉ AACSB - THE INTERNATIONAL ASSOCIATION
FOR MANAGEMENT EDUCATION,
AFFILIÉ A LA CHAMBRE DE COMMERCE ET D'INDUSTRIE
DE VERSAILLES VAL D'OISE - YVELINES.
WEB : WWW.ESSEC.FR
October 4, 2001
QUALITY UNCERTAINTY AND WELFARE IN A SEARCH
ECONOMY
Damien Besancenot¤ and Radu Vranceanuy
Abstract
Equilibrium search models carried a step further the neoclassical analysis of decentralized economies,
by formalizing in an explicit way the acquisition of price information as a costly activity. In a
classical study, Peter Diamond proved that a search economy hosting homogenous agents cannot
reach spontaneously the Walrasian equilibrium: to the contrary, the resulting equilibrium has rather
dramatic implications in terms of welfare, as …rms post a single monopoly price and reap all consumers’
surplus. In this paper, we show that additional uncertainty on product quality may bring about a
Pareto-improved allocation in the search economy. If at least some …rms want to satisfy the demand
of their more skeptical clients, they will post a low price, to the bene…t of the other consumers.
Several types of Nash equilibria are put forward: one of them presents a non-degenerated distribution
of prices.
JEL Classi…cation: L15, D83, D62
Key words: Quality, Imperfect information, Equilibrium search, Welfare.
¤
Université Panthéon-Assas (Paris 2) and ERMES, 92 rue d’Assas, 75270 Paris. Email: [email protected].
y
ESSEC, Department of Economics, BP 105, 95021 Cergy Pontoise, France. Email: [email protected]
1
Introduction
Trade coordination in decentralized economies requires an ongoing process of information
gathering, sorting and processing. In particular, consumers need time and sometimes use
their shoe soles to learn prices posted by spatially separated sellers. The neoclassical paradigm
has been for years subject to criticism for paying lip service to this essential feature of contemporary decentralized economies (Stiglitz, 1994). When economists …nally addressed this
issue and introduced small costs of acquiring price information in models of exchange, they
found out that the spontaneous emergence of the much celebrated Walrasian equilibrium can
no longer be taken for granted.1
For instance, in a classical paper, Peter Diamond has shown that in a one-good economy
where homogenous consumers search for the lowest price, homogenous …rms should post a
single price, equal to consumer’s willingness-to-pay (Diamond, 1971). Indeed, if search is a
costly activity, a …rm that charges a price slightly higher than its rivals would not lose its
customers. In equilibrium, all …rms post the highest price, similar to the monopoly price.
Such a situation is damageable for consumers, as their surplus is completely whipped o¤;
furthermore, in a free entry environment, …rms make zero pro…ts too. However, several
authors put forward the possibility of non-degenerated distributions of prices and of positive
gains from trade, provided that some heterogeneity is introduced into the original model (e.g.
Salop and Stiglitz, 1977; Reinganum, 1979; Diamond, 1987).2
This paper follow this path of research to analyze the equilibrium distribution of prices
and welfare in a standard search economy where at least some of the consumers cannot
1
Traditional studies in the economics of information are Stigler (1961) and McCall (1970). Economies
with decentralized trade were analyzed in well-known papers by Lucas (1972, 1973). Other founding papers
were gathered by Phelps (1970).
2
For instance, consumers may di¤er in their willingness-to-pay or may incur di¤erent search costs; …rms
may also have di¤erent technologies and bear di¤erent production costs.
1
correctly asses the intrinsic quality of the traded good. Consumers may face computing
di¢culties in assessing total quality of complex products.3
Sometimes …rms proceed to
technology-driven quality ameliorations. When the quality of an existing product changes,
consumers may be victims of “quality illusion” as they asses more or less correctly the
true quality level. In this line of reasoning, Nelson (1970) argued why consumers could not
correctly asses the quality of a wide class of “experience” goods, at least not before consuming
them.
In the model, a continuum of …rms and consumers engage in the decentralized trade of a
unit good of given intrinsic quality. Consumers search for the best o¤er in terms of price and
quality. If all consumers perceive correctly the true quality level, Diamond’s paradox holds:
all …rms charge the single monopoly price, and reap all consumers surplus. To the opposite,
if consumers di¤er in their quality perception, they become “heterogenous”. Hence, di¤erent
consumers have a di¤erent willingness-to-pay and a di¤erent reservation price. Firms are
aware of the distribution of reservation prices and can choose to discriminate against one
category of consumers by setting a price higher than their reservation price. We put forward
three types of Nash equilibria, in keeping with the degree of consumer confusion. Two of
them are pure-strategy equilibria, the other is a mixed-strategy equilibrium, where, although
a single quality good is sold, some …rms decide to post a low price, while the other post a
higher price.
Under our assumptions, the amount of quality uncertainty is shown to have a signi…cant
impact on economic activity (broadly de…ned as the number of successful transactions in
this economy), the number of …rms in the market and the equilibrium distribution of prices.
Furthermore, in this model consumers may bene…t from a certain degree of confusion: in
3
The paper may therefore be related to the literature on bounded rationality, according to which humans
have only a limited ability to evaluate complex situations (Simon, 1987).
2
order to satisfy the demand of the consumers with the low reservation price, in equilibrium
some …rms would post a low price, which is bene…cial to consumers with a high willingnessto-pay. This result contrasts with the …ndings of Glass (2001), who analyses a qualityimproving shock in a horizontal di¤erentiation model with heterogenous consumers in terms
of subjective valuation of quality. In this alternative context, consumer utility may decline
when quality uncertainty increases, as oligopolistic …rms collude to discriminate against
the various consumer types.4
Our opposite conclusion depends on the basic assumptions
related to the information structure of the economy; it matches the results of other studies
by Diamond (1993), Diamond and Felli (1992) or Besancenot et al. (2000) who showed that,
in a search economy, nominal shocks may erode the …rm market power and bring about
a Pareto-improved allocation. In all these models, additional uncertainty would o¤set the
perverse e¤ects on welfare stemming from price uncertainty speci…c to the search economy.
The paper is organized as follows. Section 2 introduces main assumptions, then analyzes
consumers’ optimal decision rules and the price-setting strategy of the …rms. Section 3
presents the typology of equilibria and comment on their basic features. The last section
summarizes our conclusions.
2
The model
The economy is made up of a continuum of …rms and a continuum of consumers. The measure
of consumers is normalized to unity, whereas the (endogenous) measure of …rms is equal to n.
Consumers’ search for the lowest price is sequential; they receive only one o¤er per period. If
an o¤er is accepted, the buyer leaves the market and is replaced by another customer during
the next period. Firms set prices according to a “take-it-or-leave-it” procedure (they display
binding prices before meeting consumers). Firms are free to enter the market and do it as
4
She admits that an o¤setting e¤ect may be at work if pro…ts are reinvested in future quality ameliorations.
3
long as their expected pro…ts are positive. All …rms in operation incur a positive lump-sum
cost per period. Firms produce a unit good of a homogenous quality q: This quality is private
information for …rms.
2.1
Consumer utility
The indirect utility function of the representative consumer who knows the true quality level
is:
U (t; p) = ¯ t (µq ¡ p);
(1)
where p is the price of the good, ¯ 2 ]0; 1[ is the psychological discount rate and t is the period
at which the good is consumed. The product µq can be interpreted as the willingness-to-pay
for the quality q.
If consumers do not know the true quality q, they must utilize a subjective estimate as
a decision guide. We denote by qi the perceived quality by individual i. Di¤erences between
the true and the perceived quality index may occur in the case of complex products because
bounded rational people cannot process all the relevant information. Or it may happen after
a quality-improving shock, merely because people do not know the intrinsic quality of the
new product (at least, not before consuming it).5 In this case, consumer willingness-to-pay
becomes µqi and the utility function of individual i; who consumes the commodity after t
periods, takes the form:
U i (t; qi ; p) = ¯ t(µqi ¡ p);
i 2 [0; 1]:
(2)
Utility depends in an essential way on qi; for a given price, the higher is the perceived quality,
the higher is consumer’s satisfaction.
5
In an alternative approach, variations in q would be related to consumers’ di¤erent sub jective valuations
of quality (Glass, 2001).
4
2.2
Consumer strategies
The set of prices charged by …rms is S (a subset of R+ ). Let us denote by F the probability
measure of prices. Following Sargent (1987), the discounted expected utility of consumer i
who has o¤er p in hand is denoted by V i(p) and obeys the following Bellman equation:
½
¾
Z
i
i
V (p) = max µq ¡ p; ¯ V dF ;
i
8p 2 S;
(3)
where V i(¢) is de…ned on S and depends on perceived quality by consumer i. The consumer
can either buy the good at the price p (in this case his instantaneous utility is qµ i ¡ p) or
keep on searching for a lower price for at least one more period (in this case his expected
R
utility is ¯ V i dF). Equation (3) tells us that the rational consumer chooses the best of the
two alternatives.
Given that the second term in brackets of Eq.(3) is constant, and that the …rst term
decreases in p, the consumer optimal strategy consists in selecting a reservation price pi;r
and accepting all o¤ers below this reservation price. The value function V i (¢) has then the
following expression:
8
>
>
< µqi ¡ p if p · p i;r
i
V (p) =
Z
>
>
: ¯ V idF if p > p i;r
(4)
A consumer receiving an o¤er equal to his reservation prices is indi¤erent between taking
this o¤er or continuing to search. Thus, the reservation price of the consumer i is implicitly
de…ned by:
i
i;r
µq ¡ p
=¯
Z
V idF;
(5)
where the left hand term of Eq.(5) indicates the utility of the individual accepting the o¤er
p i;r , and the right hand term indicates his expected utility if he decides to search for at least
one more period.
5
Let us suppose that S is continuous and that F admits a density function. We denote
F (¢) the cumulative distribution derived from F. After some calculations, the right hand
term of Eq.(5) takes the equivalent expression:
(
µqi ¡ p i;r = ¯ (µqi ¡ p i;r ) +
In this form, the integral
R
Z
fp·pi;r g
)
(pi;r ¡ p)dF(p) :
(6)
V i dF, indicating the expected gain from an additional search, is
written as the sum of the utility of a individual who accepts the o¤er pi;r and an expected
bonus from successful search activity. The presence of a discount factor (¯) explains why
for the optimal reservation price the individual is indi¤erent between taking this o¤er or
continuing to search. (Further inspection of this equation also shows that the solution should
be a positive reservation price.)
Di¤erentiating Eq.(6) allows us to infer an important relationship between the perceived
level of quality and the reservation price:
@pi;r
µ(1 ¡ ¯)
=
> 0:
i
@q
1 ¡ ¯(1 ¡ F (p i;r ))
(7)
The reservation price is thus a increasing function in the perceived quality level. A high
quality index implies a high reservation price and conversely. We emphasize that this result
also holds when S is a discrete set.
In order to simplify the analysis, it is assumed that only two types of agents exist:
a fraction ¸ of the population is made of “L¡consumers” characterized by a perceived low
quality level, qL; a fraction (1¡¸) of the population is made of “H¡consumers” characterized
by a perceived high quality level, qH (with qL < qH ): The ratio q H=qL can be interpreted
as a proxy for the degree of consumer confusion in this economy; it will prove to be an
important variable latter on. Situations as various as qL < q · qH (enthusiasts are right) or
qL · q < qH (pessimistic are right) are consistent with the model.
6
Then, in keeping with the result of Eq.(7), we denote by pH r the reservation price of
the H ¡consumers and by p Lr the reservation price of the L¡consumers. In this case the
probability measure G of the reservation prices is:
G = ¸±fpLr g + (1 ¡ ¸)±fpH rg :
(8)
where ±fxg indicates the Dirac measure at point x. Let denote G the cumulative distribution
inferred from G.
2.3
Pricing strategies of the …rms
As assumed, …rms incur a real lump-sum cost c per period to participate to the market.
This cost might be interpreted as a licence fee which is indexed on the general price level.
Therefore, this cost (in nominal terms) can be written as p¹c; where p¹ is the average price in
this economy. Consumers are uniformly distributed among …rms during each time period.
Let m = 1=n be the (large) number of consumers per …rm. The expected pro…t equation is:
¼(p) = ¡¹
pc + mp [1 ¡ G(p)]
h
i
= ¡¹
pc + mp (1 ¡ ¸)1fpLr<p·pH rg + ¸1fp·pLrg
(9)
The quantity sold is nil if p > pHr , is equal to (1 ¡ ¸)m if pLr < p · pHr and is equal to m
if p · p Lr :
Firms are pro…t-maximizers. Each …rm chooses its optimal price, taking as given the
prices posted by competitors. Then, the optimal price is solution to:
p¤ = arg max f¼(p)g
p
The price p > p Hr will never be chosen by a rational …rm as it involves negative pro…ts.
Strategy 1: A …rm which plans to sell (1 ¡ ¸)m must choose a price in the range pLr <
p · pHr ; obviously, the optimal price is pH r .
7
Strategy 2 : A …rm which would sell m chooses a price in the range p · pLr , the optimal
price is thus pLr :
Let us denote by s 2 [0; 1] the fraction of …rms posting the low reservation price p Lr :
The price distribution is then given by:
F = s±fpLr g + (1 ¡ s)±fpH rg
(10)
The two extreme cases s = 0 and s = 1 imply a degenerated price distribution.
2.4
Explicit reservation prices
Firstly, we determine the reservation price of consumers who perceive a low quality level
(L¡consumers). The (low) reservation price pLr is implicitly de…ned by Eq.(5), which becomes:
©
¡ ¢
¡
¢ª
µqL ¡ pLr = ¯ sV L pLr + (1 ¡ s)V L p Hr
©
ª
= ¯ s(µqL ¡ p Lr ) + (1 ¡ s)(µqL ¡ pLr )
(11)
Eq.(11) can be solved for the reservation price:
p Lr = µqL
(12)
In equilibrium, the surplus of the L¡consumers is zero.
Next, we calculate the explicit reservation price of consumers who perceive a high quality
(H¡consumers). Their (high) reservation price p Hr is implicitly de…ned by Eq.(5):
©
¡ ¢
¡
¢ª
µqH ¡ pH r = ¯ sV H pLr + (1 ¡ s)V H pHr
The reservation price is:
©
ª
= ¯ s(µqH ¡ pLr ) + (1 ¡ s)(µqH ¡ pHr )
pHr = µqH ¡
µ¯s
(qH ¡ qL)
1 ¡ ¯(1 ¡ s)
This last equation shows that for s > 0; the H ¡consumer gets a positive surplus.
8
(13)
(14)
2.5
The welfare function
In the purpose of parsimony, the equilibrium analysis in terms of welfare will build on an utilitarian welfare function, which plainly sums …rm pro…ts and surpluses of various consumers.
But under the free entry condition pro…ts are nil, thus social welfare and consumer surplus
coincide. With two types of consumers, social welfare W can be written as the weighted sum
of expected surpluses:
©
ª
©
ª
W = ¸ µqL ¡ p Lr + (1 ¡ ¸) µqH ¡ p Hr
(15)
where the two terms between brackets are respectively the expected utility of an L¡consumer
entering the market and the expected utility of a H¡consumer (they have no o¤er in hands
yet). According to Eq.(12) µqL ¡ pLr = 0; thus the welfare function depends only on the
H ¡consumers surplus:
©
ª
W = (1 ¡ ¸) µqH ¡ pHr
(16)
Finally, in keeping with Equation (14), the welfare function can be written in an alternative
way as:
W=
(1 ¡ ¸)µ¯s H
(q ¡ qL)
1 ¡ ¯(1 ¡ s)
(17)
which is positive whenever s > 0 and ¸ < 1:
3
Equilibria
An equilibrium is a situation in which the strategies of consumers and …rms are mutually
consistent. Consumers’ strategies are summarized by their reservation prices. Firms choose
a price such as to maximize pro…ts, taking as given the decisions of the other …rms. In
equilibrium, a …rm which deviates from the generalized strategy would incur a loss. For
a given fraction ¸ of L¡consumers, three types of equilibria may occur contingent on the
9
relative gap between the high and the low levels of perceived quality.6
3.1
Pure strategy equilibrium s = 1: all …rms post pLr
If all …rms follow the pure strategy p = pLr ; s = 1 and, according to Eq. (9), the pro…t of
each one is:
¼ s=1(pLr ) = mpLr ¡ p¹c
(18)
= mµqL ¡ pc
¹
(19)
where the average price is p¹ = µqL : If a …rm deviates from this strategy and charges pHr , its
pro…t would be:
¼ s=1(pHr ) = m(1 ¡ ¸)pHr ¡ p¹c
(20)
where p Hr is given by Eq.(14).
The situation in which all …rms post the price p Lr is a Nash equilibrium if and only if
¼ s=1(pHr ) < ¼ s=1(pLr ); i.e. no …rm can gain from unilaterally deviating (i.e. from charging
a high reservation price):
qH
1 ¡ ¯(1 ¡ ¸)
·
L
q
(1 ¡ ¸)(1 ¡ ¯)
(21)
(see also Figure 1).
According to condition (21), …rms decide to post the low reservation price and to sell the
largest quantity (that is m) when the gap between the high and the low perceived quality is
“small” or when the proportion ¸ of L¡consumers is “high”. No …rm would post a high price
because the positive e¤ect on pro…ts of the price increase does not compensate the adverse
e¤ect of the reduction in the quantity sold.
According to Eq. (9), pro…t per …rm is an increasing function in the measure of consumers
per …rm m; or, given that m = 1=n; a decreasing function in the measure of …rms n. By
6
The restrictive assumption of a predetermined ¸ facilitates the understanding while not altering the main
insights. Of course, the three regimes may be characterized if both q H =qL and ¸ were allowed to vary: The
three equilibria should then be depicted in a two dimensional space.
10
assumption, …rms freely enter this market as long as they obtain positive pro…ts. Hence,
pro…ts in equilibrium must be nil: ¼s=1(pLr ) = 0. Replacing m by 1=n and p¹ by µqL in
Eq.(18), then equating pro…ts to zero, we get Eq.(22) which de…nes the measure of …rms in
the economy:
n = 1=c
(22)
In the post-reform equilibrium, the economic activity (number of successful transactions)
and the number of …rms are unchanged.
According to Eq. (17), social welfare is equal to:
Ws=1 = ¯µ(1 ¡ ¸)(qH ¡ qL)
(23)
In keeping with the utilitarian criterion, this equilibrium is better than the perfect information equilibrium where qH = qL = q. Social welfare increases with the fraction (1 ¡ ¸) of the
H ¡consumers and with the di¤erence between the two perceived levels of quality.
3.2
Pure strategy equilibrium s = 0 : all …rms post pHr
If all …rms adopt the pure strategy p = pHr ; s = 0. Then, according to Eq.(13), the
reservation price of the H ¡consumers is: pHr = µqH : The nominal pro…t of each …rm is
then:
¼ s=0(pHr ) = m(1 ¡ ¸)p Hr ¡ p¹c
= m(1 ¡ ¸)µqH ¡ p¹c:
(24)
(25)
where p¹ = p Hr : If a …rm deviates from this strategy and charges pLr ; (i.e. the reservation
price of L¡consumers), its pro…t becomes:
¼ s=0(pLr ) = mµqL ¡ p¹c
11
The equilibrium where all …rms post pHr is individually rational if and only if ¼s=0(pHr ) ¸
¼ s=0(pLr ); that is:
qH
1
¸
L
q
1 ¡¸
(26)
According to condition (26), …rms decide to post the high reservation price and sell only the
quantity (1 ¡ ¸)m when the gap between the high and the low levels of perceived quality is
“large”.
Under the free entry condition, pro…ts are driven to zero: ¼s=0(pHr ) = 0. Setting pro…ts
de…ned by Eq.(24) to zero we obtain Eq.(27) which de…nes the measure of …rms:
1 ¡¸
c
n=
(27)
The activity level and the number of …rms is lower in this case than in the previous one.
In this case, W s=0 = 0: there is no welfare improvement as compared to the perfect
information case. H¡consumers have a zero surplus and L¡consumers inde…nitely postpone
their purchases: they have a zero surplus too.
3.3
Nash equilibrium in mixed-strategy: 0 < s < 1
In Figure 1, we show the interval for which either equilibrium s = 0 or equilibrium s = 1
may emerge.
Strategy 1: p=p L
1
1
1−λ
Mixed-strategy
1−β(1−λ)
(1−λ)(1−β)
Strategy 2: p=p H
Figure 1: Pure and mixed-strategy equilibria
12
qH /qL
As
1
1 ¡ ¯(1 ¡ ¸)
<
; if
1 ¡ ¸ (1 ¡ ¸)(1 ¡ ¯)
·
¸
qH
1
1 ¡ ¯(1 ¡ ¸)
2
;
qL
1 ¡ ¸ (1 ¡ ¸)(1 ¡ ¯)
(28)
both equilibria are possible.
In this case, the next logical step is to study the Nash equilibrium in mixed-strategy
associated to this interval where a fraction s < 1 of …rms post pLr ; while the other (1 ¡ s)
post p Hr :
From Equation (9), the pro…t of a …rm posting pLr is:
¼s2(0;1) (pLr ) = mpLr ¡ pc
¹
(29)
and the pro…t of a …rm posting pHr is:
¼ s2(0;1) (pHr ) = m(1 ¡ ¸)pHr ¡ pc
¹
(30)
In equilibrium, the pro…t of a …rm posting pLr should be equal to the pro…t of a …rm posting
p Hr : Equality:
¼ s2(0;1) (p Lr ) = ¼s2(0;1) (p Hr )
(31)
p Lr = (1 ¡ ¸)pHr
(32)
is similar to:
µ¯s
Replacing pLr = µqL and pHr = µqH ¡ 1¡¯(1¡s)
(qH ¡qL); after a few calculations, we obtain:
s=
µ ¶µ
¶· H
¸
1
1 ¡¯
q
(1
¡
¸)
¡
1
¸
¯
qL
(33)
which is an increasing function in (qH =qL ):
·
¸
1
1 ¡ ¯(1 ¡ ¸)
H L
It can be checked that q =q 2
;
) s 2 [0; 1]:
(1 ¡ ¸) (1 ¡ ¸)(1 ¡ ¯)
The level of activity in the mixed strategy case is higher than in the pure-strategy equi-
librium s = 0 but lower than in the pure strategy equilibrium s = 1; …rms match only a
fraction 1 ¡ ¸(1 ¡ s) of the total demand.
13
In the mixed-strategy equilibrium the average price is:
p¹ = spLr + (1 ¡ s)pHr
(34)
Under the free entry condition, ¼ s2(0;1) (p Lr ) = 0; thus:
m
pLr
= c;
p¹
(35)
and given that in keeping with Equation (32) pH r =pLr = 1=(1 ¡ ¸); the measure of …rms is:
1
n=
c
µ
1¡ ¸
1 ¡ ¸s
¶
(36)
As expected, the number of …rms in the mixed-strategy equilibrium is now between the
number of …rms in the two pure-strategy equilibria.
Replacing in Equation (17) the value of s such as de…ned in Equation (33), social welfare
is equal to:
W s2(0;1) = µf(1 ¡ ¸)qH ¡ qLg
(37)
Given conditions (21) and (26), it can be checked that 0 · W s2(0;1) · Ws=1 :
In this intermediate region, consumers get a positive surplus if the pure-strategy equilibrium s = 1 occurs; they are also better-o¤ (compared with the no uncertainty case) if the
mixed-strategy equilibrium emerges. If at least some …rms post a low price in order to retain
the most skeptical clients, (some of) the other consumers may get a positive surplus.
4
Conclusion
This paper analyzed how imperfect information on quality in‡uences the equilibrium allocation of goods in a search economy. The basic setting follows Diamond (1971) in considering
a large number of consumers searching for the lowest price. In the presence of search costs
and no uncertainty about the quality of the traded good, …rms post the monopoly price and
reap all consumer surplus. In the model at hand, suboptimal behavior of some consumers
14
may generate a positive externality for the others if the wedge between the high and the low
perceived quality levels is not too signi…cant. For instance, if some consumers underestimate
the quality level in use and consequently choose a low reservation price, …rms may want to
post a low price such as to match their demand. In this case, the other consumers …nd prices
that are lower than their own reservation price and get a positive surplus.
A mixed-strategy equilibrium may also emerge if the degree of consumer confusion is
neither too weak, nor too strong. In this case, the distribution of prices is not degenerated:
…rms will post di¤erent prices for a single quality item. Among those consumers who think
(be them right or not) that the quality has improved, some of them may “got a bargain” if
they have the chance to buy the good for a price lower than their willingness-to-pay.
Contrary to a widespread belief, additional uncertainty on product quality may bring
about a Pareto-improved allocation in the typical search economy where consumers spend
time to gather price information. If the Walrasian auctioneer is on leave, a not too important
doze of quality uncertainty may improve social welfare.
5
References
Besancenot, Damien, Guillaume Rocheteau and Radu Vranceanu, 2000, Search, price illusion
and welfare, Journal of Macroeconomics, 22, 1, pp. 109-124.
Diamond, Peter A., 1993, Search, sticky prices, and in‡ation, Review of Economic Studies,
60, pp. 53-68.
Diamond, Peter A., 1987, Consumer di¤erences and prices in a search model, Quarterly
Journal of Economics, 102, pp. 429-436.
Diamond, Peter A., 1971, A model of price adjustment, Journal of Economic Theory, 3, pp.
156-168.
Diamond, Peter A. and Leonardo Felli, 1992, Search, sticky prices and de‡ation, MIT
15
(mimeo).
Glass, Amy J., 2001, Price discrimination and quality improvement, Canadian Journal of
Economics, 34, 2, pp. 549-569.
Lucas, Robert E., 1973, Some international evidence on the output-in‡ation trade-o¤s, American Economic Review, 63, pp. 326-334.
Lucas, Robert E., 1972, Expectations and the neutrality of money, Journal of Economic
Theory, 4, pp. 103-124.
McCall, John J., 1970, Economics of information and job search, Quarterly Journal of Economics, 84, pp. 113-126.
Nelson, Phillip, 1970, Information and consumer behavior, Journal of Political Economy, 78,
pp. 311-329.
Phelps, Edmund S., 1970, The New Microeconomics in In‡ation and Unemployment Theory,
W.W.Norton, New York.
Reinganum, Jennifer, 1979, A simple model of equilibrium price dispersion, Journal of Political Economy, 87, pp. 851-858.
Salop, Steven and Joseph E. Stiglitz, 1977, Bargains and ripo¤s: a model of monopolistically
competitive price distortion, Review of Economic Studies, 44, pp. 493- 510.
Sargent, Thomas, 1987, Dynamic Macroeconomic Theory, Harvard University Press.
Simon, Herbert, 1987, Bounded rationality, The New Palgrave: A Dictionary of Economics,
vol.1., eds. John Eatwell, Murray Milgate and Peter Newman, London, Macmillan, pp.
266-268.
Stigler, George, J., 1961, The economics of information, Journal of Political Economy, 69, 3,
pp. 213-215.
Stiglitz, Joseph E., 1994, Wither socialism?, MIT Press, Cambridge and London.
16
ESSEC
CE NTRE
DE RECHERCHE
LISTE DES DOCUMENTS DE RECHERCHE DU CENTRE DE RECHERCHE DE L’ESSEC
(Pour se procurer ces documents, s’adresser au CENTRE DE RECHERCHE DE L’ESSEC)
LISTE OF ESSEC RESEARCH CENTER WORKING PAPERS
(Contact the ESSEC RESEARCH CENTER for information on how to obtain copies of these papers)
[email protected]
1997
97001 BESANCENOT D., VRANCEANU Radu
Reputation in a Model of Economy-wide Privatization.
97002 GURVIEZ P.
The Trust Concept in the Brand-consumers Relationship.
97003 POTULNY S.
L’utilitarisme cognitif de John Stuart Mill.
97004 LONGIN François
From Value at Risk to Stress Testing: The Extreme Value Approach.
97005 BIBARD Laurent, PRORIOL G.
Machiavel : entre pensée du pouvoir et philosophie de la modernité.
97006 LONGIN François
Value at Risk: une nouvelle méthode fondée sur la théorie des valeurs extrêmes.
97007 CONTENSOU François, VRANCEANU Radu
Effects of Working Time Constraints on Employment: A Two-sector Model.
97008 BESANCENOT D., VRANCEANU Radu
Reputation in a Model of Exchange Rate Policy with Incomplete Information.
97009 AKOKA Jacky, BRIOLAT Dominique, WATTIAU Isabelle
La reconfiguration des processus inter-organisationnels.
97010 NGUYEN. P
Bank Regulation by Capital Adequacy and Cash Reserves Requirements.
97011 LONGIN François
Beyond the VaR.
97012 LONGIN François
Optimal Margin Level in Futures Markets: A Method Based on Extreme Price Movements.
97013 GROUT DE BEAUFORT Viviane
Maastricth II ou la copie à réviser.
97014 ALBIGOT J.G., GROUT DE BEAUFORT V., BONFILLON P.O., RIEGER B .
Perspectives communautaires et européennes sur la réduction du temps de travail.
97015 DEMEESTERE René, LORINO Philippe, MOTTIS Nicolas
Business Process Management: Case Studies of Different Companies and Hypotheses for Further
Research.
Page 1
97016 PERETTI Jean-Marie, HOURQUET P.G., ALIS D.
Hétérogénéité de la perception des déterminants de l’équité dans un contexte international.
97017 NYECK Simon, ROUX Elyette
WWW as a Communication Tool for Luxury Brands: Compared Perceptions of Consumers and
Managers.
97018 NAPPI-CHOULET Ingrid
L’analyse économique du fonctionnement des marchés immobiliers.
97019 BESANCENOT D., ROCHETEAU G., VRANCEANU Radu
Effects of Currency Unit Substitution in a Search Equilibrium Model.
97020 BOUCHIKHI Hamid
Living with and Building on Complexity: A Constructivist Perspective on Organizations.
97021 GROUT DE BEAUFORT V., GRENOT S., TIXIER A . TSE K.L
Essai sur le Parlement Européen.
97022 BOULIER J.F., DALAUD R., LONGIN François
Application de la théorie des valeurs extrêmes aux marchés financiers.
97023 LORINO Philippe
Théorie stratégique : des approches fondées sur les ressources aux approches fondées sur les processus.
97024 VRANCEANU Radu
Investment through Retained Earnings and Employment in Transitional Economies.
97025 INGHAM M., XUEREB Jean-Marc
The Evolution of Market Knowledge in New High Technology Firms: An Organizational Learning
Perspective.
97026 KOENING Christian
Les alliances inter-entreprises et la coopération émergente.
97027 LEMPEREUR Alain
Retour sur la négociation de positions : pourquoi intégrer l’autre dans mon équation personnelle ?
97028 GATTO Riccardo
Hypothesis Testing by Symbolic Computation.
97029 GATTO Riccardo , JAMMALAMADAKA S. Rao
A conditional Saddlepoint Approximation for Testing Problems.
97030 ROSSI (de) F.X., GATTO Riccardo
High-order Asymptotic Expansions for Robust Tests.
97031 LEMPEREUR Alain
Negotiation and Mediation in France: The Challenge of Skill-based Learnings and Interdisciplinary
Research in Legal Education.
97032 LEMPEREUR Alain
Pédagogie de la négociation : allier théorie et pratique.
97033 WARIN T.
Crédibilité des politiques monétaires en économie ouverte.
97034 FRANCOIS P.
Bond Evaluation with Default Risk: A Review of the Continuous Time Approach.
97035 FOURCANS André, VRANCEANU Radu
Fiscal Coordination in the EMU: A Theoretical and Policy Perspective.
97036 AKOKA Jacky, WATTIAU Isabelle
MeRCI: An Expert System for Software Reverse Engineering.
97037 MNOOKIN R. (traduit par LEMPEREUR Alain)
Page 2
Surmonter les obstacles dans la résolution des conflits.
97038 LARDINOIT Thierry, DERBAIX D.
An Experimental Study of the Effectiveness of Sport Sponsorship Stimuli.
97039 LONGIN François, SOLNIK B.
Dependences Structure of International Equity Markets during Extremely Volatile Periods.
97040 LONGIN François
Stress Testing : application de la théorie des valeurs extrêmes aux marchés des changes.
1998
98001 TISSOT (de) Olivier
Quelques observations sur les problèmes juridiques posés par la rémunération des artistes interprètes.
98002 MOTTIS Nicolas, PONSSARD J.P.
Incitations et création de valeur dans l’entreprise. Faut-il réinventer Taylor ?
98003 LIOUI A., PONCET Patrice
Trading on Interest Rate Derivatives and the Costs of Marking-to-market.
98004 DEMEESTERE René
La comptabilité de gestion : une modélisation de l’entreprise ?
98005 TISSOT (de) Olivier
La mise en œuvre du droit à rémunération d’un comédien ayant « doublé » une œuvre audiovisuelle
er
(film cinématographique ou fiction télévisée ) avant le 1 janvier 1986.
98006 KUESTER Sabine, HOMBURG C., ROBERTSON T.S.
Retaliatory Behavior to New Product Entry.
98007 MONTAGUTI E., KUESTER Sabine, ROBERTSON T.S.
Déterminants of « Take-off » Time for Emerging Technologies: A Conceptual Model and Propositional
Inventory.
98008 KUESTER Sabine, HOMBURG C .
An Economic Model of Organizational Buying Behavior.
98009 BOURGUIGNON Annick
Images of Performance: Accounting is not Enough.
98010 BESANCENOT D., VRANCEANU Radu
A model of Manager Corruption in Developing Countries with Macroeconomic Implications.
98011 VRANCEANU Radu, WARIN T.
Une étude théorique de la coordination budgétaire en union monétaire.
98012 BANDYOPADHYAU D. K.
A Multiple Criteria Decision Making Approach for Information System Project Section.
98013 NGUYEN P., PORTAIT Roland
Dynamic Mean-variance Efficiency and Strategic Asset Allocation with a Solvency Constraint.
98014 CONTENSOU François
Heures supplémentaires et captation du surplus des travailleurs.
98015 GOMEZ M.L.
De l’apprentissage organisationnel à la construction de connaissances organisationnelles.
98016 BOUYSSOU Denis
Using DEA as a Tool for MCDM: some Remarks.
98017 INDJEHAGOPIAN Jean-Pierre, LANTZ F., SIMON V.
Page 3
Dynamique des prix sur le marché des fiouls domestiques en Europe.
98019 PELISSIER-TANON Arnaud
La division du travail, une affaire de prudence.
98020 PELISSIER-TANON Arnaud
Prudence et qualité totale. L’apport de la philosophie morale classique à l’étude du ressort psychologique
par lequel les produits satisfont les besoins de leurs utilisateurs.
98021 BRIOLAT Dominique, AKOKA Jacky, WATTIAU Isabelle
Le commerce électronique sur Internet. Mythe ou réalité ?
98022 DARMON René
Equitable Pay for the Sales Force.
98023 CONTENSOU François, VRANCEANU Radu
Working Time in a Model of Wage-hours Negociation.
98024 BIBARD Laurent
La notion de démocratie.
98025 BIBARD Laurent
Recherche et expertise.
98026 LEMPEREUR Alain
Les étapes du processus de conciliation.
98027 INDJEHAGOPIAN Jean-Pierre, LANTZ F., SIMON V.
Exchange Rate and Medium Distillates Distribution Margins.
98028 LEMPEREUR Alain
Dialogue national pour l’Europe. Essai sur l’identité européenne des français.
98029 TIXIER Maud
What are the Implications of Differing Perceptions in Western, Central and Eastern Europe for Emerging
Management.
98030 TIXIER Maud
Internal Communication and Structural Change. The Case of the European Public Service: Privatisation
And Deregulation.
98031 NAPPI-CHOULET Ingrid
La crise des bureaux : retournement de cycle ou bulle ? Une revue internationale des recherches.
98032 DEMEESTERE René
La comptabilité de gestion dans le secteur public en France.
98033 LIOUI A., PONCET Patrice
The Minimum Variance Hedge Ratio Revisited with Stochastic Interest Rates.
98034 LIOUI A., PONCET Patrice
Is the Bernoulli Speculator always Myobic in a Complete Information Economy?
98035 LIOUI A., PONCET Patrice
More on the Optimal Portfolio Choice under Stochastic Interest Rates.
98036 FAUCHER Hubert
The Value of Dependency is Plant Breeding: A Game Theoretic Analysis.
98037 BOUCHIKHI Hamid, ROND (de) Mark., LEROUX V.
Alliances as Social Facts: A Constructivist of Inter-Organizational Collaboration.
98038 BOUCHIKHI Hamid, KIMBERLY John R.
In Search of Substance: Content and Dynamics of Organizational Identity.
98039 BRIOLAT Dominique, AKOKA Jacky, COMYN-WATTIAU Isabelle
Electronic Commerce on the Internet in France. An Explanatory Survey.
Page 4
98040 CONTENSOU François, VRANCEANU Radu
Réduction de la durée du travail et complémentarité des niveaux de qualification.
98041 TIXIER Daniel
La globalisation de la relation Producteurs-Distributeurs.
98042 BOURGUIGNON Annick
L’évaluation de la performance : un instrument de gestion éclaté.
98043 BOURGUIGNON Annick
Benchmarking: from Intentions to Perceptions.
98044 BOURGUIGNON Annick
Management Accounting and Value Creation: Value, Yes, but What Value?
98045 VRANCEANU Radu
A Simple Matching Model of Unemployment and Working Time Determination with Policy Implications.
98046 PORTAIT Roland, BAJEUX-BESNAINOU Isabelle
Pricing Contingent Claims in Incomplete Markets Using the Numeraire Portfolio.
98047 TAKAGI Junko
Changes in Institutional Logics in the US. Health Care Sector: A Discourse Analysis.
98048 TAKAGI Junko
Changing Policies and Professionals: A Symbolic Framework Approach to Organizational Effects on
Physician Autonomy.
98049 LORINO Philippe
L’apprentissage organisationnel bloquée (Groupe Bull 1986-1992) : du signe porteur d’apprentissage au
Piège de l’habitude et de la représentation-miroir.
98050 TAKAGI Junko, ALLES G.
Uncertainty, Symbolic Frameworks and Worker Discomfort with Change.
1999
99001 CHOFFRAY Jean-Marie
Innovation et entreprenariat : De l’idée… au Spin-Off.
99002 TAKAGI Junko
Physician Mobility and Attidudes across Organizational Work Settings between 1987 and 1991.
99003 GUYOT Marc, VRANCEANU Radu
La réduction des budgets de la défense en Europe : économie budgétaire ou concurrence budgétaire ?
99004 CONTENSOU François, LEE Janghyuk
Interactions on the Quality of Services in Franchise Chains: Externalities and Free-riding Incentives.
99005 LIOUI Abraham, PONCET Patrice
International Bond Portfolio Diversification.
99006 GUIOTTO Paolo, RONCORONI Andrea
Infinite Dimensional HJM Dynamics for the Term Structure of Interest Rates.
99007 GROUT de BEAUFORT Viviane, BERNET Anne-Cécile
Les OPA en Allemagne.
99008 GROUT de BEAUFORT Viviane, GENEST Elodie
Les OPA aux Pays-Bas.
99009 GROUT de BEAUFORT Viviane
Les OPA en Italie.
Page 5
99010 GROUT de BEAUFORT Viviane, LEVY M.
Les OPA au Royaume-Uni.
99011 GROUT de BEAUFORT Viviane, GENEST Elodie
Les OPA en Suède.
99012 BOUCHIKHI Hamid, KIMBERLY John R.
st
The Customized Workplace: A New Management Paradigm for the 21 Century.
99013 BOURGUIGNON Annick
The Perception of Performance Evaluation Criteria (1): Perception Styles
99014 BOURGUIGNON Annick
Performance et contrôle de gestion.
99015 BAJEUX-BESNAINOU Isabelle, JORDAN J., PORTAIT Roland
Dynamic Asset Allocation for Stocks, Bonds and Cash over Long Horizons.
99016 BAJEUX-BESNAINOU Isabelle, JORDAN J., PORTAIT Roland
On the Bonds-stock Asset Allocation Puzzle.
99017 TIXIER Daniel
La logistique est-elle l’avenir du Marketing ?
99018 FOURCANS André, WARIN Thierry
Euroland versus USA: A Theoretical Framework for Monetary Strategies.
99019 GATTO Riccardo, JAMMALAMADAKA S.R.
Saddlepoint Approximations and Inference for Wrapped α-stable Circular Models.
99020 MOTTIS Nicolas, PONSSARD Jean-Pierre
Création de valeur et politique de rémunération. Enjeux et pratiques.
99021 STOLOWY Nicole
Les aspects contemporains du droit processuel : règles communes à toutes les juridictions et procédures
devant le Tribunal de Grande Instance.
99022 STOLOWY Nicole
Les juridictions civiles d’exception et l’étude des processus dans le droit judiciaire privé.
99023 GATTO Riccardo
Multivariate Saddlepoint Test for Wrapped Normal Models.
99024 LORINO Philippe, PEYROLLE Jean-Claude
Enquête sur le facteur X. L’autonomie de l’activité pour le management des ressources humaines et pour
le contrôle de gestion.
99025 SALLEZ Alain
Les critères de métropolisation et les éléments de comparaison entre Lyon et d’autres métropoles
françaises.
99026 STOLOWY Nicole
Réflexions sur l’actualité des procédures pénales et administratives.
99027 MOTTIS Nicolas, THEVENET Maurice
Accréditation et Enseignement supérieur : certifier un service comme les autres…
99028 CERDIN Jean-Luc
International Adjustment of French Expatriate Managers.
99029 BEAUFORT Viviane, CARREY Eric
L’union européenne et la politique étrangère et de sécurité commune : la difficile voie de la construction
d’une identité de défense européenne.
Page 6
99030 STOLOWY Nicole
How French Law Treats Fraudulent Bankruptcy.
99031 CHEVALIER Anne, LONGIN François
Coût d’investissement à la bourse de Paris.
99032 LORINO Philippe
Les indicateurs de performance dans le pilotage organisationnel.
99033 LARDINOIT Thierry, QUESTER Pascale
Prominent vs Non Prominent Bands: Their Respective Effect on Sponsorship Effectiveness.
99034 CONTENSOU François, VRANCEANU Radu
Working Time and Unemployment in an Efficiency Wage Model.
99035 EL OUARDIGHI Fouad
La théorie statistique de la décision (I).
2000
00001
CHAU Minh, LIM Terence
The Dynamic Response of Stock Prices Under Asymetric Information and Inventory Costs: Theory and
Evidence
00002
BIBARD Laurent
Matérialisme et spiritualité
00003
BIBARD Laurent
La crise du monde moderne ou le divorce de l’occident.
00004
MATHE Hervé
Exploring the Role of Space and Architecture in Business Education.
00005
MATHE Hervé
Customer Service: Building Highly Innovative Organizations that Deliver Value.
00006
BEAUFORT (de) Viviane
L’Union Européenne et la question autrichienne, ses conséquences éventuelles sur le champ de révision
de la CIG.
00007
MOTTIS Nicolas, PONSSARD Jean-Pierre
Value Creation and Compensation Policy Implications and Practices.
00009
BOURGUIGNON Annick
The Perception of Performance Evaluation Criteria (2): Determinants of Perception Styles.
00010
EL OUARDIGHI Fouad
The Dynamics of Cooperation.
00011
CHOFFRAY Jean-Marie
Innovation et entrepreneuriat : De l’Idée…au Spin-Off. (Version révisée du DR 99001).
00012
LE BON Joël
De l’intelligence économique à la veille marketing et commerciale : vers une nécessaire mise au point
conceptuelle et théorique.
00013
ROND (de) Mark
Reviewer 198 and Next Generation Theories in Strategy.
00014
BIBARD Laurent
Amérique latine : identité, culture et management.
00016
BIBARD Laurent
Les sciences de gestion et l’action.
Page 7
00017
BEAUFORT (de) V.
Les OPA au Danemark.
00018
BEAUFORT (de) V.
Les OPA en Belgique.
00019
BEAUFORT (de) V.
Les OPA en Finlande.
00020
BEAUFORT (de) V.
Les OPA en Irlande.
00021
BEAUFORT (de) V.
Les OPA au Luxembourg.
00022
BEAUFORT (de) V.
Les OPA au Portugal.
00023
BEAUFORT (de) V.
Les OPA en Autriche.
00024
KORCHIA Mickael
Brand Image and Brand Associations.
00025
MOTTIS Nicolas, PONSSARD Jean-Pierre
L’impact des FIE sur les firmes françaises et allemandes : épiphénomène ou influence réelle ?
00026
BIBARD Laurent
Penser la paix entre hommes et femmes.
00027
BIBARD Laurent
Sciences et éthique (Notule pour une conférence).
00028
MARTEL Jocelyn, C.G. FISHER Timothy
Empirical Estimates of Filtering Failure in Court-supervised Reorganization.
00029
MARTEL Jocelyn
Faillite et réorganisation financière : comparaison internationale et évidence empirique.
00030
MARTEL Jocelyn, C.G. FISHER Timothy
The Effect of Bankruptcy Reform on the Number of Reorganization Proposals.
00031
MARTEL Jocelyn, C.G. FISHER Timothy
The Bankruptcy Decision: Empirical Evidence from Canada.
00032
CONTENSOU François
Profit-sharing Constraints, Efforts Output and Welfare.
00033
CHARLETY-LEPERS Patricia, SOUAM Saïd
Analyse économique des fusions horizontales.
00034
BOUYSSOU Denis, PIRLOT Marc
A Characterization of Asymmetric Concordance Relations.
00035
BOUYSSOU Denis, PIRLOT Marc
Nontransitive Decomposable Conjoint Measurement.
00036
MARTEL Jocelyn, C.G. FISHER Timothy
A Comparison of Business Bankruptcies across Industries in Canada, 1981-2000.
2001
01001
DEMEESTERE René
Pour une vue pragmatique de la comptabilité.
Page 8
01002
DECLERCK Francis
Non Disponible.
01003
EL OUARDIGHI Fouad, GANNON Frédéric
The Dynamics of Optimal Cooperation.
01004
DARMON René
Optimal Salesforce Quota Plans Under Salesperson Job Equity Constraints.
01005
BOURGUIGNON Annick, MALLERET Véronique, NORREKLIT Hanne
Balanced Scorecard versus French tableau de bord : Beyond Dispute, a Cultural and Ideological
Perspective.
01006
CERDIN Jean-Luc
Vers la collecte de données via Internet : Cas d’une recherche sur l’expatriation.
01012
VRANCEANU Radu
Globalization and Growth: New Evidence from Central and Eastern Europe.
01013
BIBARD Laurent
De quoi s’occupe la sociologie ?
01014
BIBARD Laurent
Introduction aux questions que posent les rapports entre éthique et entreprise.
01015
BIBARD Laurent
Quel XXIème siècle pour l’humanité ?
01016
MOTTIS Nicolas, PONSSARD Jean-Pierre
Value-based Management at the Profit Center Level.
01017
BESANCENOT Damien, KUYNH Kim, VRANCEANU Radu
Public Debt : From Insolvency to Illiquidity Default.
01018
BIBARD Laurent
Ethique de la vie bonne et théorie du sujet : nature et liberté, ou la question du corps.
01019
INDJEHAGOPIAN Jean-Pierre, JUAN S . LANTZ F., PHILIPPE F.
La pénétration du Diesel en France : tendances et ruptures.
01020
BARONI Michel, BARTHELEMY Fabrice, MOKRANE Mahdi
Physical Real Estates: Risk Factors and Investor Behaviour.
01021
01022
BESANCENOT Damien, VRANCEANU Radu
Quality Leaps and Price Distribution in an Equilibrium Search model
01023
BIBARD Laurent
Gestion et Politique
01024
BESANCENOT Damien, VRANCEANU Radu
Technological Change, Acquisition of Skills and Wages in a search Economy
01025
BESANCENOT Damien, VRANCEANU Radu
Quality Uncertainty and Welfare in a search Economy
01026
MOTTIS N. , PONSARD J.P.,
L’impact des FIE sur le pilotage de l’entreprise
01027
TAPIERO Charles, VALOIS Pierre
The inverse Range Process in a Random Volatibility Random Walk
01028
ZARLOWSKI Ph., MOTTIS N.
Making Managers into Owners An Experimental Research on the impact of Incentive Schemes on
Shareolder Value Creation
Page 9
01029
BESANCENOT Damien, VRANCEANU Radu
Incertitude, bien-être et distribution des salaires dans un modèle de recherche d’emploi
Page 10