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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Work in progress, please do not quote!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
This paper investigates the firms’ incentives to invest in informative and/or
comparative advertising, in an horizontally differentiated oligopolistic market. We
show that in equilibrium, the firms’ optimal decision is to invest in a combination of
informative and comparative advertising. The expenditure levels on each type of
advertising are determined by the degree of substitution between the 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: alipranti@stud.soc.uoc.gr ‡Department of Economics, University of Cyprus; e-mail: mitrokostas.evangelos@ucy.ac.cy §Corresponding author. Department of Economics, University of Crete, Univ. Campus at Gallos,
Rethymnon 74100, Greece, Tel: +30-28310-77407, Fax: +30-28310-77406 {petrakis@rector.uoc.gr}.
2
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 tend 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)
3
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 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 differentiated products, where consumers do not possess any information
about the products. Firms strategically use informative advertising in order to transmit
all the relevant information that helps consumers to identify the product that covers
better their needs. Therefore, the use of informative advertising tends to 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. Thus, the use of comparative advertising not only increases
consumers’ valuation for the advertised product but also decreases 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, independently and simultaneously, upon the type(s) of advertising to launch as
well as the investment level on each type of advertising that they launch. In the
second stage firms compete by setting their quantities.4
Regarding the first question, we argue that in 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.
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 levels in informative
4 In section 5 we also consider price competition.
4
advertising tend to decrease when the products are poor substitutes while, they tend to
increase as the products tend to be perfect substitutes. It is well know, that as the
product substitutability increases, the market competition enhances. Thus, each firm
has strong incentives to invest in a combination of informative and comparative
advertising in order to enlarge 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, the
lower market competition, when the products are poor substitutes, leads firms to
invest less in both informative and comparative advertising in order to avoid the
detrimental effect of the high advertising costs.
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 positive relationship that we
obtain between each firm’s investment in advertising and its output, leads to higher
firms’ total production. Clearly, firms find themselves in a prisoner’s dilemma
situation where they end up being worse 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 consumers’ surplus, due to the higher output production and the better informed
consumers, dominate the detrimental effect that the increased competition has over
the profits. On the contrary, when the degree of competition is high the opposite
holds.5
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 leads them to
5 Note that the above results still hold under price competition. 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.
5
overinvest also in informative advertising in order to confront with the fiercer
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
weakens price competition by enhancing the degree of product differentiation and
leads 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
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 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.
6
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 four ways. First, unlike the bulk of the literature that approaches comparative
advertising exogenously, we examine the firms’ incentives to invest in comparative
and/or informative advertising endogenously by considering the investment level in
each type of advertising as a firm’s strategic decision. Second, we provide results over
the optimal advertising portfolio (the optimal allocation of firms’ advertising
expenditures between comparative and informative advertising) that a firm is going to
use when both of these advertising strategies are available in the industry. Third, by
considering a duopolistic market with horizontally differentiated products we provide
results on the impact that the degree of product substitutability has on the investment
levels in each type of advertising. Fourth, 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.
7
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 higher 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 contrary, 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 detrimental 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)
8
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: )( (.) 22iiii bcqC . 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:
)()( 22iiiijijiii bcqqqq 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(s) to launch as well as the
investment level on each type of advertising that they launch in order to promote their 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.
9
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 The Benchmark Case without any 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 horizontally differentiated products, where each firm chooses its
output, in order to maximize its profits given by ΠiC = iiji cqqqq )( .
Taking the first order conditions, we evaluate the reaction function of each firm, given
by:
2
)(cq
qRq jj
Cii
(4)
Due to symmetry, we obtain that the equilibrium price; output and profit are,
respectively,
2
cqC ,
2
)1( cpC ,
2
22
)(2
)()(
cα
qCC (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 consumers’ surplus and the
total welfare are given,
2
22
)(2
)()1()1(
c
qCS CnetC ,
2
2
)(2
)()3(
c
TW C (6)
3.2 Endogenous selection 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,
10
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
c)( jiij
jCIii
qqRq
(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 increase 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
)()(
i
jCi
i
jCIi
q
qR
q
qR, implying that ( )CI
i 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,
2
j
4
)()(2))(2((.)
ijjiiCI
i
cq (8)
Using the above equation the following observations are in order: Firstly,
04
22
i
CIiq
and 02
1
i
CIiq
indicate that an increase in firm i’s
advertising expenditures tends to increase its output. Secondly, 02
1
j
CIiq
shows the negative relationship between the firm j’s investments in comparative
advertising and the firm i’s output. In particular, 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)
)()4(
)]()(2))(2[((.)max 22
22
2j*
,ii
ijjiii b
c
ii
11
Applying first order conditions, we get the best reply functions for both informative
and comparative advertising given by:
4)4(
]))(2()-)(2[(2)(
22
ji
b
c jji (10)
)2](1)2([
2)2()-)(2()(
2
j
b
c ijji (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(
)(22
*
b
ci (12)
02)2)(2(
2))((22
*
b
ci (13)
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,
12
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 γ
(equivalently, the lower values of the degree of competition) there exist a negative
relationship between the firms’ investment levels in informative advertising and the
degree of product substitutability, 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 product substitutability. Further, we observe that the optimal investment mix
)2(
2*
*
i
i is decreasing in the degree of product substitutability γ and it is
independent of the effectiveness of the advertising technology.
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 increases. Therefore, each firm has strong
incentives to invest in both informative and comparative advertising in order to
enlarge its market share by two alternative ways: first, by informing the previously
uninformed consumers and second by convincing consumers, through the
comparison, that its product is superior than the rival’s one. However, the lower
market competition when the products are poor substitutes, i.e for the lower values of
γ, leads firms to invest less both in informative and comparative advertising.
13
In addition, 0))2)(2(2(
)2)(2(222
2*
bbi , 0
))2)(2(2(
)2)(2(22
3*
bbi
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 non-monotonic in the
degree of product substitutability. It is decreasing (increasing) in the degree of
product substitutability for low (high) γ. Moreover, it increases as the advertising
technology becomes more effective (lower b).
ii) The equilibrium investment in comparative advertising is increasing in the degree
of product substitutability γ. Moreover, it increases as the advertising technology
becomes more effective (lower b).
Plugging (12) and (13) into (7) and (3), firm’s equilibrium output and profits are
given,
02)2)(2(
)4()(2
2
b
cbq CI
i (14)
0]2)2)(2([
]8)4()4([)(22
222
b
bbcCIi (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.
14
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. Thus, firms’ decision to invest in both types of
advertising leads them to a prisoner’s dilemma situation, where they end up to be
worse off.
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 intensified 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 negative relationship between b and advertising
expenditures along with the positive relationship between the output and each firms’
advertising levels, observed by Lemma 1 and the analysis after (8), we have that a less
effective advertising technology (higher b) leads to lower advertising investments and
thus, to lower equilibrium output.
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
15
connected to the advertising effectiveness parameter b.12 Clearly, as the competition
increases, 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 (higher b), 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 detrimental 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 technology
prevents firms from overinvesting in such marketing practices and as a consequence,
decreases market competition and leads to higher firms’ profits. The following
Lemma summarizes:
Lemma 2. Equilibrium output and profits are decreasing in the degree of
substitutability between products γ. Equilibrium output increases while, equilibrium
profits decrease, as the advertising technology becomes more effective (lower b).
12 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.
16
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 iCSTW (16)
With CS and 2Πi* corresponding to the consumers surplus and the overall market
profits respectively. In particular, the consumer surplus for the representative
consumer is given by the following expression:
jjiijijijijjijiiCI qpqpqqqqqqCS 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( CICI qCS (18)
Further, with respect to (16), (18) and (14), the total welfare can be written as:
22
22
]22)2)(-([
])4(216-4)-3)(([)(
b
bbcTW CI (19)
By comparing the equilibrium values of the 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 derives13
Proposition 3.
i) In equilibrium, consumers’ surplus and social welfare when firms invest in
both informative and comparative advertising are higher than the
corresponding values of the benchmark case, without advertising activities.
Hence, CCI CSCS , always hold.
13 For the proof see in the appendix.
17
ii) In equilibrium, social welfare when firms invest in informative and
comparative advertising is higher than the corresponding values of the
benchmark case without advertising activities for the lower values of γ
( ]4.0,0[ ) while, the opposite holds if ]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 CCI CSCS
for all the given values of the parameters γ and b. The rationale behind this result is
based on the dual beneficial effect of advertising. Firstly, firms’ investment in
advertising leads to an increase in consumers’ valuation of the products, that acts
beneficially to the consumers’ surplus. Secondly, the increased competition between
the firms, leads to higher total production, that makes 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 poor substitutes the beneficial effect of advertising on the
consumers’ surplus dominates the detrimental effect of the lower firms’ profitability
while, the opposite is true when the products are close substitutes.
Further, we observe that the consumers’ surplus, when firms invest in both
informative and comparative advertising, increases as the advertising technology
becomes more effective (lower b), 0
b
CS CI
and decreases as the products tend to
be perfect substitutes, 0
CICS.14 The intuition behind the latter result is
straightforward. First, as the products tend to be perfect substitutes, i.e γ→1, the
optimal investment mix *
*
i
i
tend to decrease that is, firms tend to invest
proportionally more in comparative than in informative advertising. Thus, the
relatively higher firms’ expenditures on comparative advertising that aim mainly to
alter the consumers’ valuation about the rival’s firm product than to transmit
information, have a detrimental impact on the consumers’ surplus. Second, as the
products tend to be perfect substitutes, the equilibrium output of each firm decreases
which tends to decline the consumers’ surplus.
14After 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
18
Finally, using (19) we obtain that the social welfare is decreasing in all the values
of the product substitutability γ and in the lower values of the advertising
effectiveness parameter b while, it is increasing for the higher values of b since,
0
CITW, 0
b
TW CI
for ]4.0,0[ while, 0
b
TW CI
for ]1,4.0( .15 It is
obvious that for a less effective advertising technology, i.e, higher values of b, the
positive effect of profits due to the lower firms’ investments in advertising dominates
the negative effect of the lower 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, 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 court16(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).
15 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
16 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.
19
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
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
)()( ij
jINii
qcqRq
(21)
Therefore by solving the system of foc, we obtain equilibrium output of the second
stage, given by:
2
j
4
2))(2(
iIN
i
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(
]))(2[(2)(
22
b
c jINj
INi
(24)
Exploiting symmetry we have that equilibrium level of investment in informative
advertising,
01)2(
)(2
*
b
cINi (25)
2
22
2j
)4(
]μ2))(2[(max i
iINi b
c
i
20
By comparing the equilibrium advertising investment 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 derives17
Proposition 5: Firms’ expenditures on informative advertising under the mix
advertising case are always higher than that of the mere informative case (except if
γ=0, in which case they are equal).
The intuition behind this result is that the use of comparative advertising intensifies
market competition which in turn, leads firms to invest even more 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, consumers’ surplus and total welfare respectively are given by:
1)2(
)2)((2
*
b
cbq IN
i , 1)2(
)(2
2*
b
cbINi
22
222
]1)2([
)2())(1(
b
cbCS IN ,
22
22
]1)2([
)](2)3()2([
b
cbbTW IN (26)
17 For the proof see in the appendix.
21
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: Equilibrium output and consumers’ surplus under the mere
informative case are lower than those of the mix advertising case (informative and
comparative) but they are higher than those of the benchmark case. Moreover,
equilibrium profits and total welfare are higher than those of both the mix advertising
and the benchmark case. Hence, the following inequalities hold:
i. CINCI qqq , for all γ > 0.
ii. CICIN for all γ.
iii. CINCI CSCSCS , for all γ > 0.
iv. CIN TWTW and CIIN TWTW for all γ
v. ,CCI TWTW if and only if ]4.0,0[
The following observations are in order. First, regarding output, given the positive
relationship between the output and advertising levels along with the results presented
in proposition 5, it is clear that the higher advertising expenditures 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 worse 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. As a consequence, comparative advertising can be characterized as
the case of “wasteful advertising” and firms would prefer this aggressive type of
advertising to be prohibited.18
18 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
22
On the contrary, when the firms invest solely in informative advertising, the
beneficial effect of the higher firms’ demand due to the advertising expenditures
dominates the detrimental effects of the advertising costs and the fiercer competition.
Therefore, firms end up being 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 holds for all 0 then CINCI CSCSCS holds also. Thus, the
firms’ investment in advertising (informative and comparative) acts beneficially to
consumers since it provides 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 ppq , 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
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.
23
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 that 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
product differentiation, taking as basic premise, that informative 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 equilibrium firms’ optimal decision is to invest in both
informative and comparative advertising. Further, we show that the firms’
expenditures on comparative advertising are positively connected to the degree of
product substitutability γ. In contrast, firms’ expenditures on informative advertising
are U-shaped with respect to γ that is, they tend to decrease when the products are
poor substitutes while, 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 end up to be
worse 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
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.
24
both informative and comparative advertising is beneficial for the consumers, since it
leads to higher 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 main results
would change under cost and/or demand asymmetries among firms. Since both of the
scenarios described above are not easy tasks, their analysis awaits for further work.
25
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
)( jiijj
CIii
qcqRq
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( CC qCS while by the
(18) we have that 2])[1( CICI qCS . Therefore, since CIq > Cq always holds, it can
be easily checked that CCI 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,
26
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([
)]}(2)22(2[)2{(
bb
cbbCIi
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 .
27
Consumer Surplus: Consumer Surplus can be expressed as 2* ])[1( qCS 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
bbbcTWTW 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
bbbcTWTW CIN
The above equation is always positive for all the given values of γ and b. Thus, we
conclude that CIN TWTW always hold.
28
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