Comparative versus Informative Advertising in ... (F.11)_tcm4-50088.pdf · Comparative versus...

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Work in progress, please do not quote!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: [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]}.

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.


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 .


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


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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