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The advantage of being first and competition between firms
International Journal of Industrial Organization I (1983) 353-364. North-Holland
THE ADVANTAGE OF BEING FIRST AND COMPETITION BETWEEN FIRMS Cecilia A. C O N R A D * Duke University, Durham, NC 27706, USA
Final version received August 1983 It is frequently suggested that the first brand in a product market enjoys a price advantage over its imitators due to imperfect information about product quality. This article considers the effect
of this advantage on prices and market shares in a dominant firm price leadership model. An established firm with a price advantage faces free entry by firms producing unbranded products (generics). In equilibrium, the first brand enjoys a market share advantage over entrants in entry and post entry periods. If the initial price disadvantage is large, entry will not occur.
1. Introduction Bain (1946) and others have argued that a pioneering brand is able to establish a reputation which later entrants cannot overcome without large promotional expenditures or drastic price cuts. 1 In a recent article, Sehmalensee (1982) has examined this hypothesis in the context of a simple model. He concludes that when product quality is uncertain, a 'profitable pioneering brand m a y be immune to subsequent entry'. Schmalensee's analysis assumes that the producer of the first brand introduced will not alter price in response to entry and that the second brand knows this in advance. This article considers the effect of a pioneer brand advantage on prices and market shares in a less passive competitive environment. It examines a dominant firm price leadership model of post entry behavior. The pioneer brand producer is modeled as the price leader who faces a large number of unbranded competitors called generics. A separate paper considers a second model in which the pioneer brand faces entry by a single brand name competitor) This model produces results which confirm Schmalensee's conclusions. The existence of an initial price advantage for the first brand introduced enables it to charge a higher price and have a larger market share than its rival in *The paper is taken from my Ph.d. disseration at Stanford University (1982). I would like to thank James Rosse, Timothy Bresnahan, William Novshek, and John Vernon for many helpful comments. This paper has also benefited enormously from the comments of anonymous referees. tFor other referents, see U.S. Federal Trade Commission (1979).
2Com'ad(1982). 0167-7187/83/$3.00 © 1983, Eisev/er Science Publishers B.V. (North-Holland)
354
C.A. Conrad, The advantage of beingfirst
post entry periods. Two possible equilibrium strategies for the pioneer brand emerge. Depending on the size of its advantage over entrants, it may set a price which effectively impedes the entry of imitators or it may set a price which allows it to coexist with entrants. The model presented here differs from Schmalensee's in other respects. Schmalensee's model considers the problem encountered by the first brand when it is first introduced. I do not address this problem explicitly in the context of this paper. It can be demonstrated that the qualitative nature of results is not altered by including the period in which the first brand is introduced. Section 2 presents a description of consumer behavior in which the source of the initial price advantage for the established brand is asymmetric information about product quality and risk averse consumers. A product of unknown quality is inherently riskier than a product of known quality. Because it is less risky, consumers will pay a higher price for the product of known quality. Similar results are obtainable using other specifications of the source of the initial price advantage) Section 3 discusses the dominant firm price leadership model with generic entry. Empirical implications of the model are presented in section 4 and conclusions in section 5.
2. Consumer behavior
This section presents a description of consumer choice in which the first brand introduced enjoys an initial demand advantage over later entrants. 2.1. Consumer choice in the entry period
Initially, a consumer is faced with a choice between two types of products, the pioneer brand and the entrant brands. The two products offer a characteristic, q, which is available in variable amounts; q will be referred to as product quality. I assume that q is an experience characteristic. Complete information about product quality is obtained only through actual experience with the product. 4 This paper only considers the market consisting of consumers purchasing prior to t = 1 who were initially satisfied, s Hence, all consumers have complete information about the quality of the pioneer brand. The quality of entrant brands is unknown. 3In Schmalensee's model, consumers are risk neutral, but the expected quality of an unknown product is lower than that for a product of known quality. This alternative formulation will generate similar results in this model. 4Products of this type were labelled experience goods in Nelson (1970). Consumers learn quickly and obtain complete information from a single experience. 5This model is extended to include the period in which the pioneer brand is introduced in the Ph.D. dissertation of Conrad. No fundamental results are altered.
C.A. Conrad, The advantage of beingfirst
355
A consumer decides whether to try an entrant brand based on the expected addition to his utility derivable from using the brand today and on expected future increases in utility. Single period utility for a risk averse consumer is described as follows:
U = U ( q , ) + z = U l + z, achieved if consumer purchases one unit of the pioneer, and
U = U*(qi)+z = U~.+z, expected if the consumer purchases one unit of any entrant brand i. Ua and U~ are measured in constant z dollars where z is the level of satisfaction derived from consumption of z units of some outside good. The price of z is set equal to one. U1 is utility derived from consumption of the product with known quality, ql. U~ is the expected utility derived from consumption of a product with unknown quality, ql. Faced with a choice between the pioneer and a single entrant brand (subscript 2), a consumer will purchase the entrant brand when it yields a net increase in the sum of present and future utility over the pioneer. A consumer j buys the entrant brand in period one if
Ue2-P21 q-vjT1 > U 1 - P l l .
(1)
vj is a taste parameter for consumer j. Pit and P2t are prices in period t of goods 1 and 2, respectively. Tt is the sum of expected increases in future net surpluses from trying a brand of unknown quality at time t. 6 A consumer who tries the product of unknown quality in period t will know the quality of both products in t + 1 and future periods. He can select the product offering the highest net surpluses. Tt will depend on the number of repeat purchases, the expected future path of prices, and on the distribution of product quality perceived by consumers. All of these factors are exogenous to the model. Consumer expectations about future prices do not depend on prices observed today. F o r simplicity, I assume that all consumers purchase one unit per time period, each period, until a final period of consumption, L. In the context of consumer behavior, the assumption of a finite time horizon is analogous to an assumption of bounded rationality. The initial price disadvantage for entrant brands arises due to risk averse consumers and low expectations about future increases in net surpluses. Attention is restricted to me-too products. Me-too brands are imitations of ST,= ~..~+1E. max(U1-Pt,, U2-P2,)-(U1 -Pt,), where subscript t denotes the current period; ~l~eript s is any time period.
356
C.A. Conrad, The advantage of beingfirst
established brands which offer no major improvements or innovations. Recent examples include C&C Cola introduced as an alternative to Coke and Pepsi; and Datril, an asprin substitute. I characterize consumer expectations about a me-too product which imitates the pioneer as follows: E(qi)=q,,
(2)
and ul - vl-
T~ > O.
(3)
Consumers are assumed to be risk averse. This assumption coupled with (2) insures that U1 > U). There is a positive opportunity cost of trying a brand of unknown quality. Eq. (3) states that the opportunity cost of trying the entrant brand is greater than the expected gain in future net surpluses from being informed about product quality. Under these assumptions, the pioneer brand will attract consumers even when Pl 1 > P2x2.2. Demand in period 1 In this period all consumers choose between the pioneer and an entrant brand by the decision rule described in eq. (1). Individual choices may then be aggregated to derive demand for each product. Consumers are assumed to differ in a single characteristic which affects how they evaluate the information content of a purchase. 7 Consumers are uniformly distributed over an interval (g,g+ 1) where g > 0 with respect to v's. In the analysis in this section, I assume that g = 0. All consumers have the same income; identical expectations about future; and identical expectations about the distribution of quality for an unknown product. Differences in v may be thought of as differences in the individual household discount rates. 8 The mean tastes parameter, f, may be interpreted as directly related to the average frequency of purchase for a product category. As the time interval between purchases increases, an individual will value the future use of the product less. For a cross-section of products, those which are more frequently purchased will have higher ~'s. The endpoint consumers define the range of prices at which both products will sell in positive quantities. It is easily established that a consumer with v = 1 will not purchase the me-too entrant when (U l - P 1 1 ) - ( U e 2 - P 2 1 ) > T1. 7Similar qualitative results arise in a model in which consumers differ in risk aversion or in expectations about the quality of the unknown product. 8Schmalenseeoffersa similar interpretation.
C.A. Conrad, The advantageof beingfirst
357
A consumer with the maximum valuation of the future will not purchase the me-too entrant when the opportunity cost of trying a new product today is larger than the gain from search. Thus, at price pairs (Pl 1, P21) such that Pll --P21 < U1 - U [ - T1, the me-too entrant will have zero sales and the established brand will sell to the entire market. When the opportunity cost of trying an unknown product is negative, (Ul-Pll)-(U~-P21)<0, the consumer who doesn't value the future, v=0, will purchase the me-too entrant and the established brand will have zero sales. The consumer who is just indifferent between purchasing a product of unknown quality (the entrant) and a product of known quality (the pioneer) is identified by v~', v~*= r ( u 1
-p~l)-(u~ -
p21)I/T1.
The indifferent consumer is the individual whose relative weight of the future is equal to the ratio of the expected difference in surplus today over the gain from search realized tomorrow. Demand for the two products is written as follows: Pioneer brand Dll=N
if
Me-too entrant
(U1-U~)-Tl>pll-P21
D21 --- 0
=v*N
if ( U I - U [ ) - T l < p l l - p 2 1 < ( U 1 - U ~ 2 )
=(1 - v * ) N
=0
if ( U 1 - U [ ) < P I l - P 2 1
=N
where N is the total population of consumers. Firm l's demand falls to zero at pll=U1 so if (UI-U~)+p21>U1, demand for firm l's product is truncated at p11= U1. Demand curves are downward sloping and linear in current prices in the range of prices below, (UI - U [ ) - T1 < P l l --P21 < U1 - - U~. 2.3. Demand in period 1 < t < L Demand in post entry periods depends crucially on the information
C.A. Conrad, The advantage of being first
358
consumers obtain in period one about the quality of entrant p r o d ~ : : A s noted earlier, complete information about product quality is obtained only through actual experience with the product. Consumers learn quickly in this model formulation. Complete information is obtained through a single trial. In addition, consumers obtain information only through their own experience. There is no word of mouth transmission. These last assumptions are most restrictive than necessary for many of the model results, but they simplify the analysis. What is essential is that there is some residual uncertainty associated with a product that a consumer has not tried. One source of this uncertainty could be mistrust of a neighbor's judgement of product quality. Alternatively, the assumption may be justified by arguing that consumers who are likely to communicate with one another share common characteristics, such as v's. For example, v's might depend on education or income levels. Since consumers with the same v's make the same decisions about trying unknown products, word of mouth transmission may simply re-inforce imperfect information. A crucial assumption in this model is what happens to Tt, the sum of expected increases in future net surpluses from trying a brand of unknown quality at time t. With a finite time horizon, one might expect that Tt declines over time. As t approaches L, the information obtained from trying a product of unknown quality has applications for fewer periods. A similar argument could be made with an infinite time horizon, but depreciation of information. If there were word of mouth transmission in this model, Tt might depend on what consumers tried the unknown product in period t - 1 . Tt would no longer be exogenous. For simplicity and tractability, I assume that Tt is exogenously determined, even for t > l . Tt declines over time and T L = O . In a later section, I discuss the implications of relaxing these assumptions for model's results. In any intermediate period t, consumers are sub-divided into two groups: those who have tried a me-too product and those who haven't. Let v*_x be the taste parameter for the uniformed consumer in period t - 1 who was just indifferent between the pioneer and the entrant. The uniformed consumers in period t will be the group of consumers with tastes parameters such that vi s(0, v * l ] . The informed consumers will have tastes parameters such that vi ~(v*_ 1, 1). The consumers who know the quality of both the pioneer and entrant in period t will prefer the pioneer to the entrant if and only if Pxt
e
,
U 2 ) - v~ _ ~ T~.
C.A. Conrad, The advantage of being first
359
At the other extreme, if P I ~ - P 2 t > U1 - U~,
the entire group will buy a me-too product. Demand for the pioneer and for the me-too product from this group is downward sloping in the intermediate range of prices. Fig. 1 illustrates demand for the pioneer brand in period l
Dit
P2t
P2t- (U 1-U~}+Vt_lTt
P2t+(U1-U~)
Plt
Fig. 1
Consumers who are indifferent between the pioneer and the me-too brand consume the product they consumed in the previous period. 3. Free entry of generics This section discusses a model in which the first brand introduced faces entry by a large number of unbranded producers called generics. Generics are indistinguishable from one another. A conumer who tries a generic acquires information about all generics. In contrast, a consumer who tries a brand name product acquires information only about that brand name. Each generic faces a perfectly elastic demand for its product in every period. There is free entry of generic products in every period. With constant marginal cost c, and zero fixed costs, the price of the generic products must equal marginal cost in every period t. The producer of the first brand acts as a dominant firm in this model. It anticipates profit maximizing behavior by actual and potential generic entrants. In every period t, the producer of the first brand chooses its own price to maxim~e profits, taking into account that the price of generics will equal marginal cost.
360
C.A. Conrad, The advantage of beingfirst
3.1. Post-entry equilibrium In period L, profits for the producer of the first brand, given its expectation that the price of generics will equal marginal cost, are defined by if
7~IL= ( P l L - - C ) N
PlL < C,
=(p~L-C)v~_~N if C~plL
otherwise.
Profits are clearly maximized by choosing P lL = C + ( U 1 - U)). At this price, the producer of the first brand retains consumers who have not tried generics. In period L - l , profits for the pioneer brand producer are again maximized by retaining consumers who have not tried generics. Attracting consumers who have tried generics requires a price below marginal cost in L - 1 and retaining those consumers in period L also requires a price less than marginal cost. Hence, attracting consumers who have tried generics will not be profitable for the pioneer brand. The profit maximizing price is e
,
P~L- I =C-~-(U1--U2)--VL- 2 TL- I"
A similar argument is made for any period t > l . Again, profit maximization will never involve reattracting consumers from generics. The pioneer maximizes profits in any period t by choosing a price
p,,=C+(U,-U~)-v,* ,T,. The profit maximizing strategy for the pioneer in post entry periods will be to retain those consumers who did not try generics in period 1. Its decision about price in period 1 determines its share of the market and its price in post entry periods.
3.2. Entry period I now examine the pioneer brand's entry period response to generics when it has perfect foresight about post entry equilibria. At time of entry, all consumers will be uniformed about the quality of generics and informed about the quality of the pioneer. As discussed, we assume that this information asymmetry conveys a price advantage to the pioneer over all consumers.
C.A. Conrad, The advantage of beingfirst
361
The profit stream for the pioneer brand is
7r,~=N(plx-C +k~=z(U~-U~)-Tk) =0
if pI,
p~>C+(U1-U~),
=N(UI-U~) (P11-C) T1
TI
x ( p l , - C + ~ = 2~
(UI--U~)--v*Rk) otherwise,
where
=(u~_- u 9 T,
(Pl 1 -- C)
When
(u~-uI)L
T,<2,
profits reach their maximum at the price
p'I =C+(Ux-U~)-[L(U1-U~)T~/ 2~ Tt1, which results in generic entry. If
(Ux-U~)L/x / ~ T,>2, profits are maximized at
p*I=C+(Ut-U[)- T1. At this price, the pioneer brand retains all consumers. No generics are consumed. The critical determining factor is the ratio of the opportunity cost of search (summed over L periods) to the expected information gain from trying a n unknown product (summed over L periods),
L(U1-- 2) Tt.
C.A. Conrad, The advantageof beingfirst
362
I define this ratio to be the pioneer brand advantage (PBA). 9 It reflects the price advantage the pioneer possesses over potential entrants. The size of the PBA will depend on the 'riskiness' of trying a product of unknown quality. Where the costs of product failure are low or where consumers are less uncertain about product quality, trying the product of unknown quality may be less risky. ( U t - U ~ ) may be smaller and ~ Tt, larger. The PBA is correspondingly reduced.
3.3. Interim summary Two types of equilibria may be identified. If the pioneer's price advantage over entrants is large, it will find it profitable to set a price in period 1 which is so low as to make generic entry unprofitable. This price, p l l = C+(Ut-U~z)=Tt, will not be below marginal or average variable cost. In this case, the established brand maintains its market share in post entry periods as well. If the PBA is small, the established brand and the generic entrant coexist in equilibrium. The established brand's market share will be
MSI=L(Ui-Ue2) f 2 ~ T ~ , which is equivalent to ½ PBA. It can be shown that MS1>½. The key assumptions are that Tt's decline over time and that the pioneer brand posseses an initial price advantage over its rivals [eq. (3)]. Under these assumptions, the pioneer brand will maintain a market share advantage over generics in period 1 and in subsequent periods. The persistence of a sizeable pioneer brand advantage depends on the behavior of the T,'s over time. If the T/s are constant, no fundamental results are altered. If the T~'s increase over time, the strength of some important conclusions is reduced. First, the price premium enjoyed by the pioneer brand over generics will diminish over time. If T~ grows very large, the price premium eventually could disappear. Second, although the pioneer brand's market share is stable over time, there is no guarantee that it will dominate the market. MS1 could be less than one-half.
4. Changes in parameters In this section, I consider the effect on equilibrium price differences of shifting the distribution of consumer tastes. The distribution of consumers is altered so as to change the mean tastes parameter, f, but leave density intact. 9This definition of the PBA differs from that in my dissertation. I am grateful to an anonymous refereefor this reformulation.
C.A. Conrad, The ad~;antage of being first
363
In the previous analysis, I assumed that g, the lowest valuation of the future held by consumers, equalled zero. This assumption is now relaxed. I consider the effects of an increase in g which will increase the average valuation of the future, v. Under the new distribution of consumers the P B A gets smaller. Consumers are more willing on average to sample a new product. The pioneer brand advantage's deterioration leads to an unambiguous decline in its market share. The greater the average valuation of the future, the smaller is the advantage accruing to a pioneer brand. As discussed earlier, ~5may be interpreted as directly related to the average frequency of purchase for a product category. For a cross section of products, those which are more frequently purchased will have higher Ys. The more frequently a product is purchased, the less likely we will see a single brand equilibrium and the smaller the price difference between the pioneer and generics in an equilibrium where they coexist. 5. Conclusions This paper examines a model of price competition in which the first brand in a market has a price advantage over imitative entrants because consumers have more information about its quality. In this model: the initial price advantage for an established brand gives it a market share advantage over time and may enable it to enjoy a monopoly in the market. This model yields predictions which are consistent with observed price differences between pioneer brands and their imitators and with the pattern of market shares over time in prescription drug markets [F.T.C. Staff Report (1977)]. Several empirically testable hypotheses are proposed. The market share of the first brand introduced and its price advantage over entrants should be larger for products where there is low purchase frequency and/or high costs of product failure. A preliminary examination of cross sectional data on prescription drug price differences yielded preliminary support for these hypotheses [Conrad (1982)], but further study is needed. This analysis focused on the effects of an advantage to being first, without directly asking when the first brand will have an informational advantage over entrants. However, it does offer some insights. Factors which increase the gains from acquiring information about product quality or which decrease the cost of acquiring that information will reduce the advantage possessed by the first brand introduced. In addition, the source of advantage in this market is imperfect information about experience characteristics of a product. Where experience characteristics are less important, the informational advantage should be smaller.
364
C.A. Conrad, The advantage of beingfirst
References Bain, Joe S., 1946, Barriers to new competition (Harvard University Press, Cambridge, MA). Conrad, Cecilia A., 1982, The pioneer brand hypothesis and other topics: Product marke~s with assymetric information about product quality, Ph.D. dissertation (Stanford University, Stanford, CA). Nelson, Philip, 1970, Information and consumer behavior, Journal of Political Economy 78, 311-329. Schmalensee, Richard, 1982, Product differentiation advantages of pioneering brands, American Economic Review 72, 349-365. U.S. Federal Trade Commission, 1977, Bureau of Economics, Sales promotion and product differentiation in two prescription drug markets, by Ron Bond and David Lean, Staff report (Government Printing Office, Washington, DC). U.S. Federal Trade Commission, 1979, Bureau of Economics, Brand performance in the cigarette industry and the advantage of early entry 1913-1973, by Ira Whitten, Staff report (Government Printing Office, Washington, DC).
THE ADVANTAGE OF BEING FIRST AND COMPETITION BETWEEN FIRMS Cecilia A. C O N R A D * Duke University, Durham, NC 27706, USA
Final version received August 1983 It is frequently suggested that the first brand in a product market enjoys a price advantage over its imitators due to imperfect information about product quality. This article considers the effect
of this advantage on prices and market shares in a dominant firm price leadership model. An established firm with a price advantage faces free entry by firms producing unbranded products (generics). In equilibrium, the first brand enjoys a market share advantage over entrants in entry and post entry periods. If the initial price disadvantage is large, entry will not occur.
1. Introduction Bain (1946) and others have argued that a pioneering brand is able to establish a reputation which later entrants cannot overcome without large promotional expenditures or drastic price cuts. 1 In a recent article, Sehmalensee (1982) has examined this hypothesis in the context of a simple model. He concludes that when product quality is uncertain, a 'profitable pioneering brand m a y be immune to subsequent entry'. Schmalensee's analysis assumes that the producer of the first brand introduced will not alter price in response to entry and that the second brand knows this in advance. This article considers the effect of a pioneer brand advantage on prices and market shares in a less passive competitive environment. It examines a dominant firm price leadership model of post entry behavior. The pioneer brand producer is modeled as the price leader who faces a large number of unbranded competitors called generics. A separate paper considers a second model in which the pioneer brand faces entry by a single brand name competitor) This model produces results which confirm Schmalensee's conclusions. The existence of an initial price advantage for the first brand introduced enables it to charge a higher price and have a larger market share than its rival in *The paper is taken from my Ph.d. disseration at Stanford University (1982). I would like to thank James Rosse, Timothy Bresnahan, William Novshek, and John Vernon for many helpful comments. This paper has also benefited enormously from the comments of anonymous referees. tFor other referents, see U.S. Federal Trade Commission (1979).
2Com'ad(1982). 0167-7187/83/$3.00 © 1983, Eisev/er Science Publishers B.V. (North-Holland)
354
C.A. Conrad, The advantage of beingfirst
post entry periods. Two possible equilibrium strategies for the pioneer brand emerge. Depending on the size of its advantage over entrants, it may set a price which effectively impedes the entry of imitators or it may set a price which allows it to coexist with entrants. The model presented here differs from Schmalensee's in other respects. Schmalensee's model considers the problem encountered by the first brand when it is first introduced. I do not address this problem explicitly in the context of this paper. It can be demonstrated that the qualitative nature of results is not altered by including the period in which the first brand is introduced. Section 2 presents a description of consumer behavior in which the source of the initial price advantage for the established brand is asymmetric information about product quality and risk averse consumers. A product of unknown quality is inherently riskier than a product of known quality. Because it is less risky, consumers will pay a higher price for the product of known quality. Similar results are obtainable using other specifications of the source of the initial price advantage) Section 3 discusses the dominant firm price leadership model with generic entry. Empirical implications of the model are presented in section 4 and conclusions in section 5.
2. Consumer behavior
This section presents a description of consumer choice in which the first brand introduced enjoys an initial demand advantage over later entrants. 2.1. Consumer choice in the entry period
Initially, a consumer is faced with a choice between two types of products, the pioneer brand and the entrant brands. The two products offer a characteristic, q, which is available in variable amounts; q will be referred to as product quality. I assume that q is an experience characteristic. Complete information about product quality is obtained only through actual experience with the product. 4 This paper only considers the market consisting of consumers purchasing prior to t = 1 who were initially satisfied, s Hence, all consumers have complete information about the quality of the pioneer brand. The quality of entrant brands is unknown. 3In Schmalensee's model, consumers are risk neutral, but the expected quality of an unknown product is lower than that for a product of known quality. This alternative formulation will generate similar results in this model. 4Products of this type were labelled experience goods in Nelson (1970). Consumers learn quickly and obtain complete information from a single experience. 5This model is extended to include the period in which the pioneer brand is introduced in the Ph.D. dissertation of Conrad. No fundamental results are altered.
C.A. Conrad, The advantage of beingfirst
355
A consumer decides whether to try an entrant brand based on the expected addition to his utility derivable from using the brand today and on expected future increases in utility. Single period utility for a risk averse consumer is described as follows:
U = U ( q , ) + z = U l + z, achieved if consumer purchases one unit of the pioneer, and
U = U*(qi)+z = U~.+z, expected if the consumer purchases one unit of any entrant brand i. Ua and U~ are measured in constant z dollars where z is the level of satisfaction derived from consumption of z units of some outside good. The price of z is set equal to one. U1 is utility derived from consumption of the product with known quality, ql. U~ is the expected utility derived from consumption of a product with unknown quality, ql. Faced with a choice between the pioneer and a single entrant brand (subscript 2), a consumer will purchase the entrant brand when it yields a net increase in the sum of present and future utility over the pioneer. A consumer j buys the entrant brand in period one if
Ue2-P21 q-vjT1 > U 1 - P l l .
(1)
vj is a taste parameter for consumer j. Pit and P2t are prices in period t of goods 1 and 2, respectively. Tt is the sum of expected increases in future net surpluses from trying a brand of unknown quality at time t. 6 A consumer who tries the product of unknown quality in period t will know the quality of both products in t + 1 and future periods. He can select the product offering the highest net surpluses. Tt will depend on the number of repeat purchases, the expected future path of prices, and on the distribution of product quality perceived by consumers. All of these factors are exogenous to the model. Consumer expectations about future prices do not depend on prices observed today. F o r simplicity, I assume that all consumers purchase one unit per time period, each period, until a final period of consumption, L. In the context of consumer behavior, the assumption of a finite time horizon is analogous to an assumption of bounded rationality. The initial price disadvantage for entrant brands arises due to risk averse consumers and low expectations about future increases in net surpluses. Attention is restricted to me-too products. Me-too brands are imitations of ST,= ~..~+1E. max(U1-Pt,, U2-P2,)-(U1 -Pt,), where subscript t denotes the current period; ~l~eript s is any time period.
356
C.A. Conrad, The advantage of beingfirst
established brands which offer no major improvements or innovations. Recent examples include C&C Cola introduced as an alternative to Coke and Pepsi; and Datril, an asprin substitute. I characterize consumer expectations about a me-too product which imitates the pioneer as follows: E(qi)=q,,
(2)
and ul - vl-
T~ > O.
(3)
Consumers are assumed to be risk averse. This assumption coupled with (2) insures that U1 > U). There is a positive opportunity cost of trying a brand of unknown quality. Eq. (3) states that the opportunity cost of trying the entrant brand is greater than the expected gain in future net surpluses from being informed about product quality. Under these assumptions, the pioneer brand will attract consumers even when Pl 1 > P2x2.2. Demand in period 1 In this period all consumers choose between the pioneer and an entrant brand by the decision rule described in eq. (1). Individual choices may then be aggregated to derive demand for each product. Consumers are assumed to differ in a single characteristic which affects how they evaluate the information content of a purchase. 7 Consumers are uniformly distributed over an interval (g,g+ 1) where g > 0 with respect to v's. In the analysis in this section, I assume that g = 0. All consumers have the same income; identical expectations about future; and identical expectations about the distribution of quality for an unknown product. Differences in v may be thought of as differences in the individual household discount rates. 8 The mean tastes parameter, f, may be interpreted as directly related to the average frequency of purchase for a product category. As the time interval between purchases increases, an individual will value the future use of the product less. For a cross-section of products, those which are more frequently purchased will have higher ~'s. The endpoint consumers define the range of prices at which both products will sell in positive quantities. It is easily established that a consumer with v = 1 will not purchase the me-too entrant when (U l - P 1 1 ) - ( U e 2 - P 2 1 ) > T1. 7Similar qualitative results arise in a model in which consumers differ in risk aversion or in expectations about the quality of the unknown product. 8Schmalenseeoffersa similar interpretation.
C.A. Conrad, The advantageof beingfirst
357
A consumer with the maximum valuation of the future will not purchase the me-too entrant when the opportunity cost of trying a new product today is larger than the gain from search. Thus, at price pairs (Pl 1, P21) such that Pll --P21 < U1 - U [ - T1, the me-too entrant will have zero sales and the established brand will sell to the entire market. When the opportunity cost of trying an unknown product is negative, (Ul-Pll)-(U~-P21)<0, the consumer who doesn't value the future, v=0, will purchase the me-too entrant and the established brand will have zero sales. The consumer who is just indifferent between purchasing a product of unknown quality (the entrant) and a product of known quality (the pioneer) is identified by v~', v~*= r ( u 1
-p~l)-(u~ -
p21)I/T1.
The indifferent consumer is the individual whose relative weight of the future is equal to the ratio of the expected difference in surplus today over the gain from search realized tomorrow. Demand for the two products is written as follows: Pioneer brand Dll=N
if
Me-too entrant
(U1-U~)-Tl>pll-P21
D21 --- 0
=v*N
if ( U I - U [ ) - T l < p l l - p 2 1 < ( U 1 - U ~ 2 )
=(1 - v * ) N
=0
if ( U 1 - U [ ) < P I l - P 2 1
=N
where N is the total population of consumers. Firm l's demand falls to zero at pll=U1 so if (UI-U~)+p21>U1, demand for firm l's product is truncated at p11= U1. Demand curves are downward sloping and linear in current prices in the range of prices below, (UI - U [ ) - T1 < P l l --P21 < U1 - - U~. 2.3. Demand in period 1 < t < L Demand in post entry periods depends crucially on the information
C.A. Conrad, The advantage of being first
358
consumers obtain in period one about the quality of entrant p r o d ~ : : A s noted earlier, complete information about product quality is obtained only through actual experience with the product. Consumers learn quickly in this model formulation. Complete information is obtained through a single trial. In addition, consumers obtain information only through their own experience. There is no word of mouth transmission. These last assumptions are most restrictive than necessary for many of the model results, but they simplify the analysis. What is essential is that there is some residual uncertainty associated with a product that a consumer has not tried. One source of this uncertainty could be mistrust of a neighbor's judgement of product quality. Alternatively, the assumption may be justified by arguing that consumers who are likely to communicate with one another share common characteristics, such as v's. For example, v's might depend on education or income levels. Since consumers with the same v's make the same decisions about trying unknown products, word of mouth transmission may simply re-inforce imperfect information. A crucial assumption in this model is what happens to Tt, the sum of expected increases in future net surpluses from trying a brand of unknown quality at time t. With a finite time horizon, one might expect that Tt declines over time. As t approaches L, the information obtained from trying a product of unknown quality has applications for fewer periods. A similar argument could be made with an infinite time horizon, but depreciation of information. If there were word of mouth transmission in this model, Tt might depend on what consumers tried the unknown product in period t - 1 . Tt would no longer be exogenous. For simplicity and tractability, I assume that Tt is exogenously determined, even for t > l . Tt declines over time and T L = O . In a later section, I discuss the implications of relaxing these assumptions for model's results. In any intermediate period t, consumers are sub-divided into two groups: those who have tried a me-too product and those who haven't. Let v*_x be the taste parameter for the uniformed consumer in period t - 1 who was just indifferent between the pioneer and the entrant. The uniformed consumers in period t will be the group of consumers with tastes parameters such that vi s(0, v * l ] . The informed consumers will have tastes parameters such that vi ~(v*_ 1, 1). The consumers who know the quality of both the pioneer and entrant in period t will prefer the pioneer to the entrant if and only if Pxt
e
,
U 2 ) - v~ _ ~ T~.
C.A. Conrad, The advantage of being first
359
At the other extreme, if P I ~ - P 2 t > U1 - U~,
the entire group will buy a me-too product. Demand for the pioneer and for the me-too product from this group is downward sloping in the intermediate range of prices. Fig. 1 illustrates demand for the pioneer brand in period l
Dit
P2t
P2t- (U 1-U~}+Vt_lTt
P2t+(U1-U~)
Plt
Fig. 1
Consumers who are indifferent between the pioneer and the me-too brand consume the product they consumed in the previous period. 3. Free entry of generics This section discusses a model in which the first brand introduced faces entry by a large number of unbranded producers called generics. Generics are indistinguishable from one another. A conumer who tries a generic acquires information about all generics. In contrast, a consumer who tries a brand name product acquires information only about that brand name. Each generic faces a perfectly elastic demand for its product in every period. There is free entry of generic products in every period. With constant marginal cost c, and zero fixed costs, the price of the generic products must equal marginal cost in every period t. The producer of the first brand acts as a dominant firm in this model. It anticipates profit maximizing behavior by actual and potential generic entrants. In every period t, the producer of the first brand chooses its own price to maxim~e profits, taking into account that the price of generics will equal marginal cost.
360
C.A. Conrad, The advantage of beingfirst
3.1. Post-entry equilibrium In period L, profits for the producer of the first brand, given its expectation that the price of generics will equal marginal cost, are defined by if
7~IL= ( P l L - - C ) N
PlL < C,
=(p~L-C)v~_~N if C~plL
otherwise.
Profits are clearly maximized by choosing P lL = C + ( U 1 - U)). At this price, the producer of the first brand retains consumers who have not tried generics. In period L - l , profits for the pioneer brand producer are again maximized by retaining consumers who have not tried generics. Attracting consumers who have tried generics requires a price below marginal cost in L - 1 and retaining those consumers in period L also requires a price less than marginal cost. Hence, attracting consumers who have tried generics will not be profitable for the pioneer brand. The profit maximizing price is e
,
P~L- I =C-~-(U1--U2)--VL- 2 TL- I"
A similar argument is made for any period t > l . Again, profit maximization will never involve reattracting consumers from generics. The pioneer maximizes profits in any period t by choosing a price
p,,=C+(U,-U~)-v,* ,T,. The profit maximizing strategy for the pioneer in post entry periods will be to retain those consumers who did not try generics in period 1. Its decision about price in period 1 determines its share of the market and its price in post entry periods.
3.2. Entry period I now examine the pioneer brand's entry period response to generics when it has perfect foresight about post entry equilibria. At time of entry, all consumers will be uniformed about the quality of generics and informed about the quality of the pioneer. As discussed, we assume that this information asymmetry conveys a price advantage to the pioneer over all consumers.
C.A. Conrad, The advantage of beingfirst
361
The profit stream for the pioneer brand is
7r,~=N(plx-C +k~=z(U~-U~)-Tk) =0
if pI,
p~>C+(U1-U~),
=N(UI-U~) (P11-C) T1
TI
x ( p l , - C + ~ = 2~
(UI--U~)--v*Rk) otherwise,
where
=(u~_- u 9 T,
(Pl 1 -- C)
When
(u~-uI)L
T,<2,
profits reach their maximum at the price
p'I =C+(Ux-U~)-[L(U1-U~)T~/ 2~ Tt1, which results in generic entry. If
(Ux-U~)L/x / ~ T,>2, profits are maximized at
p*I=C+(Ut-U[)- T1. At this price, the pioneer brand retains all consumers. No generics are consumed. The critical determining factor is the ratio of the opportunity cost of search (summed over L periods) to the expected information gain from trying a n unknown product (summed over L periods),
L(U1-- 2) Tt.
C.A. Conrad, The advantageof beingfirst
362
I define this ratio to be the pioneer brand advantage (PBA). 9 It reflects the price advantage the pioneer possesses over potential entrants. The size of the PBA will depend on the 'riskiness' of trying a product of unknown quality. Where the costs of product failure are low or where consumers are less uncertain about product quality, trying the product of unknown quality may be less risky. ( U t - U ~ ) may be smaller and ~ Tt, larger. The PBA is correspondingly reduced.
3.3. Interim summary Two types of equilibria may be identified. If the pioneer's price advantage over entrants is large, it will find it profitable to set a price in period 1 which is so low as to make generic entry unprofitable. This price, p l l = C+(Ut-U~z)=Tt, will not be below marginal or average variable cost. In this case, the established brand maintains its market share in post entry periods as well. If the PBA is small, the established brand and the generic entrant coexist in equilibrium. The established brand's market share will be
MSI=L(Ui-Ue2) f 2 ~ T ~ , which is equivalent to ½ PBA. It can be shown that MS1>½. The key assumptions are that Tt's decline over time and that the pioneer brand posseses an initial price advantage over its rivals [eq. (3)]. Under these assumptions, the pioneer brand will maintain a market share advantage over generics in period 1 and in subsequent periods. The persistence of a sizeable pioneer brand advantage depends on the behavior of the T,'s over time. If the T/s are constant, no fundamental results are altered. If the T~'s increase over time, the strength of some important conclusions is reduced. First, the price premium enjoyed by the pioneer brand over generics will diminish over time. If T~ grows very large, the price premium eventually could disappear. Second, although the pioneer brand's market share is stable over time, there is no guarantee that it will dominate the market. MS1 could be less than one-half.
4. Changes in parameters In this section, I consider the effect on equilibrium price differences of shifting the distribution of consumer tastes. The distribution of consumers is altered so as to change the mean tastes parameter, f, but leave density intact. 9This definition of the PBA differs from that in my dissertation. I am grateful to an anonymous refereefor this reformulation.
C.A. Conrad, The ad~;antage of being first
363
In the previous analysis, I assumed that g, the lowest valuation of the future held by consumers, equalled zero. This assumption is now relaxed. I consider the effects of an increase in g which will increase the average valuation of the future, v. Under the new distribution of consumers the P B A gets smaller. Consumers are more willing on average to sample a new product. The pioneer brand advantage's deterioration leads to an unambiguous decline in its market share. The greater the average valuation of the future, the smaller is the advantage accruing to a pioneer brand. As discussed earlier, ~5may be interpreted as directly related to the average frequency of purchase for a product category. For a cross section of products, those which are more frequently purchased will have higher Ys. The more frequently a product is purchased, the less likely we will see a single brand equilibrium and the smaller the price difference between the pioneer and generics in an equilibrium where they coexist. 5. Conclusions This paper examines a model of price competition in which the first brand in a market has a price advantage over imitative entrants because consumers have more information about its quality. In this model: the initial price advantage for an established brand gives it a market share advantage over time and may enable it to enjoy a monopoly in the market. This model yields predictions which are consistent with observed price differences between pioneer brands and their imitators and with the pattern of market shares over time in prescription drug markets [F.T.C. Staff Report (1977)]. Several empirically testable hypotheses are proposed. The market share of the first brand introduced and its price advantage over entrants should be larger for products where there is low purchase frequency and/or high costs of product failure. A preliminary examination of cross sectional data on prescription drug price differences yielded preliminary support for these hypotheses [Conrad (1982)], but further study is needed. This analysis focused on the effects of an advantage to being first, without directly asking when the first brand will have an informational advantage over entrants. However, it does offer some insights. Factors which increase the gains from acquiring information about product quality or which decrease the cost of acquiring that information will reduce the advantage possessed by the first brand introduced. In addition, the source of advantage in this market is imperfect information about experience characteristics of a product. Where experience characteristics are less important, the informational advantage should be smaller.
364
C.A. Conrad, The advantage of beingfirst
References Bain, Joe S., 1946, Barriers to new competition (Harvard University Press, Cambridge, MA). Conrad, Cecilia A., 1982, The pioneer brand hypothesis and other topics: Product marke~s with assymetric information about product quality, Ph.D. dissertation (Stanford University, Stanford, CA). Nelson, Philip, 1970, Information and consumer behavior, Journal of Political Economy 78, 311-329. Schmalensee, Richard, 1982, Product differentiation advantages of pioneering brands, American Economic Review 72, 349-365. U.S. Federal Trade Commission, 1977, Bureau of Economics, Sales promotion and product differentiation in two prescription drug markets, by Ron Bond and David Lean, Staff report (Government Printing Office, Washington, DC). U.S. Federal Trade Commission, 1979, Bureau of Economics, Brand performance in the cigarette industry and the advantage of early entry 1913-1973, by Ira Whitten, Staff report (Government Printing Office, Washington, DC).