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Comparative versus Informative Advertising in Oligopolistic
Markets*
Maria Alipranti† Evangelos Mitrokostas‡ Emmanuel Petrakis §
Work in progress, please do not quote
Abstract
The present paper investigates the firms’ incentives to invest in informative and/or
comparative advertising, in an oligopolistic market with horizontal and vertical
product differentiation. We show that, in equilibrium the firms’ optimal decision is to
invest in a combination of informative and comparative advertising where, the
expenditure levels on each type of advertising are being determined by the degree of
substitution between products. Further, through the comparison with the benchmark
case without advertising activities and the mere informative advertising case, we show
that firms’ investment in both types of advertising always leads to higher output and
lower profits. Finally, the impact of advertising on social welfare is also discussed.
Keywords: Informative Advertising, Comparative Advertising, Oligopoly, Product
Differentiation.
JEL Classification: L13, M37
* Acknowlegements: The authors wish to thank Simon Anderson and all the participants at 8th
Conference on Research on Economic Theory and Econometrics, Tinos 2009, and ASSET Meetings
2009 at Istanbul for their helpful comments and suggestions. Full responsibility for all shortcomings is
ours. †Department of Economics, University of Crete; e-mail: [email protected] ‡Department of Economics, University of Cyprus; e-mail: [email protected] §Corresponding author. Department of Economics, University of Crete, Univ. Campus at Gallos,
Rethymnon 74100, Greece, Tel: +30-28310-77407, Fax: +30-28310-77406 {[email protected]}.
1. Introduction.
Comparative advertising, “the form of advertising that compares rivals brands on
objectively measurable attributes or price, and identifies the rival brand by name,
illustration or other distinctive information”1, has received increased attention by
business, academics and policy makers since, this “aggressive” advertising form has
emerged as a prevalent marketing practice.2 The advertising wars of Pepsi and Coke,
Ducking Donuts and Starbucks, or the advertising campaign of Avis, “We try harder”,
are few examples of the extended use of comparative advertising.3
However, the empirical evidence so far, regarding the effectiveness of
comparative ads, is inconclusive. On the one hand, comparative ads tent to be more
effective than the non comparative in inducing consumers’ attention, message and
brand awareness, favourable brand attitudes and purchase intentions, [Grewal et
al.(1997), Jung and Sharon (2002)]. On the other hand, apart from legal risks, they
may enhance consumers’ mistrust and lead to misidentifications of the sponsoring
brands, [Goodwin and Etgar (1980), Wilkie and Farris (1975), Prasad (1976), Barone
and Miniard (1999)].
Given the above evidence, a number of questions arise over the firms’ attitude
towards the use of such an aggressive advertising form along with the traditional
advertising techniques. This papers aims to shed some light into this issue by
exploring endogenously the firms’ incentives to invest in comparative and/or
informative advertising along with the consequences of such investments in the
market outcomes and the social welfare. In particular, we aim to address the following
four questions.
First, which is the optimal firms’ decision upon the type of advertising and the
expenditure level on each type that firms are willing to undertake in order to promote
their products? This question is motivated by the alternative strategic use that
1 Statement of policy regarding comparative advertising, Federal Trade Commission, Washington, D.C., August13, 1979. 2 Pechmann and Stewart (1990) showed that at the United States the 60 percent of all advertising contained indirect comparative claims, 20 percent contained direct comparative claims and only 20 percent contained no comparative claims while, Muehling et al. (1990) suggested that almost 40 percent of all advertising content is comparative. The difference between direct and indirect comparative ads is based on whether the competitor is explicitly named (or precisely indentified by logos and images) or not. 3 For more details and examples see Barigozzi and Peitz (2006)
informative and comparative advertising has. Informative advertising is strategically
used by firms as a mean through which they convey product information to
consumers (Bagwell 2007); while comparative advertising is mainly used as a mean
to promote the superiority of the advertised product against the rival products.
Second, how does the degree of substitutability between products affect the firms’
investment levels in each type of advertising in the equilibrium? Third, how does
firms’ investment in both types of advertising affect their market performance
comparing to the benchmark case without advertising activities? The fourth question
is relevant to the societal effects of the different types of advertising.
To address the above questions, we consider an oligopolistic market with
horizontally and vertically differentiated products, where a portion of consumers are
initially informed about a characteristic of the product while, the other are initially
uniformed. Firms’ strategically use informative advertising in order to transmit all the
relevant information about the product attributes to consumers and thus, to increase
the proportion of the informed consumers. Equivalently, we can say that the use of
informative advertising help consumers identify the product that covers better their
needs and therefore it increase consumers valuation of the advertised product. On the
contrary, comparative advertising is strategically used by the firms in order to present
their product as superior to the rivals’ one. Therefore, the use of comparative
advertising not only increases consumers’ valuation for the advertised product but
also diminishes consumers’ valuation of the targeted product. However, despite the
differences between these two marketing strategies they are both accompanied by a
sufficiently high advertising cost. In this content, we consider a two stage game where
in the first stage firms decide upon the type and the level of each type of advertising
that they are going to undertake while, in the second stage they compete by setting
their quantities.4
Regarding the first question, we argue that in the equilibrium, firms’ optimal
decision is to invest in both informative and comparative advertising. Clearly, firms
are willing to undertake both types of advertising in order to increase their demand
not only, by attracting consumers through the use of informative advertising but also,
by decreasing the rival’s demand through the comparison.
4 In section 5 we also consider price competition.
As far as the second question is considered, we show that the firms’ investment
level in comparative advertising is positively connected to the degree of product
substitutability. In addition, we show that the firms’ investment level in informative
advertising tend to decrease when the products are not close substitutes while, it tend
to increase as the products tend to be perfect substitutes. It is well know, that as the
products tend to be close substitutes, the market competition augments. Therefore,
each firm has strong incentives to invest in a combination of informative and
comparative advertising in order to increase its market share by, informing the
initially uninformed consumers about the characteristics of its product and by
convincing them, through the comparison, that its product is superior to the rival’s
one. On the contrary, when the products tend to be independent, the alternative
characteristics of goods are easily recognized by the consumers and thus, firms tend to
decrease their investments in informative advertising. Further, a comparison between
goods is not effective any more.
Considering now the market outcomes, we observe that firms’ expenditures on
both types of advertising always lead to a higher output level and lower profits
comparing to those obtained at the benchmark case without any advertising activities.
In particular, the increased competition due to the firms’ investment in both types of
advertising leads to lower firms’ profitability while, the strategic complementarity
that we obtain between each firm’s investment in advertising and its output, leads to
higher firms’ total production. Clearly, firms end up in a prisoner’s dilemma situation
where they conclude to be worst off.
Further, regarding the welfare effects of the expenditures on advertising, we show
that in equilibrium, if the degree of competition is low, the social welfare when the
firms invest in both types of advertising is higher than that of the benchmark case
while, the opposite holds if the degree of competition is high. This is so because when
the market competition is low, the beneficial effect that the use of advertising has over
the net consumers’ surplus, due to the higher output production and the better
informed consumers, dominate the diminishing effect that the increased competition
has over the profits. On the contrary, when the degree of competition is high the
opposite holds.5
5 Note that the above results still hold under price competition.
Expanding our basic analysis, we further analyze the case where firms invest
solely in informative advertising.6 Comparing the equilibrium results of this case with
those obtained when the firms invest in both types of advertising, we argue that the
existence of comparative advertising in the firms’ sets of strategies lead them to
overinvest also in informative advertising in order to confront with the increased
competition that the use of comparative ads cause. Moreover, we show that the use of
both informative and comparative advertising leads always to higher output, lower
firms’ profits, higher net consumers’ surplus and lower social welfare.
The existed literature on the economic analysis of comparative advertising,
despite its significance and its extended use in practice, is limited. Aluf and Shy
(2001) using a Hotteling model, where comparative advertising increases the
transportation cost to the rival’s product, show that the use of comparative ads weaken
price competition by enhancing the degree of product differentiation and lead to
higher prices and profits. In a different vein, Barigozzi et al. (2006), examine
comparative advertising as a mean to signal quality. In particular, they consider a
market where an entrant, whose quality is unknown, decides between the use of
generic advertising, that is standard money burning to signal quality, or comparative
advertising, that implies comparison over the qualities of the two firms, in order to
face the incumbent whose quality is known.7 They conclude that the entrant’s
incentives to use comparative advertising are close related with the quality of his
product and the penalty that he is going to pay if the content of his advertising
campaign is manipulative8. In the same perspective, Emons and Fluet (2008) examine
also the signaling role of comparative advertising in a duopolistic market where both
firms use comparative advertising to highlight their quality differential and the cost of
advertising increases as the firms move away from the truth.
Anderson and Renault (2009) consider advertising as a mean through which
firms’ can disclosure information about horizontal match characteristics of the
products. In their context, comparative advertising can be used by a firm in order to
6 This configuration also reflects the case where consumers perceive comparative advertising as a manipulating firms’ marketing practice which does not capture any trustworthy information. 7 The signaling role of advertising is based on the idea that high advertising spending work as a device designed to signal high quality (e.g Nelson, (1974); Kihlstrom and Riordan, (1984); Milgrom and Roberts, 1986). 8 They assumed that when the entrant uses comparative advertising, the incumbent has the opportunity to go to the court and obtain gains if the court verdict is that the advertising is manipulative and the entrant’s true quality is low.
reveal information about the rival’s product attributes that the latter might not wish to
communicate. They show that when the products are of similar quality firms have
incentives to advertise only their own goods. Thus, comparative advertising plays no
role since, full product information is provided regardless. On the other hand, when
the products are of sufficiently different qualities, only the low quality firm has strong
incentives to use comparative advertising (if it is legal) in order to reveal the
horizontal attributes of both goods and thus, to have the chance by improving its
consumer base to survive in the market.
The present paper contributes to the existed literature on comparative advertising
in three ways. First, unlike the bulk of the literature that approaches comparative
advertising exogenously, we examine the firms’ incentives to invest in comparative
and informative advertising endogenously by considering the investment level in each
type of advertising as a strategic firm’s decision. Second, by considering a duopolistic
market with both horizontally and vertically differentiated products we provide results
on the impact that the degree of product substitutability has on the investment levels
in each type of advertising. Third, by extending our analysis under Bertrand
competition framework we reveal that even if the equilibrium results do not change
qualitatively from those obtained under Cournot competition framework, the intensive
competition when the firms compete in prices requires more advertising restrictions in
order firms to remain active on the market.9
The rest of the paper is organized as follows. In Section 2, we present our basic
model. In the section 3, we adduce the equilibrium analysis and the comparison with
the benchmark case without advertising activities. Section 4, includes the welfare
analysis. In section 5, we consider the comparison between our basic model and the
case of mere informative advertising. In section 6, we consider the extension of our
model under Bertrand competition. Finally, section 7 concludes.
9 This is in line to Peters (1984) and Bester and Petrakis (1995) and who claim that firms may be better off when there exist advertising restrictions.
2. The Basic Model. We consider an oligopolistic market that consists of two firms, denoted by i,j =1,2,
i j, each producing one brand of differentiated good. On the demand side, we
assume a unit mass population of consumers composed by individuals who have
homogenous preferences. In particular, following Häckner (2000), the utility function
of the representative consumer is given by:
mqqqqqqqqU jijijijijiiji ]γ2[2
1)()(),( 22
j (1)
where, qi, i =1,2 represents the quantity of good i, bought by the representative
consumer and m is the respective quantity of the “composite good”. The parameter
]1,0[ is a measure of the degree of substitutability, with γ→0 corresponding to the
case of (almost) independent goods and γ→1 to the case of (almost) homogeneous
goods. Alternatively, the parameter γ can be interpreted as the degree of competition
in the market with higher γ corresponding to lower degree of competition between
firms and vice versa. Further, i represents the investment level in informative
advertising while, i denotes the investment level in comparative advertising. Notice
that in our setup, the firms’ expenditures on informative advertising give to the
initially uninformed consumers the relative information to identify the product that
covers better their needs and thus, it increases their valuation for the advertised
product. On the other hand, comparative advertising has a dual effect. First, it
increases the consumers’ valuation of the advertised product. Second, it decreases the
consumers’ valuation of the targeted product of the rival firm (Chakrabarti and Haller,
2007). In other words, following Anderson et al. (2008), the firms’ expenditures on
comparative ads are beneficial not only due to the direct effect of promoting as
superior their own product but also due to the diminishing effect on the rival’s
product.
Solving the utility maximization problem of the representative consumer we
obtain the inverse demand function faced by each firm:
jijiii qqp , i =1,2, ; i j (2)
where pi, pj are the firms’ prices, while the price of the “composite good” has been
normalized to unity. Note that the firm i’s investment in informative and comparative
advertising shifts its demand curve outwards. On the contrary, the firm j’s investment
in comparative advertising has a detrimental impact on the firm i’s demand since it
shifts the demand curve of the latter inwards.
Further, we assume that firms are endowed with identical constant returns to scale
production technologies, with their marginal production cost being symmetric and
equal to c, 0< c ≤ α. In addition, we assume a quadratic advertising cost, )( 22iib ,
that implies the diminishing returns of advertising expenditures. Thus, the total cost
function of firm i is given by: )( c(.) 22iiii bqC . The parameter b reflects the
effectiveness of the advertising technology on shifting consumers’ demand. A higher
b denotes a less effective advertising technology: the higher the b, the higher the
required expenditures to obtain a given shift on consumers demand. To guarantee
well-behaved interior solutions in all cases we make the following assumption
throughout the paper:
Assumption 1: 22
2
)4(
84
b
Assumption 1 indicates that the effectiveness of advertising investments is not too
high; otherwise firms would have incentives to overinvest in advertising in order to
increase their demand that may lead both of them out of the market. 10
As it follows, the firm i’s net profits can be expressed as:
)(c)( 22iiiijijiii bqqqq i =1, 2; i j (3)
Therefore, the advertising investments by firm i ( ,i i ), lead to higher consumers
valuation for its product and thus, to higher demand while, at the same time they
increase firm i’s overall cost. On the contrary, it is clear that the comparative
advertising expenditures made by firm j ( j ) have a diminishing effect in firm i’s
demand and its overall profitability.
We consider a two stage game with the following timing. In the first stage, firms
decide independently and simultaneously upon the type and the investment level in
10 The assumption corresponds with Peters (1984) and Bester and Petrakis (1995) who claim that in some cases firms are better off under advertising restrictions.
each type of advertising that they are going to undertake in order to promote their
products. In the second stage, given the decisions of the previous stage, they compete
in the market by setting their outputs. The above game is solved backwards by
employing the Subgame Perfect Nash Equilibrium (SPNE) solution concept.
3. Equilibrium Analysis.
3.1 Benchmark Case: no investment in advertising.
Before proceeding to the equilibrium analysis of the basic model, we briefly discuss
the benchmark case where firms do not undertake any advertising activities, thus μi
=μj=0 and κi =κj=0. Hence, the market outcomes can be described by the standard
Cournot game with differentiated products, where each firm chooses its output, in
order to maximize its profits given by ΠiC = iii qqq c)γq( j .
Taking the first order conditions, we evaluate the reaction function of each firm, given
by:
2
cγq)( j
jCii qRq (4)
Due to symmetry, we obtain that the equilibrium price; output and profit are,
respectively,
γ2
c
a
qC , γ2
γ)c1(
a
pC , 2
22
γ)(2
c)-(α)(
CC q (5)
Finally, since we have assume a unit mass population of consumers composed by
individuals who have identical preferences, it turns out that each consumer buys a
quantity q=qC of each good. Further, using (1) and (5), the net consumers’ surplus and
the total welfare are given,
2
22
γ)(2
c)-(α)1()1(
Cnet
C qCS , 2
2
γ)(2
c)-(α)3(
CTW (6)
3.2 Endogenous choice of advertising.
We proceed our analysis with case of the firms’ endogenous selection of
advertising. In the last stage of the game each firm chooses its output qi, taking as
given the rival’s output qj along with the expenses on each type of advertising (μi,j,
κi,j), decided in the first stage of the game, in order to maximize its profits given by
(3).
From the first order conditions of (3), the reaction function of firm i is given by:
22
q)( j jii
jCIii
cqRq
(7)
Comparing )( jCIi qR with the reaction function of the no advertising case )( j
Ci qR ,
in which only the left term of (7) appears, we observe the dual effect that the use of
advertising has over the output. On the one hand, firm i’s expenditures on informative
and comparative advertising (μi, κi) tend to augment its demand and thus, its
production and equilibrium output. On the contrary, the rival’s firm investment in
comparative advertising (κj) tends to decrease equilibrium output. Note also that the
slope of firm i’s reaction curve is ( ) ( )
2
CI Ci j i j
i i
R q R qq q
, implying that
( )CIi jR q is an outward and parallel shift of the respective curve in the benchmark
case.
Solving the system of reaction functions (7), we obtain the equilibrium output on
the second stage,
2j
4
)()(2))(2((.)
ijjiiCIi
cq (8)
Using the above equation the following observations are in order: Firstly,
04
22
i
CIiq and 0
2
1
i
CIiq indicate strategic complementarity
between the firm i’s informative and comparative advertising investments and its
output. Hence, an increase in firm i’s advertising expenditures is going to increase its
output. Secondly, 02
1
j
CIiq shows strategic substitutability between the
firm j’s comparative advertising expenditures and firm i’s output. Therefore, firm j by
increasing its comparative advertising investment has the opportunity to decrease firm
i’s output.
In the first stage of the game, firm i chooses the expenditure level of each type of
advertising ( i , i ) in order to maximize its profits. Thus, firm’s i maximization
problem is:
(9)
Applying first order conditions, we get the best reply functions for both informative
and comparative advertising given by:
4)4(
]))(2(c)-α)(2[(2)(
22ji
bj
ji (10)
)2](1)2([
2)2(c)-α)(2()( 2
j
bij
ji (11)
As it follows from the best reply functions, 04)4(
222
bj
i ,
01)2(
12
bj
i , 0
j
i
, 0
j
i
that implies the existence of
strategic substitutability between the level of informative and comparative advertising
expenditures with the corresponding values of the rival’s firm. Clearly each firm is
going to increase its investment in both informative and comparative advertising in
order to reduce the advertising investment of the rival firm and thus, to possess
comparative advantage. Moreover, we observe strategic complementarity between
each firm’s investment in informative and comparative advertising since,
04)4(
)2(222
bi
i and 0)1)2()(2(
22
bi
i . Hence, an
increase in the firm i’s investment in comparative advertising is accompanied by a
higher investment in comparative advertising and vice versa.
By imposing symmetry and solving the first order conditions system, we obtain
firm i’s equilibrium investment level for both informative and comparative
advertising,
02)2)(2(
c)-α(22
*
bi (12)
02)2)(2(
2)c)(-α(22
*
bi (13)
)()4(
)]()(2))(2[((.)max 22
22
2j*
,ii
ijjiii b
c
ii
From (12) and (13) we observe that firms endogenous choice is to invest both in
informative and in comparative advertising. The intuition behind this result is that,
given the strategic complementary between the informative and comparative
advertising, firms are willing to undertake both types of advertising in order to
increase their demand not only by attracting consumers through the use of informative
advertising but also by decreasing the rival’s demand through the comparison. Hence,
the following proposition can be stated:
Proposition 1: In equilibrium, firms’ endogenous choice is to invest in a combination
of informative and comparative advertising.
Note also that, 22
2*
])2)(2(2[
])2()2)(2(2[2
b
bbi <0 for ]66.0,0[ while
0*
i for ]1,66.0( . It is obvious that for the relative low values of
competition there exist a negative relationship between the firms’ investment levels in
informative advertising and the degree of competition, while for higher values
66.0 the opposite holds. Further, 0])2)(2(2[
2)2(222
2*
b
bi for all the
given values of γ thus, the equilibrium comparative advertising expenditures are
positively related to the degree of competition.
Clearly, market competition is fiercer when γ is high and this makes firms’
incentives to invest in advertising even stronger. In particular, the intuition behind the
above results is that when the products tend to be close substitutes, i.e for the higher
values of γ, the market competition augments. Therefore, each firm has strong
incentives to invest in both informative and comparative advertising in order to
increase its market share by two alternative ways: first, by informing the portion of
the previously uninformed consumers and second by convincing consumers, through
the comparison, that its product is superior than the rival’s one. However, when the
products are not close substitutes, i.e for the lower values of γ, the alternative
characteristics of the goods are easily recognized by the consumers and thus, firms
tend to decrease their investments in informative advertising. Further, a comparison
between them is not effective any more.
In addition, 0))2)(2(2(
)2)(2(222
2*
bbi , 0
))2)(2(2(
)2)(2(22
3*
bb
i
show that the more effective the advertising technology is, i.e, the lower values of b,
the higher is the investment in advertising, ceteris paribus. The following lemma
summarizes:
Lemma 1.
i) The equilibrium investment in informative advertising is decreasing in the degree of
competition for ]66.0,0[ , while it is increasing in the degree of competition for
(0.66,1] . Moreover it is always decreasing in the effectiveness degree of
advertising technology (b).
ii) The equilibrium investment in comparative advertising is increasing in the degree
of competition (γ) while, it is decreasing in the effectiveness degree of advertising
technology (b).
Plugging (12) and (13) into (7) and (3), firm’s equilibrium output and profits are
given,
02)2)(2(
)4c)(-α(2
2
b
bq CI
i (14)
0]2)2)(2([
]}8)4()4{b[b(c)-α(22
222
bCI
i (15)
By comparing the equilibrium values of output and profits in the case where firms
invest both in informative and comparative advertising, with the ones obtained in the
benchmark the following proposition derives,11
11 For the extended proof see at the appendix.
Proposition 2:
i) Equilibrium output is higher when firms invest both in informative and comparative
advertising, than that of the benchmark without any advertising activities. That is,
CIq >qC always holds.
ii) Equilibrium profits are lower when firms invest both in informative and
comparative advertising, than that of the benchmark without any advertising
activities. That is, ΠCI < C always holds.
It is clear that the increased competition due to the firms’ investments in
advertising leads to higher output production and lower firms’ profits than those
obtained at the benchmark case. Hence, firms conclude in a prisoners’ dilemma
situation that leads them to be worst off. As a consequence, the optimal decision of
firms to invest in a combination of comparative and informative advertising can be
characterized as the case of “wasteful advertising”12.
Further, using (14) we observe that the equilibrium output is negatively connected
with both the degree of competition γ and the advertising effectiveness parameter b
since, 0))2)(2(2(
])4(4[22
22*
b
bbqi and 0))2)(2(2(
)4(222
2*
bb
qi .
The explanation behind this result is based on two facts. First, the augment
competition leads firms to produce lower output. Note that the firm i's reaction curve,
given by the analysis after (7) ( )
2
CIi j
i
R qq
, has a negative slope, therefore an
increase in γ tend to decrease the slope of the reaction curve and as a consequence,
leads to a lower equilibrium output. Second, given the strategic complementarity
between the output and the advertising levels along with the strategic substitutability
between advertising and effectiveness parameter b, observed by the analysis after (8)
and Lemma 1, we have that an increase in b leads to lower advertising investments
and thus, to lower equilibrium output.
12 The term of wasteful advertising was first introduced by Pigou 1924, in order to describe the prisoner’s dilemma which arises when competing firms in a market invest equal efforts in advertising in order to attract the favor of the public from the others. As Pigou first showed this concludes in a prisoner’s dilemma where none of the firms gains anything at all.
Moreover, by (15) we have that 0
CIi , while 0
b
CIi hence, the equilibrium
profits are negatively connected with the degree of competition γ and positively
connected to the advertising effectiveness parameter b.13 Clearly, as the competition
augments, i.e for the higher values of γ, firms’ obtain lower profitability. On the
contrary, we observe that the lower the effectiveness of advertising is, the higher is
the profitability of firms. The rationale behind the latter result is as follows. First,
following Lemma 1 we show that the higher the b is, the lower are the firms’
expenditures on informative and comparative advertising. Hence, given the profit
function (3), firms’ lower investment in advertising has a diminishing effect on their
demand and thus, on their profits. On the contrary, lower firms’ advertising
expenditures implies lower firms’ total cost and thus, higher firms’ profits. In
addition, it is noteworthy that the lower firms’ investment in comparative advertising
declines the diminishing effect on each firm’s demand due to rival’s comparative
advertising and therefore, it acts beneficially to profits. The equilibrium results reveal
that the positive effect on profits by the lower advertising investments dominates.
This is in line with the Proposition 2 since, a less effective advertising prevents firms
from overinvesting in such marketing practices and as a consequence, diminishes
market competition and leads to higher firms’ profits. The following Lemma
summarizes:
Lemma 2. Equilibrium output is decreasing both in the degree of substitutability
between products γ and in the advertising effectiveness parameter b, while
equilibrium profits are decreasing in γ but increasing in b.
13 After some manipulations it can be testified that,
0))2)(2(2(
16)]4(2)8()2)(2([32
2
b
bb
CIi and
0))2)(2(2(
)]2)4(()2(2)4()2(2[232
2322
b
bbbCIi always hold.
4. Welfare Analysis. In this section we discuss the impact of the firms’ decision to investment in both
informative and comparative advertising on the social welfare. Total welfare is
defined as the sum of consumers and producers surplus:
*2 inetCSTW (16)
with CSnet and 2Πi* corresponding to the net consumers surplus and the overall market
profits respectively. In particular, the net consumer surplus for the representative
consumer is given by the following expression:
jjiijijijijjijiiCInet qpqpqqqqqaqCS 2
2
1 22 (17)
By imposing symmetry, we have that CICIj
CIi qqq , *** ji , *** ji and
CICIj
CIi ppp . Thus, (17) can be written as:
2])[1( CICInet qCS (18)
Further, with respect to (16), (18) and (14), the total welfare can be written as:
22
22
]22)2)(-[b(
]})4(216-4)-3)(b{[b()c(
CITW (19)
By comparing the equilibrium values of the net consumers’ surplus and the social
welfare in the case when firms invest both in informative and comparative
advertising, with the ones obtained in the benchmark case the following Proposition
derives14
Proposition 3.
i) In equilibrium net consumers’ surplus and social welfare are higher if firms
invest in informative and comparative advertising than the corresponding
values at the benchmark case in which firms do not undertake any advertising
activities. Hence, Cnet
CInet CSCS , always hold.
14 For the proof see in the appendix.
ii) In equilibrium if the degree of competition is low ( ]4.0,0[ ), social welfare
is higher when firms invest in informative and comparative advertising than
the corresponding values at the benchmark case in which firms do not
undertake any advertising activities. The opposite holds if the degree of
competition is high ( ]1,4.0( ).
We turn now to discuss the main arguments that drive the above results. By using (6)
and (18), and since CIq >qC always holds, it can be easily checked that Cnet
CInet CSCS
for all the given values of the parameters γ and b. The rationale behind this result is
based on the dual beneficially effect of advertising. Firstly, firms’ investment in
advertising leads to more and better informed consumers which acts beneficially to
the net consumers’ surplus. Secondly, the increased competition among the firms,
leads to higher total production, that make consumers better off. Note also, that for
]4.0,0[ CCI TWTW holds while, for ]1,4.0( CCI TWTW . Clearly, when the
products are not close substitutes the beneficially effect of the higher net consumers’
surplus when firms invest in advertising dominates the diminishing effect of the lower
firms’ profitability. On the contrary, as the substitutability between products increases
the diminishing effect of the lower profits dominates the beneficially effect of the
higher net consumers’ surplus.
Further we observe that the net consumers’ surplus when the firms’ invest in both
informative and comparative advertising is diminishing both in the degree of
competition and the advertising effectiveness since, 0
CInetCS and 0
b
CS CInet
always hold.15 The intuition behind the latter result is straightforward. First, for a
given effectiveness of advertising, as the products tend to be homogeneous the overall
expenditure on advertising tend to decrease. Thus, we conclude in less informed
consumers that has a detrimental impact on the net consumers’ surplus. Second, as the
products tend to be perfect substitutes, the equilibrium output of each firm decreases
which tends to decline the net consumers’ surplus.
Finally, using (19) we obtain that the social welfare is decreasing in all the values
of the market competition γ and in the lower values of the advertising effectiveness b
15After some mathematical manipulation one can easily observe that
0))2)(2(2(
)]}54(2)4([8){4(32
2222
b
bbCSCInet
,0
))2)(2(2(
)4)(1(432
22
b
bb
CS CInet
while, it is increasing for the higher values of b since,
0CITW
,
0
bTW CI
for ]4.0,0[ while, 0
bTW CI
for ]1,4.0( .16 It is obvious that
for the higher values of b the positive effect of profits due to the lower firms’
investments in advertising dominates the negative effect of the lower net consumers’
surplus. However, in absolute values the total welfare tend to decrease and thus, the
proportional decrease on the total welfare due to the increased competition dominates.
We summarize our findings in the follow proposition:
Proposition 4: In equilibrium, net consumers’ surplus is decreasing in both the
degree of substitutability between products γ and in the advertising effectiveness
parameter b while, the social welfare is decreasing in γ and in the lower values of b
(that is, when ]4.0,0[ ) but is increasing for the higher values of b (that is,
when ]1,4.0( )
5. The case of mere informative advertising.
In this section we consider the comparison between the case where firms invest in
both types of advertising and the case where firms invest only in informative
advertising. The latter case has been motivated by two alternative facts. First, even if
the countries legislation framework does not prohibit the use of comparative
advertising, firms tend to avoid this aggressive marketing practice because of the high
risk to be accused for an attempt to mislead consumers and be prosecuted by the rival
to the court17 [see for details, Barigozzi and Peitz (2006); Barigozzi, et al. (2006)].
Second, the fact that consumers may perceive a firm’s comparative advertising
campaign as manipulative and thus, as a non trustworthy source of information [see
for details, Wilkie and Farris (1975); Barone and Miniard (1999)].
In the mere informative case we assume that κi =κj=0, therefore firm i’s inverse
demand is given now by: jiiINi qqp . Hence, in the final market
16 After some mathematical manipulation one can easily observe that
0))2)(2(2(
))]}2(34(3[2)4()2()2(8){2(32
232
b
bbbTW CI ,0
))2)(2(2(
]8)4([4)3168()2(232
32
b
bb
TW CI
17 In 2000 Papa John’s was forced by the court to pay over 468.000$ in damages to Pizza Hut due to the advertising campaign “Better ingredients. Better pizza” that has been judged as misleading since, such claims can not be proved.
competition stage, where firms compete by setting their outputs, firm i solves the
maximization program,
2)(max iiijiiINi
qbcqqqq
i
(20)
The best reply function of firm i is
2
)q()( j i
jINii
cqRq
(21)
Therefore by solving the system of foc, we obtain equilibrium output of the second
stage, given by:
2
j
4
2))(2(
iINi
cq (22)
Note that equilibrium output in the case where firms invest only in informative
advertising is decreasing as the rival’s investment in advertising increases and
products tend to be close substitutes.
In the first stage of the game, the maximization program of the firm i is given by:
(23)
Applying first order conditions we have that the best reply function in informative
advertising is given by:
4)4(
]c)-α)(2[(2)(
22
bjIN
jINi (24)
Exploiting symmetry we have that equilibrium level of investment in informative
advertising,
01)2(
c)-α(2
*
b
INi (25)
By comparing the equilibrium investment in informative advertising in the case were
firms invest solely in informative advertising, with the corresponding values in the
case where firms invest in both informative and comparative advertising the following
Proposition derives18
18 For the proof see in the appendix.
2
22
2j
)4(
]μ2))(2[(max i
iINi b
c
i
Proposition 5: Firms’ expenditures level on informative advertising under the mix
advertising case equals that of the mere informative case when the products are
independent (γ=0), while it is always higher for all the other given values of γ.
The intuition behind this result is that the use of comparative advertising augments
market competition which in turn, leads firms to overinvest also in informative
advertising.
Note that in contrast to the analysis regarding Lemma 1 where, the expenditure
levels in informative advertising was negatively connected to the degree of
competition for ]66.0,0( , in the case of mere informative advertising we have that
0]1)2([
)2(222
*
b
bINi hold for all the given values of γ. The reason for the
latter is that since firms do not have any more the comparative advertising in their set
of strategies and thus, they are not threaten by the comparative advertising of the
rival, they choose to invest less in advertising when the market competition augments,
i.e for the higher values of γ, in order to avoid the negative consequences of
advertising cost. Moreover, 0]1)2([
)2(222
2*
bb
INi . This replicates our
arguments considering Lemma 1.
By substituting (25) to (22), (20), (18) and (16) the equilibrium values for output,
profits net consumers’ surplus and total welfare respectively are given by:
1)2(
)2c)(-α(2
*
b
bq IN
i , 1)2(
c)-α(2
2*
b
bINi
22
222
]1)2([
)2(c)-α)(1(
b
bCS net
IN , 22
22
]1)2([
c)-α](2)3()2([
b
bbTW IN (26)
Further, comparing the equilibrium values of output, profits, consumers’ surplus and
total welfare in the case when firms invest only in informative advertising, with the
ones obtained in the case where the firms invest only in informative advertising and
the benchmark the following Proposition derives
Proposition 6: If firms invest only in informative advertising, equilibrium output and
net consumers’ surplus are lower than if firms invest in both informative and
comparative advertising but higher than the benchmark. Profits and total welfare are
higher than if firms invest in both informative and comparative advertising and the
benchmark. Hence, the following inequalities hold:
CINCI qqq , INCI qq for γ = 0
CICIN
CINCI CSCSCS , INCI CSCS for γ = 0
CIN TWTW and CIIN TWTW while, forTWTW CCI , ]4.0,0[ and
forTWTW CIC , ]1,4.0(
The following observations are in order. First, regarding output, given the
strategic complementarity between the level of advertising and output along with the
results presented in proposition 5, it is clear that the higher levels of advertising
investment when firms invest in both types of advertising lead to higher levels of
output comparing to those obtained in all the other cases. Second, considering the
equilibrium profits, it is obvious that when firms invest in both informative and
comparative advertising they conclude to be worst off. The explanation behind the
latter is that the use of comparative advertising leads to intensified competition both
in advertising and output level and thus, leads to overinvestment in advertising, higher
total production and lower profits. On the contrary, when the firms invest solely in
informative advertising, the beneficial effect of the increased firms’ demand due to
the advertising expenditures dominates the diminishing effects of the advertising costs
and the fiercer competition. Hence, firms conclude to be better off. From all the above
it is clear that firms’ optimal choice to invest both in informative and comparative
advertising leads them to a prisoner’s dilemma situation where they obtain the lower
profits.
Continuing our analysis, considering consumers’ surplus, we have from the
analysis after (18) that it is positively related to the output level. Further since
CINCI qqq always holds CINCI CSCSCS holds also. Thus, the firms’
investment in advertising (informative and comparative) acts beneficial to consumers
since it provide more information and leads to higher total production. Finally,
regarding total welfare it is obvious that the effect of the higher firms’ profitability
when they invest only in informative advertising dominates the effect of the higher
consumers’ surplus when firms invest in a combination of informative and
comparative advertising and the benchmark.
6. Extensions
6.1 Bertrand Competition.
In this section we consider the case where firms in the last stage of the game compete
by choosing their prices. In this case each firm i faces the linear demand function
)1())(1()1( 2 jijijii ppaq , 10 . Keeping all the other modeling
specifications fixed, we observe that all of our main results still hold under Bertrand
market competition and the intuitive arguments are in line with the respective ones in
the Cournot case. In particular, we show that firms in the equilibrium have always
strong incentives to invest in both informative and comparative advertising for all the
given values of the substitutability parameter γ. However, we observe that the
assumption over the advertising effectiveness parameter b, changes from
22
2
)4(
84
b under Cournot competition to
)1()4(
82427222
432
b under
Bertrand competition.19 Thus, our model possesses a price setting equilibrium only if
the cost of advertising is significantly higher than that of Cournot. The intuition
behind this result is derived directly by the fact that the Bertrand competition is
“harder” than Cournot. Thus, as the advertising tends to be ineffective firms tend to
invest less in advertising which protects them by the impacts of the existing prisoners’
dilemma.
7. Conclusions
In this paper, we have endogenously investigate the firms’ incentives to invest in
informative and comparative advertising in an oligopolistic market with horizontal
and vertical product differentiation, taking as basic premise, that informative
19 One can easily observe after some manipulations that the assumption over the effectiveness parameter b under Bertrand competition is stricter than that under Cournot competition.
advertising is used by firms as a mean to transmit information to consumers while,
comparative advertising is mainly used in order present the advertised product as
superior to the rival’s one.
We argue that in the equilibrium firms’ optimal decision is to invest in both
informative and comparative advertising. Further, we show that while the firms’
expenditures on comparative advertising are positively connected to the degree of
product substitutability, the firms’ expenditures on informative advertising tend to
decrease when the products are not close substitutes and they tend to increase as the
products tend to be perfect substitutes. Our main findings also hold under Bertrand
competition if the advertising effectiveness parameter b is sufficiently high.
Moreover, by comparing the equilibrium outcomes when firms invest in a
combination of informative and comparative advertising with those obtained at the
benchmark case without advertising activities and those of the mere informative
advertising case, we show that firms’ endogenous choice to invest in both types of
advertising always leads them to higher output production and lower profitability.
Thus, firms find themselves in a prisoner’s dilemma situation where they conclude to
be worst off. Hence, comparative advertising can be characterized as “wasteful
advertising” since both of the firms would be better off, if this aggressive form of
advertising has been prohibited. On the contrary, our analysis reveals that the use of
both informative and comparative advertising is beneficial to consumers, since it leads
to higher net consumers’ surplus due to the higher output and the improved
information that consumers possess.
Throughout the paper we have restricted our attention to a duopolistic market.
Therefore, it would be challenging to extend our analysis by examine how the
equilibrium results may change when there exist more than two competing firms in
the market since, in a situation like that the use of comparative advertising may
emerge a free-rider problem. Further, it would be interesting enough to relax our
maintain assumption about firms’ symmetry and to investigate how the size of a firm
could alter its incentives to invest in comparative and informative advertising. Since
both of the scenarios described above are not easy tasks, their analysis awaits for
further work.
8. Appendix
8.1 Proof of Proposition 2
Output: Taking the firm i’s reaction curve when the firms invest in both informative
and comparative advertising we have that,
22
q)( j jii
jCIii
cqRq
Comparing )( jCIi qR with the reaction function of the benchmark case without
advertising activities )( jCi qR , in which only the left term of above equation appears,
and due to the symmetry of the game that implies that at the equilibrium the optimal
expenditure on comparative advertising is equal for both firms, κ*i = κ*
j= κ*, (the
effect of each firm’s investment in comparative advertising neutralize one another), it
is obvious that CIq > Cq always holds since at the equilibrium, only the beneficial
effect of informative advertising over the output exists.
Profits:
By evaluating the difference between the equilibrium profits of the case where firms
invest both in comparative and informative advertising given in (15) and the profits of
the benchmark case given in (5) we have that,
0]2)2)(2([)2(
]4)8()2([)(222
22
b
bcCCI
Clearly from the above equation, since both the nominator and the denominator are
positive for all the given values of the parameters b and γ, C > CI always holds.
8.2 Proof of Proposition 3
Consumers’ Surplus: By equation (6) we have that 2])[1( CCnet qCS while by the
(18) we have that 2])[1( CICInet qCS . Therefore, since CIq > Cq always holds, it can
be easily checked that Cnet
CInet CSCS for all the given values of the parameters γ and b.
Total Welfare: Taking the difference between the social welfare when firms invest in both informative and comparative advertising given in (19) and that of the benchmark case given in (6) we have that,
222
22
]2)2)(2([)2(
)463()2(2)3(4
b
bTWTW CCI
From the above equation it can be easily testified, after some manipulations, that for
]4.0,0[ CCI TWTW holds while, for ]1,4.0( CCI TWTW .
8.3 Proof of Proposition 5
Taking the difference between the equilibrium expenditure level in informative advertising when firms invest solely in informative advertising and the corresponding value obtained when the firms invest both in informative and comparative advertising we have that,
]2)2()2(][1)2([
)()2(222
2**
bb
cbINCI
The above equation turn to be positive for all the ]1,0( while it is zero for γ=0.
Thus, ** INCI with equality when γ=0
8.4 Proof of Proposition 6
Output: Using (14) and (26) we have that
]2)2()2(][1)2([
))(2(22
**
bb
cbqq INCI
The above equation is always positive for ]1,0( while, it is equal to zero when
γ=0. Therefore, ** INCI qq with equality when γ=0. Further from Proposition 2 we
have that CIq > Cq always hold. Thus, CINCI qqq , INCI qq for γ = 0.
Profits: Given equations (15),(26) we have that,
222
222
]2)2)(2(][1)2([
c)-α]}(2)22(2[)2{(
bb
bbCIi
INi
The above equation always exceed zero, thus IN >ΠCI holds for all the given values
of parameters γ and b. Further, from Proposition 2 we have that C > CI always
holds. Therefore, CICIN .
Consumer Surplus: Consumer Surplus can be expressed as 2*])[1( qCSnet in
addition we have show that CINCI qqq , INCI qq for γ = 0. Hence, it is obvious that
CINCI CSCSCS , INCI CSCS for γ = 0.
Social Welfare: Using equations (19), (26) we have that,
2222
222
]2)2)(2([]1)2([
))]2(4)(2(2))3(12(16(2[)2()(
bb
bbbcaTWTW CIIN
The above exceeds zero for the given values of γ and b. Thus, CIIN TWTW Further,
using (6) and (26) we have that,
222
2232
]1)2([)2(
))]2(4)(2(2))3(12(16(2][3)2(2[)(
b
bbbcaTWTW CIN
The above equation is always positive for all the given values of γ and b. Thus, we
conclude that CIN TWTW always hold.
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