Product Differentiation Advantages of Pioneering Brands
`
`This essay presents and explores a rela-
`tively simple market model in which rational
`buyer behavior in the face of imperfect infor-
`mation about product quality can give long-
`lived advantages to pioneering brands. The
`analysis has some implications for the varia-
`tion in the strength of such advantages across
`markets with different basic conditions. Two
`sorts of evidence provide the motivation for
`this research.
`First, Joe Bain's seminal empirical study
`of conditions of entry led him to conclude
`that "the advantage to established sellers
`accruing from buyer preferences for their
`products as opposed to potential entrant
`products is on average larger and more fre-
`quent in occurrence at large values than any
`other barrier to entry" (p. 216). Treating
`advertising as a proxy for product differenti-
`ation, a large literature has attempted to test
`this assertion by relating advertising to prof-
`itability in cross section.' It is interesting to
`note, however, that Bain concluded that
`advertising was not the main force at work:
`
`these things might seem to
`All of
`suggest the existence of fundamental
`technical considerations, institutional
`developments, and more or less funda-
`mental consumer traits which make
`possible or even very probable the de-
`velopment of strong and stable prod-
`uct-preference patterns. They may also
`
`*Professor of applied economics, Sloan School of
`Management, Massachusetts Institute of Technology. I
`am grateful to the U.S. Federal Trade Commission for
`its support of this research. I am also grateful for helpful
`comments to Steven Salop, a referee, the managing
`editor, and seminar audiences at MIT, Chicago, Harvard,
`Princeton, Rochester, the Department of Justice, the
`Federal Trade Commission, and the Santa Barbara and
`San Diego campuses of the University of California.
`Naturally, only I can be held accountable for this essay's
`shortcomings and the opinions it expresses.
`'William S. Comanor and Thomas A. Wilson and
`Harold Demsetz provide interesting overviews of this
`literature; see also my forthcoming essay, especially
`Section 3.
`
`suggest that advertising per se is not
`necessarily the main or even the most
`important key to the product differ-
`entiation problem. . . .
`[P. 1431
`
`Bain did not explicitly describe any mecha-
`nism by which product differentiation ad-
`vantages might be created, but a number of
`his remarks pointed toward buyer uncer-
`tainty about product quality as centrally
`involved.
`Second, conventional wisdom in market-
`ing and scattered recent empirical research
`support the notion that there are important
`advantages to being the first entrant in some
`sorts of markets. Marketers usually predict
`little success for "me too" brands, those
`claiming to be identical to established brands
`but selling at a lower price.3 The success of
`generic and private-label brands of some
`consumer products makes it clear that the
`strength of any handicap under which such
`brands operate must vary considerably across
`markets of different sorts. Ronald Bond and
`David Lean (1977, 1979) find that important
`and long-lived advantages are enjoyed by
`pioneering brands of prescription drugs,
`advantages that can be overcome by later
`entrants only if
`they offer distinct ther-
`apeutic benefits, not just lower prices. Ira
`Whittin's study of cigarette market segments
`points in this same direction, as do the
`cross-section analysis of marketing costs by
`Robert Buzzell and Paul Farris, and the study
`of order-of-entry effects reported by Glen
`Urban and his associates.
`The next section describes the assumptions
`and notation employed and outlines the
`analysis of Sections II-V. Buyer learning
`about quality takes place over time, so that
`buyers and sellers generally face dynamic
`decision problems when quality information
`
`*see pp. 1 16, 140, and 142, as well as other discus-
`sions in ch. 4.
`
`3 ~ o r typical statements, see Kenneth Runyon, p. 214,
`or J. 0. Peckharn.
`
`Copyright O 2001 All Rights Reserved
`
`ALCON 2029
`Apotex Corp. v. Alcon Research, Ltd.
`Case IPR2013-00428
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`is incomplete. In order to render those prob-
`lems more or less tractable, a number of
`rather drastic simplifying assumptions are
`made. Like most exercises in economic the-
`ory, this analysis should thus be thought of
`as a parable illustrating a general principle,
`not as a literal description of any particular
`piece of reality.4 The findings and some of
`their implications for research and for public
`policy are summarized in Section VI.
`
`I. Assumptions and Notation
`
`Consider a narrowly defined product class,
`like freeze-dried instant coffee or stainless
`steel razor blades, such that individual con-
`sumers can be sensibly modeled as using at
`most one brand in the class at any instant. It
`is assumed for simplicity that brands in this
`class either "work" or "don't work"; they
`either perform as a brand in this class should,
`or they fail to perform acceptably. This makes
`it possible to describe uncertainty about the
`quality of a new brand by a single parame-
`ter, the subjective probability that it won't
`work. It is assumed that these products are
`what Phillip Nelson (1970) christened "expe-
`rience goods," so that the only way a con-
`sumer can resolve uncertainty about quality
`is to purchase a brand and try it. One trial is
`both necessary and sufficient to determine
`whether or not any single brand works.
`Consumers differ in their valuation of
`products in this class. Let the function Q(v),
`0 < v < V, give the number of consumers
`willing to pay at least v for a brand in this
`class that is certain to work. Each consumer
`values a unit that doesn't work at - cpv, with
`cp a nonnegative constant. (One might have
`cp > 0 for a bleach that could ruin clothes, for
`instance.) Consumers are perfectly informed
`
`4~ number of related works deserve mention here.
`Christian von Weizskher, ch. 5, considers a basically
`competitive model of this sort of situation. The Bond
`and Lean (1979) model of first-entrant advantages relies
`heavily on assumptions about buyers' response to ad-
`vertising. Cecelia Conrad presents a dynamic model
`resembling mine in some aspects, but she neglects the
`first brand's problems of getting buyers to learn about
`it. The development here traces its ancestry to the
`simple model in the Appendix of my 1979 article. Carl
`Shapiro's recent work has a number of formal similari-
`ties to mine.
`
`except about product quality, so that neither
`informative nor persuasive advertising oc-
`curs.
`The time between purchases is assumed
`constant and equal to one period, so that
`trial of a new brand consumes the entire
`normal interpurchase time. This assumption
`can be altered without changing the basic
`results, as long as the cost of learning about
`a new brand's quality is not made negligible
`relative to current and expected future unit
`price. Let the one-period discount rate, as-
`sumed the same for all consumers, be r. All
`else equal, more frequent purchase implies a
`smaller value of r. Consumers are assumed
`to be risk neutral, to have infinite horizons,
`and to behave rationally in a sense to be
`made precise shortly.
`The analysis below considers a two-stage
`scenario. In the first stage, a pioneering brand
`enters the market and attains steady-state
`equilibrium. I have in mind here the first
`appearance of a distinctly new product, like
`stainless steel razor blades. It is assumed that
`the first brand actually works for all buyers.
`If buyers knew enough about the costs of
`producing working and nonworking brands,
`and if they were very sophisticated, they
`might attempt to infer the pioneering brand's
`quality from its price or simply from its
`existence. It avoids serious game-theoretic
`problems and does little violence to reality,
`especially in the case of new products, to
`assume that buyers do not have enough in-
`formation to behave in this fa~hion.~ Instead,
`
`it is simply assumed that prior to the intro-
`duction of the first brand, all consumers
`have subjective probability a that it will not
`work, and all act to maximize the discounted
`value of expected utility. Trial of a new
`brand of unknown quality yields both an
`immediate utility payoff and information,
`the value of which depends on future prices
`of the brand. Section I1 analyzes the first
`
`5 ~ y 1978 article defends neglect of such signalling
`
`considerations in this general context. This assumption
`and the assumption that information sources such as
`word-of-mouth do not exist seem most plausible when
`quality is subjective, so that consumers can disagree
`about whether a brand actually works. In the interests
`of simplicity, I have not attempted to incorporate this
`sort of preference heterogeneity explicitly.
`
`

`
`V O L . 72 NO. 3
`
`SCHMALENSEE: PRODUCT DIFFERENTIATION O F BRANDS
`
`351
`
`brand's pricing problem under the extreme
`assumption that buyers have static expecta-
`tions about prices. Section IV examines the
`implications of the polar opposite extreme
`assumption of perfect foresight. Neither as-
`sumption is especially attractive, but to-
`gether they should at least bound actual
`buyer expectations.
`In the second stage of the scenario consid-
`ered here, a second, objectively identical
`brand appears on the market. Innovation is
`ruled out in order to focus on the effects of
`order of entry and on related barriers to
`imitation. The second brand is also assumed
`to have exactly the same cost structure as the
`first. Two additional simplifying assump-
`tions are made. First, it is initially assumed
`that the second brand is subjectively identi-
`cal to the first at the introductory stage, so
`that the same value of n applies. It is
`straightforward to relax this assumption, and
`this is done in Section V. Second. it is as-
`sumed that the first brand does n6t change
`prices in response to entry and that the sec-
`ond brand knows this in advance. This is a
`much more passive response to new competi-
`tion than is usually considered plau~ible.~ In
`an undifferentiated world, this behavior
`would permit the second brand to undercut
`the first by an arbitrarily small amount, steal
`all the first brand's customers, and duplicate
`its profit performance. Regardless of cost
`conditions, it would thus make it impossible
`for the first brand to earn positive profits
`without attracting new entry. Despite this
`assumption, it is shown below that the addi-
`tion of uncertainty about quality can make a
`profitable pioneering brand immune to sub-
`sequent entry. This assumption permits us to
`avoid (at least in this essay) modeling the
`complicated dynamic game between the first
`and second brands that would be played
`after the latter's entry.7
`Section I11 analyzes the second brand's
`pricing problem for the case of static expec-
`tations and demonstrates that brand's order-
`
`%ee, for instance, Avinash Dixit and the references
`he cites.
`'Conrad's paper illustrates the seriousness of these
`complications. It may be necessary to make basic changes
`in the model presented here in order to obtain a tracta-
`ble post-entry game.
`
`of-entry disadvantage. Section IV shows that
`our basic conclusions are equally valid in the
`polar opposite extreme case of perfect buyer
`foresight. The consequences of relaxing the
`assumptions that buyers assign the same ini-
`tial probability of inadequacy to both first
`and second brands, that they know for cer-
`tain the value to them of a working brand,
`and that purchase is necessary to get infor-
`mation about quality are explored in Sec-
`tion V.
`In my forthcoming essay, this basic setup
`is analyzed under the assumption that buyers
`correctly expect sellers never to change price.
`This very ad hoc pricing restriction drasti-
`cally simplifies the model and turns out not
`to alter the basic nature of its conclusions.
`Since both brands actually work, each sells
`forever to those consumers who try it when it
`is introduced and to no others. Both brands
`then have well-defined demand curves, with
`the second brand's curve depending on the
`first brand's price. It is shown that the sec-
`ond brand's demand curve has the first
`brand's price as its intercept. It coincides
`with the first brand's demand curve only for
`prices distinctly below the first brand's price.
`This means that with economies of scale, the
`(common) long-run average cost schedule can
`lie everywhere above the second brand's de-
`mand schedule even though the first brand is
`earning positive profits. The analysis below
`obtains essentially the same results without
`restricting price changes. Since the second
`brand's demand curve turns out not to be
`easily defined in general, however, there does
`not seem to be a simple graphical description
`of the second brand's disadvantage.
`
`11. Pricing the Pioneering Brand
`
`In this section and the next, buyers have
`static expectations; they expect the most re-
`cently observed price to hold forever, even if
`price has changed in the past. Suppose that
`in order to try a new brand, a consumer
`ceases for the trial period to use a substitute
`that yields a nonnegative surplus, s. Assum-
`ing away income effects and indivisibilities,
`one can take s = 0 for the first brand.
`If a consumer would be willing to pay v
`for a working brand in this class, immediate
`
`Copyright O 2001 All Rights Reserved
`
`

`
`352
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`T H E AMERICAN ECONOMIC REVIEW
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`J U N E I982
`
`trial of a new brand selling at price p is
`rational if and only if the following inequal-
`ity is satisfied:
`
`x [(v - p)(l + r)/r] a s ( l + r)/r.
`The first bracketed term on the left gives
`discounted surplus if the new brand is tried,
`doesn't work, and the consumer switches
`back to the substitute. The second term on
`the left capitalizes the stream of surplus asso-
`ciated with buying a brand that works at
`price p forever, and the term on the right
`gives the capitalized benefit of continuing to
`purchase the substitute.
`Inequality (1) can be rewritten simply as
`
`where the important quantity 7 is defined by
`7 = nr(1+ +)/(I + r - n).
`(3)
`If 7 = 0, condition (2) indicates that the new
`brand will be purchased if and only if its net
`surplus, v - p, exceeds s. Larger values of 7
`always discourage trial of a new brand. As
`one would expect, r is increasing in both n
`and +, as these contribute to the expected
`cost of trial. Larger values of r, which corre-
`spond to lower purchase frequency, also in-
`crease 7. The lower is purchase frequency,
`the more important is any single purchase
`relative to the entire future stream of
`purchases. This makes the risk associated
`with trying a new brand loom larger relative
`to the alternative of sticking forever with the
`substitute. If r 2 1, condition (2) shows that
`trial is so subjectively risky that it never
`occurs at positive p. To rule this out, let us
`assume 0 < r < 1 in all that follows.
`If the first brand on the market charges
`price p, and all buyers with v > p are sure
`that it works, its sales equal Q(p). Let II(p)
`be the per period profit function correspond-
`ing to this demand curve. When the first
`brand initially appears on the market, nobody
`
`'one can derive condition (1) with s = 0 more rigor-
`ously by letting buyer utility be the sum of utility from
`this product class (either zero, o, or - + u ) and income
`left over to spend on other goods. It is then straightfor-
`ward to show that trial of the pioneering brand is
`optimal if and only if (1) holds with s = 0.
`
`is sure that it works, and condition (2), with
`s = 0, implies that a price p will produce
`sales of Q[p/(l- T)]. Let the profit function
`corresponding to this less-attractive intro- ,
`ductory-period demand curve be IIO(p), and
`assume both profit functions are globally ,
`strictly concave.
`In period 1, let P = V(1- T), and in later
`periods let P equal the lowest price previ-
`ously charged. The demand curve for the
`pioneering brand then has the general shape
`of the solid kinked curve in Figure 1. If
`p < c, some new buyers are reached, and
`profits equal IIO(p). If p 2 Z/(l- r), the
`only buyers are those who have purchased
`the brand at least once before, and profits
`are given by IT(p). If P G p < u ( 1 - r),
`current profits could obviously be increased,
`and no new customers are being informed, so
`that prices in this range can never be opti-
`mal.
`If the pioneering brand adopts a monopoly
`Q-constant strategy, it maximizes profit sub-
`ject to the constraint that it sell to the same
`buyers in all periods. This constraint implies
`that it charges a first-period price p0 and a
`price p in all later periods such that p0 =
`p(1- 7). (See Figure 1.) The optimal values
`can then be obtained by maxi-
`of p and
`mizing {IIO[p(l - 7)] + (l/r)II[p]). This
`sort of
`low/high pricing sequence corre-
`sponds roughly to what is called "penetra-
`tion pricing" in the marketing and managerial
`economics literat~u-e.9 One can show that if
`marginal production cost is positive, a mo-
`nopoly Q-constant policy yields an output
`level below that which would be chosen by
`an ordinary monopolist with profit function
`II(p) because of the extra marginal cost that
`the pioneering firm must incur in order to
`persuade buyers (by means of a low price) to
`try its ex ante risky product.
`In Appendix A, it is shown that the mo-
`nopoly Q-constant strategy just described is
`the best dynamic pricing policy for the first
`brand, as long as no thought is given to
`possible subsequent entry. In order to high-
`light those aspects of later entrants' prob-
`'see Joel Dean for a brief discussion and a compari-
`son with the alternative high/low strategy usually called
`"cream-skimming" and more commonly associated with
`durable goods.
`
`

`
`VOL. 72 NO. 3
`
`SCHMALENSEE: PRODUCT DIFFERENTIATION OF BRANDS
`
`FIGURE 1. SINGLE PERIOD DEMAND FOR THE PIONEERING BRAND
`
`Q -
`
`lems that arise naturally, I assume away any
`such thoughts on the part of the first brand.
`Allowing the pioneering brand to price stra-
`tegically could only strengthen the results
`obtained belaw at a high cost in added com-
`plexity. On the other hand, little is gained by
`confining the first brand to the monopoly
`Q-constant strategy defined above. It is thus
`assumed below only that the first entrant
`follows some Q-constant policy, charging
`price Pl(l - 7) in the first period and PI in
`all periods thereafter, and selling Q(P,) in all
`periods. Under any such policy, the levelized
`per period equivalent to the first brand's
`average revenue stream is simply
`
`111. Demand Conditions Facing a Later Entrant
`
`Because the first brand has followed a
`Q-constant policy, the second brand faces
`two and only two distinct types of con-
`sumers. If the first brand's price is P,, those
`consumers with v G PI have never tried the
`first brand. If the second brand then charges
`introductory pricep, the condition for trial is
`again given by (2) with s = 0, as for the first
`brand:
`
`Consumers with high v's are a second type
`of buyer, as they have already tried brand
`one and found it to work. Because purchase
`of brand one yields a surplus of (v - PI), the
`
`Copvright O 2001 All Rights Reserved
`
`

`
`THE AMERICAN ECONOMIC REVIEW
`
`J U N E 1982
`
`condition for trial is given by (2) with s = v
`- PI: lo
`
`Condition (5b) shows that consumers with
`large values of v are least likely to try brand
`two, even though they were most likely to try
`brand one. Their high valuation of brand
`one, after they have made the investment of
`trying it, gives them a high opportunity cost
`of trying brand two.
`The demand conditions facing brand two
`in its first period are depicted in Figure 2.
`Prior to the second brand's appearance, the
`first brand (assumed to have completed the
`
`''one can derive condition (5b) more formally using
`the framework sketched in fn. 8, above. The difference
`is that the alternative to trying the second brand yields
`utility of u from this product class for certain at a price
`of P,.
`
`introductory phase of a Q-constant policy)
`charges PI and sells Q(Pl). If the second
`brand charges an introductory price of P:,
`its first-period customers are those with v's
`between the two intersection points of the
`line with the heavy kinked curve. As
`p = P:
`Figure 2 is drawn, the second brand sells
`
`in its first period. This is less than the first
`brand would have sold had it charged P:
`during its introductory period. Only if P:
`is
`less than (PI - rV) are the second brand's
`introductory sales equal to those the first
`brand would have achieved at the same price.
`If the second brand undercuts the first
`brand's price sequence, P,(1- r ) for one
`period and PI thereafter, by an arbitrarily
`small amount, it will sell only to those buyers
`with 0's arbitrarily close to PI. Such a policy
`would give the second brand a levelized aver-
`
`

`
`VOL. 72 NO. 3
`
`SCHMALENSEE: PRODUCT DI1 7FERENTIA TION OF BRANDS
`
`355
`
`age revenue equal to that of the first brand,
`6, but it would make essentially zero sales.
`Under constant returns, entry will occur in
`spite of this disadvaniage (though at arbi-
`trarily small scale) if PI exceeds unit cost."
`With fixed costs or other economiesOf scale,
`however, it should be clear that P, can be
`above the first firm's average cost (at output
`Q(P,)) without provoking entry.
`If the second brand charges any first-period
`price between P1(l - r ) and PI - rV, it makes
`fewer sales than the first brand would have
`made at the same introductory price. Since
`first-~eriod sales translate into informed
`buye;s willing to pay more because they
`know the brand works, this difference is the
`heart of the second brand's disadvantage. If
`the first seller of fluoride tooth~aste can
`persuade those who care a lot about cavities
`to try one tube, and if the taste is acceptable
`to most consumers, the second brand of fluo-
`ride tooth~aste will find it much harder to
`get a trial: It will be compared to a known,
`acceptable fluoride toothpaste, while the first
`brand was compared only to "ordinary"
`toothpaste.
`If the second brand charges an introduc-
`tory price less than P, - rV, which is dis-
`tinctly less than the first brand's introduc-
`tory price, it thereby persuades all those who
`would have tried the first brand at that same
`price to try it. (That is, as Figure 2 should
`make clear, its first-period demand is given
`by Q[P;/(~ - r)], the same function that
`held for the first brand at all prices.) It then
`has essentially the same second-period op-
`tions the first brand would have had. (The
`second brand cannot sell anything if it
`charges a price above P,, but this is not
`likely to be a relevant alternative.) If the first
`brand could have earned positive profit with
`a Q-constant strategy beginning with a very
`low first-period price, the second brand will
`find entrv of the same sort attractive. Even
`with congtant costs, however, it is obviously
`
`possible for the first brand to be highly
`profitable but entry at drastically lower prices
`to be unprofitable.
`The preceding discussion establishes the
`existence of a barrier to entry. Profitable
`entry deterrence can occur in this model
`even though potential entrants have the ex-
`ceptionally optimistic expectation that the
`first brand's price will never change, even if
`they steal all its customers. In order to in-
`vestigate the importance of this barrier in
`general, it would be necessary to calculate
`the second brand's optimal price policy and
`the consequences of following it. This turns
`out to be very difficult. The argument in
`Appendix A establishing that the first brand's
`optimal policy involves only one price change
`can be applied to the second brand also. The
`problem is that it is not always optimal for
`the second brand to follow a (2-constant
`policy.
`The nature of the difficulty here can be
`understood by examining the second brand's
`demand curve for periods after the first, as
`shown by the heavy kinked curve in Figure
`3. As above, P is the lowest price this brand
`has ever previously charged, and P, is the
`first brand's price. Figure 3 is drawn assum-
`ing P > PI - rV. The flat portion of the de-
`man2 curve at price P, corresponds to those
`consumers who have tried both brands and
`know that both work. The segment AB re-
`flects those who have tried only the second
`brand because they found the first too ex-
`pensive. A reduction in P increases the length
`of the flat segment (moves point A to the
`right) as well as that of the declining seg-
`ment. If the optimal introductory price is
`above PI - rV, it may be optimal to follow a
`Q-constant policy and go to a point like B
`thereafter. On the other hand, since a low
`introductory price increases the number of
`brand one's customers who engage in trial, it
`may be optimal to set a low introductory
`price for this purpose and then move to a
`point like A in Figure 3.12 Finally, since a
`
`"Note that if entry occurs at small scale, the pioneer-
`ing brand loses only a few of its customers, so that the
`present value of its excess profits may still be positive.
`Thus even without scale economies, entry may not drive
`the pioneering brand to a zero (discounted) profit posi-
`tion. I am indebted to Dennis Carlton for this observa-
`tion.
`
`"1f the first brand has followed a monopoly Q-con-
`stant policy, PI exceeds the static, perfect information
`monopoly price, as Appendix A shows. Thus marginal
`revenue just to the right of point A in Figure 3 exceeds
`the first brand's equilibrium marginal cost. If the second
`brand's marginal cost at the relevant output is no larger,
`
`Co~vrinht O 2001 All Rinhts Reserved
`
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`
`T H E AMERICAN ECONOMIC REVIEW
`
`JUNE 1982
`
`reduction in the introductory price moves the
`whole segment AB to the right, it may be
`optimal to move to a point in the interior of
`that segment for periods after the first. If the
`optimal introductory price is below P1 - TV,
`on the other hand, point A is unchanged by
`marginal variations in that price, and a Q-
`constant policy must be optimal. There are
`thus four distinct strategy types that may be
`optimal for the second brand in any particu-
`lar situation, and it is apparently necessary
`in general to compare the profit streams they
`yield for given cost and demand functions
`and fixed P, in order to choose among them.
`In lieu of any further general analysis, the
`remainder of this section examines the impli-
`cations of a fairly tractable special case. Sup-
`pose that both brands have fixed, one-time
`setup costs F and zero variable costs. Let
`consumers' valuations be uniformly distrib-
`uted over the unit interval, and let the scale
`of the market be normalized so that Q(v) = 1
`- u. It is fairly straightforward to show that
`
`some equilibrium sales to new customers may thus be
`optimal.
`
`the present value of the first brand's profits
`(assuming no subsequent entry), W,, is maxi-
`mized by a Q-constant policy with P, = 1/2.
`Let W2 be the maximum present value ob-
`tainable by the second brand, given that the
`first brand has followed the monopoly Q-
`constant policy. It is shown in Appendix B
`that if r <1, 7 < 1/3, and 7(1+4r)< 1, the
`second brand optimally follows a Q-constant
`policy, and the net present values of the two
`brands are related by
`
`If 7 = 0, W2 = W,; there is no quality un-
`certainty and there is obviously no barrier. If
`F = 0, so that there are no scale economies,
`W, is positive if and only if Wl is positive.
`The second brand is generally less profitable
`than the first, but its entry is not thereby
`deterred under our assumptions. In general,
`it is clearly possible for W, and F to be
`positive and yet for W2 to be negative. The
`parameter 7 completely describes the magni-
`
`

`
`VOL. 72 NO. 3
`
`SCHMA LENSEE: PRODUCT DIFFERENTIATION OF BRANDS
`
`357
`
`tude of the second brand's demand disad-
`vantage in this example. The larger is T, the
`harder it is in general for both first and
`second brands to induce trial, and the worse
`is the relative position of the second brand.
`
`IV. Implications of Perfect Foresight
`
`The assumvtion of static expectations used
`above no doubt understates buyer sophisti-
`cation in many situations. Experienced
`consumers havi certainly observed low/
`high "penetration pricing" more than once.
`Moreover, new products are sometimes
`introduced at prices that are labeled "Intro-
`ductory" and that sometimes are even d e
`scribed as being some definite amount below
`"Regular List Price." Though it undoubtedly
`overstates both buyer sophistication and seller
`predictability in many situations, the as-
`sumption of perfect foresight regarding price
`changes does illuminate the general implica-
`tions of forward-looking behavior. It is an
`extreme assumption that is fairly tractable
`and should serve, along with the opposite
`extreme assumption of static expectations, to
`bound actual consumer behavior in this con-
`text.
`Under perfect foresight, any consumer's
`purchasing behavior depends on the entire
`future time path of prices. But this picture
`becomes descriptively less plausible the more
`complex the time path considered. Moreover,
`one rarely observes "penetration pricing"
`strategies for new brands involving complex
`sequences of price changes. Thus nothing of
`empirical relevance is likely to be lost if we
`allow sellers only one price change, from an
`introductory price of p0 to a "regular" price
`of p. Similarly, to facilitate comparison with
`the analysis above, all brands are restricted
`to strategies in which p0 G P . ' ~
`If for some buyer s G ( v - p ), a new brand
`will be tried in its introductory period, if at
`all, with the intention of buying it thereafter
`if it works. The condition for this sort of
`
`trial, following the development of (I), is14
`
`(7)
`
`p G v - s
`
`and
`
`m[(- +v - +(s/r)]
`
`+(I- m>[(v - PO)
`+ (V - P)/r] 2 s ( l + r)/r.
`Condition (7) can be usefully rewritten as
`
`and p =
`
`pOr + p(1- m)
`r + ( l - a )
`
`~ v ( 1 - 7 ) - s .
`
`It is possible for consumers with s
`(v - p )
`nonetheless to try a new brand in the first
`period, with no intention of repurchasing it,
`is low enough. The condition for first-
`if
`period-only purchase of this sort is simply
`that first-period expected net benefits be
`positive:
`
`and
`
`G v[l - r(l+ +)] - s
`
`where the last equality serves to define 7'.
`Referring to (3), it is clear that T'> T. Let us
`assume that risk is sufficiently moderate that
`r1 < 1, SO that first-period-only purchase is at
`least possible in principle.
`To consider the first brand's pricing prob-
`lem, set s = 0 in conditions (7)-(9), as in
`Section 11. Appendix C establishes that the
`first brand optimally follows a Q-constant
`strategy under the assumptions here. That is,
`it charges Pl(l - 7') in the first period and P,
`thereafter, selling Q(P,) in all periods. The
`introductory price is kept low even though
`buyers have perfect foresight because of the
`seller's better information about quality.
`Buyers assume that they will repurchase the
`
`131 conjecture that a strategy of this form is in fact
`optimal here, but I have not proven this to be true. Note
`that if > p, some consumers may rationally wait until
`the second period to buy.
`
`I4~hese conditions, both as they apply to the first
`brand and to later brands, can be derived more rigor-
`ously as outlined in fnn. 8 and 10, above.
`
`Co~vriaht O 2001 All Riahts Reserved
`
`

`
`358
`
`THE AMERICAN ECONOMIC RE VIEW
`
`JUNE 1982
`
`product only with probability (1 - a), so that
`the second-period price is multiplied by this
`probability in condition (8), while the seller
`knows that they will repurchase for certain.
`The seller thus makes the second-period price
`as high as possible (given the optimal sales
`path) relative to the first-period price to take
`advantage of buyers' underweighting of the
`second and subsequent periods.
`The first-brand's levelized average revenue
`under a Q-constant policy is given by (4)
`with r f in place of r . Since r' is greater than
`7, levelized average revenue at any P, (i.e., at
`any sales volume) is less under perfect fore-
`sight than under static expectations. It is
`harder to persuade rational consumers to try
`a risky new product if they know that today's
`low introductory price is temporary than if
`they expect it to hold forever, all else equal.
`Now suppose the first brand has followed
`a Q-constant strategy and becomes estab-
`lished, an