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Cournot and Bertrand Competitionwhen Advertising Rotates Demand: TheCase of Honda and ScionVictor J. Tremblay a , Carol Horton Tremblay a & KosinIsariyawongse ba Department of Economics , Oregon State University , Corvallis ,Oregon 97331b Department of Business and Economics , Edinboro University ,Edinboro , PA 16444Published online: 01 Feb 2013.

To cite this article: Victor J. Tremblay , Carol Horton Tremblay & Kosin Isariyawongse(2013) Cournot and Bertrand Competition when Advertising Rotates Demand: The Case ofHonda and Scion, International Journal of the Economics of Business, 20:1, 125-141, DOI:10.1080/13571516.2012.750045

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Cournot and Bertrand Competition when Advertising

Rotates Demand: The Case of Honda and Scion

VICTOR J. TREMBLAY, CAROL HORTON TREMBLAY andKOSIN ISARIYAWONGSE

ABSTRACT We develop a model to explain why firm behavior differs in the market forsmall cars. Firms such as Honda compete in output (Cournot) and produce marketingcampaigns with universal appeal, while firms such as Scion compete in price (Ber-trand) and produce targeted marketing campaigns. We show that this mixture of Cour-not and Bertrand behavior can occur when advertising rotates demand. Whenbehaving as a Cournot-type firm such as Honda, it is more profitable to pursue amass-market advertising campaign that rotates demand counterclockwise when it facesrelatively low unit costs and a flat demand function. When behaving as a Bertrand-type firm such as Scion, it pays to pursue a niche-market advertising campaign thatrotates demand clockwise when it faces relatively high unit costs and a steep demand.

Key Words: Cournot–Bertrand Model; Mass-Market Advertising; Niche-MarketAdvertising; Demand Rotation; Automobile Industry.

JEL classifications: L13, L62, M37.

1. Introduction

In the market for small cars, firms choose very different strategic paths. Inmany industries, all firms within the same industry engage in either output orprice competition. In the small car market, however, firms such as Honda andSubaru set production targets and let prices adjust to clear the market.

We wish to thank Rolf Fare, Dan Stone, and seminar participants at Central European Universityand Pacific Lutheran University for providing helpful comments on an earlier version of the paper.We would also like to acknowledge the useful suggestions received in the anonymous refereeingprocess.

Victor J. Tremblay, Department of Economics, Oregon State University, Corvallis, Oregon 97331; e-mail:v.tremblay@oregonstate.edu. Carol Horton Tremblay, Department of Economics, Oregon State University,Corvallis, Oregon 97331; e-mail: ctremblay@oregonstate.edu. Kosin Isariyawongse, Department of Businessand Economics, Edinboro University, Edinboro, PA 16444; e-mail: kisariyawongse@edinboro.edu.

Int. J. of the Economics of Business,Vol. 20, No. 1, February 2013, pp. 125–141

1357-1516 Print/1466-1829 Online/13/010125–17� 2013 International Journal of the Economics of Business

http://dx.doi.org/10.1080/13571516.2012.750045

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Alternatively, Saturn and Scion first set prices and then fill consumer orders atthese pre-established prices. That is, Honda and Subaru behave as Cournot-type firms, while Saturn and Scion behave as Bertrand-type firms.

Suppliers of small cars also differ in their marketing choices. Honda’s auto-mobiles and advertising campaigns are designed to have relatively broadappeal, emphasizing characteristics such as product quality and fuel economy.On the other hand, Scion’s cars and advertising campaigns target a small nicheaudience of young men who live in urban areas. To accomplish this, Scionreplaces big-budget broadcast advertising with targeted internet ads, sponsor-ship of local events, and street-corner test drives.

Our primary objective is to develop a model that explains these asym-metric strategic choices. Our model builds on two lines of work. The first isthe classic duopoly model developed by Singh and Vives (1984), whichshows that when firms produce differentiated products, face sufficiently sim-ilar demand and cost conditions, and have the option of competing in out-put or price, they will choose output over price competition (i.e., Cournotdominates Bertrand). This outcome can be overturned, however, dependingon the nature of technology, the timing of strategic interaction, and givensufficient demand, cost or strategic asymmetry between firms (Arya et al.,2008; Hackner, 2000; Kreps and Scheinkman, 1983; Tremblay, Tremblay, andIsariyawongse, 2011; Tremblay, Tremblay, and Tremblay, 2011; Zanchettin,2006). There is increasing interest in static and dynamic models of the mixedcase of Cournot and Bertrand behavior, which Tremblay and Tremblay(2011) call Cournot–Bertrand models. All of these models ignore advertising,however.

The second line of research on which our model is built derives fromthe taxonomy of advertising developed by Johnson and Myatt (2006), onethat allows advertising to rotate demand.1 They show that when a firmchooses to serve a large fraction of potential consumers, called a “mass-mar-ket” position by Johnson and Myatt, it will prefer to develop a product withvertical characteristics that have universal appeal, such as high product reli-ability, and will use advertising to inform consumers of these characteristics.This type of advertising campaign will reduce the dispersion of consumervaluations for the product and cause the demand function to rotate counter-clockwise. In contrast, a firm that pursues a small “niche” market of poten-tial consumers is more likely to develop an advertising campaign thatpromotes an idiosyncratic characteristic that appeals to targeted consumers,such as a youthful image. This type of advertising campaign will increasethe dispersion of consumer valuations for the product and cause demand torotate clockwise.

In the sections that follow, we develop a duopoly model where firms com-pete in advertising and in output or price. One firm has the cost and marketingcharacteristics of Honda, and the other firm has the cost and marketing charac-teristics of Scion. Although the small car market is interesting in its own right,it serves here as an example of our modeling approach. Our main goal is toshow that under a reasonable set of demand and cost conditions, it is optimalfor one firm to compete in output and choose a mass-market advertising posi-tion and for the other firm to compete in price and pursue a niche-marketadvertising position.

126 V.J. Tremblay et al.

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2. Honda and Scion: Motives for their Strategic Choices

2.1. The Strategic Differences between Honda and Scion

Honda entered the US small car market in the early 1970s, and its success grewwith the introduction of the Honda Civic in the 1973 model year. Scion is arelatively new Toyota division or nameplate that entered the US market in the2003 model year.2 Since then, these firms have competed in advertising andoutput/price. Firms use advertising to provide consumers with presale infor-mation about product characteristics and image. Once this information is com-municated, firms then sell cars to consumers.3

At the selling stage, Honda dealers compete in output, while Scion dealerscompete in price. That is, Honda dealers first set monthly inventories and thenlet price adjust to meet sales goals and clear the market.4 Being a relatively lateentrant that is interested in marketing to consumers in urban areas, Scion facesa high cost of setting up new dealerships. As a result, the company sells Scionsat existing Toyota dealerships. These dealers hold very little inventory of Scionautomobiles, so consumers place orders on cars that are delivered at a laterdate. In addition, prices are posted and are non-negotiable. Scion calls this“pure pricing.”

Although Honda and Scion both produce small cars, their product designand marketing goals are quite different. Honda is the fifth largest auto pro-ducer in the United States, with a market share of 11.5% in 2007.5 Hondabuilds small cars with few accessories that are known for reliability and fueleconomy rather than style. For example, Consumer Reports ranks Hondasamong the most reliable cars in the world, while Car and Driver, a leadingautomobile magazine, gives the 2009 Hondas low marks for styling and road-side appeal.6 Honda ads emphasize the quality and high fuel economy of itsautomobiles, vertical characteristics that are valued by everyone, rather than ahorizontal characteristic such as a racing engine that appeals to a limited num-ber of consumers. By promoting vertical rather than horizontal characteristics,Honda ads generally appeal to the masses rather than a particular subgroup ofpotential consumers.

Alternatively, Scion serves a smaller segment of the market, with a marketshare of only about 1.7% in 2007. With the increase in the average age of Toy-ota buyers, Toyota introduced the Scion brand to attract consumers who havetypically shunned Toyota automobiles: hip male consumers from Generation Y(born from 1977 to 1995) who live in urban areas. To attract them, each yearScion offers 40 to 150 optional accessories (e.g., custom-colored parts andupholstery and a variety of steering wheel and tail light options), which allowbuyers to customize their vehicles. To reach its targeted audience, Scionreplaces big-budget, mass-market ads with ads in movie theaters, sponsorshipsof local events, street-corner test drives, and internet postings aimed at youngmale consumers from urban areas. In the marketing literature, this is called“guerrilla marketing” (Levinson, 2007).

Many of the major advertisers in the United States are automobile companies.Among the leading 25 national advertisers in 2007, 6 are automobile companies:GM ranks 4th, Ford 6th, Toyota 13th, Chrysler 14th, Nissan 20th, and Honda 23rd.As well as choosing very different types of advertising messages, Honda andScion also spend widely different amounts on advertising. In 2007, for example,Honda spent $706 per car on advertising, while Scion spent only $227 per car.

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Table 1 summarizes the main differences in characteristics between Hondaand Scion. At the selling stage, Honda competes in output while Scion com-petes in price. Honda chooses a high-volume (mass-market) position andadvertises more intensively than Scion. Honda’s advertising messages empha-size the vertical characteristics of its automobiles and, therefore, have universalappeal. In contrast, Scion focuses on a low-volume (niche-market) position,developing cars and an advertising strategy that appeal to young male con-sumers.

2.2. The Motives for the Strategic Decisions of Honda and Scion

Kreps and Scheinkman (1983) show how technological considerations canaffect firm decisions to compete in output versus price. They demonstrate thatwhen production takes place before market transactions, firms will compete inoutput; when production takes place after demand determination, firms willcompete in price. Tremblay, Tremblay, and Isariyawongse (forthcoming)extend this idea to identify conditions under which one firm will compete inoutput and the other in price. They show that if firms compete in a two-stagegame and firm 1 chooses output in the first stage, then firm 2 will be indiffer-ent between competing in output or in price in the second stage. That is, adynamic Cournot–Bertrand outcome is just as likely as a dynamic Cournot–Cournot (i.e., Stackelberg) outcome. They also show that a static Cournot–Ber-trand outcome will occur if one firm has a relatively high cost of competing inoutput.

Although both explanations may play a role in the Honda and Scion case,the cost argument appears more relevant. Fixed costs are higher for outputcompetition than price competition because output competition requires adealer to have sufficient inventory and a large car lot relative to a firm thatcompetes in price and receives a car from the factory only after a customerorder is placed. Scion is a relatively new brand, and when it was introduced,existing Toyota dealers faced a capacity constraint, with sales lots already fullof new Toyotas and used cars. By choosing to compete in price and shippingto order, little inventory is required, giving Scion relatively low fixed costs. IfScion chose to compete in output, its fixed costs would have been substantiallyhigher because Toyota dealers would have had to expand their capacity, whichwould be costly in urban areas where Scion’s targeted consumers reside.Palmeri et al. (2003) argue that this is the reason why Scion chose the low-inventory and pure-pricing strategic approach.

Table 1. Important strategic differences between Honda and Scion

Honda Scion

Choice variable at the selling stage Output Price

Product design Universal appeal Idiosyncratic appeal

Few accessories Many custom accessories

Advertising

Type “Mass-market” “Guerrilla or niche-market”

Theme Quality and fuel economy Quirky and hip image

Spending $706 per car $227 per car

US market share 11.5% 1.7%

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In contrast, Honda has established brands and dealers that have competedin output for decades. Switching to price competition would incur a switchingcost, as Honda has existing storage capacity that may be costly to liquidate.With sufficiently high switching costs or sufficiently low fixed costs associatedwith holding inventory, such a firm will prefer output competition over pricecompetition, at least in the short run. Given that Honda is the high-volumeproducer with greater experience, one might also expect it to have a lower unitcost due to learning-by-doing.

The original product design of their automobiles provides further motiva-tion for Honda and Scion to compete differently. That is, Honda customers haveno choice of individual accessories, as each model comes in three trim levels.The DX version is the basic model. The LX version adds a set of features,including remote door locks, electronic trunk release, air conditioning, andcruise control. The EX version adds rear disk brakes, a moonroof, power seatingadjustment, and a navigation system. Thus Honda dealers would need to holdrelatively little inventory to have cars in stock with these three trim levels. Incontrast, Scion would need a huge inventory to make available cars with everypossible set of options.7 Consistent with Kreps and Scheinkman (1983), techno-logical factors determine whether firms compete in output or in price. In thiscase, however, technological asymmetries cause firms within the same industryto make different choices (as in Tremblay, Tremblay, and Isariyawongse, forth-coming). Honda mass produces cars before bringing them to market, causing itto compete in output. Scion produces a custom car for each individual customeronly after an order is placed, causing it to compete in price.

3. A Cournot–Bertrand Model with Advertising

In this section, we develop the model and identify parameter values that sup-port the behavior of firms with the characteristics of Honda (H) and Scion (S).To simplify the analysis, each firm is assumed to produce a single substitutegood with characteristics that are predetermined. Firms compete in a two-stagegame. In the first stage, they must decide on the type of advertising campaignand the level of advertising expenditures. Regarding type, a firm must decidewhether its advertising will appeal to a mass-market audience or a niche-mar-ket audience. In the second stage, they compete in either output (Cournot) orprice (Bertrand). Firm i faces a unit cost (ci) and a fixed cost of production (Fi),where i = H or S. Firm i’s output is defined as qi, its price as pi, and its adver-tising expenditures as Ai.

We modify the duopoly models of Dixit (1979) and Singh and Vives (1984)by allowing advertising to rotate demand, as in Johnson and Myatt (2006).Demand functions are linear, but unlike previous studies, we allow a firm’sown advertising to change the intercept and slope of demand. Because H willcompete in output and S will compete in price in the second stage of the game,demand is written in terms of the strategic variables: Ai, qH, and pS.

pHðqH;AH; pSÞ ¼ aHðAHÞ � bðAHÞqH þ pS; ð1Þ

qSðpS;AS; qHÞ ¼ aSðASÞ � dðASÞpS � qH; ð2Þ

Cournot and Bertrand Competition when Advertising Rotates Demand 129

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where the demand intercept (ai) and slope parameters (b and d) are functionsof advertising.8 Mass-market advertising will cause inverse demand to rotatecounterclockwise by lowering aH and b for H and by raising aS and d for S. Incontrast, niche-market advertising will cause inverse demand to rotate clock-wise.9 Given this specification, firm profits (i) are

pH ¼ ðpH � cHÞqH � FH � wAH

¼ ½aHðAHÞ � bðAHÞqH þ ps � cH�qH � FH � wAH; ð3Þ

ps ¼ ðpS � cSÞqS � FS � wAS ¼ ðpS � cSÞ½aSðASÞ � dðASÞpS � qH� � FS � wAS; ð4Þ

where w is the exogenous price of a single advertising message.

3.1. A Simple Monopoly Example when Advertising Rotates Demand

To illustrate this advertising taxonomy, assume that cS and FS are sufficientlyhigh so that H is a simple monopolist. In this example, we let aH = hH +hHb(AH). Dropping the subscripts for convenience, the firm’s inverse demandis p = (h + hb) – bq. Because b is a function of advertising, both the intercept(h + hb) and the slope (b) change with advertising. In this specification, therotation point is fixed at h, with p = h when q ¼ h 8 b � ½0;1Þ; we identify theoutput level at this point as qh. Notice that the inverse demand function rotatesclockwise around h as b increases.

The firm competes in two periods. In the first period, it chooses a mass-market or a niche-market type of campaign and the level of advertising expen-ditures. In the second period, the firm chooses its optimal output or price. Thefirm is assumed to be sequentially rational and use backwards induction toidentify its optimal action at each period or stage (Mas-Colell et al., 1995, pp.268–77). This involves solving for optimal behavior in the second period andthen determining the optimal behavior in the first period, given that the firmaccurately anticipates its behavior in the later period. In other words, we deter-mine the profit-maximizing price and quantity (p⁄, q⁄) and then determine theprofit-maximizing level and type of advertising given p⁄ and q⁄. Firm profitsare p = (h + hb – bq – c)q – F – wA, and the firm’s profit maximizing values inthe second-stage problem are:

p� ¼ hþ bhþ c

2ð5Þ

q� ¼ hþ bh� c

2bð6Þ

p� ¼ ðhþ bh� cÞ24b

� F � wA ð7Þ

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The second-order condition requires b > 0.Next, the firm solves its first period problem, given p⁄ above. The firm has

the option of choosing a mass-market advertising campaign that lowers b or aniche-market advertising campaign that increases b. We assume that once atype of advertising is chosen, advertising spending causes a smooth change inb within the interval 0 < b1 � b � b2 < 1. We also let w be positive but lowenough to assure that advertising is profitable. Given equation (7), the firm’sfirst-order condition with respect to advertising is

dp�

dA¼ @R

@b

@b

@A� w ¼ 0 ð8Þ

where R = (h + bh – c)2/(4b), and in this model oR/ob = op⁄/ob.An important feature of the model is that the profit function is convex in

b.10 Thus the firm will choose a type and level of advertising that produces anextreme value of b (b⁄), with b⁄ e {b1, b2} when w is sufficiently low. A mass-market advertising campaign that lowers b to b1 will be preferred when themarginal consumer, located at q⁄, is to the right of qh. This is because a flatterdemand raises the willingness to pay for the marginal consumer; thusop⁄/ob < 0. The reverse is true when the marginal consumer is to the left of qh.In order to raise the marginal consumer’s willingness to pay in this case, thefirm will pursue a niche-market strategy that increases b to b2 because op⁄/ob> 0. This illustrates Johnson and Myatt’s (2006) Proposition 1: the monopolistwill choose an extreme marketing position when mass-market and niche-mar-ket advertising campaigns can rotate demand.

Which type of marketing campaign is optimal depends upon parametervalues. Firm participation requires that c < h + hb, which we assume to hold.When q⁄ is to the right of qh (i.e., q⁄ > qh = h), c < h – hb. In this case, op⁄/ob <0, and the firm will pursue a mass-market campaign that lowers b. When q⁄ isto the left of qh, c > h – hb and op⁄/ob > 0. Thus the firm will pursue a niche-market campaign that increases b.11

To illustrate this point, we consider the case where c = 0 and h = 12. Whenb = 0.5, the firm will choose a mass-market campaign because q⁄ = 18 > qh =12. If the profit maximizing level of mass-market advertising lowers b to 0.4,

0 2 4 6 8 10 12 14 16 18 20 22 24

6

8

10

12

14

16

18 p

q

pA*pB*

qA* qB*

D2 (b = 0.4)

D1 (b = 0.5)

BA

Figure 1. Inverse demand and mass-market advertising.

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firm profits change from 162 to 176.4 – wA⁄. As long as w is sufficiently low,profits rise with a mass-market advertising campaign that lowers b. Figure 1illustrates the inverse demand functions when b = 0.5 (D1) and when b = 0.4(D2). It shows that the movement from D1 to D2 leads to an increase in thewillingness to pay of the marginal consumer (located at qA

⁄) and, therefore, anincrease in gross profit. Alternatively, when b = 2.0, the firm will choose aniche-market campaign because q⁄ = 9 < qh = 12. In this case, if the profit maxi-mizing level of niche-market advertising raises b to 2.5, profits change from162 to 176.4 – wA⁄. Again, this type of advertising raises profits as long as w issufficiently low. As illustrated in Figure 2, this advertising campaign results ina steeper inverse demand function (moving from D1 to D2), which leads to anincrease in the willingness to pay of the marginal consumer (located at qA

⁄)and an increase in gross profit.

The relevant parameter space for b and c is delineated in Figure 3. Threeregions are important. (1) Region Z1 identifies parameter values where it isunprofitable for the firm to participate. (2) In region Y1, parameter values makeit profitable to pursue a niche-market campaign. (3) In region X1, parametervalues make it profitable to pursue a mass-market campaign. This implies thatthe monopolist will be more likely to pursue a mass-market (niche-market)campaign when marginal cost is sufficiently low (high) and the original inversedemand function is sufficiently flat (steep).

3.2. The Cournot–Bertrand Duopoly when Advertising Rotates Demand

Now we consider the case where it is profitable for both H and S to partici-pate. We fix the rotation point for each firm as in the monopoly case, such thataH = hH + hHb and aS = hS + hSd. Respective demands for firms H and Sbecome

pH ¼ hH þ hHb� bqH þ pS; ð9Þ

qS ¼ hS þ hSd � dpS � qH; ð10Þ

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

10

20

30

40 p

q

pB*pA*

qA* qB*

B

A

D1 (b = 2)

D2 (b = 2.5)

Figure 2. Inverse demand and niche-market advertising.

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where b = b(AH), and d = d(AS).12 With two firms, pH = hH when qH = hH and

pS = 0, and qS = hS when pS = hS and qH = 0. Notice that if H uses advertisingto increase b, its inverse demand function becomes steeper; if S uses advertising toincrease d, its inverse demand function becomes flatter (but its demand functionbecomes steeper). This implies that if H and S pursue a mass-market (niche-market) advertising campaign, then H’s advertising lowers (raises) b and S’sadvertising raises (lowers) d, which will rotate each firm’s inverse demandfunction counterclockwise (clockwise).13

Technological asymmetries explain why H competes in output and Scompetes in price, the Cournot–Bertrand outcome. As discussed above, itpays a mass-producing car company such as H to compete in output, and itpays a custom-car company such as S to compete in price. Another potentialexplanation is that the fixed costs associated with output competition maybe sufficiently high for S and sufficiently low for H. A final feature of thetechnology is that cS is likely to be greater than cH because H is the high-volume and more experienced producer. We make use of this fact later inthe analysis.

Firms have perfect and complete information and use backwards inductionto reach the subgame perfect Nash equilibrium. This involves identifying theNash equilibrium to the second period problem first. Then we solve for theNash equilibrium in the first period, assuming that firms correctly anticipatethe Nash equilibrium in the second period. In the second period, firm first-order conditions are:

@pH

@qH¼ hH þ bhH � 2bqH þ pS � cH ¼ 0; ð11Þ

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

-3

-2

-1

0

1

2

3

4

5

6

7

8

9

10

11

12C

b

X1

Y1

Z1

Figure 3. Parameter space that supports mass-market and niche-marketadvertising campaigns. Note that X1 identifies the parameter space that

supports a mass-market advertising campaign. Y1 identifies the parameterspace that supports a niche-market advertising campaign. The participation

constraint is not met in region Z1.

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@pS

@pS¼ hS þ dhS � 2dpS � qH þ dcS ¼ 0: ð12Þ

Solving these simultaneously for the strategic variables and substitutingthem into the demand and profit equations produces the Nash equilibrium inthe second period:

p�H ¼ cHð1þ 2bdÞ þ bðaþ dhSÞc

; ð13Þ

p�S ¼2bdcS þ b� hH

c; ð14Þ

q�H ¼ a� dð2cH � hSÞc

; ð15Þ

q�S ¼d½b� cSð1þ 2bdÞ � hH�

c; ð16Þ

p�H ¼ b½a� dð2cH � hSÞ�2

c2� FH � wAH; ð17Þ

p�S ¼

d½b� cSð1þ 2bdÞ � hH�2c2

� FS � wAS; ð18Þ

where a � ½dcS þ hS þ 2dhHð1þ bÞ�; b � ½cH � bhH þ 2bhSð1þ dÞ�; and c � ð1þ4bdÞ. For the Nash equilibrium to be stable, both b and d must be greater than0.5.14 To assure firm participation, hi must be sufficiently large relative to ci. Asdiscussed above, price competition is more profitable than output competitionfor S if there are sufficient technological asymmetries. In addition, price compe-tition for S becomes more profitable as hH diminishes.

Our goal is to identify parameter values that are consistent with theobserved behavior of Honda and Scion. One example is to let hS = 2hH = 12, cH= 0, cS = 10, b = 2, and d = 1, which we define as the benchmark values ofparameters. We choose them for two reasons. First, the resulting Nash equilib-rium is consistent with the fact that H has a larger market share and a strategicadvantage over S if the difference in fixed costs between firms is not too great:pH

⁄ = 15.56 > pS⁄ = 13.11, qH

⁄ = 7.78 > qS⁄ = 3.11, pH

⁄ = 120.99 – FH, and pS⁄ =

9.68 � FS. Second, we will see that these values can support H’s choice of amass-market advertising campaign and S’s choice of a niche-market advertis-ing campaign.

Because firms have perfect and complete information, sequential rationalityensures that firms will choose the optimal types and levels of advertising given

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the anticipated Nash equilibrium in the second period. We assume that once atype of advertising is chosen, advertising causes smooth changes in parametervalues at a decreasing rate within the intervals 0.5 < b1 � b � b2 < 1 and 0.5 <d1 � d � d2 < 1. Again, w is positive but sufficiently low so that advertising isprofitable for both firms. In order to identify parameter values for H (cH and b)that will support its mass-market advertising choice, all other parameters arefixed at their benchmark values.

Proposition 1 H will pursue a mass-market advertising campaign when its marginalcost (cH) is sufficiently low and demand is sufficiently flat (i.e., the initial, pre-adver-tising value of b is sufficiently low).

Proofs of all propositions can be found in the Appendix. The relevant con-straints are illustrated in Figure 4. The firm will not participate when parame-ter values lie in region Z2. Region Y2 identifies parameter values that support aniche-market strategy, and region X2 identifies parameter values that support amass-market strategy. For a mass-market strategy to be optimal for H, cH mustbe less than cS, and H’s inverse demand must be relatively flat (the initialvalue of b must be sufficiently low), parameter restrictions that are consistentwith H’s high volume position and its decision to pursue a mass-market adver-tising campaign. In this case, H will use advertising to rotate its inversedemand counterclockwise (i.e., lower b) because this raises firm profits byincreasing the willingness to pay of the marginal consumer.

We next analyze parameter values needed to support S’s advertisingbehavior. In this case, cS and d vary but all other parameters take on bench-

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.00

5

10

15

20

25

30

35

40CH

b

X2

Y2

Z2

Figure 4. Parameter space that supports mass-market and niche-marketadvertising for Honda. Note that X2 identifies the parameter space that

supports a mass-market advertising campaign. Y2 identifies the parameterspace that supports a niche-market advertising campaign. The participation

constraint is not met in region Z2.

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mark values (which are consistent with Proposition 1 above).

Proposition 2 S will pursue a niche-market advertising campaign when its marginalcost (cS) is sufficiently high and demand is sufficiently steep (i.e., the initial value of dis sufficiently low).

Figure 5 identifies the relevant parameter space. For S to participate, cS mustbe sufficiently low, identified by regions X3 and Y3. Region X3 identifiesparameter values that support a mass-market strategy, and Region Y3 identifiesparameter values that support a niche-market strategy. Thus for it to be opti-mal for S to pursue a niche-market strategy, S must have relatively high mar-ginal costs and face a relatively steep inverse demand function (i.e., the initialvalue of d is sufficiently low). This is consistent with the fact that S targets itsautomobiles to a select group of consumers, young males from urban areas,who are small in number but are likely to have relatively inelastic demandfunctions for cars with characteristics that they desire.

With the same set of benchmark values that were used above,15 we nextanalyze the effect of H’s mass-market actions and S’s niche-market actions onprices and rival profits.

Proposition 3 The mass-market advertising of H will lead to lower equilibrium pricesfor both firms and will lower S’s profits; the niche-market advertising of S will lead toa higher equilibrium price for S, will have an indeterminate effect on H’s equilibriumprice, and will raise H’s profits.

This is not surprising given that these firms pursue very different types ofadvertising. H’s advertising emphasizes universal characteristics, which appeal

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.07

8

9

10

11

12

13

14

15

16

17

18 CS

d

X3

Y3

Z3

Figure 5. Parameter space that supports mass-market and niche-marketadvertising for Scion. Note that X3 identifies the parameter space that supportsa mass-market advertising campaign. Y3 identifies the parameter space thatsupports a niche-market advertising campaign. The participation constraint is

not met in region Z3.

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to both H and S consumers and leads to tougher price competition and a netbenefit only to the advertising firm. Alternatively, S’s advertising appeals toconsumers with idiosyncratic preferences. This form of advertising leads to anincrease in profits for both firms because it effectively increases product differ-entiation by informing consumers of real differences between brands. ThusProposition 3 implies that the Nash equilibrium level of advertising will notmaximize joint profits. A trade association interested in increasing industryprofits would encourage niche-market and discourage mass-market advertis-ing.

Evaluating the welfare effect of advertising is complicated when advertis-ing changes consumer tastes (Dixit and Norman, 1978; Stivers and Tremblay,2005) and causes a change in the slope of demand (Shapiro, 1980). If oneaccepts consumer plus producer surplus as an appropriate welfare measure asin Becker and Murphy (1993) and Fisher and McGowan (1979), then thefollowing proposition holds.

Proposition 4 H advertises too much from society’s perspective when parameter val-ues are consistent with it pursuing a mass-market campaign; S advertises too littlefrom society’s perspective for all parameter values that support firm participation.

This and Proposition 3 imply that cooperation improves social welfare in thissetting.

These results can be overturned, however, when firm advertising affectsthe rotation point as well as the slope of demand. If the rotation point isendogenous, H benefits from shifting its rotation point left. This will increasedemand by raising the marginal valuation of every consumer. Thus consumerand producer surplus increase in the H market. Alternatively, S benefits fromshifting the rotation point right, which increases demand by increasing themarginal valuation of every consumer. When the rotation point is endogenousin this way, H and S will produce too little advertising from the perspective ofboth the industry and society as a whole.

4. Conclusion

The market for small cars is interesting in that firms make very different strate-gic choices. At the marketing stage, firms such as Honda pursue a mass-marketadvertising campaign, while firms such as Scion pursue a niche-market adver-tising campaign. Firms also choose very different strategic variables at the sell-ing stage, with Honda choosing output and Scion choosing price. We developa model that provides a plausible explanation for these observed behaviors.

Our model identifies conditions under which firms make asymmetric stra-tegic choices. Technological asymmetries induce one firm to compete in outputand the other to compete in price, a mixture of the Cournot and Bertrand mod-els. The Cournot-type firm produces more output and has a strategic advan-tage over the Bertrand-type firm, as long as the difference in costs is not toogreat. The model also identifies market conditions under which one firm willpursue a mass-market and the other a niche-market advertising campaign.That is, when a firm faces relatively low (high) unit costs and a relativelyflat (steep) inverse demand function, it will be more profitable to pursue amass-market (niche-market) advertising campaign that rotates demand coun-

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terclockwise (clockwise). In this setting, industry profits increase in niche-mar-ket advertising and decrease in mass-market advertising. The model alsoexplains much of the observed behavior of Honda and Scion, with Honda com-peting in output and Scion competing in price, Honda choosing mass-marketadvertising and Scion choosing niche-market advertising, and Honda having alarger market share than Scion.

The welfare implications of advertising are complicated in a model such asthis. If we assume that advertising does not change consumer tastes and doesnot affect the rotation point, then the mass-market producer advertises toomuch and the niche-market producer advertises too little from society’s per-spective. If firm advertising can change the rotation point as well as the slopeof demand, however, both firms may produce too little advertising from theperspective of industry and society.

Notes

1. Aislabie and Tisdale (1988) and Chamberlin (1933, ch. 6) also suggest that advertising mayaffect the slope of demand.

2. In reality, Honda produces cars with the Honda and Acura nameplates, and Toyota producescars with the Scion, Toyota, and Lexus nameplates. Here, Honda refers to cars with the Hondanameplate, and Scion refers to the Scion nameplate.

3. Information about the small car market and the marketing tactics of Scion and Honda is fromCiminillo (2005), Fonda et al. (2003), Garfield (2003), Morrissee (2007), Palmeri et al. (2003),Rechtin (2006), and Welch (2007).

4. In the past, large car dealers were able to price discriminate, charging higher prices to lessinformed and lower prices to more informed buyers. Bargaining such as this is less common inthe market for small cars today. First, the internet has substantially lowered the cost of obtain-ing information. For example, for a particular model of car, edmunds.com provides consumerswith information on the suggested retail price, the dealer’s cost, and the average price paid byconsumers in a particular zip code. Second, there is little difference between the suggestedretail price and the dealer cost for small cars, leaving little room for bargaining. Dealers ofsmall cars earn much of their income from extended service/warranty contracts and from ser-vicing the cars that they sell.

5. Output and market share data are obtained from Ward’s Motor Vehicle Facts & Figures (2008).Advertising data are obtained from Advertising Age at AdAge.com.

6. This information is available at ConsumerReports.com and CarandDriver.com. In Car and Dri-ver’s enthusiast rating, which evaluates such things as a car’s driving pleasure, ability to thrill,styling beauty, and the ability to impress others, the Honda Fit received a rating of 5 out of 10,the Civic a 4, and the Accord a 4. In contrast, automobiles with a high enthusiast rating includethe Ford Mustang (with a rating of 7), Dodge Challenger (8), Porsche Boxster (9), and LotusElise (10). Scions are unusual in that each car can be highly customized to a consumer’s prefer-ence.

7. This is analogous to the clothing industry, where mass-produced clothing is sold in large retailstores with a wide selection of styles. Tailors who produce custom-made clothing, however,operate in small shops with little or no inventory.

8. The Singh and Vives (1984) demand system derives from the utility function U(qH,qS) = aHqH +aSqS – (bHqH

2 + bSqS2 + 2sqHqS)/2, which produces the following inverse demand functions: pH

=aH – bHqH – sqS and pS=aS – bSqS – sqH. In order to focus on the rotational effect of advertisingand to minimize the number of demand parameters in the Cournot–Bertrand demand system,we set aH = (aHbS – aSs)/bS, b = (bHbS – s2)/bS, aS =aS/bS, d = 1/bS, and s/bS = 1. This producesthe demand system in equations (1) and (2).

9. Note that an advertising campaign that causes a non-parallel shift in demand need not have arotation point for positive values of both price and output. Following Johnson and Myatt, how-ever, we define demand rotation to mean that the rotation point occurs at a positive valuedprice–quantity pair.

10. That is, op⁄/ob = [�c2 + 2ch + h2(b2 – 1)]/(4b2) and o2p⁄/ob2 = (c – h)2/(2b3) > 0.

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11. When q⁄ = qh, c = h – hb and op⁄/ob = 0. In this case, the profit function is strictly convex in band any discrete change in b will raise profits. Thus either campaign will be profitable.

12. For simplicity, we assume that rival advertising affects a firm’s demand indirectly. This is notas restrictive as it may seem, as we will see that rival advertising still has an important effecton a firm’s equilibrium price, output, and profit.

13. In this model, a firm that chooses a mass-market position will develop products with universalappeal and use advertising to inform potential consumers of this fact. A firm that pursues aniche-market position, however, will promote the idiosyncratic qualities of its brand that appealto its targeted audience. Thus rival advertising that has no direct effect on a firm’s demandfunction will have a strategic effect and influence the Nash price, output, and profit levels ofboth firms.

14. Following Dixit (1986), this requires that |o2p1/oq12| > |o2p1/oq1op2| and |o2p2/op2

2| >|o2p2/op2oq1|. In our model, o2p1/oq1

2 = –2b, o2p1/oq1op2 = 1, o2p2/op22 = –2d, and o2p2/op2oq1

= –1.15. That is, hS = 2hH = 12, cS = 10, d = 1, and cH and b vary when analyzing H; hS = 2hH = 12,

cH = 0 and b = 2, and cS and d vary when analyzing S.

References

Aislabie, C.J., and Tisdell, Clem A. (1988) Profit maximization and marketing strategies: demandrotation and social influences, Managerial and Decision Economics, 9, pp. 77–82.

Arya, Anil, Mittendorf, Brian, and Sappington, David E.M. (2008) Outsourcing, vertical integration,and price vs. quantity competition, International Journal of Industrial Organization, 26, pp. 1–16.

Becker, Gary S., and Murphy, Kevin M. (1993) A simple theory of advertising as a good or bad,Quarterly Journal of Economics, 108, pp. 941–64.

Chamberlin, Edward (1933) The Theory of Monopolistic Competition (Cambridge: Harvard UniversityPress).

Ciminillo, Jill Anne (2005) Scion’s TV ads focus on youthful attitude, Automotive News (April 25),p. 28.

Dixit, Avinash (1979)A model of duopoly suggesting a theory of entry, Bell Journal of Economics, 10,pp. 20–32.

Dixit, Avinash (1986) Comparative statics for oligopoly, International Economic Review, 27, pp. 107–22.

Dixit, Avinash, and Norman, Victor (1978) Advertising and welfare, Bell Journal of Economics, 19,pp. 1–17.

Fisher, Franklin M., and McGowan, John J. (1979) Advertising and welfare: comment, Bell Journal ofEconomics, 10, pp. 726–7.

Fonda, Daren, Philadelphia, Desa, and Szczesny, Joseph R. (2003) Baby you can drive my car, Time(June 30), pp. 46–8.

Garfield, Bob (2003) Toyota finds attractive effort to push the plug-ugly Scion, Advertising Age(August 4), p. 29.

Hackner, Jonas (2000) A note on price and quantity competition in differentiated oligopolies, Jour-nal of Economic Theory, 93, pp. 233–9.

Johnson, Justin P., and Myatt, David P. (2006) On the simple economics of advertising, marketing,and product design, American Economic Review, 96, pp. 756–84.

Kreps, David, and Scheinkman, Jose (1983) Quantity precommitment and Bertrand competitionyield Cournot outcomes, Bell Journal of Economics, 14, pp. 326–37.

Levinson, Jay Conrad (2007) Guerrilla Marketing (New York: Mariner Books).Mas-Colell, Andreu, Whinston, Michael D., and Green, Jerry R. (1995) Microeconomic Theory (NewYork: Oxford University Press).

Morrissee, Brian (2007) Scion web strategy takes a stealth approach, Adweek (October 22), p. 12.Palmeri, Christopher, Ben Elgin, and Kathleen Kerwin (2003) Toyota’s Scion: dude, here’s your car,Business Week (June 9), p. 44.

Rechtin, Mark (2006) Scion’s dilemma: be hip – but avoid the mainstream, Automotive News (May22), pp. 432–46.

Shapiro, Carl (1980) Advertising and welfare: comment, Bell Journal of Economics, 11, pp. 49–52.Singh, Nirvikar, and Vives, Xavier (1984) Price and quantity competition in a differentiated duop-oly, Rand Journal of Economics, 15, pp. 546–54.

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Stivers, Andrew, and Tremblay, Victor J. (2005) Advertising, search costs, and welfare, InformationEconomics and Policy, 17, pp. 317–33.

Tremblay, Carol Horton, Tremblay, Mark J., and Tremblay, Victor J. (2011) A general Cournot–Ber-trand model with homogeneous goods, Theoretical Economics Letters, 1, 38–40.

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Welch, David (2007) Scion’s street credentials, Business Week (April 27), p. 11.Zanchettin, Piercarlo (2006) Differentiated duopoly with asymmetric costs, Journal of Economics andManagement Strategy, 15, pp. 999–1015.

Appendix

Proof of Proposition 1. From the Nash equilibrium in equations (13)–(18), the par-ticipation constraint for H is cH � 23 + 6b. Firm H will pursue a mass-marketadvertising campaign that lowers b when opH

⁄/ob < 0, which occurs when

cH\23� 74bþ 24b2

1� 4b: ðA1Þ

The participation constraint is met when condition (A1) holds. The right-hand sideof equation (A1) is positive, and the stability condition is met (i.e., b > 0.5) for b e(0.5, 2.73263). This identifies values of cH and b that make a mass-market campaignoptimal, which is described by area X2 in Figure 4. &

Proof of Proposition 2. From the Nash equilibrium in equations (13)–(18), the par-ticipation constraint for S is

cS\6ð5þ 8dÞ1þ 4d

: ðA2Þ

Firm S will pursue a niche-market advertising campaign that lowers d whenopS

⁄/od < 0, which occurs when

cS >6ð5� 16d þ 64d2Þ1þ 4d þ 32d2

: ðA3Þ

The right-hand side of equation (A3) is positive for all acceptable values of d. Con-ditions (A2) and (A3) are met when cS is sufficiently high and d is sufficiently low,as described by area Y3 in Fig. 5. &

Proof of Proposition 3. Regarding rival profits: From the Nash equilibrium in equa-tions (13)–(18), the mass-market advertising of H that lowers b will lower S’s profits(i.e., opS

⁄/ob > 0) when the following condition holds:

cS\6ð5þ 8dÞ1þ 4d

ðA4Þ

This condition must hold under the participation constraint. Therefore, H’s mass-market advertising campaign will always lower S’s profits. The niche-market adver-tising of S that lowers d will raise H’s profits (i.e., opH

⁄/od < 0) when cH < 23 + 6b.Because this condition must hold under the participation constraint, S’s niche-mar-ket advertising campaign will always raise H’s profits.

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Regarding prices: H’s advertising that changes b will have the following effect onNash prices:

@p�H@b

¼ 46þ 24bþ 48b2 � 2cHð1þ 4bÞ2 ; ðA5Þ

@p�S@b

¼ 2½9þ dð24þ cSÞ�ð1þ 8dÞ2 ðA6Þ

Equation (A6) is positive, and firm H’s participation constraint guarantees thatequation (A5) is positive. Thus H’s mass-market advertising that lowers b willlower Nash prices for both firms. S’s advertising that changes d will have the fol-lowing effects on Nash prices.

@p�H@d

¼ 2bð17� 18b� cHÞð1þ 4bÞ2 ; ðA7Þ

@p�S@d

¼ 4ðcS � 48Þð1þ 8dÞ2 : ðA8Þ

Equation (A7) is indeterminate, and firm S’s participation constraint guaranteesthat equation (A8) is negative. Thus S’s niche-market advertising that lowers d willraise S’s equilibrium price and may lower or raise H’s equilibrium price. &

Proof of Proposition 4. H’s advertising produces a flatter demand, which lowersS’s profits (Proposition 3) but may raise or lower total surplus in the H market.Consumer plus producer surplus will fall, however, when the following conditionholds.

cH\29þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi205þ 72bþ 144b2

p

2: ðA9Þ

This is true when condition (A1) is met, which assures that H is a mass-marketproducer. Thus when H pursues a mass-market advertising campaign, it advertisestoo much from society’s perspective. S’s advertising produces a steeper demand,which raises total surplus in the S market and increases H’s profits (Proposition 3).Thus S advertises too little from society’s perspective. &

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