Entry, Exit, Growth, and Innovation over the Product Life ...

Entry, Exit, Growth, and Innovation over the Product Life Cycle

By STEVEN KLEPPER *

Regularities concerning how entry, exit, market stmcture, and innovation varyfrom the birth of technologically progressive industries through maturity aresummarized. A model emphasizing differences infirm innovative capabilities andthe importance of firm size in appropriating the retums from innovation is de-veloped to explain the regularities. The model also explains regularities regard-ing the relationship within industries between firm size and firm innovative effort,innovative productivity, cost, and profitability. It predicts that over time firmsdevote more effort to process innovation but the number of firms and the rateand diversity of product innovation eventually wither. (JEL LIO)

A similar view has emerged from a numberof disciplinary perspectives about how tecb-nologically progressive industries evolve frombirtb tbrough maturity.' Wben industries arenew, tbere is a lot of entry, firms offer manydifferent versions of the industry's product,the rate of product innovation is high, and mar-ket shares change rapidly. Despite continuedmarket growth, subsequently entry slows, exitovertakes entry and there is a shakeout in thenumber of producers, the rate of product in-novation and the diversity of competing ver-sions of the product decline, increasing effortis devoted to improving the production pro-cess, and market shares stabilize. In some

* Department of Social and Decision Sciences. Car-negie Mellon University, Pittsburgh, PA 15213. I thankWesley Cohen. Mark Kamlet. Jon Leland. John Miller,Richard Nelson, Ken Simons, Peter Swann, Bill Williams,and participants al the 1992 Conference of the Interna-tional Joseph A. Schumpeter Society, the 1992 Conferenceon Market Processes and the Dynamics of Corporate Net-works, Wissenschaftszentnim Berlin, and the IndustrialOrganization Seminars at the University of Maryland.Berkeley, Penn State, and the London School of Econom-ics for helpful comments. The paper was greatly improvedby the unstinting suggestions of two anonymous refereesand the co-editor. Preston McAfee.

' See, for example. Oliver E. Williamson's (1975) ac-count of how economists depict the evolution of new in-dustries, Kim B. Clark's (1985) description of howtechnology and internal firm organizalion change over thecourse of industry evolution, and how a business consult-ant. Philip G. Drew (1987). describes the way businessschools depict the evolution of indusLries.

quarters, this evolutionary pattem has come tobe known as the product life cycle (PLC).

While numerous authors have contributed tothis description, perhaps the mosi influentialhave been William J. Abemathy and James M.Utterback.^ Building on the work of Dennis C.Mueller and John E. Tilton (1969) and usingthe automobile industry as a leading case,they depict the PLC as driven by the way newtechnologies evolve. They stress that when aproduct is introduced, there is considerable un-certaitity about user preferences (even amongthe users themselves) and the technologicalmeans of satisfying them. As a result, manyfirms producing different variants of the prod-uct enter the market and competition focuseson product innovation. As users experimentwith the alternative versions of the product andproducers leam about bow to improve tbeproduct, opportunities to improve the productare depleted and a defacto product standard,dubbed a dominant design, emerges. Produc-ers wbo are unable to produce efficiently thedominant design exit, contributing to a shake-out in the number of producers. The depletionof opportunities to improve the product cou-pled with locked-in of the dominant designleads to a decrease in product innovation. Thisin tum reduces producers' fears that invest-ments in the production process will be ren-dered obsolete by technological change in tbe

' See in particular James M. Utterback and William J.Abemathy (1975) and Abemathy and Utterback (1978).

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VOL 86 NO. 3 KLEPPER: INNOVATION OVER THE PRODUCT UFE CYCLE 563

product. Consequently, they increase their at-tention to the production process and investmore in capital-intensive methods of produc-tion, which reinforces the shakeout of produc-ers by increasing the minimum efficient sizefirm.

While this view has helped to popularize thePLC, it rests critically on the notion of a dom-inant design, an imprecise concept that doesnot appear to apply to all new products, es-pecially ones for which buyer tastes are di-verse (Micbael E. Porter, 1983). Furthermore,it incorporates some questionable assumptionsabout tecbnological change. It assumes thatproduct and process innovation are inextrica-bly linked and tbat firms will not attend to theproduction process until product innovationhas slowed sufficiently. Yet the history of theautomobile industry and others, such as tiresand antibiotics, itidicates that great improve-ments were made in the production processwell before the emergence of any kind of dom-inant design (S. Klepper and Kenneth L.Simons, 1993). Indeed, many of these im-provements were based on human and physi-cal investments that were not renderedobsolete by subsequent major product inno-vations. The dominant-design view also min-imizes the infiuence of industry demand onincentives to innovate, attributing tbe slow-down in product innovation and rise in processinnovation entirely to tbe depletion of oppor-tunities for product innovation and the emer-gence of a dominant design. While the relativeimportance of demand and supply factors hasbeen hotly debated (David C. Mowery andNatban Rosenberg, 1982), it has never beenquestioned tbat demand factors play an im-portant role in shaping the rate and directionof technological change.

This paper proposes a new explanation forthe PLC. Empirical regularities characterizingtbe PLC are first identified. A formal model isthen constructed to explain the regularities.The model builds on recent theories of indus-try evolution (Richard R. Nelson and SidneyG. Winter. 1982; Boyan Jovanovic. 1982) andefforts to model the link between market struc-ture and R&D (Nelson and Winter, 1978;Partha Dasgupta and Joseph Stiglitz, 1980;Therese M. Flaherty, 1980). The model fo-cuses on the role of firm innovative capabili-

ties and size in conditioning firm R&Dspending, innovation, and market structure.Following various theoretical models of asym-metric industry structure (Flaherty; AvnerShaked and John Sutton, 1987), it incorpo-rates the notion that the value of a unit costreduction achieved through innovation is pro-portional to the level of output produced bythe firm. Coupled with convex adjustmentcosts, this imparts an advantage to the earliestentrants which eventually causes a cessationin entry and a shakeout in the number of pro-ducers. It also provides firms with a greaterincentive to engage in process innovation asthey grow, which leads to an increase overtime in their efforts to improve the productionprocess. Firms are also assumed to have differentcapabilities that lead them to pursue differenttypes of product innovations, a theme promotedby Nelson (I98I) and used by Wesley M.Cohen and Klepper (1992) to explain differ-ences within industrie.s in firm R&D intensities.This provides tbe basis for explaining the declinein product innovation that occurs over time. Unk-ing it to the decline in the number of competitorsbrought about by the shakeout of producers. Itis shown that the model can also explain variouscross-sectional regularities that have accumu-lated concerning the relationship witbin indus-tries between firm size and firm R&D effort,R&D productivity, cost, and profitability. Thus,the model provides a unified explanation for awide range of temporal and cross-sectional reg-ularities conceming industry evolution and firmbehavior.

The paper is organized as follows. In Sec-tion I, the prominent features of the PLC aresummarized. In Section II, the model is spec-ified. In Section III. preliminary implicationsof the model are developed. In Section IV, themodel is shown to explain all the prominentfeatures of the PLC. In Section V, the modelis used to explain various cross-sectional reg-ularities between firm size, R&D, and firmperformance. In Section VI, the implicationsof the model are discussed and extensions ofthe model are considered.

1. The Nature of the Product Life Cycle

The depiction of industry evolution con-veyed in the PLC is based upon case studies

S64 THE AMERICAN ECONOMIC REVIEW JUNE 1996

and quantitative analyses of the evolution ofnew industries. In this section, six regularitiesconcerning how entry, exit, market structure,and technological change vary from the birth oftechnologically progressive industries throughmaturity are summarized. While every industryhas its idiosyncrasies, these regularities providea composite picture of the evolution of techno-logically progressive industries.

The first two regularities pertain to entry andexit. Michael Gort and Klepper (1982) andKlepper and Elizabeth Graddy (1990) exam-ine the annual time path in the number of pro-ducers for 46 major new products beginningwith their commercial inception. Utterbackand Fernando F. Suarez (1993) also considerthe time path in the number of producers aswell as the paths in the number of entrants andexits for 8 products subject to considerabletechnological change. Klepper and Simons(1993) review the entry and exit paths for 2of the products studied by Utterback andSudrez and 2 other products subject to consid-erable tecbnological change. Two patternsemerge from these studies concerning the na-ture of industry evolution in technologicallyprogressive industries:

At the beginning of the industry, the numberof entrants may rise over time or it may at-tain a peak at the start of the industry andthen decline over time, but in both casesthe number of entrants eventually becomessmall.

The number of producers grows initially andthen reaches a peak, after which it declinessteadily despite continued growth in indus-try output.'

'These are general tendencies, and exceptions can al-ways be found Of greater significance is the possibilitythat these patterns reflecl a bias in the way new productsare typically defined. If these patterns tend to be inter-rupted by major innovations but the innovations are de-fined as creating new products subject to their own productlife cycles, the patterns could be artifactual. The bulk ofthe new products that have been studied, however, did notexperience such major innovations until many years afterthey were introduced, and their evolution was generallycharacterized by long initial periods during which itiecharacteristic patterns in entry and the number of firmswere observed.

Slwcv rif I Jf^nl Fim» SljihilI

ProdiKI RAD f ,>vcr li

FIGURE I. TEMPORAL PAITKRN.S oh ENTRY, NUMBER OF

PRODUCERS, MARKET SHARES, AND INNOVATION

These patterns are illustrated in Figure 1.Two alternative paths for entry are depicted.In both cases, entry eventually becomes smalland the number of firms rises initial ly and thendeclines over time. Related to these two pat-terns are regularities in the way firm marketshares change over time. Although market-share data over an extended time period are notavailable for many products, Edwin Mansfield(1962) and Burton H. Klein (1977 pp. 8 9 -128) have examined how the market shares ofthe leading producers of automobiles, tires,aircraft, petroleum, and steel changed overtime. Their findings, which accord with a num-ber of case studies, suggest a third regularitywhich is noted in Figure 1:

Eventually the rate of change of the marketshares of the largest firms declines and theleadership of the industry stabilizes.

The other three regularities about tbe PLCpertain to technological change. Because tech-nological change is more difficult to quantify,the regularities are based on a number of casestudies'* and two samples of innovations for a

•* These include Abemathy (1978) and Abemathy et al.(1983) for automobiles, Klein (1977} for automobiles andaircraft, Tilton (1971) and Jerome Kraus (197.1) for tran-sistors, Kenneth Flamm (1988) and Philip Anderson andMichael J. Tushman (1990) for computers. Arthur A.Bright (1949) and James R. Bright (i9.i8) for lightbulbs. Thomas J, Prusa and James A, Schmltz (1991) forPC software, and Abemathy and Ulterback (1978) andUtterback and Suarez (1993) for collections of products.For further detail, see Klepper (1992).

VOL 86 NO 3 KLEPPER: INNOVATION OVER THE PRODUCT UFE CYCLE 565

limited number of industries in the UnitedStates (Utterback and Abemathy, 1975) andthe United Kingdom (C. De Bresson and J.Townsend, 1981 ). These studies suggest thatfor industries with rich opportunities for bothproduct and process R&D, three patterns inproduct and process innovation can be identi-fied:'

The diversity of competing versions of theproduct and the number of major productinnovations tend lo reach a peak during thegrowth in the number of producers and thenfall over time.

Over time, producers devote increasing effortto process relative to product innovation.

During the period of growth in the number ofproducers, the most recent entrants accountfor a disproportionate share of productinnovations.

These three regularities are also noted inFigure 1. Together, the six regularities laid outabove and summarized in Figure I provide thefocus for the theoretical analysis of the paper.

II. The Model

The model depicts the evolution from birththrough maturity of an industry with rich op-

^ The three patterns are ascribed only to products withrich opportunities for both product and process innovationbecause Ihe bulk of the producls for which patterns ininnovation have been studied are, noi surprisingly, oneswiih such characteristics. Indeed, Abemathy (1978 p. 84).K. Paviii and R. Rothwell (1976). and Porter (1983 pp.23-24), among others, contend that products without richopportunilies for both producl and process innovalion donol follow ihe prolotypical PLC. Examples ciled as ex-ceptions lo the PLC include synthetic fibers and plastics,which are claimed to be relatively homogeneous and pri-marily subject to process bul nol producl innovation, andheavy electrical equipment, which is produced in smallbatches and is claimed to be subject primarily lo productand nol proce.ss innovation. While no evidence is pre-sented to buttress these claims and nol all observers sub-scribe to them (for example, see David A Hounshell(19881 regarding synthetic fibers), it is important to rec-ognize that the evidence regarding innovation during thePLC is primarily based on products with rich opponunitiesfor both product and process innovation. This is reflectedin the model, which presupposes that the joinl nature ofproduct and process innovation drives the PLC.

portunities for product and process innovation.Two aspects of innovation are featured. First,following Jacob Schmookler (1966) and anumber of theoretical models (for example.Dasgupta and Stiglitz, 1980; Shaked and Sutton.1987), the demand for a firm's product is as-sumed to condition its incentive to innovate.This is assumed to be manifested differentlyfor process and product innovation. Processinnovation is principally designed to lower afirm's average cost of production. Since tbevalue of a reduction in average cost is propor-tional to the total output of the firm, it is as-sumed that the incentive for process innovationis conditioned by the total quantity demandedof the firm's product. Product innovations, incontrast, are often designed to attract new buy-ers for a product. Accordingly, it is assumedthat the incentive for product innovation isconditioned by the demand of new buyers.Second, firms are assumed to be randomly en-dowed with distinctive capabilities wbich in-fluence tbe kinds of innovations tbey develop.The idea of distinctive firm competencies liesat the heart of the business-strategy literature(Porter, 1980) and its relevance for innovationappears prominently in many industry casestudies.'' It is assumed that ibese differences incapabilities manifest themselves principally inproduct innovations, where firms often spe-cialize in innovations that service distinctivetypes of users (Eric von Hippel, 1988). Incontrast, process innovations tend to be incre-mental and based on information that firmscommonly generate tbrougb production (com-pare Bright, 1958; Samuel Hollander, 1965).

The model is stylized to highlight the twofeatured aspects of innovation. It has the fol-lowing structure. Time is discrete. In eachperiod, incumbent firms decide whether to

" For example, a number of studies emphasize how sig-nilicant innovations can be traced back to expenise ac-quired fortuitously. This is featured in Hugh G. J, Aitken's(1985) analysis of early radio innovations, Flamm s(1988) discussion of the influence of gttvemmcnt spon-sored cryptography efforts during World War II on sub-sequent innovation by computer firms, and Klein's (1977pp. 89-109) di.scussion of the skills brought into theautomobile industry at the tum of the century by entre-preneurs with experience in mass production and inter-changeable parts manufacture.

THE AMERICAN ECONOMIC REVIEW JUNE 1996

remain in the industry and a limited number ofpotential entrants decide whether to enter. Allfirms produce a standard product. They decidehow much process R&D to perform, which de-termines the average cost of the standard prod-uct. They also decide how much product R&Dto perform. Firms randomly differ in theirproduct innovation expertise, which influencestheir success at product R&D. In each period,successful product innovators develop a dis-tinctive product innovation which they com-bine with the standard product to market aunique, distinctive product. Di.stinctive prod-ucts appeal to all buyers, but only new buyerspay the premiums for them, with each distinc-tive product sold to a different class of newbuyers. All firms monitor the product inno-vations of their rivals. This enables them toimitate all product innovations one period afterthey are introduced and incorporate them intothe standard product at no additional produc-tion cost. When the last period's product in-novations are incorporated into the standardproduct, buyers of the distinctive products be-come buyers of the standard product and thedemand for the standard product by all otherbuyers increases, causing the demand curvefor the standard product to shift to the right.Producers share in the expansion in demandfor the standard product in proportion to theirprior output and decide how much further toexpand their output subject to a cost of ad-justment. All decisions are made to maximizecurrent profits, firms are price takers, and ineach period the price of the standard productclears the market.

The model is formally specified as follows.In each period t, there are K, potential entrants.As firms enter and others randomly developthe innovative capabilities required to enter, K,changes. A priori no restrictions are placed onwhether K, rises or falls over time; this maydiffer across industries and also within indus-tries over time. Each potential entrant is ran-domly endowed with innovative expertisewhich it cannot modify over time. Let s, de-note the innovation expertise of firm /, whichit knows prior to entry, and A,,,,., the maximumpossible innovation expertise. To simplify thedynamics of the model, it is assumed that ineach period there are one or more potentialentrants with innovative expertise j ^ ^ , and the

cumulative distribution of innovative expertiseis the same for the potential entrants in eachperiod. This distribution is denoted as H(s),where His) is assumed to be continuous forall s < s,,,^^ and //(.v,,,aJ = 1 by definition.

The firm's innovative expertise influencesits success at product R&D. Tbe probability offirm / developing a product innovation in pe-riod t iss, + g(rd;,), wbere rd,, is its spendingon product R&D and the function ^'(rd,,) re-flects the opportunities for product innovation.Each successful innovator adds its innovationto the standard product and markets a distinc-tive variant of the industry's product, which itsells at a price exceeding the price of the stan-dard product, reflecting the value of its inno-vation. Distinctive variants are assumed toappeal to all buyers but only new buyers havea positive demand for them at the pricescharged, with each distinctive variant pur-chased by a different class of new buyers. Af-ter one period, all product innovations arecopied and incorporated into the standardproduct, so successful innovators have a one-period monopoly over their distinctive variants.Let G denote the one-period gross monopolyprofit (before subtracting the amount spent onproduct R&D) earned by each seller of a dis-tinctive variant. It is assumed that ^'(rd,,) > 0and g"(rd,,) < 0 for all rd,, > 0., reflectingdiminishing retums, and that g'(O)G > I,which ensures rd,, > 0 for all i, /. In order tobe able to imitate costlessly the innovations ofits rivals, which is required to market a dis-tinctive product variant and also the standardproduct, firms monitor the innovations of theirrivals at a cost of F per period. Thus, if a firmengaged in only product innovation and didnot produce the standard product, its expectedprofits in period / would be [5, + g(rd;,)lG -rd;, - F. To simplify the model, it is assumedtha tF>[5 , +g( rd , , ) ]C-rd , , for all rd,,. Thisensures that in order to have nonnegative ex-pected profits, all firms must produce the stan-dard product.

Let Q, = f,(p,) denote the total market de-mand for the standard product in period t,where Q, is the quantity demanded, p, is theprice of the standard product, and/(/?,) is themarket demand schedule for the standardproduct in period t. Over time, f(p,) shifts tothe right at every price as last period's product


innovations are incorporated into the standardproduct. It is assumed that/,(p,) is continuousand downward sloping for all t. Let Q,, denotethe output of the standard product by firm / inperiod /. It is determined as follows. Assumingthat p, falls over time (this will be shown inthe next section), the total quantity demanded,Q,, expands over time. AU firms sell the samestandard product at the same price. New buy-ers are assumed to choose a seller based on astochastic leaming process in which the prob-ability of a firm attracting a new buyer is pro-portional to its sales of the standard product inthe prior period, 0,,- i. It is assumed that it isoptimal for a buyer to continue purchasingfrom the same firm as long as the firm remainsin the market. Accordingly, it is assumed thatincumbents in period t experience a rise intheir sales of the standard product from Qi,. iin period/ - I to 0,,_ i ( C / 0 , - 1 ) in period/,where Q,/Q, -1 denotes the growth in the totalquantity demanded of the standard productfrom period t - \ tot. If desired, the firm canexpand its output further, resulting in an in-crease in its market share of the standard prod-uct relative to period t - L To do so, it mustincur an adjustment cost of m{Aq,,), whereAg,, is the expansion in its output in j>eriod tabove Q^, liQJQ,- , ) . The ftinction m{Aq,,)is such that m'(0) = 0, m'(.Aq^,) > 0 for allA^,, > 0, and m"(A^,,) > 0 for all Ag,, ^ 0,with m' (A^,,) growing without bound as A*y,,increases, reflecting increasing marginal ad-justment costs.^

The average cost of production of the stan-dard product for firm i is assumed to be inde-pendent of Q,, and equal to c - /(re,,), wherere,, is the amount spent on process R&D byfirm i in period / and the function /(re,,) re-flects the opportunities for process innovation.Following Flaherty (1980), cost in period / isa function only of process R&D in period t. Itis assumed that as re,, increases, /(re,,) asymp-totically approaches an upper bound and

' If a firm wants to expand its market share, it will nor-mally have to incur mariteting costs to attract customersfrom its rivals. The assumption tbat m"(Ag,,) > 0 reflectsthe idea that the more the firm wants to increase its marketshare in any given period, the greater the marketing costsrequired for expansion at the margin.

/'(rc,,) > 0 and /"(re,,) < 0 for all re,, s 0,reflecting diminishing retums. Further, it is as-sumed that /'(O)0n.m > 1. where Q^.^ is thesmallest level of output ever produced by anyfirm. This ensures rc,, > 0 for all /, t.

Given the assumptions, the expected profitof firm / in per iod/ ,£(n, , ) , can be expressedas

(1)

X [p,-C + I(TCi,)]

- rc,, - m(Aq,,) - F,

where [s, + g(rd,,)]G - rd;, is the firm'sexpected net profit from product R&D aftersubtracting the cost of its product R&D,[Q,.-^iQ,fQ,-^) + Aq,,][p,-c + /(rc,,)] -rc,, - m{Aq,,) is its net profit from producingthe standard product after subtracting both itsspending on process R&D and the costs of ad-justing its output, and F is the cost of moni-toring the innovations of its rivals. Expression(1) applies to entrants in period / as well asincumbents, with 0;,_ , = 0 for entrants. Allfirms are assumed to be atomistic and pricetakers. In each period / they can project themarket-clearing price for the standard product,p,, but are uncertain about future prices and tbustheir prospects for survival. Accordingly, it isassumed they decide whether to be in the in-dustry and if so, rd,,, rc,,, and A^,,, to maximizecurrent expected profits, E(t\^,). Let rd,*,rc,T, and Aq* denote the profit-maximizingchoices of rd,,, rc,,, and Aq,, and E(Ut) theexpected profits of the firm at these choices.Potential entrants enter if £(11*) > 0, are in-different about entering if £( 11 *) = 0, and donot enter if E{U*) < 0, where A^,, definestheir initial output of the standard product ifthey enter. Similarly, incumbents stay in theindustry if ^ ( n * ) > 0, are indifferent aboutstaying in if ^(n,*) = 0, and exit if £ ( n * ) <0. Once incumbents exit, their output of thestandard product is lost.

The industry is assumed to start in period 1when demand and technology for the productare such that there exists a price pi forwhich the quantity supplied by firms with


nonnegative expected profits equals the quan-tity demanded, 0 , , where Qi > 0. Similarly,in every suhsequent period p, is assumed toclear the market. This requires that the quan-tity demanded in period /, Q, = f,{p,), equalsthe quantity supplied hy producers in period ttaking p, as given:

(2)

where the index /, /of the summation denotesthat the summation is over firms / in the marketin period t. In terms of the actual mechanismgoverning the change in price from period / -1 to r, the dynamics of the model are simplifiedby assuming that for all incumbent firms inperiod t, dE(X\*)ldp, > 0 for all prices p,within a broad neighborhood of z?,-,," withthe equilibrium price constrained to He in thisbroad neighborhood. The existence of such aprice in each period satisfying equation (2) isdemonstrated in the next section. As will beshown, market clearing is achieved throughthe effects of p, on Q,, Ag,,, and on entry andexit in period /.''

* This condition requires that in each period (, ihe lowerp, then the lower the maximum possible expected prolilsof each firm, assuming the firm can sell as much of thestandard product as it wants at />,. The price of the standardproduct affects £(11*) in two ways: through its effect onihe profil per unit of the standard product, p, — c -^ /(re,,),and through its effect on each firm's output of ihe standardproduct via the total quantity demanded of the standardproduct. Q,. These two effects work in opposite direc-tions— the lower p, then the lower the firm's profit perunit on the standard product, ceteris pahbus. but thegreater the firm's total output of the standard product, cet-eris paribus. Given that /(re,,) is bounded, al .sufficientlylow prices E(W*) must be less than zero for all firms.hence at sufficiently low prices the first effect must dom-inate the second and dEin*,)ldp. > 0. If df,{p,)/dp, = 0 atthe relevant prices (that is. the price elasticity of dematidequaled zero), then p, would have no effect on the firm'soutput of the standard product and it is easy to see fromequation (1) that dE{U,,)/dp, > 0 for all prices. More gen-erally, if suitable constraints are placed on the functiondf,ip,)/dp, at the relevant prices then dE(n*)/dp, > 0 forall prices within a broad neighborhood of p, ,.

" Note thai if exit occurs in period ( then S, , Q,, - i <2,,,-I Q,,-t = Q:-\. where the index /, ; - I denotessummation over firms in the market in period t - 1. Asdeveloped in the next section, exit will be necessary forthe market to clear in each period.

The model is stylized to keep it tractable andto highlight the two key features of innovationthat underlie it. Product innovations are as-sumed to be introduced into distinctive ver-sions of the product and then incorporated intothe products of all firms, which conforms tothe way many products evolve over time.'"This preserves the notion of an industry inwhich all firms produce the same productwhile allowing for (limited) product differ-entiation. Each product innovation is assumedto be sold to a different class of new buyers toreflect the idea that firms have different kindsof innovative expertise that lead them to ser-vice different groups of buyers. Coupled withthe assumption that product innovations do notaffect the demand for the standard product,this ensures that the incentive to engage inproduct innovation is determined solely by thedemand of new buyers." Differences in firminnovative abilities are structured so that theydo not affect the firm's output of the standardproduct nor the amount spent on product orprocess R&D. Consequently, the fimi's outputof the standard product is related to the firm'sR&D .spending only through its effects on thereturns from process R&D, which highlightsthe influence of the demand for the standardproduct on process R&D. Opportunities for in-novation, as reflected in the functions g(rd,v)and /(re,,), are assumed constant to abstractfrom the effects of changing technological op-portunities on the firm's R&D spending. Alldecisions are based on current expected profitsand process innovations are not cumulative tosimplify the dynamics of the model and toreflect the limited horizons of firms in new in-dustries. Many of these assumptions are re-considered in the conclusion, where it isargued that the spirit and principal implica-tions of the model would not change if theassumptions were relaxed.

'" For example, in automobiles innovations such as theelectric starter and the inexpensive closed body were in-troduced into distinctive mcxiels and then copied widelyby all manufacturers.

" This abstracts from strategic incentives to innovateassociated with the preemption of rivals (Richard J.Gilbert and David M. G. Newbery, 1982) and cannibalismol prior innovations (Jennifer Reinganum. 1983. 1985).

VOL 86 NO. 3 KLEPPER: INNOVATION OVER THE PRODUCT LIFE CYCLE 569

ni. Preliminary Results

In order to facilitate the proof of later re-sults, a series of intermediate implications ofthe model are developed as lemmas. In deriv-ing these lemmas, it is assumed that there ex-ists a price p, in each period that clears themarket given the choices firms make about en-try, exit, rdy,, rc ,̂, and Aq,, taking p, as given.The existence of such a path for price is estab-lished at the end of this section.

The first results pertain to firms in the mar-ket in period t, including firms that entered themarket during period t as well as earlier en-trants. Differentiating (1) with respect to rd,,,re,,, and A^,, establishes the following first-order conditions for an interior maximum foreach firm / in the market in period /:

(3)

(4)

(5)

g'it6*)G= 1

m 'iAq*) = p, - c-\- /(re*).

where optimal values are denoted by an aster-isk. Furthermore, for a firm to be in the marketin period t, its expected profits in period t mustbe nonnegative. Given the assumption of F >[Si + g(rd,,)]G - rd,, for all rd,,, a necessarycondition for £(11,,) ^ 0 is that for each firmi in the market in period /:

(6) J, - c + /(re,*) > 0.

Assuming -i"iTC*)[Q,,.dQJQ, i) + Aq*]X m"(Aqt) > / ' ( re*)- to ensure that the jointsolution of (4) and (5) for re,, and Aq,, is a max-imum, the solutions to equations (3 ) - (6 ) willsatisfy the second-order conditions. Conse-quently, for each firm i and period r, rd,t > 0,re* > 0, and Aq* > 0, with these choicessatisfying equations ( 3 ) - ( 6 ) . Thus, all finnsin the market in period t perform product andprocess R&D and increase their market shareof the standard product relative to period t - i.

Conditions (3) - (6) imply two resultswhich reflect the simplified nature of themodel.

LEMMA 1: For all i and t, rd,* = rd * whereTd* satisfies g'(Td*)G - I.

PROOF:The profit-maximizing value of rd,, is de-

fined by equation (3) . which is the same forall firms and does not change over time. Con-sequently, all firms spend the same amountrd* on product R&D, where rd* satisfies(3) .

Analogous io EiU*), let Vf,=[Qi,-,i Q,l(3, .,) + Aq*Mp, - c + /(re*)] - re* -miAq*,) denote the firm's (incremental)profit from the standard product. Lemma 1 im-plies that the firm's incremental profit earnedfrom product R&D in each period, [s, +^(rd,,)]G - rd,,, remains constant over time.Consequently, changes in the firm's expectedprofits over time arise only from changes inV *. Accordingly, most of the analysis of themodel focuses on the standard product.

The second result indicates that in each pe-riod t, firms in each entry cohort make thesame choices for re,, and A^,, and have thesame output and incremental profits from thestandard product. Letting the values of thesevariables for entry cohort k in period t he de-noted as ret, Aq), Q), and V), the followingresult is established.

LEMMA 2: For all firms i that entered in pe-riod k and are still in the market in period t s:k. re,* = rcj. A^,,* = AqU Q,, = Q), andV,,*= Vl

PROOF:Since Q,,-\ = 0 for entrants in period r.

equations (4) and (5) imply re* and Aq*,hence Q,, and V*, must be the same for allentrants in t. It then follows from (4) and (5)thai re*. A^,*, Q,,, and V* must be the samefor these firms in every period they are in themarket.

Lemmas 1 and 2 imply that in each periodt the expected profits of firms that entered inthe same period differ only according to theirproduct-innovation expertise s,. Consequently,in each period the distribution of Ei U,,) acrossfirms in the same entry cohort will be the sameas the distribution of .v, for these firms.

The firm's output in the prior period. 0,, _ i.will determine its choice of re,, and Ag,, andhence V,,. This is reflected in Lemma 3.

570 THE AMERICA/^ ECONOMIC REVIEW JUNE 1996

LEMMA 3: For each firm i in the market inperiod t, the larger Q,, _ / then the larger rc ,̂,Aq,,. and V̂ ,.

PROOF:Differentiating ( 3 ) - ( 5 ) with respect to

Q,, _ I and rearranging yields

t/dQ,,.,=g"(Tdt)Gm"{^q*)l'

where D is the determinant of the matrix ofsecond partials of E(n,,) with respect to rd,,,re,,, and Aq,, evaluated at rd*, re*, andA^*. Since b < 0 based on the second-orderconditions and p, - t + /(re*) > 0 based on(6), eaeh of these derivatives is positive.Therefore, the larger Q,, _ i then the greater re,,,Aq,,, and V,,.

Since Aq* is determined by Qi,-\ andAq* > 0 for all /, /, Lemmas 2 and 3 implythat in each period / the age of the firm fullydetermines re,,, A^,,. V,,, and Q,,, with eachgreater the older the firm. Coupled withLemma 1, this imphes that in each period tdifferences across firms in £"(n,,) are fully de-termined by two factors: the age of the firmand its product innovation expertise s,.

Lemma I establishes the time path of rdj, foreach firm while Lemmas 2 and 3 establish howre,,, Aq,,, Q,,, and V,, vary across fimis in eachperiod. It is also possible to investigate howre,,, A^,,,Q,,.and V,, change over time for eachfirm. For incumbents, Q,, and re,, change overtime as follows.

LEMMA 4: For each firm i in the market inperiods t - J and t, Q,, > Q,,^ i and re,, >

PROOF:Since A^,, > 0 for all i, t, it follows that

Qii > Qii - I for a l l ' ' ''• Rewriting equation (4)as &,/'(rc,*) = 1. it follows from Q,, > Q,,- , .and /"(rc;,) < 0 for all re,, that re,, > rc,,_ ,.

The time paths for A^,, and V̂ , for incum-bents cannot be so easily characterized. Equa-tion (5) indicates that for each incumbent A^ ,̂will change over time according to the timepath of p, - c + /(re,,), the firm's profit perunit of the standard product. The change in V,,over time will also depend on the time path in/7, - t 4- /(re,,). Lemma 4 implies that /(re,,)rises over time, but Lemma 5 below indicatesPt falls over time. Consequently, without fur-ther assumptions it cannot be determinedwhether A^,, and V,, generally rise or fall overtime for incumbents.

That p, must fall over time can be easilyestablished.

LEMMA 5: For each period t, p, < p, -1.

PROOF:Recall that it was assumed that for each in-

cumbent firm i in period t, dE(Ut)fdp, > 0for all prices p, within a broad neighborhoodof p, - I, with the equilibrium price in period tlying in this neighborhood. Lemma 5 is estab-lished by showing that for all prices p, ^ p,^^in this neighborhood, the market cannot clearin period /. Supposep, = p,-\. Then, Q,, mustexceed Q,, _ i for all producers in period t — \.This implies £(n,T) > E(Y\*,..\) ^ 0 for allproducers in period t — 1 and hence that noincumbent would exit in period t. The samecondition must be true for all prices p, > p,- iwithin a broad neighborhood ofp,- i given thatdE(n*, )/dp, > 0 for all such prices. But everyfirm that remains in the industry will expandits market share, hence the market cannot clearif all firms remain in the industry. Therefore,p, must be less than p, \.

In order for every firm that remains in themarket to expand its market share, some firmsmust exit in every period. This will occur onlyif price falls over time. It must fall sufficientlyin each period t that E(U*) falls below zerofor some firms in the market in period / — I,causing these firms to exit.

VOL S6 NO. S KLEPPER: INNOVATION OVER THE PRODUCT UFE CYCLE 571

Using/>, < p, 1, it is possible to character-ize how the size of entrants. A^;, the processR&D of entrants, rcj, and the profits of en-trants from the standard product, V',, changeover time. Let .v' denote the minimum productinnovation expertise in period / among firmsthat entered in period k ^ t. U is also possibleto characterize how s',, the minimum productinnovation expertise among entrants, changesover time. Over time, rcj, Aq',, V',, and s',change as follows.

LEMMA 6: For all periods I > k, rcJ <rcl, Aq', < Aql Vf < VJ, and s', > .vJ.

PROOF:The choices of re,, and Aq^, for entrants in

period t must satisfy equations ( 3 ) - ( 6 ) withQ,,- \ = 0. These equations differ across pe-riods only because p, falls over time. To seehow changes in p, affect rcj. Aq',, and alsoV;.sel (?,, I ̂ Oin (3 ) - ( 5 ) and differentiatewith respect to p,. This yields

drct/dp, = g"ird*)Gr(Tc*)/D> 0

= g"(rd*)Grirc*)Aq*/D>0

dVTJdp, = dVrjOp, = Aqt > 0.

Given that p, < p, ,, it follows that re',,Aq',, and V; must fall over time. Furthermore,if V J falls over time, the marginal entrant musteam greater incremental profits from productinnovation over time, which implies s', mustrise over time.

Lemma 6 indicates that the minimum in-novative expertise required for entry risesover time. Lemma 7 indicates that it eventu-ally rises to the point where no further entryoccurs.

LEMMA 7: After some period, s', > i,,,,,, andno firms enter the industry.

PROOF:Recall thai it was assumed that the distri-

bution of innovative expertise H(s) was suchthat at least one potential entrant in every entry

cohort had innovative expertise .v,,,̂ ,. If s', <J,,,,,, for all t then in every period EiU*) ^ 0for potential entrants with innovation expertise,v,,,,,. hence £ ( n * ) > 0 for all prior entrantswith innovative expertise s^,,^. Consequently,no incumbent with innovative expertise s,,,^^would ever exil the industry. Since A^,, > 0for all firms that remain in the industry, firmswith innovative expertise .v,,,̂ , will expand theirmarket share in every period. This cannot,however, occur indefinitely, as eventuallythese firms would capture the entire marketand would not be able lo expand further with-out some of them exiting. This requires p,eventually to fall to a level such that £"(11,̂ ) <0 for some incumbents with innovative exper-tise .V,,,,,,. At this point £(11*) < 0 for all po-tential entrants with .v, = .v,,,..,. Since p, failsover time, after this point EiU*) will con-tinue to he negative for potential entrants with•V, = J,njx. hence s', will exceed s^^^ and no fur-ther entry will occur.

One final result that will be useful concernshow .?* differs across entry cohorts in each pe-riod. This is summarized as follows.

LEMMA 8: In each period t, s', > sJ for

PROOF:In each period, £(11,,) ^ 0 for producers.

Given that V* is lower the younger the firmba.sed on Lemma 3, it follows that the mini-mum s, required for survival must be greaterfor younger firms. Coupled with the fact thatentrants start with higher minimum productinnovation experti.se than all prior entry co-horts based on Lemma 6. it follows that theyounger the cohort of firms then the greaterthe minimum product innovation expertise ofthe cohort.

The various lemmas indicate how: ( I ) theprice of the standard product changes overtime; (2) the initial values of rd,,, re,,, A^^,,and V,, change over time for entrants; and (3)the values of rd,,. re,,, and Q,, change over timefor incumbents. Summarizing results, overtime p, declines, rdy, remains the same for en-trants and incumbents, re,,, A^,,, and V,, de-cline over time for entrants. .vJ rises over time

m THE AMERICAN ECONOMIC REVIEW JUNE 1996

for entrants, and re,, and Q,, rise over time forincumbents after entry. The other time paths,which involve how A^,,, V,,, and EiU,,)change over time for incumbents after entry,cannot be characterized generally. The onlypattern that must hold is that in each period.V,, and £(n, ,) must fall for some firms.

It was assumed that a price/J, existed in eaehperiod such that the market cleared given thechoices of firms taking p, as given. This willnow be established via induction. It was as-sumed that such a price existed in period I —this was how period I was defined. Supposesuch a price exists in period / — 1. It will beshown that a market-clearing price p, thenmust exist in period t given the choices offirms taking this price p, as given. Given thatthe market cleared in period / — I. ^ , _ , =Sy.. I Qi, I. where the summation is overfirms in the market in period / - I. In period/, p, must satisfy equation (2), which can beexpressed as

(7) f.iP.)\ I -

- X Aq, = 0.

where the summation is over firms in the mar-ket in period /. In the proof of Lemma 5 it wasestablished that p, must he less than p, i andmust induce some firms to exit; otherwise I -2,.; Q,,- \IQi 1 = 0 since the market cleared inperiod / - I and equation (7) would be violatedgiven that Aq,, > 0 for each firm in the market.Given the assumption of dEiYl* )ldp, > 0. thelower p, then the more flrms for whichEin*) < 0 and thus the greater the number offirms exiting in period t. The more firms thatexit then the greater (I - I.,,Q,, \IQ,-\] andthe smaller 2,., Aq^, in equation (7). Further-more, the smaller/?, then the greater/(;>,) andthe smaller Aq,, for each firm, which reinforcesthe effect of exit on the market-clearing condi-tion. Thus, as p, decreases relative to p,-\,f,ip,){\ - X,,, G , - . / G - i } rises and 2,,, Aq,,falls in equation (7). Given that /(re,,) isbounded, at a low enough price £( n,t) < 0 foreach firm and all firms would exit the industry.Thus. atalowenoughprice/(p,)| I -1.,jQ,, ,/Q,-[) - 2,j A^;, > 0, whereas for prices p, ^

0. Given that/(p,) and Aq,, are continuous func-tions of p, and all firms are assumed to beatomistic and indifferent about being in the in- .dustry when £ ( n * ) - 0, it then follows thatthere must be a price p, which satisfies equation(7) and thus clears the market in period / . ' '

Note that the existence of such a path forprice does not depend on positive entry in eachperiod, nor does it depend on the time paths inthe number of entrants, number of exits, andnumber of firms. These time paths are ad-dressed in the next section.

IV. The Regularities of the PLC

Six propositions are developed in this sec-tion corresponding to each of the empiricalregularities summarized in Section 2.

Consider the first regularity about entry overtime. Let £, denote the number of entrants inperiod t. The possible fime paths in £, impliedby the model are characterized in Proposition 1.

PROPOSITION 1: Initially the number ofentrants may rise or decline, but eventually itwill decline to zero.

PROOF:The entry process is such that E, = K,i\ —

His',)). Lemma 6 indicates J! rises over time.Hence £, will fall over time unless A', rises overtime at a sufficient rate, which cannot be ruledout a priori. Therefore, initially £, may rise or

'- The assumption that all firms are atomistic ensuresIhe continuity of f,{p,){ I - I.,,Q,,.,/(), , \ - S,, A^,, asa function of/>, and hence the existence of a price p, sat-isfying equation (7). A similar assumption is invoked inJovancivic and Glenn H. MLicDonald (1994) and Hugo A.Hopenhayn (1993) in their mtidels of industry shakeouts(ihese are discussed funher below). Allcmalivcly, if firmswere nonatomislic then ihe quantity supplied, S, , ()„ ,IQ,/Q, i) + - , , At/,,, could exceed ihc quantiiy demanded,

f,(p,). at all prices p, insuf'tkient ID induce [he marginalfirm lo exit but could fall short of the quantity demandedat all prices sufficient to induce the marginal firm to exit.Then, there would be no price that would clear the marketin period l. Although beyond the scope of the paper, non-atomistic finns might be accommodated by allowing firmsto maintain backlogs of unfilled orders so thai unsatisfieddemand at the equilibrium price in period / was satisfiedthrough firm expansion in subsequent perioils.

VOL H6 NO. 3 KLEPPER: INNOVATION OVER THE PRODUCT UFE CYCLE 573

_ fall over time. Lemma 7 indicates that in eithercase, E, will eventually decline to 0.

Proposition I can account for the two entrypatterns reflected in Figure I. Intuitively, inevery period, incumbents have a lower averagecost than entrants because they spend more onprocess R&D due to the greater output overwhich they can apply the benefits of their R&D.Entrants can nonetheless gain a foothold in theindustry if they can earn sufficient profits fromdeveloping a distinctive product variant, whichrequires sufficient product-innovation expertises,. Over time, though, price is driven downand the advantage of incumbents over entrantsgrows, increasing the product-innovation ex-pertise required for entry to be profitable. Thisreduces the percentage of potential entrantsthat enter over time, although the number ofentrants can rise at any time if the number ofpotential entrants K, rises sufficiently. Even-tually, price is driven to a level such that re-gardless of their product-innovation expertise,the expected profits of all potential entrants areless than or equal to 0 and entry ceases.

The second regularity indicates that initiallyIhe total number of firms rises but eventuallypeaks and then declines steadily, as reflectedin Figure I. Proposition 2 indicates how thiscan be explained by the model.

PROPOSITION 2: Initially the number offirms may rise over time, but eventually it willdecline steadily.

PROOF:It was shown that p, must fall over time in

Lemma 5, and by a sufficient amount to causesome firms to exit in every period. Coupledwith Lemma 7, which indicates entry musteventually stop, this implies that after someperiod the number of firms steadily declines.To see how the number of firms could rise overtime at some point prior to this, consider with-out loss of generality the change in the numberof firms between periods I and 2. This changeequals the number of entrants in period 2, ^2(1 -H{sl)). minus the number of exits in period2, A',(W(.sl) - H{.s\)). The only constraimon the numher of entrants and exits comesfrom the requirement that the market mustclear in period 2. All incumbents that remain

in the industry in period 2 expand their marketshare. Therefore, in order for the market toclear in period 2, the total output of entrantsin period 2, K2{ 1 - His-:))Aql, must be lessthan the output exiters in period 2 would haveproduced if they had remained in the industryand maintained their market share, K,{H{s\) -His\))(Q,/Q,)Aq\. Since Aql < Aq\ basedon Lemma 6, this condition can be satisfiedeven if A:3( I - H{sl)) > Kf(H(s\) -His\)). Thus, initially the number of firmsmay rise. Note that the number of firms couldrise from period I to 2 even if A', < AT,. whichwould ensure that the number of entrants inperiod 2. K2(\ - H(sl)), was less than thenumber of entrants in period I, A:I(I -H(s\)). Thus, the number of firms could riseinitially even if the number of entrants fell.

Intuitively, over time price falls, the moreinnovative incumbents expand, and the less in-novative incumbents exit and are replaced bymore innovative, smaller entrant. This can re-sult in a rise in the number of producers. How-ever, as incumbents continue to grow their ad-vantages eventually become insurmountableand entry ceases. Exit continues, though, as thelargest firms with the greatest innovative ex-pertise expand their market share and push theless fit firms out of the market. Consequently,eventually the number of firms decline.s overtime.

Consider next the third regularity regardinghow the market shares of the leaders changeover time. Proposition 3 indicates that the rateof change of the market shares of all incum-bents must eventually slow.

PROPOSITION 3: As each firm grows large,eventually the change in its market share,Aq,,/Q,, will decline over time.

PROOF:Given that Q, is nondecreasing over time,

Aq,,IQ, will decline over time if Aq,, declinesover time. Equation (5) indicates that Ag,, isbased on the firm's profit margin on the stan-dard product,;?, - c -\- /(re,,). For incumbentsthat remain in the industry, re,, will grow overtime, causing /(re,,) to grow. Eventually,though, /(re,,) will asymptotically approach itsupper bound, and the rise in /(re,,) will

574 THE AMERICAN ECONOMIC REVIEW JUNE 1996

approach zero. In contrast. Lemma 5 indicate.sthat p, wi]l fall in every period to accommodatethe desires of incumbents to expand. There-fore, for incumbents that remain in the indus-try, p, - c + /(rc,,) will eventually decline,causing the increase in their market share,Aq,,IQ,, to decline.

Intuitively, in every period incumbents ex-pand. The rate al which they expand dependson their profit margin on the standard product.With the marginal product of process R&Deventually approaching zero, all firms even-tually experience a decline in their profit mar-gin. This will induce them to decrease the rateat which they expand their market share. Sincethe largest firms perform the most processR&D, they will be the first to decrease the rateat which they expand their market share. Sub-sequently, smaller firms will follow."

The other three regularities pertain to the na-ture of innovation over the PLC. Regardingfirst the trend over time in the rate of productinnovation, it is straightforward to establishthe following.

PROPOSITION 4: Afier entry ceases, the ex-pected number of product innovations of allfirms, %_, (.V, + girdu)), declines over time.

PROOF:Since rd,, = rd* for all firms according to

Lemma I, .r, + g(rd,,) remains the same forany firm i that remains in the market. Conse-

"Ni)le. though, ihat there is nothing in the mode! toensure that the largest firms remain in the market in everyperiod. Exit will occur in every period, and ihere is nothingin the model to rule oul exit from the firsi cohort, whichcontains the largest limis. Nonetheless, it is possible luestablish thai the largest cohorts will be subjecl to the low-esl rate of cxil in the following sense. In each cohort thaiexperiences exit, the firms with the lea.st innovative ex-pertise will exit. Eventually, whole entry cohorts becomeextinct. This will occur for entry cohort k when .s', theminimum innovation expertise required for survival, ex-ceeds .v,,,̂ .. Based on L^mma 8. s' will exceed ,v,,,̂ . first forthe youngest cohorts, which always have the greatest min-imum product-innovation expertise. Thus, once entryceases the youngest cohorts, which are also the smallest.will experience ihc greatest rales of exit. This accords withthe findings of numerous studies (for example, David S.Evans, 1987; Timothy Dunne et a l , 1989).

quently, once entry ceases, 2 , , , ( J , + J?(rd,v))declines over time as the number of firmsfalls.

Proposition 4 explains the eventual declinein the rate of product innovation in new in-dustries reflected in the fourth regularity.Since each firm performs a constant amountof product innovation over time, once entryceases and the number of firms declines thenthe expected number of product innovationsmust decline. Corresponding to this is a de-cline in the number of distinctive variants ofthe product for sale. This explains the otherpart of the fourth regularity concerning thedecline in the number of competing versionsof the product that eventually occurs in newindustries. Note that prior to the shakeout inthe number of producers, the number of firmsincreases over time as more innovative en-trants displace larger, less innovative incum-bents. This causes the number of competingversions of the product to rise over time.Thus, initially the market induces a rise in thediversity of competing product versions,which eventually gives way to a steady de-cline in this diversity. In this sense, the emer-gence of a "dominant design" for a productcan be interpreted as the result rather than thecause of the shakeout in the number of pro-ducers. In effect, the private benefits of largesize eventually compromise the diversity ofcompeting product versions in the market.Since all product innovations are introducedin competing versions of the product and sub-sequently incorporated into the standardproduct, over time the rate of product inno-vation in the standard product will also de-cline as the number of firms falls.

Consider next the trend over time in the ef-fort devoted to process and product R&D. Itis easy to establish the following.

PROPOSITION 5: For each finn i that re-mains in the market in period t. rc,,/rd,, >rc,, - |/rd,, _,.

PROOF:For each firm. Lemma 1 indicates rd,, is con-

stant over time and Lemma 4 indicates that rc,,rises over time. Hence rc,,/rd,, must rise overtime.

WOL. 86 NO. 3 KLEPPER: INNOVATION OVER THE PRODUCT UFE CYCLE 575

. Proposition 5 establishes that over timeevery firm that remains in the market in-creases its effort on process relative to prod-uct R&D, which explains the fifth regularity.Intuitively, since the returns to product R&Dare independent of firm size while the returnsto process R&D are a direct function of firmsize, as firms grow they increase their efforton process relative to product R&D. This isjust an extreme case of the general idea thatthe returns to product R&D are less depen-dent on the output of the firm (prior to theR&D) than the returns to process R&D. Inthis sense process and product R&D, whichare often collapsed into one based on an ap-peal to a Lancasterian attributes framework,are different.

Proposition 5 applies to individual firms.Eventually the trends at the firm level mustalso be mirrored at the market level. Once en-try ceases, the smallest firms are dispropor-tionately driven from the market given theircost disadvantage. These firms have the high-est ratio of product to process R&D becau.sethey conduct the least amount of processR&D. Thus, as they disproportionately exitand incumbents increase their level of process

- relative to product R&D, the ratio of total pro-cess to total product R&D for all firms rises.'"*Note, though, that once entry ceases the total

. process R&D of all firms might decline overtime, just at a slower rate than the decline intotal product R&D."

The last regularity concerning innovationis that entrants tend to account for a dispro-portionate share of product innovations rel-ative to incumbents. Let if = 2,,(j[, -l-

) denote the expected number of

'"" Prior to entry ceasing, there is a counteracting forceat the level of the market to the trend in the ratio of firmprocess to product R&D: smaller, more innovative en-trants displace larger, less innovative incumbents. Becausethe entrants are smaller, they have a higher ratio of productto process R&D than the incumbents, which contributestoward a higher ratio of product to process R&D at themarket level. Thus, it is possible that prior to entry ceas-ing, the ratio of process to product R&D at the marketlevel might fall over time. Once eniry ceases, however,the ratio must rise.

'•̂ Whetherthe total amount of process R&D of all firmsdeclines over time depends on the rate at which incumbentfirmsexpand their process R&D relative to the rate of firmexit, which is not determined within the model.

innovations per firm in period / of firms thatentered in period k, where N\ is the numberof firms in period / that entered in period kand the summation is over these firms. Prop-osition 6 indicates that ij must be greater theyounger the cohort.

PROPOSITION 6: For all periods t. (J < i\for k< I.

PROOF:Since all firms spend the same amount on

product R&D, the expected number of inno-vations per firm, s, + g(rd,,), is determinedexclusively by s,. This implies that on averagethe expected number of innovations per firmin each entry cohort will be determined by theaverage innovative expertise of firms in the co-hort. For each period /, Lemma 8 indicates thatthe minimum innovative expertise of cohort k,,sf, is greater the younger the cohort (that is,the larger k). Therefore, the average value ofs, will be greater the younger the cohort, hencei) < i'.foT k < I.

Proposition 6 implies that entrants will bemore innovative on average than incum-bents, which explains the last regularity. In-tuitively, the most recent entrants are smallerthan ail other firms and thus earn the leastprofits from the standard product. The onlyway they survive given this disadvantage isif they are more innovative on average thanincumbents. Thus, it is not necessary to ap-peal to some kind of disadvantage of size ininnovation, or to entrants having a greaterincentive than incumbents to innovate be-cause they have less to protect (compareReinganum, 1983. 1985). to explain thegreater innovativeness of entrants. Rather,the greater innovativeness of entrants maybe attributable to the selection process gov-erning the evolution of the market coupledwith an advantage of large firm size in ap-propriating the returns from R&D. Indeed, ifincumbents either had strategic disincentivesto innovate or were less efficient at innova-tion because of their larger size, then oppor-tunities for profitable entry would persistover time, which is not consistent with thefirst regularity concerning entry eventuallybecoming small.


V. Cross-Sectional Implications of the Model

In this section it is shown that the model canexplain various cross-sectional regularities re-garding how within industries R&D effort,R&D productivity, cost, and profitability dif-fer across firms according to their size. Sincethe model was not set up to explain these reg-ularities, its ability to explain them can beviewed as support for its account of the PLC.

A simple cross-sectlonai implication of themodel is that larger firms should perform moretotal R&D and also devote a greater fractionof their R&D to process innovation.

PROPOSITION 7: For each period t, thelarger the output of the firm at the start of theperiod, Qi, - I, then the greater its total spend-ing on R&D, rd,, + re,,, and the greater thefraction of its total R&D devoted to processinnovation, rc,,/(rd;, 4- re,,)-

PROOF:This follows directly from Lemmas 1 and 3.

There have been numerous studies of therelationship between total R&D spending andcontemporaneous firm size. It has been re-peatedly found that R&D and contemporane-ous firm size are closely related, with firm sizeexplaining over 50 percent of the variation infirm R&D in more R&D-intensive industries(see Cohen and Klepper [1996b] for a reviewof these studies). In terms of the compositionof firm R&D, F. M. Scherer (1991) analyzesthe patents issued to firms in the Federal TradeCommission Line of Business Program in the10-month period from June 1976 to March1977. Assigning these patents to business unitsand classifying them according to whetherthey are process or product patents, Schererfinds that among business units witb patents,the fraction of patents that are process in-creases with the sales of the business unit.Based on the assumption that the returns toprocess R&D are more closely tied to the sizeof the firm than the returns to product R&D,Cohen and Klepper (1996a) develop addi-tional predictions at the level of the industryabout the relationship between the fraction ofpatents tbat are process and business unit sales.Using Scherer's data, they find support for

Proposition 7 at tbe level of tbe industry aswell as for their more detailed predictions.

The intuition bebind Proposition 7 is simple:the larger tbe firm then the greater the returnsfrom process R&D, hence the greater the effortdevoted to R&D in general and process in par-ticular. Alternatively stated, the larger the firmthen the greater the output over which it canaverage the fixed costs of (process) R&D,hence the greater its R&D effort. This impliesthai the close relationship between R&D andfirm size is indicative of an advantage of size.In contrast, most studies have interpreted theclose relationship to indicate no advantage ofsize. They note that R&D does not tend to risemore than proportionally with firm size, whichimplies that increasing the average firm sizewould not increase total industry R&D spend-ing. This has been widely interpreted to implythere are no advantages of large firm size inR&D (William L. Baldwin and John T. Scott,1987 p. 111). But as Cohen and Klepper(1996b) emphasize, witbout sucb an advan-tage it is difficult to explain why there is aclose relationship between R&D and firmsize."'

In addition to predictions about R&D effortand firm size, the model has distinctive impli-cations about bow firm size and R&D produc-tivity are related.

PROPOSITION 8: For each period t, the av-erage product of process R&D, /(rc,,)/rc,,,and the average product of product R&D,iSi + girdi,))lrdi,. vary inversely with the sizeof the firm, Q^,.

"' Note ihat in the model there is no innale advantageof firm size in R&D. as Cohen and Klepper i 1996b) pointout in a related setting. The advantage of kirge firm sizestems from the inability of firms to sell their innovationsin disembodied form and the coslliness of rapid growth.In the absence of these restrictions, successful innovationscould be embodied in ihe entire industry output throughthe sale of the innovations and/or the expansion of suc-cessful innovators, and Ihc contemporaneous size of thefirm would have no bearing on the firm's incentives toconduct R&D. While many other models assume, eitherimplicitly or explicitly, thai innovations cannoi be soldand ihus link Ihe returns to innovation to the size of theinnovator, few assume any restrictions on finn growth.


PROOF:Given that /"(rc^,) < 0 for all re,,, the larger

re,, then the lower will be /(rc,,)/rc,,. In eachperiod /. the larger the finn then the greater its

'spending on process R&D. Therefore, /(re,,)/re,, will vary inversely with Q,,. Regardingproduct R&D, Proposition 6 indicates that theexpected number of innovations per firm isgreater for smaller firms. Since all firms spendthe same amount on product R&D, this impliesthat (.V, + g(rd,,))/rd,, must be inversely re-lated to the size of the firm, Q,,.

Proposition 8 is consistent with the findingsof studies that examine the relationship be-tween total R&D effort and the number of pat-ents and/or innovations per unit of R&D. JohnBound et ai. (1984) find that for publiclytraded firms, the number of patents per dollarof R&D is considerably greater for firms withsmaller R&D budgets. Examining this rela-tionship within industries using data from acomprehensive census of innovations in 1982conducted for the Small Business Administra-tion, Zoltan J. Acs and David B. Audretsch(1991) generally find an inverse relationshipacross firms between the number of innova-

. tions per dollar of R&D and total R&D spend-ing. If in addition total R&D spending doesnot rise more than proportionally with firmsize within industries, as ha.s generally beenfound, then Proposition 8 further implies that(he total product of R&D will not rise in pro-portion to firm size. Equivalentiy stated,within industries larger firms will account fora disproportionately small share of process andproduct innovations relative to their size. Thisis consistent with Acs and Audretsch's find-ings (1988, 1991) based on the Small Busi-ness Administration data, especially for moreR&D intensive industries, with Scherer's(1965) findings concerning the rate of patent-ing among large firms, and with the observa-tions of Alice Patricia White (1983) for theselect group of dominant firms she analyzes.

This interpretation runs counter to the con-ventional interpretation of the inverse relation-ship between R&D productivity and firm size.This finding has been widely interpreted as afurther sign of the lack of an advantage of firmsize in R&D (see. for example, Acs andAudretsch, 1991). Not only do large firms not

spend disproportionately more on R&D thansmaller firms, but they appear to get less outof their R&D s]jending than smaller firms, sug-gesting they are actually less efficient at R&Dthan their smaller counterparts. This interpre-tation, though, raises more questions than itanswers. If larger firms are less efficient atR&D, why do they conduct more R&D thansmaller firms? Even more fundamentally, howare large firms able to survive and prosper inR&D intensive industries if they are less effi-cient at R&D than smaller firms?

These questions are readily answered by themodel. All firms have the same R&D produc-tivity in the model in the sense that the func-tions gird,,) and /(re,,), which calibrate theproductivity of product and process R&D re-spectively, are the same for all firms. Thelower average productivity of both productand process R&D in larger firms is a reflectionof the competitive advantages conferred byfirm size. By applying their (process) R&D toa larger level of output, larger firms are ableto appropriate a greater fraction of the valueof their (process) R&D than smaller firms.This induces them to undertake more processR&D than smaller firms. Given the diminish-ing returns to R&D, by undertaking more pro-cess R&D larger firms march further down themarginal-product schedule of process R&D,causing the average product of their processR&D to be lower than in smaller firms. At thesame time, by undertaking more process R&Dand getting a larger return from their processR&D than smaller firms, they eam greater prof-its from process R&D than smaller firms. Thisis why they prosper despite the lower averageproductivity of their R&D than smaller firms.The greater profits they eam from processR&D also enables them to survive with lessaverage product-innovation expertise thansmaller firms, which explains why they gen-erate fewer product innovations per dollar ofproduct R&D than smaller firms.'^

' ' Richard J. Rosen (1991) recently proposed an alter-native explanation for why large firms accouni for a dis-proportionalely small share of innovations relative to theirsales which also relies on large size conferring an advan-tage in appropriating the returns from R&D. His expla-nation, however, also relies on a stylized depiction of the


The model has further implications regard-ing how the advantages conferred by size inR&D will be reflected in firm cost and profit-ability. Il predicts that larger firms will havelower average cost.

PROPOSITION 9: For each period t, firmaverage cost c - 1(TC.,) varies inversely withQ...

PROOF:Since re,, varies directly with Q,, and / ' (re,,) >

0 for all re,,, it follows directly that c - /(re,,)varies inversely with Q,,.

This prediction is consistent with the find-ings of Richard E. Caves and David R. Barton(1990). who use plant data from the Censusof Manufacturers to estimate production func-tions for 4-digit SIC manufacturing industries.Allowing productivity to differ across plants,they find that for the average industry largerplants are more productive than smaller plants.In light of the high correlation between plantand business size, this finding is supportive ofProposition 9. Consistent with the role of R&Din the model in imparting a lower cost to largerfirms. Caves and Barton (p. 126) find the re-lationship between productivity and plant sizeto be stronger in more R&D intensive indus-tries. Proposition 9 is also consistent with E.Ralph Biggadike's (1979 pp. 65-66) findingsabout entrants. Using detailed data on newbusiness units of a subset of firms in the PIMSdata set, Biggadike finds that entrants tend tostart with a pronounced production-cost dis-advantage that declines over time as the en-trants capture a larger share of the market.

The model has further implications regard-ing how the advantages conferred by firm sizein R&D will be reflected in firm cost andprofitability.

returns to risky R&D projects which suggests, counter lothe evidence assembled in Mansfield (1981), that largefirms will account for a disproportionately small share ofriskier R&D. As Ihe model indicates, as long as R&D issubject to diminishing retums and large finn size providesan advantage in appropriating ihe retums lo R&D. Ihereis little need to resort to oiher styiizations to account forthe disproportionately small number of innovations ac-counted for by larger firms.

PROPOSITION 10: The large.st and most _profitable firms will come from the first cohortof entrants. These firms will increase theirmarket shares over time and consistently eam _supernormal profits.

PROOF:Firms that entered in period 1 with innova-

tive expertise 5n,ax will always be larger thanall subsequent entrants and will eam greaterprofits than all other firms. Consequently, theywill consistently eam supemormal profits andwill never exit. Since A^,, > 0 for ail incum-bents, over time these firms will also increasetheir market shares.

Proposition 10 implies that the marketshares of the largest and most profitable firmsin the industry will not decline over time. Fur-thermore., although the profits of these firmsmay decline over time as price falls, they willconsistently eam supemormal profits. Thesepredictions are consistent with Mueller's(1986) findings conceming the persistence ofmarket share and profitabihty among the larg-est manufacturing firms over the period 1950-1972. Mueller finds that a number of thesefirms maintained their market shares over this22-year period. While the average profitabilityof tbese firms declined over time, they werestill eaming supemormal retums on invest-ment in 1972. Consistent with the role playedby R&D in the model in conferring an advan-tage to larger firms. Mueller finds tbat the per-sistence of market share and profitability wasstronger for firms in more R&D-intensive in-dustries. Proposition 10 also predicts that themost successful and long-lived firms will dis-proportionately come from the earliest entrycohorts. This is consistent with the findings ofKlepper and Simons (1993) conceming fourproducts that experienced sharp shakeouts: au-tos, tires, televisions, and penicillin. They findthat the chances of surviving at least 10 yearswere significantly greater for the earliest en-trants, particularly in autos and tires, and thaton average the largest firms entered earlier.

In summary, the cross-sectional regularitiesindicate that the larger the firm then the greaterits spending on R&D. the greater the fractionof its R&D devoted to process innovation, thesmaller the number of patents and innovations

VOL 86 NO. J KLEPPER: INNOVATION OVER THE PRODUCT UFE CYCLE 579

it generates per dollar of R&D, and the lowerits average costs. Furthermore, earlier entrant.stend to grow larger and survive longer. Sinceall of these patterns are predicted by the

'model, they provide support for it. The extentof the support., though, depends on the degreeto which these same patterns can be explainedby other theories, particularly theories thatcan account for various features of the PLC.The most relevant alternative theories are thedominant design view reviewed in the introduc-tion (compare Utterbaek and Suarez, 1993),which explains many features of the PLC, andtheories recently advanced in Jovanovic andMacDonald (1994) and Hopenhayn (1993) toexplain shakeouts.

Each of these theories posits technology-based mechanisms which increase exit and/ormake entry harder, contributing to a shakeout.In Utterback and Suarez (1993) the mecha-nism is a dominant design, which leads to exitof firms less able to manage the productionprocess for the dominant design. In Jovanovicand MacDonald ( 1994) it is a major (exoge-nous ) technological change which leads to exitof firms Ihat are unable to innovate in the newregime. In Hopenhayn (1993) it is a slowdownin product innovation that favors firms that in-vest in process innovation, in the manner ofthe dominant design theory.'**

While the theories do not directly addressthe cross-sectional regularities, they can none-theless be used to speak to them. In each the-ory, the firms that prosper and remain in theindustry during the shakeout are the better in-novators. It might be expected these firmswould spend more on R&D, particularly pro-cess R&D in the Utterback and Suarez (1993)and Hopenhayn (1993) models, have lowercosts, and grow to be larger. This could ex-plain the cross-sectional regularities involvingfirm size and lotal R&D, (he fraction of R&Ddevoted to process innovation, and averagecost. The other two regularities, however, aremore difficult for the alternative theories to ex-plain. If larger firms are better innovators, they

'" Hopenhayn (I9W) also posits other, nontechnology-based mechanisms that could trigger a shakeoul. These arenot considered because they cannot address the cross-sectional regularities involving R&D,

might be expected lo generate at least as many,if not more, innovations per dollar of R&Dthan the smaller firms. Yet the cross-sectionalregularities indicate that the number of patentsand innovations per dollar of R&D declineswith firm size. In terms of the significance ofeariy entry, none of the theories emphasizesthe importance of entry liming in conditioningthe length of survival of firms that enteredprior to the shakeout.''' Yet the cross-sectionalregularities indicate that among products ex-periencing sharp shakeouts. the date of entrywas an important determinant of the length ofsurvival for the preshakeout entrants.-"

Thus, the alternative theories cannot readilyexplain all the regularities. This does not implythat the forces they feature are nol operative.Indeed, these forces are largely complemen-tary to the ones featured in the model. Judgingfrom the cross-sectional regularities, however,the model appears to capture important forcesthat are not present in the other theories.

VI. Implications and Extensions

The notion that entry, exit, market structure,and innovation foHow a common pattern fornew products has become part of the folklore-of a number of disciplines, including econom-ics. Although the features of this pattern arebased on a limited number of products andmuch of the evidence is impressionistic, theyappear to resonate with our experience. De-spite its popularity, though, there are manyskeptics about the PLC. both in terms of itslogic and its universality. The principal pur-pose of this paper was to shore up its logical

'" In each theory ihe shakeoul is triggered by eventswhich change the basis for competition among incum-bents, which if anything might be expected to underminethe value of prior experience.

-" Moreover, it does not appear to be the shakeout itselfwhich accounts for this effect. Klepper (1996) tinds thatdifferences in survival rates for ihe preshakeoul entrantswere most pronounced when they were older and had sur-vived a number of years of the shakeout. In the model,this can be explained by the selection process (compareKlepper, 1996). On average, later entrants are better in-novators. At young ages, this tan offset the disadvantageof late entry for firm survival, but as firms age and theselection process continues to operate, eventually later en-trants must experience higher hazard rates.


foundations by showing how a simple modelcould explain all the central features of thePLC.

The proposed model grounds the PLC withtwo simple forces. One is that the ability toappropriate the returns to process R&D de-pends centrally on the size of the firm. Theother is that firms possess different types ofexpertise which lead them to pursue differenttypes of product innovations. The advantageof size in process R&D causes firm processR&D to rise over time and eventually puts en-trants at such a cost disadvantage that entry isforeclosed. After entry ceases, firms competeon the hasis of their sizx anH also their inno-vative prowess. As firms exit and the numberof firms falls, the diversity of product R&D iscompromised, cau.sing the number of productinnovations and the diversity of competingproduct variants to decline. The same twoforces also explain the relationship within in-dustries between firm size and total R&Dspending, relative spending on product andprocess R&D, the productivity of R&D, av-erage cost, and profitability. The ability of themode! to explain these cross-sectional regu-larities in addition to the temporal patterns thatdefine the PLC provides support for its expla-nation of the PLC. It also lends credence to thePLC as a leading case that captures (he salientfeatures of the evolution of technologicallyprogressive industries.

A number of stylizations were invoked tohighlight the two key forces featured in themodel. Perhaps the most noteworthy were theassumptions that average cost was a functionof only contemporaneous process R&D, de-cisions were made solely on the basis of short-term profits, and all innovations were ultimatelyembodied in the industry's standard product.Although relaxing these assumptions wouldcomplicate the model, it need not fundamen-tally alter the ability of the model to explainthe PLC. Regarding process innovation, sup-pose process improvements were allowed tocumulate. If all process improvements wereassumed to be costle.ssly imitated one periodafter they were introduced, firm differences inaverage cost would still be a function of onlydifferences in contemporaneous firm spendingon process R&D. Firm average costs wouldequal c, - /(re,,), where c, reflects the cumu-

lative effect on cost of all past process inno-vations by ail firms. This change would notfundamentally affect the model."' Even if costdifferences across firms were allowed to cu-mulate, it would only reinforce the advantages *of the largest firms. If firms were allowed tobe forward looking, all firms would acceleratethe growth in their output to take account ofthe advantages of size in R&D and accord-ingly undertake greater process R&D in eachperiod (Klepper. 1992). But given the costs ofexpanding output, firms would still grow byfinite rales in each period and it would still beadvantageous to enter earlier. Indeed, the firmsthat would accelerate the growth in their out-put the most would be those that expected tosurvive longest, which would be the firms thatentered earliest with the greatest innovativeexpertise. Thus, allowing firms to be forwardlooking would not alter the advantages of earlyentry and greater innovation expenise and thuswould not fundamentally alter the model. Fi-nally, suppose some product innovations werenot embodied in the standard product butformed the basis for separate product niches.If all permanent product variants could becostlessly imitated one period after they weredeveloped and process innovation lowered theaverage cost of all product variants, then theimplications of the model would not change.All firms would produce all product variantsand the incentives for process R&D would de-pend on the total output of all variants."

The depiction in the model of how marketstructure and performance evolve over timefor new products is different from the conven-tional industrial organization paradigm onstructure and performance. Historically, indus-try characteristics were seen as shaping the na-ture of firm cost functions and barriers toentry, which in tum determined structure andperformance. With few exceptions, firm dif-ferences within industries were thought to be

-' The only implication of the model that would changeis Proposilion ?•, which would require further structuringof the mode] lo establish.

-- The only way the mixiel would be fundamentally al-tered is if each producl niche required its own process R&D.In this case, each product niche would be analogous to aseparate industry, and the model would no longer be amode! of industiy evolution but of industry fragmentation.

VOL 86 NO. 3 KLEFPER. INNOVATION OVER THE PRODUCT UFE CYCLE 581

irrelevant (Mueller, 1986 pp. 223-24). In re-cent years, however, it has been recognizedthat firm differences may be at the root of anumber of important phenomena, such as thepositive correlation across industries betweenindustry concentration ratios and mean firmprofitability (Harold Demsetz, 1973). Themodel takes this approach a step further byembedding differences in firm capabilities inan evolutionary setting In which expansion inoutput at any given moment is subject to in-creasing marginal costs and firm size impartsan advantage in certain types of R&D. Theresult is a world in which initial firm differ-ences get magnified as size begets size, whichimparts an advantage to early entry and leadsto an eventual decline in the number of firmsand the rate of product innovation.-'

The starkness of the model precludes anydepartures from this evolutionary pattern. Thiscan be remedied by allowing for randomevents that alter the relative standing of incum-bents and potential entrants. For example, ifcohorts differ in terms of the distribution oftheir innovative expertise or if the innovativeexpertise of incumbents is undermined by cer-tain types of technological changes, then laterentrants may leapfrog over the industry leadersand the firms that eventually dominate the in-dustry may not come from the earliest cohortof entrants.'^ Some products are described aseventually becoming commodities, which couldbe accounted for in the model by allowing tech-nological opportunities for innovation eventuallyto dry up. Incumbent firm product and processR&D would then eventually decline to zero andthe advantages of early entry would eventuallybe eliminated, allowing the number of firms tostabilize before the shakeout of producers hadrun its full course. The model could also be gen-eralized to include other activities, such as mar-keting and advertising, that could substitute forprocess R&D in imparting an advantage tolarger firms (Sutton. 1991).-' While these

generalizations would no doubt enrich themodel and allow it to accommodate departuresfrom the PLC that have been observed in sometechnologically progressive industries (com-pare Klepper, 1992), even in its stark form themodel is able to address a wide range of reg-ularities. It demonstrates that many aspects ofindustry evolution and heterogeneity withinindustries in firm R&D effort and profitabilitycan be explained by coupling random differ-ences in firm capabilities with advantages offirm size conferred by R&D.

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