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Electronic copy of this paper is available at: http://ssrn.com/abstract=963229
Asymmetric Information and
Overinvestment in Quality
Paul Belleflamme,
Martin Peitz
Working Paper 49/2007
Bruchsal, January 2007
ISSN 1613-6691 (print version)
ISSN 1613-6705 (online version)
Prof. Dr. Martin Peitz is Professor of Economics and Quantitative Methods at International
University in Germany, Bruchsal.
Prof. Paul Belleflamme, Ph.D. is Associate Professor at Université Catholique de Louvain.
Contact: martin.peitz@i-u.de, belleflamme@core.ucl.ac.be
School of Business Administration
Electronic copy of this paper is available at: http://ssrn.com/abstract=963229
Asymmetric Information and
Overinvestment in Quality
Paul Belleflamme∗
Université Catholique de Louvain
Martin Peitz†
International University in Germany and University of Mannheim
This version: January 2007
Abstract
According to standard economic wisdom, asymmetric information
about product quality leads to a quality deterioration in the market.
Suppose that a higher investment level makes the realization of high
quality more likely. Then, if consumers observe the investment (but
not the realization of product quality) before purchase, they can infer
the probability distribution of high and low quality that may be put on
themarket. This,asweshow,maymakethefirm overinvest in quality
compared to a market with full information.
Keywords: asymmetric information, product quality
JEL-Classificati on : D82, D92, L15
∗CORE and IAG-Louvain School of Management, Université Catholique de Louvain,
34 Voie du Roman Pays, B-1348 Louvain la Neuve, Belgium, belleflamme@core.ucl.ac.be.
†Department of Economics, University of Mannheim, 68131 Mannheim, Germany,
Martin.Peitz@i-u.de; also affiliatedwithCEPR,CESifoandENCORE.
1 Introduction
We exa m ine t he effects of asymmetric information on firms’ incentives to
invest in the quality of their product. Asymmetric information prevails be-
cause consumers cannot ascertain the quality of the product before they buy
it. However, through a risky investment, firms have the ability to increase
the average quality of their product. Consumers can observe the investment
level and thereby, obtain information about the expected quality in the mar-
ket. Using a simple model, we show that in such a situation, firms might
end up investing more in quality under asymmetric information than under
full information.
We provide two simple arguments that support the overinvestment re-
sult. First, under asymmetric information low quality is always put on the
market whereas it is not offered if the willingness-to-pay is below the cost
under full information. From an ex ante point of view, the firm can then
increase its profits by overinvesting compared to the full information case
because this reveals to consumers that the risk of obtaining low quality is
reduced, which is reflected in the price. Second, we have to take the partic-
ipation constraint of the high-quality firm into account if it is more costly
to produce high quality than low quality. Under asymmetric information,
the price that can be charged increases in the probability that high quality
will result. To make sure that high quality stays in the market, this price
has to be above the cost of high quality because otherwise a lemons problem
arises. The existence of the lemons problem, in turn, may make it optimal
for the firm to distort the investment level upward.
Key requisite for our result is the consumers’ ability to draw inferences
from investment levels on expected product quality. For instance, pharma-
ceutical firms provide information about their input in research and devel-
opment for a particular prescription drug, apparently to make prescribing
doctors and hospital pharmacists think that their product is likely to be suc-
cessful. In the cosmetics industry, the leading company, L’Oréal, emphasizes
in its advertisement campaigns the large number of patents it files every year
(over 500 in 2005) and how much it invests in cosmetic and dermatological
research (3% of sales or $625 million in 2005), so as to convince consumers
1
of its commitment to market high-quality products. Hollywood studios hire
well-known actors with the idea that these actors lead to better movies on
average. Producers of wines, organic food and other food products invest in
production processes (and inform consumers about these investments) with
the idea that the adoption of such processes leads to better products on
average.
The type of investment we have in mind can also be exemplified by a
firm’s effort to meet standards for quality management systems, such as ISO
9000. The ISO 9000 certification does not guarantee the quality of end prod-
ucts and services; rather, it certifies that consistent business processes are
being applied. That is, it proves that the firm (actually, any type of organi-
zation) has put in place the necessary processes (i.e., a quality management
system) “to fulfil the customer’s quality requirements, and applicable reg-
ulatory requirements, while aiming to enhance customer satisfaction, and
achieve continual improvement of its performance in pursuit of these ob-
jectives.”1Cole (1998, p. 68) confirms our view by suggesting that firms
may make ISO 9000 “their primary instrument for signaling quality to their
customers.”2
While there is an abundant economic literature on quality in asymmet-
ric information situations, we are not aware of work that obtains a result
similar to ours.3Inspired by previous work that alludes to the adverse se-
1Taken from www.iso.org (ISO 9000. Understanding the basics).
2However, firms may also seek certification simply in compliance with requirements of
major customers or regulators. To disentangle the relative importance of these two moti-
vations, Anderson et al. (1999) estimate a probit model of ISO 9000 certification. They
show that the signaling motivation is indeed important: the desirability of communicating
quality outcomes to external parties provides incremental explanatory power for the cer-
tification decision (even after including compliance motivations for seeking certification).
Quality management systems seem thus to correspond to the type of investments we refer
to in our model.
3This literature starts with Akerlof’s (1970) “lemons’ principle”, according to which
adverse selection (resulting from asymmetric information) causes the bad quality to drive
the good quality out of the market. Various ways have then been explored to remedy, or at
least alleviate, the underprovision of quality that prevails under asymmetric information.
For instance, Leland (1979) has explored the role of minimum quality standards as a policy
to cope with the underprovision of quality. Price and advertising signals are other means
by which firms may reduce the asymmetric information and convince consumers of the
2
lection problem arising from an unmodeled investment in quality (see, e.g.,
Milgrom and Roberts, 1986), we explicitly model that the level of the in-
vestment affects the probability distribution over quality and show that due
to asymmetric information, the firm may overinvest in quality.
In an important paper, de Meza and Webb (1987) obtain an overinvest-
ment result of a different sort. They consider a competitive market in which
entrepreneurs face an asymmetric information problem when asking for out-
side finance. Entrepreneurs have to make the same level of investment to
enter the market but they differ in the probability to be successful. De
Meza and Webb show that too many entrepreneurs invest. In their model
the overinvestment result directly stems from the adverse selection frame-
work that makes high-quality projects draw in low-quality projects.4Hence,
in their model more aggregate investment lowers average quality. This is in
line with the general tenor in the literature that asymmetric information
problems tend to lead to a quality deterioration. By contrast, in our model,
in which a higher investment level increases the probability of high quality,
asymmetric information may lead to higher quality.
Creane (2006) considers a market in which an unlimited number of ho-
mogeneous firms decide whether to enter with uncertain quality. After entry,
firms observe the quality; high quality is more costly than low quality. The
number of firms, determined by the free entry condition according to which
high and low quality firms stay in the market, is not sustainable because
the participation constraint of high-quality firmsisviolated,andthuswould
lead to adverse selection. Therefore firmsenterinsmallernumberandob-
tain positive equilibrium profits under free entry. While Creane considers
entry for a given investment level we analyze the situation for a given firm
good quality of their product; see, e.g., the seminal contributions by Nelson (1974) and
Milgrom and Roberts (1986). In a price-signalling context, Shieh (1993) has analyzed the
investment incentives in cost-reducing innovations under asymmetric information, where
neither the investment nor product quality is observable to consumers. He shows that
asymmetric information about quality may strengthen the firm’s incentive to invest in
cost-reducing innovation.
4In a related model, Lensink and Sterken (2001) also obtain an overinvestment result,
which however stems from the possibility to delay the investment decision and not from
the heterogeneity of expected returns of projects.
3
in which the probability distribution over quality is continuously affected by
the investment level.
The paper is organized as follows: in Section 2, we lay out the model; in
Section 3, we analyse the benchmark of full information; in Section 4, we de-
velop the asymmetric information case and we contrast it to the benchmark
in order to establish our main result (which we illustrate through a numer-
ical example); in Section 5, we reconsider the analysis introducing outside
options; we conclude in Section 6.
2Themodel
Suppose a single seller offers a product to a unit mass of buyers. The seller’s
opportunity cost is cs,wheres∈{L, H}is the quality of the product. High
quality is assumed to be more costly than low quality, cH>c
L.There
is a unit mass of buyers who are assumed to be identical and have unit
demand. The valuation of each buyer is assumed to be rs.Bydefinition,
high quality is more valuable than low quality, rH>r
L.DenoteI(λ)the
investment that is needed to obtain that with probability λthe product is of
high quality. We view this investment as a commitment to meet on average
a certain reliability of the product. Suppose that I(λ)=(k/2)λ2,which
satisfies I0>0,I00 >0,andlimλ→0I0(λ)=0. As stated in the introduction,
I(λ)can be interpreted as efforts to meet standards for quality management
systems.
We consider the following three-stage game: at stage 1, the firm invests I
in quality; at stage 2, after learning the quality realization it sets its price; at
stage 3, buyers form beliefs about product quality and make their purchasing
decision. As we will explore below, under full information the firm chooses
a strictly positive investment level if rH−cH>r
L−cLand zero investment
if the reverse inequality holds. Note that in our setting the full-information
solution implements the firstbestallocation(thisisduetothefactthatthe
firm fully extracts all surplus); thus deviations from the firstbestarethe
result of asymmetric information.
If the quality choice and the underlying investment decision cannot be
observed by consumers, the firm has no means to convince consumers that its
4
product is of high quality; the firm will therefore invest zero. This confirms
that in markets in which firms choose quality, firms tend to provide too low
a quality from a social point of view.
What we investigate is whether a risky investment in quality, where the
investment is observable to consumers, results in the same type of quality
trap as before. Clearly, the situation we envisage now potentially allows
consumers to obtain information about the expected quality in the market,
since consumers observe the investment effort and have a clear understanding
of the relationship between investment spending and expected quality. We
assume that the high quality is socially beneficial, i.e. rH>c
H.Wemake
no such assumption for the low quality; rather, we want to contrast the
cases where the low quality is either socially beneficial (rL>c
L)ornot
(rL<c
L). To simplify the exposition, and with minimum loss of generality,
we also assume that the high quality is socially more beneficial than the low
quality, rH−cH>r
L−cL(which is trivially satisfied when the low quality
is not socially beneficial). We restict attention to equilibria in which the
firm extracts all rents so that price is equal to expected surplus.5
3 Full information benchmark
We first analyze the full information case (i.e., consumers observe the in-
vestment and the realization of quality). We distinguish between two cases:
(1) rL>c
Lso that under full information also low quality is put on the
market and (2) rL<c
Lso that under full information low quality is not put
on the market.
In case (1), the firm’s maximization problem is maxλEπ1=λ(rH−
cH)+(1−λ)(rL−cL)−(k/2)λ2.Solvingthefirst-order condition of profit
maximization, we obtain as the probability for high-quality: (rH−cH−
rL+cL)/k. Notethatwehaveaninteriorsolutionifk>r
H−cH−rL+cL
(otherwise the probability is 1).6We al so check th a t the firm’s expected
5In a modified model in which the number of consumers exceeds the number of available
units and in which consumers bid for the product, equilibrium price is necessarily equal
to expected surplus (see e.g. Tadelis, 1999).
6From our assumption that rH−cH>r
L−cL, the probability is necessarily strictly
5
profit evaluated at λ=(rH−cH−rL+cL)/k is positive:
Eπ1|λ=(rH−cH−rL+cL)/k =1
2k(rH−cH−rL+cL)2+(rL−cL)>0(1)
In sum, the probability for high quality under full information in case (1) is
λf
1=(1
k[(rH−cH)−(rL−cL)] if k>r
H−cH−rL+cL≡k0,
1if k≤k0.(2)
In case (2), the firm’s problem is maxλEπ2=λ(rH−cH)−(k/2)λ2,
which yields the following profit-maximizing probability for high-quality:
(rH−cH)/k > 0. Notethatwehaveaninteriorsolutionaslongask>
rH−cH(otherwise the probability is 1)andthatthefirm’s expected profit
evaluated at λ=(rH−cH)/k is positive. We can then define the probability
for high quality under full information in case (2) as
λf
2≡(1
k(rH−cH)if k>r
H−cH≡k1,
1if k≤k1.(3)
4 Asymmetric information
Consider now the situation of asymmetric information in which consumers
observe Ibut not the realization of quality. We analyze perfect Bayesian
equilibria of the game in which the firm observes quality after stage 1 and
consumers only observe the investment level (and price) but not the realized
quality. We start with the situation where consumers expect any quality
realization to be put on the market (clearly, if high quality is put on the
market, so is low quality since its costs are lower). The expected surplus is
thus λrH+(1−λ)rL, which is the price the firm will set at stage 2. Hence,
expected profits at stage 1 are
λ[λrH+(1−λ)rL−cH]+(1−λ)[λrH+(1−λ)rL−cL]−(k/2)λ2
=λ(rH−cH)+(1−λ)(rL−cL)−(k/2)λ2.
Solving the first-order condition of profit maximization, we obtain as the
probability for high-quality:
λa≡1
k(rH−cH−rL+cL).(4)
positive.
6
As we have seen above, λa<1provided that k>k
0. Moreover, from
expression (1), we know that the firm’s expected profitevaluatedatλ=λa
is positive in case (1) but might be negative in case (2) as rL−cL<0.
Therefore, in case (2), the firm is better offby entering the market than not
being active as long as λa(rH−cH)+(1−λa)(rL−cL)−(k/2) (λa)2>0,or
k<(rH−cH−rL+cL)2
2(cL−rL)≡k2.
Itiseasilycheckedthatincase(2),k1<k
0<k
2.
Comparing expression (4) with expressions (2) and (3), we observe that,
when consumers expect both qualities to be put on the market, the proba-
bility for high-quality is weakly greater under asymmetric information than
under full information. Investment incentives are not affected by consumer
information if rL≥cL(λa=λf
1) but are stronger under asymmetric in-
formation if the reverse inequality holds. Indeed, in the latter case, we
observe that low-quality products are not released on the market under full
information, but that low quality is always consumed under asymmetric in-
formation. Since this expected lower quality is reflected in price and since
low quality is produced at costs above the consumers’ willingness to pay,
the firm has an incentive to reduce the probability of low quality products
through higher investments. It is only when the investment cost is very high
(i.e., k>k
2)thatthefirm prefers not to invest under asymmetric informa-
tion while it keeps on investing under full information. The results for case
(2) are summarized in the following table (where λa
2denotes the probability
of high quality under asymmetric information in case (2)).
k≤k1k1<k≤k0k0<k≤k2k>k
2
λa
2=λf
2=1 λa
2=1>λ
f
2λa
2=λa>λ
f
2λa
2=0<λ
f
2
The previous results were derived under the assumption that a high qual-
ity product stays in the market under asymmetric information. However,
at stage 2, the firm may not be interested in offering high quality on the
market, while it is always willing to do so under full information (under
our assumption that rH>c
H). For a high-quality firm to make positive
operating profits, the price must exceed costs, i.e. λrH+(1−λ)rL−cH≥0,
7
which is equivalent to
λ≥e
λ≡cH−rL
rH−rL
.
Hence, the firm will indeed implement λaif λa≥e
λ, which can be rewritten
as
λa≥e
λ⇐⇒ k≤rH−rL
cH−rL
(rH−cH−rL+cL)≡k3.
If k>k
3and the firm implemented λa, consumers would know that a
high-quality firm would not participate, so that their beliefs about product
quality would not be confirmed. Consumers expect a sufficiently high prob-
ability that the product is of low-quality, which reduces their willingness to
pay. Hence, the firm cannot charge a sufficiently high price to cover its cost
in case it is of high quality. In such a case (i.e., λa<e
λor k>k
3), the
firm has the option to increase its investment expenditure, so as to increase
the probability of high quality up to e
λ. The condition for this option to be
profitable for the firm differs according to whether we are in case (1) or in
case (2).
In case (1), as rL>c
L,thefirm may alternatively invest zero and offer
low quality on the market. The former action is more profitable than the
latter if e
λ(rH−cH)+(1−e
λ)(rL−cL)−(k/2)e
λ2>r
L−cLor, equivalently,
e
λ[(rH−cH)−(rL−cL)] −(k/2)e
λ2>0.Solvingforkwe must have k<
2[(rH−cH)−(rL−cL)]/e
λ,whichis
k<2rH−rL
cH−rL
[(rH−cH)−(rL−cL)] = 2k3.
Noting that k3>k
0(since, by assumption rH>c
H), we now have a com-
plete picture of the probability of high quality in case (1) under asymmetric
information. We contrast it with the solution under full information in the
following table:
k≤k0k0<k≤k3k3<k≤2k32k3<k
λa
1=λf
1=1 λa
1=λf
1<1λa
1>λ
f
1λa
1=0<λ
f
1
In case (2), with rL<c
L, overinvestment is profitable if e
λ(rH−cH)+
(1 −e
λ)(rL−cL)−(k/2)e
λ2>0, which is equivalent to
k<2(rH−rL)(cH−cL)(rH−cH)
(cH−rL)2≡k4.
8
Summarizing our previous findings, we have that the probability of high
quality under asymmetric information in case (2), λa
2,isequaltoλaas long
as (i) k>k
0(otherwise, it is equal to 1), (ii) k<k
2(otherwise, it is equal to
0), and (iii) k<k
3. If the latter condition is not met, the firm will increase
the probability of high quality up to e
λas long as k<k
4. To get a complete
picture, we need to rank the thresholds k0,k1,k2,k3and k4.Wedetailthis
ranking in the appendix, which allows us to state the following proposition,
wherewedefine
∆≡−
(cH−rL)(rH−cH)
(2rH−cH−rL).
Proposition 1 If consumers observe investments in the quality of products
but not the quality itself, a firm invests strictly more in quality under asym-
metric information than under full information, provided that (1) rL−cL>0
and k3<k≤2k3or (2a) ∆<r
L−cL<0and k1<k≤k4,or(2b)
rL−cL<∆and k1<k≤k2.
The three situations of over-investment are depicted in Figure 1. To
get the intuition behind our result, let us restate the two arguments. First,
we have seen that ignoring the participation constraint of the high-quality
firm, investment incentives weakly increase under asymmetric information
compared to full information. The reason for the potential overinvestment
is that a low-quality firm stays in the market under asymmetric information
even though its value is less than the cost because it is sold at the expected
and not the actual value. The fact that the product may be of low quality is
takenintoaccountbyconsumersandthusreflected in the price. Therefore,
by investing more, the firm can convince consumers that the risk of obtain-
ing low quality is reduced. Secondly, taking into account the participation
constraint of a high-quality firm, investments under given beliefs may be
insufficient to make selling high quality worthwhile. This implies that λa
cannot be the equilibrium belief at the investment level I(λa).Tomake
the participation of the high-quality firm worthwhile, the firm has to distort
its investment upward in order to convince consumers that a high-quality
outcome is more likely, in which case they are willing to pay more. Thirdly,
at the investment stage the firm has to compare profits with such an upward
distorted investment to the outside option (which is either zero or to sell low
9
rL
k3
k1
2k3
k0
k
cL
rL<cL+∆
k4
k2
rH-cH+cL
2b
1
2a
Figure 1: Overinvestment under asymmetric information
quality). It may be profitable to overinvest. It is only when investments are
too costly (i.e. k>2k3for rL>c
Lor k>k
2or k4for rL<c
L)thatthe
standard underinvestment result under asymmetric information holds.
Anumerical example (which gives parameter values to all parameters ex-
cept k) illustrates our results for cases (1) and (2a). Take rH=10,cH=6,
and cL=2. WetaketwovaluesforrL:eitherrL=3>c
L(case (1))
or rL=1<c
L(case (2a)). Consider first case (1) with rL=3. Under
full information, the firm would choose its investment such that λf
1=3/k.
As we have seen above, under asymmetric information and provided that
consumers expect that products are sold on the market independent of the
realization of the random variable, the firm would invest such that λa=λf
1.
However, for a high-quality firm to make positive operating profits the price
must exceed costs, i.e. λrH+(1−λ)rL−cH≥0, which becomes λ≥e
λ≡3/7
10
under our parameter values. Hence, the firm will indeed implement λaif
λa≥e
λ. Otherwise, if the firm implemented λa, consumers would know
that a high-quality firm would not participate so that their beliefs about
product quality would not be confirmed. Consumers expect a sufficiently
high probability that the product is of low-quality which reduces their will-
ingness to pay. Hence, the firm cannot charge a sufficiently high price to
cover its cost in case it is of high quality. The firmcanthenincreaseits
investment expenditure to increase the probability of high quality. Expected
quality is higher than under full information if e
λ=3/7>3/k =λf
1,which
is equivalent to k>k
3=7. To be an equilibrium strategy also at the
investment stage, expected profits must be greater than rL−cL=1,i.e.
4λ+(1−λ)−(k/2)λ2≥1.Evaluatedat
e
λ=3/7,thisisequivalentto
k≤2k3=14. Hence, for parameter values k∈(7,14] the firm invests
strictly more under asymmetric than under full information.
Suppose now that rL=1,sothatweareincase(2a). Wecheckthat
cL−rL=1<∆=20/13,sothatk2>k
3. Under full information, the firm
would choose its investment such that λf
2=4/k. Hence, k1=4. Redoing the
computations under asymmetric information, we find that k0=5,k3=9,
k4'11.5and k2=12.5. Take, e.g., k=10and compute the various
thresholds on λ:7
e
λ=5
9>λ
a=1
2>λ
f
2=2
5.
Hence, for parameter values k∈(4,11.5] the firm invests strictly more
under asymmetric information than under full information. For an interme-
diate range of investment cost levels (k∈(9,11.5))thefirm has to further
increase its investment in order to convince consumers that a high-quality
product will be put on the market. Only if investment costs are too high
(k>11.5), investment under asymmetric information breaks down to zero
and is therefore less than under full information. Figure 2 illustrates our
results in case (2a), where rL<c
L.8
7We have checked that expected profits at stage 1 under h
λare positive (namely, h
λ(rH−
cH)+(1−h
λ)(rL−cL)−(k/2)h
λ2=19/81).
8Although the firm invests more under asymmetric information, it can easily be checked
that it always makes at least as much profits under full information than under asymmetric
information.
11
λa
λf
λ
1
λ
~
k3k4k
k1 k0
Figure 2: Investment in quality in case (2a)
5 The analysis with outside options
Our analysis can be criticized for the fact that under asymmetric informa-
tion, high quality is less profitable than low quality since both are sold at
the same price, while low quality is cheaper to produce. If a successful in-
vestment enables the firm not only to produce high but also low quality, the
firm will always deviate to low quality due to the moral hazard problem.
This in turn would imply that a firm does not have any incentive to invest
under high quality because a higher investment does not contain information
about the expected product quality that will be put on the market. How-
ever, if the production cost of high and low quality is the same whereas high
and low quality give different values for an outside option, a high quality
firm does not have an incentive to deviate to low quality (provided that its
production costs do not increase in quality).9We can then show that our
qualitative findings from above are confirmed.
Let vHand vLdenote the value of the outside option for high and low
quality, respectively, while cdenotes the production cost which is indepen-
9We can think of the outside option as a costly action taken by the firm; in particular,
it may use the services of a third-party certifyer, who certifies realized product quality (on
the logic of third-party certification, see e.g. Biglaiser, 1993). If this action fully reveals
its product quality the firm can sell high quality under full information at a price vH.In
particular, rH−vHconstitutes the cost of certification.
12
dent of quality. By the nature of the problem, rH>v
H>v
L. In addition,
we assume that the value of the outside option for high quality exceeds pro-
duction costs, vH>c. We can then replicate the analysis of Section 3. First,
we obtain the probability for high quality under full information as
λf≡(1
k(rH−c)if rL<c,
1
k(rH−rL)if rL≥c,
and we define ˆ
k0≡rH−c. Next, we turn to the analysis under asymmetric
information and consider first the case rL≥c. In analogy to Section 4, we
obtain that ˆ
λa=(1/k)(rH−rL)and b
˜
λ=(vH−rL)/(rH−rL),wherethe
latter expression comes from the condition that the price λrH+(1−λ)rL
has to exceed the value of the outside option for a high-quality product vH.
We then can calculate the critical value of kabove which overinvestment
with b
˜
λ>ˆ
λamay be required to solve the adverse selection problem:
ˆ
k3=(rH−rL)2
vH−rL
.
For an investment I(λ)with λ≤ˆ
λato be worthwhile we must have that
the profit is non-negative for rL<c. We obtain that this is the case for all
k≤ˆ
k2where
ˆ
k2=(rH−rL)2
2(c−rL),
which is always greater than ˆ
k0. Hence, the non-negativity condition is not
binding for all k≤ˆ
k3if ˆ
k2>ˆ
k3.ThisisequivalenttovH+rL>2c.
Consider now k>ˆ
k3.ForrL>c,anupwarddistortionoftheinvest-
ment gives greater profitthanoffering low quality in the market at zero
investment, i.e. λrH+(1−λ)rL−c−(k/2)λ2>r
L−c,aslongask<2ˆ
k3.
For rL≤c, an upward distortion of the investment gives greater profit
than being inactive with zero investment, i.e. λrH+(1−λ)rL−c−(k/2)λ2>
0,aslongask<ˆ
k4where10
ˆ
k4=2vH−c
vH−rL
(rH−rL)2
vH−rL
.
10The inequality can be rewritten as 2[λ(rH−rL)+rL−c]/λ2>k.Toobtain
ˆ
k4,we
substitute the expression for e
˜
λ. Clearly, ˆ
k4>ˆ
k3is equivalent to (vH+rL)/2>cbecause
in this case profits at ˆ
λaare strictly positive, so that an upward distortion that solves the
adverse selection problem is worthwhile.
13
We thus obtain the following result:
Proposition 2 Suppose that a successful investment allows the firm to choose
between high and low quality, which are produced at equal cost, but that high
quality has a higher value than an outside option. If consumers observe in-
vestments in the reliability of products but not reliability itself, a firm invests
strictly more in reliability (or quality) under asymmetric information than
under full information, provided that (1) rL>cand ˆ
k3<k≤ˆ
k4,or(2)
rL<cand ˆ
k0<k≤max nˆ
k2,ˆ
k3o.
6Conclusion
We have provided a counter-example to the belief that asymmetric informa-
tion about product quality reduces the incentives to provide higher quality;
we have shown that the reverse may actually be true. It obtains in situations
where firms have the possibility to make a risky and observable investment
to increase the average quality (reliability) of their products. An example of
such investments could be the effort to obtain the ISO 9000 certification for
the firm’s quality management system. Although consumers do not observe
the realization of quality, they observe how much the firm has invested and,
thereby, infer useful information about the expected quality on the market.
Knowing this, a firm producing high quality may overinvest in the quality or
reliability of its product to convince consumers that high quality is indeed
very likely to be put on the market; this avoids the lemons problem and
thus may be the firm’s optimal strategy. Also, if selling low quality has a
negative social value, the firm may want to reduce the probability of low
quality realization compared to the full-information world, because under
full information low quality would not be put on the market, whereas in an
adverse selection environment low quality is always offered. We have thus
identified two simple reasons for overinvestment in quality under asymmetric
information.
14
7 Appendix. ProofofProposition1
Most of the proof is in the main text. The missing part concerns the ranking
of the thresholds k0to k4in case (2). We already know that k3>k
0.Afew
lines of computation establish that
k3>k
2⇐⇒ rL−cL<−(cH−rL)(rH−cH)
(2rH−cH−rL)≡∆,
k2−k4=(rLrH−2cLrH−r2
L+rLcL+rHcH−c2
H+cLcH)2
2(cL−rL)(cH−rL)2>0,
k2−k3
k4−k3=(rH−cH−rL+cL)(cH−rL)
2(rH−rL)(cL−rL)>0.
(Note that the last two inequalities hold because we are in case (2) where
cL>r
L). We need then to distinguish among two cases.
1. If k2<k
3, then the firm prefers to exit the market (k>k
2)before
λabecomes inferior to e
λ(k>k
3). Then, if k0<k
2,wehavethat
λa
2=1for k≤k0,λa
2=λafor k0<k≤k2and λa
2=0for k>k
2;
otherwise, if k0>k
2,wehavethatλa
2=1for k≤k2and λa
2=0
for k>k
2. Comparing with expression (3) and recalling that (i)
k0,k
2>k
1and (ii) λa>λ
f
2for k>k
1,wehavethatinbothcases,the
firm invests strictly more under asymmetric information than under
full information if k1<k≤k2.
2. If k2>k
3,wealsohavethatk4>k
3(as k2−k3and k4−k3have
the same sign). Then, λa
2=1for k≤k0,λa
2=λafor k0<k≤k3,
λa
2=e
λfor k3<k≤k4and λa
2=0for k>k
4. It follows that the
firm invests strictly more under asymmetric information than under
full information if k1<k≤k4.
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