Cournot and Bertrand Competition when Advertising Rotates Demand ...

Cournot and Bertrand Competition when Advertising Rotates Demand: The Case of Honda and Scion

Victor J. Tremblay, Carol Horton Tremblay*, and Kosin Isariyawongse Department of Economics Oregon State University Corvallis, OR 97331-3612

September 3, 2009

Running head: Cournot-Bertrand Competition with Advertising

Acknowledgements: We wish to thank Rolf Färe and Dan Stone for providing helpful comments on an earlier version of the paper.

*

Corresponding Author: Department of Economics, 303 Ballard Extension Hall, Oregon State University, Corvallis, OR, 97331-3612. Phone: 541-737-1468. Fax: 541-737-5917. Email: [email protected].

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Abstract: We develop a model which explains why firm behavior differs in the market for small cars. Firms such as Honda compete in output (Cournot) and produce marketing campaigns with universal appeal, while firms such as Scion compete in price (Bertrand) and produce targeted marketing campaigns. We show that mixed Cournot and Bertrand behavior can occur when advertising rotates demand. Whether pursuing a Cournot or Bertrand strategy, it is more profitable to pursue a mass-market (niche-market) advertising campaign that rotates demand counterclockwise (clockwise) when it faces relatively low (high) unit costs and a relatively flat (steep) inverse demand function.

Keywords: Mixed output-price competition, demand rotation, mass-market advertising, nichemarket advertising, automobile industry.

JEL Classifications: L13, L62, M37.

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1. Introduction In the market for small cars, firms choose very different strategic paths. In most industries, firms engage in either output or price competition. In the small car market, however, firms such as Honda and Subaru set production targets and let prices adjust to clear the market. Alternatively, Saturn and Scion first set prices and then fill consumer orders at these preestablished prices. That is, firms such as Honda behave as Cournot-type firms, while firms such as Scion behave as Bertrand-type firms. Suppliers of small cars also differ in their marketing choices. For example, Honda’s products and advertising campaigns are designed to have relatively broad appeal, emphasizing characteristics such as product quality and fuel economy. On the other hand, Scion’s products and advertising campaigns target a small niche audience of young men who live in urban areas. To accomplish this, Scion tries to reach younger buyers by replacing big-budget broadcast advertising with targeted internet ads, sponsorship of local events, and street-corner test drives. Our primary objective is to develop a model that explains these asymmetric strategic choices. Our model builds on two lines of work. The first is the classic duopoly model developed by Singh and Vives (1984), which shows that when firms produce differentiated products, face sufficiently similar demand and cost conditions, and have the option of competing in output or price, they will choose output over price competition (i.e., Cournot dominates Bertrand). This outcome can be overturned, however, with sufficient demand, cost, or strategic asymmetry between firms (Häckner, 2000; Zanchettin, 2006; Arya et al., 2008; Tremblay et al.,

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2008). In particular, Tremblay et al. show that in the case of a cost asymmetry or a dynamic setting, one firm may choose output competition while the other firm chooses price competition, an outcome they identify as Cournot-Bertrand. All of these models ignore advertising, however. The second line of research on which our model is built derives from the taxonomy of advertising developed by Aislabie and Tisdell (1988) and Johnson and Myatt (2006), one which allows advertising to rotate demand.1 They show that when a firm chooses to serve a large fraction of potential consumers, called a “mass-market” position by Johnson and Myatt, it will prefer to develop a product with characteristics that have universal appeal, such as high product reliability, and will use advertising to inform consumers of these vertical characteristics. This type of advertising campaign will reduce the dispersion of consumer valuations for the product and cause the demand function to rotate counterclockwise. In contrast, a firm that pursues a small “niche” market of potential consumers is more likely to develop an advertising campaign that promotes an idiosyncratic characteristic that appeals to targeted consumers, such as a youthful image. This type of advertising campaign will increase the dispersion of consumer valuations for the product and cause demand to rotate clockwise. In the sections that follow, we develop a duopoly model where firms compete in advertising and in output or price. One firm has the cost and marketing characteristics of Honda, and the other firm has the cost and marketing characteristics of Scion. Although the small car market is interesting in its own right, it serves here as an example of our general model. Our main goal is to show that under a reasonable set of demand and cost conditions, it is optimal for one firm to compete in output and choose a mass-market advertising position and for the other firm to compete in price and pursue a niche-market advertising position.

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2. The Strategic Choices of Honda and Scion Honda entered the U.S. small car market in the early 1970s, and its success grew with the introduction of the Honda Civic in the 1973 model year. Scion is a relatively new Toyota division or nameplate that entered the U.S. market in the 2003 model year.2 Since then, these firms have competed in advertising and output/price. Firms use advertising to provide consumers with presale information about product characteristics and image. Once this information is communicated, firms then sell cars to consumers.3 At the selling stage, Honda dealers compete in output, while Scion dealers compete in price. That is, Honda dealers first set monthly inventories and then adjust price to meet sales goals and clear the market.4 Being a relatively late entrant that is interested in marketing to consumers in urban areas, Scion faces a high cost of setting up new dealerships. As a result, the company sells Scions at existing Toyota dealerships. These dealers hold very little inventory, so most consumers place orders on cars that are delivered at a later date. In addition, prices are posted and are non-negotiable. Scion calls this “pure pricing.” Tremblay et al. (2008) show that cost asymmetries and dynamic play can induce one firm to compete in output and the other in price, and both explanations may be relevant to the HondaScion case. They show that if firms compete in a two stage game and firm 1 chooses output in the first stage, then firm 2 will be indifferent between competing in output or in price in the second stage. That is, a dynamic Cournot-Bertrand outcome is just as likely as a dynamic Cournot-Cournot (i.e. Stackelberg) outcome. They also show that a Cournot-Bertrand outcome will occur if one firm has a relatively high cost of competing in output.5 Although both explanations may play a role, the cost argument appears more relevant to Honda and Scion. Fixed costs are higher for output competition than price competition, because

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output competition requires a dealer to have sufficient inventory and a large car lot relative to a firm that competes in price and receives a car from the factory only after a customer order is placed. Scion is a relatively new brand, and when it was introduced existing Toyota dealers faced a capacity constraint, with sales lots already full of new Toyotas and used cars. By choosing to compete in price and shipping to order, little inventory is required, giving Scion relatively low fixed costs. If Scion chose to compete in output, its fixed costs would have been substantially higher, because Toyota dealers would have had to expand their capacity which would 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 strategy option. In contrast, Honda has established brands and dealers that have competed in output for decades. Switching to price competition would incur a switching cost, as Honda has existing storage capacity which may be costly to liquidate. With sufficiently high switching costs or sufficiently low fixed costs associated with holding inventory, Tremblay et al. (2008) show that such a firm will prefer output competition over price competition. Although Honda and Scion both produce small cars, their marketing goals are quite different. Honda is the fifth largest auto producer in the U.S., with a market share of 11.5 percent in 2007.6 Honda builds small cars that are known for reliability and fuel economy rather than style. For example, Consumer Reports ranks Hondas among the most reliable cars in the world, while Car and Driver, a leading automobile magazine, gives the 2009 Hondas low marks for styling and roadside appeal.7 Honda ads emphasize the quality and high fuel economy of its automobiles, vertical characteristics that are valued by everyone, rather than a horizontal characteristic that has limited appeal. By promoting vertical rather than horizontal

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characteristics, Honda ads generally appeal to the masses rather than a particular subgroup of potential consumers. Alternatively, Scion pursues a smaller segment of the market, with a market share of about 1.7 percent in 2007. With the increase in the average age of Toyota buyers, Toyota introduced the Scion brand to attract consumers who have typically shunned Toyota automobiles: hip male consumers from Generation Y (born from 1977 to 1995) who live in urban areas. To attract them, each year Scion offers 40 to 150 optional accessories (e.g., customcolored parts and upholstery and a variety of steering wheel and tail light options), which allow buyers to customize their vehicles. To reach its targeted audience, Scion replaces big-budget, mass-market ads with ads in movie theaters, sponsorships of local events, street-corner test drives, and internet postings aimed at young male consumers from urban areas. In the marketing literature, this is called “guerrilla marketing” (Levinson, 2007). Many of the major advertisers in the U.S. 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 and Scion 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. To summarize, Honda and Scion clearly make very different strategic choices. Honda chooses a high-volume (mass-market) position and advertises more intensively than Scion. Honda’s advertising messages emphasize the vertical characteristics of its automobiles and, therefore, have universal appeal. Scion clearly focuses on a low-volume (niche-market) position,

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developing cars and an advertising strategy that appeal to young male consumers. At the selling stage, Honda competes in output, while Scion competes in price.

3. A Cournot-Bertrand Model with Advertising In this section, we develop the model and identify parameter values that support 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 substitute good and compete in a two stage game. In the first stage they must decide on the type of advertising campaign and the level of advertising expenditures. Regarding type, a firm must decide whether its advertising will appeal to a massmarket audience or a niche-market audience. In the second stage, they compete in either output (Cournot) or price (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 advertising expenditures as Ai. We modify the classic duopoly model of Singh and Vives (1984) by allowing advertising to rotate demand, as in Aislabie and Tisdell (1988) and Johnson and Myatt (2006). Unlike the linear demand functions of Singh and Vives, we allow a firm’s own advertising to change the intercept and slope of demand. Because H will compete in output and S will compete in price in equilibrium in the second stage of the game, demand is written in terms of the strategic variables: Ai, qH, and pS. , ,

, ,

, ,

1 2

where the demand intercept, ai, and slopes, b and d, are functions of advertising.8 That is, advertising is an endogenous variable that can influence both the intercept and slope of demand.

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Mass-market advertising will cause inverse demand to rotate counterclockwise by lowering aH and b for H and by raising aS and d for S. In contrast, niche-market advertising will cause inverse demand to rotate clockwise.9 Given this specification, firm profits (pi) are

,

3

,

4

where w is the exogenous price of advertising.

A Simple Monopoly Example when Advertising Rotates Demand To illustrate this advertising taxonomy, let cS and FS be sufficiently high so that H is a simple monopolist. In this example, we let aH = zH + zH b(AH). Dropping the subscripts for convenience, the firm’s inverse demand is p = (z + zb) – bq and profits are p = (z + zb – bq – c)q – F – wA. In this specification, the rotation point is fixed at z, with p = z when q = z " b ε(0, ∞);10 we identify the output level at this point as qz. Notice that the inverse demand function rotates clockwise around z 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 expenditures. In the second period the firm chooses its optimal output and price. Using backwards induction, the optimal values in the later stage problem are: 2 2

5 6

9

7

2 The second-order condition requires b > 0.

The firm can look forward and reason back, so in the first stage the firm will choose the optimal type and level of advertising given p* above. The firm has the option of choosing a mass-market advertising campaign that lowers b or a niche-market advertising campaign that increases b. We assume that once a type of advertising is chosen, advertising spending causes a smooth change in b within the interval 0 < b1 ≤ b ≤ b2 < ∞. We also let w be positive but not excessively high so that advertising is profitable. Given equation (7), the firm’s first-order condition with respect to advertising is 0,

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where R = (z + bz – c)2/(2b), and in this model ∂R/∂b = ∂p*/∂b. An important feature of the model is that the profit function is convex in b.11 Thus, the firm will choose a type and level of advertising that produces an extreme value of b (b*), with b* ε {b1, b2} when w is sufficiently low. A mass-market advertising campaign that lowers b to b1 will be preferred when the marginal consumer, located at q*, is to the right of qz. This is because a flatter demand raises the willingness to pay for the marginal consumer; thus, ∂p*/∂b < 0. The reverse is true when the marginal consumer is to the left of qz. In order to raise the marginal consumer’s willingness to pay in this case, the firm will pursue a niche-market strategy that increases b to b2 because ∂p*/∂b > 0. This illustrates Johnson and Myatt’s (2006) Proposition 1: the monopolist will choose an extreme marketing position when mass-market and niche-market advertising campaigns can rotate demand.

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Which type of marketing campaign is optimal depends upon parameter values. Firm participation requires that c ≤ z + zb, which we assume to hold. When q* is to the right of qz (i.e., q* > qz = z), c < z – zb. In this case, ∂p*/∂b < 0, and the firm will pursue a mass-market campaign that lowers b. When q* is to the left of qz, c > z – zb and ∂p*/∂b > 0. Thus, the firm will pursue a niche-market campaign that increases b.12 To illustrate this point, we consider the case where c = 0 and z = 12. When b = 0.5, the firm will choose a mass-market campaign because q* = 18 > qz = 12. If the profit maximizing level of mass-market advertising lowers b to 0.4, 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 1 illustrates 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 the willingness to pay of the marginal consumer (located at qA*) and, therefore, an increase in gross profit. Alternatively, when b = 2.0, the firm will choose a niche-market campaign because q* = 9 < qz = 12. In this case, if the profit maximizing level of niche-market advertising raises b to 2.5, profits change from 162 to 176.4 – wA*. Again, this type of advertising raises profits as long as w is sufficiently low. As illustrated in Figure 2, this advertising campaign results in a flatter inverse demand function (moving from D1 to D2), which leads to an increase 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. Three regions are important: (1) Region Z1 identifies parameter values where it is unprofitable for the firm to participate. (2) In region Y1, parameter values make it profitable to pursue a niche-market campaign. (3) In region X1, parameter values make it profitable to pursue a mass-market campaign. This implies that the monopolist will be more likely to pursue a mass-market (niche-

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market) campaign when marginal cost is sufficiently low (high) and the inverse demand function is sufficiently flat (steep).

The Cournot-Bertrand Duopoly when Advertising Rotates Demand Now we consider the case where it is profitable for both H and S to participate. We fix the rotation point for each firm as in the monopoly case, such that aH = zH + zHb and aS = zS + zSd. Respective demands for firms H and S become , ,

9 10

where b = b(AH), and d = d(AS). With two firms, pH = zH when qH = zH and pS = 0, and qS = zS when pS = zS and qH = 0. Notice that if H uses advertising to increase b, its inverse demand function becomes steeper; if S uses advertising to increase d, its inverse demand function becomes flatter (but its demand function becomes steeper). This implies that if H and S pursue a mass-market (niche-market) advertising campaign, then H’s advertising campaign will lower (raise) b and S’s advertising campaign will raise (lower) d, which will rotate each firm’s inverse demand function counterclockwise (clockwise).13 We next consider appropriate restrictions on costs. Consistent with the fact that H competes in output and S competes in price, we assume that fixed costs are appropriately asymmetric. That is, fixed costs associated with output competition are sufficiently high for S and are sufficiently low for H. This produces the Cournot-Bertrand outcome in the final stage of the game as in Tremblay et al. (2008). Because S pursues a low-volume (niche) strategy and H pursues a high-volume (mass-market) strategy, we assume that cS > cH > 0. This is reasonable

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because H, the high-volume and more experienced producer, may have lower unit costs due to learning-by-doing. Firms have perfect and complete information and use backwards induction to reach the subgame perfect Nash equilibrium. When H competes in output and S competes in price, the Nash equilibrium in the last stage of the game is 1

2

H

1 2

S

1

4 2

H

S

H

S

where α ≡

1

,

4

4

,

12

,

13

1 2 1 4

,

2 1 4

14

,

1 2 1 4 2

11

15

,

1

and β ≡

16

2

1

. For the Nash

equilibrium to be stable, both b and d must be greater than ½.14 To assure firm participation, zi must be sufficiently large relative to ci. For S, Cournot dominates Bertrand behavior unless demand and cost conditions are sufficiently asymmetric. As discussed above, asymmetric fixed costs can induce S to compete in price. One the demand side, price competition for S is more profitable when zS is large relative to zH.

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For a reasonable set of parameter values, this stage game is consistent with much of H and S’s behavior. For example, let zS = 2zH = 12, cH = 0, cS = 10, b = 2, and d = 1, which we define as the benchmark values of parameters. In this case, pH* = 15.56 > pS* = 13.11, qH* = 7.78 > qS* = 3.11, pH* = 120.99 – FH, and pS* = 9.68 - FS. This result is consistent with the fact that H has a larger market share than S. In addition, H will have a strategic advantage over S if the difference in fixed costs between firms is not too great. Because firms have perfect and complete information, in the first stage they will choose the optimal types and levels of advertising given the anticipated Nash equilibrium in the final stage. We assume that once a type of advertising is chosen, advertising causes smooth changes in parameter values at a decreasing rate within the intervals ½ < b1 ≤ b ≤ b2 < ∞ and ½ < d1 ≤ d ≤ d2 < ∞. Again, w is positive but sufficiently low so that advertising is profitable 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 are fixed at their benchmark values.

Proposition 1: H will pursue a mass-market advertising campaign that uses advertising to lower b when cH and b are sufficiently low.

Proofs of all propositions can be found in the appendix. The relevant constraints are illustrated in Figure 4. To assure firm participation, cH must be sufficiently low (regions X2 and Y2). Region Y2 identifies parameter values that support a niche-market strategy, and region X2 identifies parameter values that support a mass-market strategy. For a mass-market strategy to be optimal, cH must be less than cS and inverse demand must be relatively flat (b must be sufficiently low), parameter restrictions that are consistent with H’s mass-market and high-volume position. In

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this case, H will use advertising to rotate its inverse demand counterclockwise (i.e., lower b), because this raises firm profits by increasing the willingness to pay of the marginal consumer. We next analyze parameter values needed to support S’s advertising behavior. In this case, cS and d vary but all other parameters take on benchmark values (which are consistent with Proposition 1 above).

Proposition 2: S will pursue a niche-market advertising campaign that uses advertising to lower d when cS is sufficiently high and d is sufficiently low.

Figure 5 identifies the relevant parameter space. For S to participate, cS must be sufficiently low, identified by regions X3 and Y3. Region X3 identifies parameter values that support a massmarket strategy, and Region Y3 identifies parameter values that support a niche-market strategy. Thus, for it to be optimal for S to purse a niche-market strategy, S must be the high cost producer and face a relatively steep inverse demand function (i.e., d is sufficiently low). This is consistent with the fact that S targets its automobiles to a select group of consumers, young males from urban areas, who are small in number but are likely to have relatively inelastic demand functions for cars with desirable characteristics. With the same set of benchmark values that were used above,15 we next analyze the effect of H’s mass-market actions and S’s niche-market actions on prices and rival profits.

Proposition 3: The mass-market advertising of H will lead to lower equilibrium prices for both firms and will lower S’s profits; the niche-market advertising of S will lead to a higher

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equilibrium price for S, will have an indeterminate effect on H’s equilibrium price, and will raise H’s profits.

This is not surprising given that these firms pursue very different types of advertising. H’s advertising emphasizes universal characteristics, which appeal to both H and S consumers and leads to tougher price competition and a net benefit only to the advertising firm. Alternatively, S’s advertising appeals to consumers with idiosyncratic preferences. This form of advertising leads to an increase in profits for both firms because it effectively increases product differentiation by informing consumers of real differences between brands. Thus, Proposition 3 implies that the Nash equilibrium level of advertising will not maximize joint profits. A trade association interested in increasing industry profits should encourage niche-market over massmarket advertising. Evaluating the welfare effect of advertising is complicated when advertising changes consumer tastes (Dixit and Norman, 1978; Stivers and Tremblay, 2005) and causes a change in the slope of demand (Shapiro, 1980). If one accepts consumer plus producer surplus as an appropriate measure as in Fisher and McGowan (1979) and Becker and Murphy (1993), however, the following proposition holds.

Proposition 4: H advertises too much from society’s perspective when parameter values are consistent with mass-market behavior; S advertises too little from society’s perspective for all acceptable parameter values.

Thus, cooperation in advertising may actually improve social welfare in this setting.

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These results can be overturned, however, when firm advertising affects the rotation point as well as the slope of demand. If the rotation point is endogenous, H benefits from shifting its rotation point left. This will increase demand by raising the marginal valuation of every consumer. Thus, consumer and producer surplus increase in the H market. Alternatively, S benefits from shifting the rotation point right, which increases demand by increasing the marginal valuation of every consumer. When the rotation point is endogenous in this way, H and S will produce too little advertising from the perspective of both the industry and society as a whole. 4. Conclusion The market for small cars is interesting in that firms make very different strategic choices. At the marketing stage, firms such as Honda pursue a mass-market advertising campaign, while firms such as Scion pursue a niche-market advertising campaign. Firms also choose very different strategic variables at the selling stage, with Honda choosing output and Scion choosing price. We develop a model that provides a plausible explanation for these observed behaviors. Our model identifies conditions under which firms make asymmetric strategic choices. Cost asymmetries induce one firm to compete in output and the other to compete in price, a mixture of the Cournot and Bertrand models. The Cournot type firm produces more output and has a strategic advantage over the Bertrand type firm as long as the difference in costs is not too great. The model also identifies market conditions under which one firm will pursue a massmarket and the other a niche-market advertising campaign. That is, when a firm faces relatively low (high) unit costs and a relatively flat (steep) inverse demand function, it will be more profitable to pursue a mass-market (niche-market) advertising campaign that rotates demand

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counterclockwise (clockwise). In this setting, industry profits increase in niche-market advertising and decrease in mass-market advertising. The model also explains much of the observed behavior of Honda and Scion, with Honda competing in output and Scion competing in price, Honda choosing mass-market advertising and Scion choosing niche-market advertising, and Honda having a larger market share than Scion. The welfare implications of advertising are quite complicated in a model such as this. If we assume that advertising does not change consumer tastes and does not affect the rotation point, then the mass-market producer advertises too much and the niche-market producer advertises too little from society’s perspective. If firm advertising can change the rotation point as well as the slope of demand, however, both firms may produce too little advertising from the perspective of industry and society.

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Appendix Proof of Proposition 1: From the Nash equilibrium in equations (11) – (16), the participation constraint for H is cH ≤ 23 + 6b. Firm H will pursue a mass-market advertising campaign that lowers b when ∂pH*/∂b < 0, which occurs when 23 H

74 1

24

2

.

4

A1

The participation constraint is met when condition (A1) holds. The right hand side of equation (A1) is positive and the stability condition is met (i.e., b > ½) for b ε(0.5, 2.73263). This identifies values of cH and b that make a mass-market campaign optimal, which is illustrated in Figure 4.

▄

Proof of Proposition 2: From the Nash equilibrium in equations (11) – (16), the participation constraint for S is S

6 5

8

1

4

.

A2

Firm S will pursue a niche-market advertising campaign that lowers d when ∂pS*/∂d < 0, which occurs when 6 5 S

1

16 4

2

64 32

2

.

A3

The participation constraint is met when condition (A3) holds, and the right hand side of equation (A3) is positive for all acceptable values of d. Thus, (A3) identifies values of cS and d that make a niche-market campaign optimal, which is illustrated in Figure 5.

▄

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Proof of Proposition 3: Regarding Rival Profits: From the Nash equilibrium in equations (11) – (16), the massmarket advertising of H that lowers b will lower S’s profits (i.e., ∂pS*/∂b > 0) when the following condition holds: 6 5

8

1

4

S

.

A4

This condition must hold under the participation constraint. Therefore, H’s mass-market advertising campaign will always lower S’s profits. The niche-market advertising of S that lowers d will raise H’s profits (i.e., ∂pH*/∂d < 0) when cH < 23 + 6b. Because this condition must hold under the participation constraint, S’s niche-market advertising campaign will always raise H’s profits. Regarding Prices: H’s advertising that changes b will have the following effect on Nash prices. ∂pH ∂b

46

∂pS ∂b

2 9

24b 48b 1 4b 9 24 1 8d

cS

2 cH

,

.

A5

A6

Equation (A6) is positive, and Firm H’s participation constraint guarantees that equation (A5) is positive. Thus, H’s mass-market advertising that lowers b will lower Nash prices for both firms. S’s advertising that changes d will have the following effects on Nash prices. ∂pH ∂d

2b 17 18b 1 4b

∂pS ∂d

4 cS 48 . 1 8d

cH

,

A7

A8

20

Equation (A7) is indeterminate, and Firm S’s participation constraint guarantees that equation (A8) is negative. Thus, S’s niche-market advertising that lowers d will raise 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 lowers S’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 condition holds. 29 H

205

72b 2

144b2

.

A9

This holds when condition (A1) is met, which assures that H is a mass-market producer. Thus, when H pursues a mass-market advertising campaign, it advertises too 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. Thus, S advertises too little from society’s perspective.

▄

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Fonda, Daren, Desa Philadelphia, and Joseph R. Szczesny, “Baby You Can Drive My Car,” Time, June 30, 2003, 46-48. Garfield, Bob, “Toyota Finds Attractive Effort to Push the Plug-Ugly Scion,” Advertising Age, August 4, 2003, 29. Häckner, Jonas, “A Note on Price and Quantity Competition in Differentiated Oligopolies,” Journal of Economic Theory, 93 (2), August 2000, 233-239. Hamilton, Jonathan and Steven Slutsky, “Endogenous Timing in Duopoly Games: Stackelberg or Cournot Equilibria,” Games and Economic Behavior, 2 (1), March 1990, 29-46. Johnson, Justin P., and David P. Myatt, “On the Simple Economics of Advertising, Marketing, and Product Design,” American Economic Review, 96 (3), June 2006, 756-784. Kreps, David, and Jose Scheinkman, “Quantity Precommitment and Bertrand Competition Yield Cournot Outcomes,” Bell Journal of Economics, 14 (2), Autumn 1983, 326337. Levinson, Jay Conrad, Guerrilla Marketing, Mariner Books, 2007. Morrissee, Brian, “Scion Web Strategy Takes a Stealth Approach,” Adweek, October 22, 2007, 12. Palmeri, Christopher, Ben Elgin, and Kathleen Kerwin, “Toyota’s Scion: Dude, Here’s Your Car,” Business Week, June 9, 2003. Rechtin, Mark, “Scion’s Dilemma: Be Hip – but Avoid the Mainstream,” Automotive News, May 22, 2006, 432-46. Singh, Nirvikar, and Xavier Vives, “Price and Quantity Competition in a Differentiated Duopoly,” Rand Journal of Economics, 15 (4), Winter 1984, 546-554.

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Stivers, Andrew, and Victor J. Tremblay, “Advertising, Search Costs, and Welfare, Information Economics and Policy, 17 (3), July 2005, 317-333. Tremblay, Victor J., Carol Horton Tremblay, and Kosin Isariyawongse, “Endogenous Timing and Strategic Choice: The Cournot-Bertrand Model,” working paper, Oregon State University, October 3, 2008. Welch, David, “Scion’s Street Credentials,” Business Week, April 27, 2007, 11. Zanchettin, Piercarlo, “Differentiated Duopoly with Asymmetric Costs,” Journal of Economics & Management Strategy, 15 (4), Winter 2006, 999-1015.

Endnotes 1

Chamberlin (1933, Ch. 6) also suggests that advertising may affect the price elasticity of

demand. 2

In reality, Honda produces cars with the Honda and Acura nameplates, and Toyota

produces cars with the Scion, Toyota, and Lexus nameplates. Here, Honda refers to cars with the Honda nameplate, and Scion refers to the Scion nameplate. 3

Information about the small car market and the marketing tactics of Scion and Honda is

from Fonda et al. (2003), Garfield (2003), Palmeri et al. (2003), Ciminillo (2005), Rechtin (2006), Morrissee (2007), and Welch (2007). 4

In the past, large car dealers were able to price discriminate, charging higher prices to

less informed and lower prices to more informed buyers. Bargaining such as this is less common in the market for small cars today. First, the internet has substantially lowered the cost of

24

obtaining information. For example, for a particular model of car, edmunds.com provides consumers with information on the suggested retail price, the dealer’s cost, and the average price paid by consumers in a particular zip code. Second, there is little difference between the suggested retail price and the dealer cost for small cars, leaving little room for bargaining. Dealers of small cars earn much of their income from extended service/warranty contracts and from servicing the cars that they sell. 5

Kreps and Scheinkman (1983) argue that it is “witless” to choose one static oligopoly

model (e.g., Cournot) over another (Bertrand), as it is an empirical question whether or not firms compete in output or price. Honda and Scion provide one example that is consistent with the Cournot-Bertrand model. 6

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. 7

This information is available at ConsumerReports.com and CarandDriver.com. In Car

and Driver’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 ratings include the Ford Mustang (with a rating of 7), Dodge Challenger (8), Porsche Boxster (9), and Lotis Elise (10). Scions are unusual in that each car can by highly customized to a consumer’s preference. 8

The Singh and Vives demand system derives from the utility function U(qH, qS) = αHqH

+ αSqS – (βHqH2 + βSqS2 + 2γqHqS)/2, which produces the following inverse demand functions: pH = αH – βHqH – γqS and pS = αS – βSqS – γqH. In order to focus on the rotational effect of

25

advertising and to minimize the number of demand parameters in the Cournot-Bertrand demand system, we set aH = (αHβS – αSγ)/βS, b = (βHβS – γ2)/βS, aS = αS/βS, d = 1/βS, and γ/βS = 1. This produces the demand system in equations (1) and (2). 9

Note that an advertising campaign that causes a non-parallel shift in demand need not

have a rotation point for positive values of both price and output. Following Johnson and Myatt, however, we define demand rotation to mean that the rotation point occurs at a positive valued price-quantity pair. 10

In Johnson and Myatt’s (2006) framework, however, the rotation point need not be

fixed. 11

That is, ∂p*/∂b = [-c2 + 2cz + z2(b2 – 1)]/(4b2) and ∂2p*/∂b2 = (c – z)2/(2b3) > 0.

12

When q* = qz, c = z – zb and ∂p*/∂b = 0. Because the profit function is strictly convex

in b, any discrete change in b will raise profits. Thus, either campaign will be profitable. 13

In this model, a firm that chooses a mass-market position will develop products with

universal appeal and use advertising to inform potential consumers of this fact. A firm that pursues a niche-market position, however, will promote the idiosyncratic qualities of its brand that appeal to its targeted audience. Thus, rival advertising will have no direct effect on a firm’s demand function, even though it will have a strategic effect and influence the Nash price, output, and profit levels of both firms. 14

Following Dixit (1986), this requires that |∂2p1/∂q12| > |∂2p1/∂q1∂p2| and |∂2p2/∂p22| >

|∂2p2/∂p2∂q1|. In our model, ∂2p1/∂q12 = -2b, ∂2p1/∂q1∂p2 = 1, ∂2p2/∂p22 = -2d, and ∂2p2/∂p2∂q1 = 1.

26 15

That is, zS = 2zH = 6, cS = 10, d = 1, and cH and b vary when analyzing H; zS = 2zH = 6,

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

Figure 1. Inverse Demand and Mass-Market Advertising

p

18 16 14

z

12

pA* pB*

10

A

B

8

D2 (b = 0.4)

6 0

2

4

6

8

10

12

14

16

18

qA*

20

22

qB*

24

D1 (b = 0.5) q

Figure 2. Inverse Demand and Niche-Market Advertising

p

40

30

B

pB*20 pA*

A z

10

D1 (b = 2) 0

1

2

3

4

5

6

7

8

9

qB*qA*

10

11

12

13

14

15

16

D2 (b = 2.5) q

Figure 3. Parameter Space that Supports Mass-Market and Niche-Market Advertising Campaigns C

12 11

Z1

10 9 8 7

Y1

6 5 4 3

X1

2 1 0 -1 -2

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

b

-3

Note that X1 identifies the parameter space that supports a Mass-Market Advertising Campaign. Y1 identifies the parameter space that supports a Niche-Market Advertising Campaign. The participation constraint is not met in region Z1.

Figure 4. Parameter Space that Supports Mass-Market and Niche-Market Advertising for Honda CH

40

Z2

35

30

25

20

Y2

15

10

5

0

X2 0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

b Note that X2 identifies the parameter space that supports a Mass-Market Advertising Campaign. Y2 identifies the parameter space that supports a Niche-Market Advertising Campaign. The participation constraint is not met in region Z2.

Figure 5. Parameter Space that Supports Mass-Market and Niche-Market Advertising for Scion CS

18

Z3

17 16 15 14 13

Y3

12 11 10 9

X3

8 7

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

d Note that X3 identifies the parameter space that supports a Mass-Market Advertising Campaign. Y3 identifies the parameter space that supports a Niche-Market Advertising Campaign. The participation constraint is not met in region Z3.