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(Klepper 1996) steven klepper, “entry, exit, growth, and innovation over the

This document summarizes six regularities seen over the product life cycle of technologically progressive industries: 1) Entry rates are high when industries are new, then slow over time. 2) Exit rates are initially low but eventually overtake entry rates, leading to a shakeout in the number of producers. 3) The rate of product innovation and diversity of product versions is highest when industries are new, then declines over time. 4) Effort devoted to improving production processes increases over time. 5) Market shares stabilize once early fluctuations diminish. 6) The number of firms, rate of product innovation, and diversity of products eventually declines, while process innovation efforts continue to grow.

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American Economic Association Entry, Exit, Growth, and Innovation over the Product Life Cycle Author(s): Steven Klepper Reviewed work(s): Source: The American Economic Review, Vol. 86, No. 3 (Jun., 1996), pp. 562-583 Published by: American Economic Association Stable URL: http://www.jstor.org/stable/2118212 . Accessed: 09/10/2012 08:02 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. . American Economic Association is collaborating with JSTOR to digitize, preserve and extend access to The American Economic Review. http://www.jstor.org
Entry,Exit,Growth,and Innovationover the ProductLifeCycle By STEVEN KLEPPER* Regularities concerning how entry, exit, marketstructure, and innovation vary from the birth of technologically progressive industries through maturity are summarized.A model emphasizingdifferences infirm innovativecapabilities and the importance of firm size in appropriating the returnsfrom innovation is de- veloped to explain the regularities. Themodel also explains regularities regard- ing the relationshipwithinindustriesbetweenfirm size andfirm innovativeeffort, innovative productivity, cost, and profitability. It predicts that over timefirms devote more effort to process innovation but the number of firms and the rate and diversity of product innovationeventually wither. (JEL L10) A similarviewhasemergedfromanumber of disciplinaryperspectivesabouthow tech- nologicallyprogressiveindustriesevolvefrom birththroughmaturity.'Whenindustriesare new,thereis a lot of entry,firns offermany differentversionsof the industry'sproduct, therateofproductinnovationishigh,andmar- ket shareschangerapidly.Despitecontinued marketgrowth,subsequentlyentryslows,exit overtakesentryandthereis a shakeoutin the numberof producers,therateof productin- novationandthe diversityof competingver- sionsof theproductdecline,increasingeffort is devotedto improvingthe productionpro- cess, and marketshares stabilize.In some quarters,thisevolutionarypatternhascometo be knownas theproductlife cycle (PLC). Whilenumerousauthorshavecontributedto this description,perhapsthe mostinfluential havebeenWilliamJ.AbernathyandJamesM. Utterback.2Buildingontheworkof DennisC. MuellerandJohnE. Tilton(1969) andusing the automobileindustryas a leading case, theydepictthePLCasdrivenbythewaynew technologiesevolve. Theystressthatwhena productis introduced,thereisconsiderableun- certaintyaboutuserpreferences(even among the usersthemselves)and the technological meansof satisfyingthem.As a result,many firmsproducingdifferentvariantsof theprod- uctenterthemarketandcompetitionfocuses on productinnovation.As usersexperiment withthealternativeversionsoftheproductand producerslearn abouthow to improvethe product,opportunitiesto improvetheproduct aredepletedanda defactoproductstandard, dubbeda dominantdesign,emerges.Produc-' ers who areunableto produceefficientlythe dominantdesignexit,contributingto a shake- outinthenumberof producers.Thedepletion of opportunitiesto improvethe productcou- pled with locked-inof the dominantdesign leadstoadecreaseinproductinnovation.This in turnreducesproducers'fearsthatinvest- mentsin the productionprocesswill be ren- deredobsoleteby technologicalchangein the * Department of Social and Decision Sciences, Car- negie Mellon University, Pittsburgh,PA 15213. I thank Wesley Cohen, Mark Kamlet, Jon Leland, John Miller, RichardNelson, Ken Simons, PeterSwann,Bill Williams, and participantsat the 1992 Conference of the Interna- tionalJosephA. SchumpeterSociety, the 1992Conference on MarketProcesses andthe Dynamics of CorporateNet- works, WissenschaftszentrumBerlin, and the Industrial Organization Seminars at the University of Maryland, Berkeley, Penn State,andthe LondonSchool of Econom- ics for helpfulcomments.Thepaperwas greatlyimproved by the unstintingsuggestions of two anonymousreferees and the co-editor, PrestonMcAfee. '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 how technology andinternalfirmorganizationchange over the course of industryevolution, andhow a business consult- ant, Philip G. Drew (1987), describes the way business schools depict the evolution of industries. 2 See in particularJames M. Utterbackand William J. Abernathy(1975) and AbernathyandUtterback(1978). 562
VOL.86 NO. 3 KLEPPER:INNOVATIONOVERTHE PRODUCT LIFE CYCLE 563 product.Consequently,theyincreasetheirat- tentionto the productionprocessandinvest morein capital-intensivemethodsof produc- tion,whichreinforcestheshakeoutof produc- ers by increasingthe minimumefficientsize firm. Whilethisviewhashelpedtopopularizethe PLC,itrestscriticallyonthenotionof adom- inantdesign,an impreciseconceptthatdoes not appearto applyto all new products,es- peciallyones for whichbuyertastesare di- verse(MichaelE.Porter,1983).Furthermore, itincorporatessomequestionableassumptions abouttechnologicalchange.It assumesthat productandprocessinnovationareinextrica- blylinkedandthatfirmswill notattendto the productionprocess until productinnovation hasslowedsufficiently.Yetthehistoryof the automobileindustryandothers,suchas tires andantibiotics,indicatesthatgreatimprove- mentswere madein the productionprocess wellbeforetheemergenceofanykindofdom- inant design (S. Klepperand KennethL. Simons, 1993). Indeed,many of these im- provementswerebasedon humanandphysi- cal investments that were not rendered obsoleteby subsequentmajorproductinno- vations.Thedominant-designview also min- imizes the influenceof industrydemandon incentivesto innovate,attributingthe slow- downinproductinnovationandriseinprocess innovationentirelyto thedepletionof oppor- tunitiesforproductinnovationandthe emer- genceof adominantdesign.Whiletherelative importanceof demandandsupplyfactorshas been hotly debated(David C. Moweryand NathanRosenberg,1982), it has neverbeen questionedthatdemandfactorsplay an im- portantrolein shapingthe rateanddirection of technologicalchange. Thispaperproposesa new explanationfor thePLC.Empiricalregularitiescharacterizing thePLCarefirstidentified.A formalmodelis then constructedto explainthe regularities. Themodelbuildson recenttheoriesof indus- tryevolution(RichardR. NelsonandSidney G.Winter,1982;BoyanJovanovic,1982)and effortstomodelthelinkbetweenmarketstruc- ture and R&D (Nelson and Winter, 1978; ParthaDasguptaand JosephStiglitz, 1980; ThereseM. Flaherty,1980). The modelfo- cuseson theroleof firminnovativecapabili- ties and size in conditioningfirm R&D spending,innovation,and marketstructure. Followingvarioustheoreticalmodelsof asym- metric industrystructure(Flaherty;Avner ShakedandJohnSutton,1987), it incorpo- ratesthe notionthatthe valueof a unitcost reductionachievedthroughinnovationis pro- portionalto the level of outputproducedby the firm. Coupledwith convex adjustment costs,thisimpartsanadvantageto theearliest entrantswhicheventuallycausesa cessation in entryanda shakeoutin thenumberof pro- ducers.It also providesfirmswith a greater incentiveto engagein processinnovationas they grow, which leads to an increaseover timeintheireffortstoimprovetheproduction process.Firnsarealsoassumedtohavedifferent capabilitiesthatleadthemto pursuedifferent typesof productinnovations,athemepromoted by Nelson (1981) and used by Wesley M. CohenandKlepper(1992) to explaindiffer- enceswithinindustriesinfirmR&Dintensities. Thisprovidesthebasisforexplainingthedecline inproductinnovationthatoccursovertime,link- ingittothedeclineinthenumberofcompetitors broughtaboutby theshakeoutof producers.It is shownthatthemodelcanalsoexplainvarious cross-sectionalregularitiesthathave accumu- latedconcerningtherelationshipwithinindus- triesbetweenfirmsize andfirmR&Deffort, R&Dproductivity,cost,andprofitability.Thus, themodelprovidesa unifiedexplanationfora widerangeof temporalandcross-sectionalreg- ularitiesconcerningindustryevolutionandfinn behavior. Thepaperis organizedas follows.In Sec- tionI, theprominentfeaturesof thePLCare summarized.InSectionII,themodelis spec- ified.In SectionIII,preliminaryimplications of themodelaredeveloped.InSectionIV,the modelis shownto explainall the prominent featuresof thePLC.In SectionV, themodel is usedto explainvariouscross-sectionalreg- ularitiesbetweenfirm size, R&D, and firm performance.In SectionVI, the implications of themodelarediscussedandextensionsof themodelareconsidered. I. TheNatureof theProductLifeCycle The depictionof industryevolutioncon- veyedin thePLCis baseduponcase studies
564 THEAMERICANECONOMICREVIEW JUNE 1996 andquantitativeanalysesof the evolutionof newindustries.Inthissection,six regularities concerninghow entry,exit, marketstructure, andtechnologicalchangevaryfromthebirthof technologicallyprogressiveindustriesthrough maturityaresummarized.Whileeveryitidustry hasitsidiosyncrasies,theseregularitiesprovide a compositepictureof theevolutionof techno- logicallyprogressiveindustries. Thefirsttworegularitiespertaintoentryand exit. MichaelGortand Klepper(1982) and KlepperandElizabethGraddy(1990) exam- inetheannualtimepathinthenumberof pro- ducersfor 46 majornew productsbeginning with their commercialinception.Utterback andFernandoF. Suarez(1993) alsoconsider the timepathin the numberof producersas wellasthepathsinthenumberof entrantsand exits for 8 productssubjectto considerable technologicalchange. Klepperand Simons (1993) reviewthe entryandexit pathsfor 2 of the productsstudied by Utterbackand Suarezand2 otherproductssubjecttoconsid- erabletechnological change. Two patterns emergefromthesestudiesconcerningthena- tureof industryevolutionin technologically progressiveindustries: At thebeginningof theindustry,thenumber of entrantsmayriseovertimeorit mayat- taina peakat the startof the industryand then declineover time, but in both cases thenumberof entrantseventuallybecomes small. Thenumberof producersgrowsinitiallyand thenreachesa peak,afterwhichit declines steadilydespitecontinuedgrowthin indus- tryoutput.3 EntrantsAccountfor MarketSharesof LargestFitmsStabilize--_ DisproportionateAmount of ProductInnovation ProductR&D overtime ProcessR&D overtimc E Rut = > pathI Entrypath2 Numberofproducers 0 Time FIGURE 1. TEMPORAL PATTERNS OF ENTRY, NUMBER OF PRODUCERS, MARKET SHARES, AND INNOVATION These patternsare illustratedin Figure1. Two alternativepathsfor entryaredepicted. Inbothcases,entryeventuallybecomessmall andthenumberof firmsrisesinitiallyandthen declinesovertime.Relatedto thesetwo pat- ternsareregularitiesin the way firmmarket shareschangeover time. Althoughmarket- sharedataoveranextendedtimeperiodarenot availableformanyproducts,EdwinMansfield (1962) and Burton H. Klein (1977 pp. 89- 128) have examined how the marketsharesof the leadingproducersof automobiles,tires, aircraft,petroleum,and steel changedover time.Theirfindings,whichaccordwithanum- berof case studies,suggesta thirdregularity whichis notedin Figure1: Eventuallythe rateof changeof the market sharesof thelargestfirmsdeclinesandthe leadershipof theindustrystabilizes. The otherthreeregularitiesaboutthe PLC pertaintotechnologicalchange.Becausetech- nologicalchangeis moredifficultto quantify, theregularitiesarebasedon a numberof case studies4andtwo samplesof innovationsfora 'These are general tendencies, and exceptions can al- ways be found. Of greater significance is the possibility thatthese patternsreflect a bias in the way new products are typically defined. If these patterns tend to be inter- ruptedby major innovations but the innovations are de- finedascreatingnew productssubjectto theirown product life cycles, the patternscould be artifactual.The bulk of the new productsthathave been studied,however, did not experience such majorinnovations until many years after they were introduced,and their evolution was generally characterized by long initial periods during which the characteristicpatternsin entry and the number of firms were observed. 'These include Abernathy(1978) andAbernathyet al. (1983) for automobiles, Klein (1977) for automobilesand aircraft,Tilton (1971) and Jerome Kraus(1973) for tran- sistors, Kenneth Flamm (1988) and Philip Anderson and Michael J. Tushman (1990) for computers, Arthur A. Bright (1949) and James R. Bright (1958) for light bulbs, Thomas J. Prusaand James A. Schmitz (1991) for PC software, and Abernathy and Utterback (1978) and Utterbackand Suarez (1993) for collections of products. For furtherdetail, see Klepper(1992).
VOL.86 NO. 3 KLEPPER:INNOVATIONOVERTHE PRODUCT LIFE CYCLE 565 limited number of industries in the United States (Utterback and Abernathy, 1975) and the United Kingdom (C. De Bresson and J. Townsend, 1981). These studies suggest that for industrieswith rich opportunitiesfor both product and process R&D, three patterns in productand process innovation can be identi- fied:5 The diversity of competing versions of the product and the number of major product innovations tend to reach a peak duringthe growthin the numberof producersandthen fall over time. Over time, producersdevote increasing effort to process relative to productinnovation. During the period of growth in the numberof producers,the most recent entrantsaccount for a disproportionate share of product innovations. These three regularities are also noted in Figure 1. Together,the six regularitieslaid out above andsummarizedin Figure 1providethe focus for the theoreticalanalysis of the paper. II. TheModel The model depicts the evolution from birth throughmaturityof an industrywith rich op- portunitiesfor productandprocess innovation. Two aspects of innovation are featured.First, following Jacob Schmookler (1966) and a number of theoretical models (for example, DasguptaandStiglitz,1980;ShakedandSutton, 1987), the demand for a firm's productis as- sumed to condition its incentive to innovate. This is assumed to be manifested differently for process and product innovation. Process innovation is principally designed to lower a firm's average cost of production. Since the value of a reductionin averagecost is propor- tional to the total outputof the firm, it is as- sumedthatthe incentiveforprocessinnovation is conditioned by the total quantitydemanded of the firm's product.Productinnovations, in contrast,areoften designed to attractnew buy- ers for a product. Accordingly, it is assumed that the incentive for product innovation is conditioned by the demand of new buyers. Second, firmsareassumedto be randomlyen- dowed with distinctive capabilities which in- fluence the kinds of innovationsthey develop. The idea of distinctive firm competencies lies at the heatt of the business-strategy literature (Porter, 1980) andits relevancefor innovation appears prominently in many industry case studies.6It is assumedthatthese differences in capabilitiesmanifest themselves principallyin product innovations, where firms often spe- cialize in innovations that service distinctive types of users (Eric von Hippel, 1988). In contrast,process innovations tend to be incre- mental and based on information that firms commonly generatethroughproduction(com- pare Bright, 1958; Samuel Hollander, 1965). The model is stylized to highlight the two featured aspects of innovation. It has the fol- lowing structure. Time is discrete. In each period, incumbent firms decide whether to ' The threepatternsare ascribedonly to productswith richopportunitiesforboth productandprocess innovation because the bulk of the products for which patterns in innovation have been studied are, not surprisingly,ones with such characteristics.Indeed,Abernathy(1978 p. 84), K. Pavitt and R. Rothwell (1976), and Porter (1983 pp. 23-24), among others,contendthatproductswithoutrich opportunitiesfor both productand process innovation do not follow the prototypical PLC. Examples cited as ex- ceptions to the PLC include synthetic fibers and plastics, which are claimed to be relatively homogeneous and pri- marily subjectto process but not productinnovation, and heavy electrical equipment, which is produced in small batches and is claimed to be subject primarilyto product and not process innovation. While no evidence is pre- sented to buttressthese claims and not all observers sub- scribe to them (for example, see David A. Hounshell [1988] regardingsynthetic fibers), it is importantto rec- ognize that the evidence regardinginnovation during the PLCis primarilybasedon productswithrichopportunities for both productandprocess innovation.This is reflected in the model, which presupposes that the joint natureof productand process innovationdrives the PLC. 6Forexample, a numberof studiesemphasize how sig- nificant innovations can be traced back to expertise ac- quiredfortuitously.This is featuredin HughG. J.Aitken's (1985) analysis of early radio innovations, Flamm's (1988) discussion of the influence of government spon- sored cryptographyefforts during World War II on sub- sequent innovationby computerfirms, and Klein's (1977 pp. 89-109) discussion of the skills brought into the automobile industry at the 'turnof the century by entre- preneurs with experience in mass production and inter- changeable partsmanufacture.
566 THEAMERICANECONOMICREVIEW JUNE 1996 remainin the industryanda limited numberof potential entrantsdecide whetherto enter.All firmsproducea standardproduct.They decide how muchprocess R&D to perform,which de- terminesthe averagecost of the standardprod- uct. They also decide how muchproductR&D to perform. Firms randomly differ in their productinnovationexpertise,which influences their success at productR&D. In each period, successful product innovators develop a dis- tinctive product innovation which they com- bine with the standardproduct to market a unique, distinctive product. Distinctive prod- ucts appealto all buyers, but only new buyers pay the premiumsfor them, with each distinc- tive product sold to a different class of new buyers. All firms monitor the product inno- vations of their rivals. This enables them to imitateallproductinnovationsone periodafter they areintroducedand incorporatethem into the standardproductat no additionalproduc- tion cost. When the last period's product in- novations are incorporatedinto the standard product,buyers of the distinctive productsbe- come buyers of the standardproduct and the demand for the standardproductby all other buyers increases, causing the demand curve for the standardproduct to shift to the right. Producers share in the expansion in demand for the standardproductin proportionto their prior output and decide how much furtherto expand their output subject to a cost of ad- justment. All decisions are made to maximize currentprofits, firms are price takers, and in each period the price of the standardproduct clears the market. The model is formally specified as follows. Ineachperiodt, thereareK,potentialentrants. As firms enter and others randomly develop the innovative capabilitiesrequiredto enter,K, changes. A priorino restrictionsareplaced on whether K, rises or falls over time; this may differ across industriesand also within indus- tries over time. Each potential entrantis ran- domly endowed with innovative expertise which it cannot modify over time. Let si de- note the innovation expertise of firm i, which it knows priorto entry, andsmax the maximum possible innovationexpertise. To simplify the dynamics of the model, it is assumed that in each period there are one or more potential entrantswith innovative expertise Smaxandthe cumulativedistributionof innovativeexpertise is the same for the potential entrantsin each period. This distributionis denoted as H(s), where H(s) is assumed to be continuous for all s < smaxand H(Smax)= 1by definition. The firm's innovative expertise influences its success atproductR&D. The probabilityof firm i developing a productinnovation in pe- riod t is si + g (rdi,), where rdi,is its spending on product R&D and the function g(rdi,) re- flects the opportunitiesfor productinnovation. Each successful innovatoradds its innovation to the standardproductand marketsa distinc- tive variantof the industry'sproduct,which it sells at a price exceeding the price of the stan- dardproduct,reflecting the value of its inno- vation. Distinctive variants are assumed to appealto all buyersbut only new buyers have a positive demand for them at the prices charged, with each distinctive variant pur- chased by a differentclass of new buyers. Af- ter one period, all product innovations are copied and incorporated into the standard product,so successful innovatorshave a one- periodmonopolyovertheirdistinctivevariants. Let G denote the one-period gross monopoly profit(before subtractingthe amountspent on productR&D) earnedby each seller of a dis- tinctivevariant.It is assumedthatg' (rdi) > 0 and g"(rdit) < 0 for all rdit 2 0, reflecting diminishing returns, and that g'(0)G > 1, which ensures rdit> 0 for all i, t. In orderto be able to imitatecostlessly the innovationsof its rivals, which is requiredto market a dis- tinctive productvariantand also the standard product,firmsmonitorthe innovationsof their rivals at a cost of F per period. Thus, if a firm engaged in only product innovation and did not producethe standardproduct,its expected profitsin period t would be [si + g(rdit)] G - rdit- F. To simplify the model, it is assumed thatF > [si + g(rdit)] G - rditfor all rdit.This ensures that in orderto have nonnegative ex- pected profits,all firmsmustproducethe stan- dardproduct. Let Qt = f(pt) denote the total marketde- mand for the standardproduct in period t, where Qt is the quantity demanded,Pt is the price of the standardproduct,andft(pt) is the market demand schedule for the standard productin period t. Over time,f (pt) shifts to the rightat every price as last period's product
VOL 86 NO. 3 KLEPPER:INNOVATIONOVERTHEPRODUCT LIFE CYCLE 567 innovations are incorporatedinto the standard product.It is assumed thatfi(p,) is continuous anddownwardsloping for all t. Let Qitdenote the outputof the standardproductby firmi in periodt. Itis determinedas follows. Assuming thatPt falls over time (this will be shown in thenext section), the totalquantitydemanded, Qt, expands over time. All firmssell the same standardproductat the same price. New buy- ers are assumed to choose a seller based on a stochastic learningprocess in which the prob- ability of a firmattractinga new buyeris pro- portionalto its sales of the standardproductin thepriorperiod,Qit - I. Itis assumedthatit is optimal for a buyer to continue purchasing fromthe same firmas long as the firmremains in the market.Accordingly, it is assumed that incumbents in period t experience a rise in their sales of the standardproductfrom Qit- I in period t - Ito Qit- I(Qt/Qt- I) in period t, where Qt/Qt - l denotes the growthin the total quantity demanded of the standard product fromperiod t - 1 to t. If desired, the firmcan expand its output further,resulting in an in- crease in its marketshareof the standardprod- uct relative to period t - 1. To do so, it must incur an adjustmentcost of m(Aqit), where Aqitis the expansion in its outputin period t above Qit- I(Qt/Qt- ). The function m(Lqit) is such thatm'(0) = 0, m'(Aqit) > 0 for all zqit > 0, and m"(Aqit) > 0 for all Aqit ' 0, with m' (Aqit) growing without bound as Aqit increases, reflecting increasing marginal ad- justment costs.7 The average cost of productionof the stan- dardproductfor firmi is assumed to be inde- pendent of Qit and equal to c - l(rcit), where rcitis the amount spent on process R&D by firm i in period t and the function l(rcit) re- flects the opportunitiesfor process innovation. Following Flaherty(1980), cost in period t is a function only of process R&D in period t. It is assumedthatas rcitincreases, l(rcit) asymp- totically approaches an upper bound and l'(rcit) > 0 and l"(rcit) < 0 for all rcit 2 0, reflectingdiminishingreturns.Further,it is as- sumed that 1'(0)QQm1,i> 1, where Qmninis the smallest level of outputever producedby any firm.This ensures rcit> 0 for all i, t. Given the assumptions, the expected profit of firmi in period t, E(IIit), can be expressed as (1) E(Hit) = [si + g(rdit)]G - rdit + [Qit_I(Qt/ Qt-l) + Aqit] X [Pt - c + I(rcit)] - rcit- m(Aqit) - F, where [si + g(rdit)]G - rdit is the firm's expected net profit from product R&D after subtracting the cost of its product R&D, I[Qit-l(QtlQt_l + Aqit [pt - c + l(rcit)I- rcit- m(Aqit)is its netprofitfromproducing thestandardproductaftersubtractingbothits spendingonprocessR&Dandthecostsof ad- justingits output,andF is the cost of moni- toringtheinnovationsof itsrivals.Expression (1) appliesto entrantsin periodt as well as incumbents,with Qit- = 0 for entrants.All firmsare assumedto be atomisticandprice takers.In each periodt they can projectthe market-clearingpriceforthestandardproduct, Pt,butareuncertainaboutfuturepricesandthus theirprospectsfor survival.Accordingly,it is assumedtheydecidewhetherto be in the in- dustryandif so,rdit,rcit,andAqit,tomaximize currentexpected profits,E(nit). Let rdi,t, rc*, and Aq* denote the profit-maximizing choices of rdit,rci,, and qit and E(HI*t) the expectedprofitsof the firmat thesechoices. Potentialentrantsenterif E(n*) > 0, arein- differentaboutenteringif E(HI*t) = 0, anddo not enter if E(HI*) < 0, where Aqit defines theirinitialoutputof the standardproductif they enter.Similarly,incumbentsstayin the industryif E(Hll*)> 0, areindifferentabout stayingin if E(HI) =0, andexit if E(HI*) < 0. Onceincumbentsexit, theiroutputof the standardproductis lost. Theindustryis assumedto startin period1 whendemandandtechnologyfortheproduct are such that there exists a price pi for which the quantitysuppliedby firms with 7If a firmwantsto expand its marketshare,it will nor- mally have to incur marketingcosts to attractcustomers from its rivals. The assumptionthatm"(Aqi,)> 0 reflects the idea thatthe morethe finn wantsto increaseits market sharein any given period, the greaterthe marketingcosts requiredfor expansion at the margin.
568 THEAMERICANECONOMICREVIEW JUNE 1996 nonnegative expected profitsequals the quan- tity demanded, Ql, where Q, > 0. Similarly, in every subsequent period p, is assumed to clear the market.This requiresthat the quan- tity demandedin period t, Q, = f,(p,), equals the quantitysupplied by producersin period t takingp, as given: (2) Q,= , {Qit-I(Qt/Qt-1) + /qit}, i,t where the index i, t of the summationdenotes thatthe summationis over firmsi in themarket in period t. In terms of the actualmechanism governing the change in price fromperiod t - I to t, thedynamicsof themodel aresimplified by assuming that for all incumbent firms in period t, dE(H1*)/dp, > 0 for all prices pt within a broad neighborhood of pt 8 with the equilibriumprice constrainedto lie in this broad neighborhood.The existence of such a price in each period satisfying equation(2) is demonstratedin the next section. As will be shown, market clearing is achieved through the effects of pt on Qt, Aqit, and on entryand exit in period t.9 Themodelis stylizedtokeepittractableand tohighlightthetwokeyfeaturesof innovation thatunderlieit. Productinnovationsare as- sumedto be introducedinto distinctivever- sionsof theproductandthenincorporatedinto the productsof all firms,whichconformsto the way manyproductsevolve over time.'0 This preservesthe notionof an industryin which all firms producethe same product while allowingfor (limited) productdiffer- entiation.Eachproductinnovationis assumed tobe soldto adifferentclassof newbuyersto reflecttheideathatfirmshavedifferentkinds of innovativeexpertisethatleadthemto ser- vice differentgroupsof buyers.Coupledwith theassumptionthatproductinnovationsdonot affect the demandfor the standardproduct, this ensuresthatthe incentiveto engage in productinnovationis determinedsolelybythe demandof new buyers."Differencesin firm innovativeabilitiesarestructuredso thatthey do notaffectthefirm'soutputof thestandard productnorthe amountspenton productor processR&D.Consequently,thefirm'soutput of thestandardproductis relatedto thefirm's R&Dspendingonlythroughits effectson the returnsfromprocessR&D,whichhighlights the influenceof the demandfor the standard productonprocessR&D.Opportunitiesforin- novation,as reflectedin thefunctionsg(rdi,) andl(rci,), are assumedconstantto abstract fromtheeffectsof changingtechnologicalop- portunitieson the firm'sR&Dspending.All decisionsarebasedoncurrentexpectedprofits andprocessinnovationsarenotcumulativeto simplifythe dynamicsof the model and to reflectthelimitedhorizonsof firmsinnewin- dustries.Manyof these assumptionsarere- consideredin the conclusion, where it is arguedthatthe spiritandprincipalimplica- tions of the model wouldnot changeif the assumptionswererelaxed. 8Thisconditionrequiresthatineachperiodt,thelower p, thenthelowerthemaximumpossibleexpectedprofits of eachfirm,assumingthefirmcan sell as muchof the standardproductasitwantsatp,.Thepriceofthestandard productaffectsE(r,*) in twoways:throughitseffecton theprofitperunitof thestandardproduct,p, - c + l(rci,), andthroughitseffectoneachfirm'soutputofthestandard productvia thetotalquantitydemandedof the standard product,Qt.Thesetwo effects workin oppositedirec- tions-the lowerpt thenthe lowerthe firm'sprofitper unit on the standardproduct,ceterisparibus,but the greaterthefirm'stotaloutputofthestandardproduct,cet- erisparibus.Giventhatl(rcj,)is bounded,at sufficiently low pricesE(rlH*)mustbe less thanzero for all firms, henceatsufficientlylowpricesthefirsteffectmustdom- inatethesecondanddE(rI,*)dpt> 0. Ifdft(pt)ldpt= 0 at therelevantprices(thatis, thepriceelasticityof demand equaledzero),thenptwouldhaveno effecton thefirm's outputof thestandardp,roductandit is easyto see from equation(1)thatdE(Hlit)ldpt> 0 forallprices.Moregen- erally,if suitableconstraintsareplacedon the function dft(pt)ldptattherelevantpricesthendE(rH*)/dpt> 0 for allpriceswithina broadneighborhoodofpt 9 Notethatif exitoccursin periodt then1j, Qit-I < li, t- I Qit-I = Q,_ ,, where the index i, t - 1 denotes summationoverfirmsin themarketin periodt - 1. As developedin thenextsection,exit will be necessaryfor themarketto clearineachperiod. '?Forexample,inautomobilesinnovationssuchasthe electricstarterandtheinexpensiveclosedbodywerein- troducedintodistinctivemodelsandthencopiedwidely byallmanufacturers. " Thisabstractsfromstrategicincentivesto innovate associatedwith the preemptionof rivals (RichardJ. GilbertandDavidM.G.Newbery,1982)andcannibalism of priorinnovations(JenniferReinganum,1983,1985).
VOL 86 NO. 3 KLEPPER:INNOVATIONOVERTHE PRODUCTLIFE CYCLE 569 III. Preliminary Results In order to facilitate the proof of later re- sults, a series of intermediateimplications of the model are developed as lemmas. In deriv- ing these lemmas, it is assumed thatthere ex- ists a price p, in each period that clears the marketgiven the choices firmsmake abouten- try, exit, rdi,,rci,, and Aqi, takingp, as given. The existence of such a pathfor price is estab- lished at the end of this section. The firstresults pertainto firmsin the mar- ket in periodt, including firmsthatenteredthe market during period t as well as earlier en- trants.Differentiating (1) with respect to rdi,, rci,, and Aqi, establishes the following first- orderconditions for an interiormaximum for each firmi in the marketin period t: (3) g'(rd1)G = 1 (4) [Qit- (Qt/Qt-i) + Aq*]l'(rc*) = 1 (5) m'(Aq*) = pt - c + l(rc *), where optimal values aredenoted by an aster- isk. Furthermore,for a firmto be in the market in periodt, its expected profitsin periodt must be nonnegative. Given the assumptionof F > [si + g(rdi,)]G - rdi, for all rdi,, a necessary condition for E(nit) 2 0 is thatfor each firm i in the marketin period t: (6) ~Pt- c + l(rcit)> Assuming -1"(rc*)[Qit-1(Qt/Qt-1) + Aq*] X m(Aq*) > lP(rc*)2 to ensure that the joint solutionof (4) and(5) forrc1,andAqi,is a max- imum, the solutionsto equations(3)- (6) will satisfy the second-order conditions. Conse- quently, for each firmi andperiod t, rd* > 0, rc* > 0, and Aq* > 0, with these choices satisfying equations (3) - (6). Thus, all firms in the marketin period t performproductand process R&D and increase their marketshare of the standardproductrelativeto periodt - 1. Conditions (3) -(6) imply two results which reflect the simplified nature of the model. LEMMA 1: For all i and t, rdi, = rd *, where rd* satisfies g'(rd *)G = 1. PROOF: The profit-maximizing value of rdi,is de- fined by equation (3), which is the same for all firmsand does not change over time. Con- sequently, all firms spend the same amount rd* on product R&D, where rd* satisfies (3). Analogous to E(fl *), letVi=V Qit- (Q Qt-1) + Aq*][p, - c + l(rc*)] - rci* m( Aq*) denote the firm's (incremental) profitfromthe standardproduct.Lemma 1im- plies that the firm's incrementalprofitearned from product R&D in each period, [si + g(rdi,)] G - rdi,,remains constant over time. Consequently, changes in the firm's expected profits over time arise only from changes in Vi*. Accordingly, most of the analysis of the model focuses on the standardproduct. The second result indicates thatin each pe- riod t, firms in each entry cohort make the same choices for rci, and Aqi, and have the same outputand incrementalprofits from the standardproduct. Letting the values of these variables for entry cohort k in period t be de- notedasrc', Aqk, Q,k,andV k, thefollowing result is established. LEMMA 2: For allfirms i thatenteredinpe- riod k and are still in the marketinperiod t > k, rci, = rck, Aqit* = AqkI Qi = Qk, and V = V t t PROOF: Since Qi - I = 0 for entrants in period t, equations (4) and (5) imply rc* and Aq , hence Qitand Vi*, must be the same for all entrantsin t. It then follows from (4) and (5) thatrc*, Aq*, Qit,and V * must be the same for these firmsin every period they are in the market. Lemmas 1 and 2 imply that in each period t the expected profits of firms that entered in the same period differ only accordingto their product-iniovationexpertisesi. Consequently, in each periodthe distributionof E(fli,) across firmsin the same entrycohortwill be the same as the distributionof si for these firms. The firm's outputin the priorperiod, Qit- I, will determine its choice of rci,and Aqi, and hence Vit.This is reflected in Lemma 3.
570 THEAMERICANECONOMICREVIEW JUNE 1996 LEMMA 3: For each firm i in the marketin period t, the larger Qi -, then the larger rci,, Aqi,, and Vi. PROOF: Differentiating (3) -(5) with respect to Qit- 1andrearrangingyields drc * / dQi,_ - = g"(rd *) Gm"(Aq *)I P(rc*) x (Qt/ Qt_) / D dzAq*ldQi,_ I = g"(rd )Gl'(rci*)2 X(Qt/ Qt- ) / D dVi*/dQit- I= a3Vi*/ a3Qit-I = [p, - c + l(rci*t) ] (Qt / Qt- 1), where D is the determinantof the matrix of secondpartialsof E(ni,) withrespectto rdi,, rci,, and Aqi, evaluated at rd*, rc*, and Aq*. Since D < 0 based on the second-order conditions andp, - c + I(rc*) > 0 based on (6), each of these derivatives is positive. Therefore,thelargerQit- Ithenthe greaterrci,, Aqi,, and Vit. Since Aq* is determined by Qit- I and Aq* > 0 for all i, t, Lemmas 2 and 3 imply that in each period t the age of the firm fully determines rci,, Aqi,, Vi,, and Qit, with each greater the older the firm. Coupled with Lemma 1, this implies that in each period t differencesacrossfirmsinE(ni,)arefullyde- termined by two factors: the age of the firm and its productinnovation expertise si. Lemma 1 establishes the time pathof rdi,for each firmwhile Lemmas2 and3 establishhow rci,, Aqi,, Qit,and Vitvary across firmsin each period. It is also possible to investigate how rci,,Aqi,, Qit,and Vitchangeovertime for each firm.For incumbents, Qitand rci,change over time as follows. LEMMA 4: For each firm i in the marketin periods t - 1 and t, Qit > Qit- and rci, > rci, -l. PROOF: Since Aqi, > 0 for all i, t, it follows that Qit> Qit- Ifor all i, t. Rewritingequation(4) as Qi,l'(rc*) = 1, it follows from Qit> Qit- and l"(rci,) < 0 for all rci,thatrci,> rci,t- . The time paths for Aqi, and Vitfor incum- bents cannotbe so easily characterized.Equa- tion (5) indicatesthatfor each incumbentAqi, will change over time according to the time path of p, - c + I(rci,), the firm's profitper unit of the standardproduct.The change in Vit over time will also depend on the time pathin Pt - c + I(rci,). Lemma 4 implies that l(rci,) rises over time, but Lemma 5 below indicates p, falls over time. Consequently, without fur- ther assumptions it cannot be determined whetherAqi,and Vitgenerally rise or fall over time for incumbents. That pt must fall over time can be easily established. LEMMA 5: For each period t,pt < p.- I PROOF: Recall thatit was assumed thatfor each in- cumbent firm i in period t, dE(n*)Idp, > O for all prices p, within a broad neighborhood of pt- I, with the equilibriumprice in period t lying in this neighborhood.Lemma5 is estab- lished by showing thatfor all pricesp, 2 pt-I in this neighborhood,the marketcannot clear in periodt. Supposep, = pt- I. Then, Qitmust exceed Qi - Ifor all producersin period t - 1. This implies E(n*) > E(n1*) 20 for all producersin period t - 1 and hence that no incumbent would exit in period t. The same condition must be truefor all pricespt > p.- I withinabroadneighborhoodofpt- Igiven that dE(n* )Idp, > 0 forall suchprices.Butevery firm that remains in the industrywill expand its marketshare,hence themarketcannotclear if all firmsremain in the industry.Therefore, pt must be less thanpt- . In order for every firm that remains in the marketto expandits marketshare,some firms must exit in every period.This will occuronly if price falls over time. It mustfall sufficiently in each period t that E(n*) falls below zero for some firms in the marketin period t - 1, causing these firmsto exit.
VOL.86 NO. 3 KLEPPER:INNOVATIONOVERTHEPRODUCT LIFE CYCLE 571 Using p, < p,- , it is possible to character- ize how the size of entrants,Aq,, the process R&D of entrants,rct, and the profits of en- trantsfrom the standardproduct, Vt, change over time. Let s' denote the minimumproduct innovation expertise in period t among firms thatenteredin period k ? t. It is also possible to characterizehow st, the minimum product innovation expertise among entrants,changes over time. Over time, rc,, Aqt, V,, and s, change as follows. LEMMA 6: For all periods I > k, rc' < rck, AqI < Aqk, VI < Vk , and sl > Sk. PROOF: The choices of rci,and Aqi, for entrantsin period t must satisfy equations (3) - (6) with Qit--= 0. These equations differ across pe- riods only because pt falls over time. To see how changesin pt affectrct, Aq,, andalso V,, set Qi1 = 0 in (3 )-(5 ) anddifferentiate with respect to pt. This yields drci*/ dp, = g"(rd *)Gl'(rc)/ D > 0 dAq /dp, - g"(rd*)Gl"(rc*)Aq* /D > 0 dV /dp, = aV a/p, = Aq* > 0. Given that pt < Pt- 1, it follows that rct, Aq,, and V must fall over time. Furthermore, if V falls over time, the marginalentrantmust earn greaterincrementalprofits from product innovation over time, which implies st must rise over time. Lemma 6 indicates that the minimum in- novative expertise required for entry rises over time. Lemma 7 indicates that it eventu- ally rises to the point where no furtherentry occurs. LEMMA 7: Aftersome period, st > sna, and nofirms enter the industry. PROOF: Recall that it was assumed that the distri- bution of innovative expertise H(s) was such thatatleast one potentialentrantin every entry cohort had innovative expertise Smax. If St ' Smax for all t then in every period E(fl*) 2 0 forpotentialentrantswith innovationexpertise Smax,hence E(II*) > 0 for all prior entrants with innovative expertise Smax.Consequently, no incumbent with innovative expertise Smax would ever exit the industry. Since Aqi, > 0 for all firms thatremain in the industry,firms with innovativeexpertiseSmaxwill expandtheir market share in every period. This cannot, however, occur indefinitely, as eventually these firms would capture the entire market and would not be able to expand furtherwith- out some of them exiting. This requires p, eventuallyto fall to a level suchthatE(fI*) < 0 for some incumbentswith innovative exper- tise smax.At this point E(H*) < 0 for all po- tential entrantswith si = Smax. Since pt falls over time, after this point E(II*) will con- tinue to be negative for potentialentrantswith Si = Smax, hence s will exceed Smaxandno fur- therentry will occur. One finalresultthatwill be useful concerns how s' differs across entrycohortsin each pe- riod. This is summarizedas follows. LEMMA 8: In each period t, s' > s' for I > k. PROOF: In each period, E(J7i,) 2 0 for producers. Given that V * is lower the younger the firm based on Lemma 3, it follows that the mini- mum si requiredfor survival must be greater for younger firms. Coupled with the fact that entrants start with higher minimum product innovation expertise than all prior entry co- horts based on Lemma 6, it follows that the younger the cohort of firms then the greater the minimum productinnovation expertise of the cohort. The various lemmas indicate how: (1) the price of the standard product changes over time; (2) the initial values of rdi,, rcit, Aqi,, and Vitchange over time for entrants;and (3) the values of rdi,,rci,,andQitchangeover time for incumbents. Summarizing results, over time pt declines, rdi,remains the same for en- trants and incumbents, rci,, Aqi,, and Vitde- cline over time for entrants,st rises over time
572 THEAMERICANECONOMICREVIEW JUNE 1996 for entrants,and rci,and Qt rise over time for incumbents after entry. The other time paths, which involve how Aqi,, V1t, and E(Ji,) change over time for incumbents after entry, cannot be characterized generally. The only patternthat must hold is that in each period, Vi,andE(Fi,) mustfallforsomefirms. Itwas assumedthatapricep, existed in each period such that the marketcleared given the choices of firms takingp, as given. This will now be establishedvia induction.It was as- sumedthatsucha priceexistedinperiod1- this was how period 1 was defined. Suppose such a price exists in period t - 1. It will be shown that a market-clearing price pt then must exist in periodt given the choices of firmstakingthispriceptas given.Giventhat the market cleared in period t - 1, Qt- = -i,-I Qit- , where the summation is over firmsin themarketin periodt - 1. Inperiod t, ptmustsatisfyequation(2), whichcanbe expressedas (7) f,(p,){ 1 - Y;Qit-I/ Qt- I i7t - X Aqit = 0, i,t wherethe summationis over firmsin the mar- ketinperiodt. Intheproofof Lemma5 itwas established thatpt must be less thanpt- and mustinducesomefirmsto exit;otherwise1 - Yi,tQit- 1/Qt- I = 0 since the marketclearedin periodt - 1 andequation(7) wouldbe violated giventhatAqi,> 0 foreachfirminthemarket. Giventheassumptionof dE(nHt*)Idpt > 0, the lower pt then the more firms for which E(l*) < 0 andthusthegreaterthenumberof finnsexitingin periodt. Themorefirmsthat exitthenthegreater{I - Yi,tQi- 1/Qt-1} and the smallerXi,tAqi,in equation(7). Further- more,thesmallerpt thenthegreaterf (pt) and the smallerAqt,for each firm,which reinforces the effect of exit on the market-clearingcondi- tion. Thus, as pt decreases relative to pt-I, f (pt){I- Yi,t Q1t-I/QIQt}rises and Ei,t Aqit falls in equation (7). Given that l(rc,t) is bounded,ata low enoughprice E(nl* ) < 0 for each firmand all firmswould exit the industry. Thus,atalow enoughpricef (p,) I1 - Yjit Q,t-I Q }-II - Yi,t Aqit > 0, whereasfor pricespt 2 p,_ 1,f(p,) {1 -Yi,t Qit- /Q,- | }-2i,tAqit < 0. Giventhatf,(pt)andAqi,arecontinuousfunc- tions of p, and all firms are assumed to be atomisticand indifferentaboutbeing in the in- dustrywhen E(ll* ) = 0, it then follows that theremustbe a pricept which satisfiesequation (7) andthusclearsthe marketin periodt.'2 Note that the existence of such a path for pricedoes notdependon positive entryin each period, nordoes it dependon the time pathsin the number of entrants,numberof exits, and number of firms. These time paths are ad- dressed in the next section. IV. TheRegularitiesof thePLC Six propositions are developed in this sec- tion corresponding to each of the empirical regularitiessummarizedin Section 2. Considerthe firstregularityaboutentryover time. Let Et denote the numberof entrantsin periodt. The possible time pathsin Etimplied by the model arecharacterizedin Proposition1. PROPOSITION 1: Initially the number of entrants may rise or decline, but eventually it will decline to zero. PROOF: The entryprocess is such thatEt = Kt(1 - H(st)). Lemma 6 indicatesst rises over time. Hence Et will fall overtime unless Ktrises over time at a sufficientrate,which cannotbe ruled out a priori.Therefore,initially E, may rise or 2 The assumption that all firms are atomistic ensures the continuity of f(p,){ 1 - .1j, Qit- ,IQt,- I-i, Aqi, as a function of p, and hence the existence of a price pt sat- isfying equation (7). A similar assumption is invoked in Jovanovic and Glenn H. MacDonald (1994) and Hugo A. Hopenhayn (1993) in their models of industryshakeouts (these arediscussed furtherbelow). Alternatively,if firms were nonatomisticthenthe quantitysupplied,Y,. Qi.- I(Q,I Q,- ) + Yi,tAqi,, could exceed the quantity demanded, f(p1), at all prices Pt insufficient to induce the marginal firmto exit but could fall shortof the quantitydemanded at all prices sufficient to induce the marginalfirmto exit. Then, therewould be no price thatwould clearthe market in periodt. Although beyond the scope of the paper,non- atomisticfirmsmightbe accommodatedby allowing firms to maintainbacklogs of unfilled ordersso thatunsatisfied demand at the equilibriumprice in period t was satisfied throughfirmexpansion in subsequentperiods.
VOL 86 NO. 3 KLEPPER:INNOVATIONOVERTHE PRODUCT LIFE CYCLE 573 fall overtime. Lemma7 indicatesthatin either case, E, will eventually decline to 0. Proposition1 can accountfor the two entry patternsreflected in Figure 1. Intuitively, in every period,incumbentshave a lower average cost thanentrantsbecause they spend more on process R&D due to the greater output over whichtheycanapplythebenefitsof theirR&D. Entrantscan nonethelessgain a foothold in the industryif they can earnsufficientprofitsfrom developinga distinctiveproductvariant,which requiressufficientproduct-innovationexpertise si. Over time, though, price is driven down andthe advantageof incumbentsover entrants grows, increasing the product-innovationex- pertiserequiredfor entryto be profitable.This reduces the percentage of potential entrants that enter over time, although the number of entrantscan rise at any time if the numberof potential entrantsK, rises sufficiently. Even- tually, price is driven to a level such that re- gardlessof theirproduct-innovationexpertise, theexpectedprofitsof all potentialentrantsare less thanor equal to 0 and entry ceases. The second regularityindicatesthatinitially the total numberof firms rises but eventually peaks and then declines steadily, as reflected in Figure 1. Proposition 2 indicates how this can be explained by the model. PROPOSITION 2: Initially the number of finns may rise over time, but eventually it will decline steadily. PROOF: It was shown thatp, must fall over time in Lemma 5, andby a sufficient amountto cause some firms to exit in every period. Coupled with Lemma 7, which indicates entry must eventually stop, this implies that after some period the numberof firms steadily declines. To see how thenumberof firmscould riseover time at some pointpriorto this, consider with- outloss of generalitythechange in the number of firmsbetween periods 1 and 2. This change equalsthenumberof entrantsinperiod2, K2(1- H(s2)), minus the numberof exits in period 2, K1(H(s )-H(s )). The only constraint on the number of entrants and exits comes from the requirement that the market must clear in period 2. All incumbents that remain in the industryin period 2 expandtheirmarket share. Therefore, in order for the market to clear in period 2, the total output of entrants in period 2, K2(1 - H(s2))Aq2, mustbe less thanthe outputexiters in period 2 would have producedif they had remainedin the industry andmaintainedtheirmarketshare,K1(H(s ) - H(s 1)l) (Q2/Q1)Aq1. Since Aq2< Aq1based on Lemma 6, this condition can be satisfied even if K2(1 - H(s2)) > K1(H(s ) - H(sl)). Thus, initially the number of firms may rise. Note thatthe numberof firmscould rise fromperiod 1 to 2 even if K2< K1,which would ensure that the number of entrantsin period 2, K2(1 - H(s2)), was less than the number of entrants in period 1, K1( 1 - H(s I)). Thus, the numberof firmscould rise initially even if the numberof entrantsfell. Intuitively, over time price falls, the more innovative incumbentsexpand,andthe less in- novative incumbentsexit and are replacedby more innovative,smallerentrants.This can re- sultin a rise in the numberof producers.How- ever, as incumbentscontinueto grow theirad- vantages eventually become insurmountable andentryceases. Exit continues,though,asthe largest firms with the greatest innovative ex- pertise expandtheirmarketshareandpush the less fit firmsout of the market.Consequently, eventually the numberof firms declines over time. Considernext the thirdregularityregarding how the market shares of the leaders change over time. Proposition3 indicates thatthe rate of change of the marketshares of all incum- bents must eventually slow. PROPOSITION 3: As eachfirm grows large, eventually the change in its market share, Aqi,/Q,, will decline over time. PROOF: Given that Q, is nondecreasing over time, Aqi,/Q, will decline over time if Aqi,declines over time. Equation (5) indicates that Aqi, is based on the firm's profitmarginon the stan- dardproduct,p, - c + I(rci,). Forincumbents thatremainin the industry,rci,will grow over time, causing l(rci,) to grow. Eventually, though,I(rci,) will asymptoticallyapproachits upper bound, and the rise in l(rci,) will
574 THEAMERICANECONOMICREVIEW JUNE 1996 approachzero. In contrast,Lemma 5 indicates thatp,will fall in every periodto accommodate the desires of incumbents to expand. There- fore, for incumbentsthatremainin the indus- try, p, - c + l(rci,) will eventually decline, causing the increase in their market share, Aqi,/Q,, to decline. Intuitively, in every period incumbents ex- pand. The rate at which they expand depends on theirprofitmarginon the standardproduct. With the marginal product of process R&D eventually approaching zero, all firms even- tually experience a decline in theirprofitmar- gin. This will induce them to decreasethe rate atwhich they expandtheirmarketshare.Since the largest firms perform the most process R&D, they will be the firstto decreasethe rate at which they expand theirmarketshare.Sub- sequently, smaller firmswill follow.' The otherthreeregularitiespertainto thena- ture of innovation over the PLC. Regarding firstthe trendover time in the rate of product innovation, it is straightforwardto establish the following. PROPOSITION 4: Afterentryceases, the ex- pected number of product innovations of all finns, 1j, (si + g(rdi,)), declines over time. PROOF: Since rdi, = rd* for all firms according to Lemma 1, si + g(rdi,) remains the same for any firm i thatremains in the market.Conse- quently, once entry ceases, li,t(si + g(rdi,)) declines over time as the number of firms falls. Proposition 4 explains the eventual decline in the rate of product innovation in new in- dustries reflected in the fourth regularity. Since each firm performs a constant amount of product innovation over time, once entry ceases and the numberof firms declines then the expected number of product innovations must decline. Corresponding to this is a de- cline in the number of distinctive variants of the product for sale. This explains the other part of the fourth regularity concerning the decline in the numberof competing versions of the product that eventually occurs in new industries. Note that prior to the shakeout in the numberof producers,the numberof firms increases over time as more innovative en- trantsdisplace larger, less innovative incum- bents. This causes the number of competing versions of the product to rise over time. Thus, initially the marketinduces a rise in the diversity 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 product can be interpretedas the result ratherthanthe cause of the shakeout in the number of pro- ducers. In effect, the private benefits of large size eventually compromise the diversity of competing product versions in the market. Since all product innovations are introduced in competing versions of the productandsub- sequently incorporated into the standard product, over time the rate of product inno- vation in the standardproduct will also de- cline as the numberof firms falls. Considernext the trendover time in the ef- fort devoted to process and product R&D. It is easy to establish the following. PROPOSITION 5: For each firm i that re- mains in the market in period t, rci,/rdi, > rci,- 1/rdi,- 1i PROOF: Foreach firm,Lemma 1indicatesrdi,is con- stantover time andLemma4 indicatesthatrci, rises over time. Hence rci,/rdi,must rise over time. 1' Note, though, that there is nothing in the model to ensurethatthe largestfirmsremainin the marketin every period.Exit will occurin every period,andthereis nothing in the model to rule out exit from the firstcohort, which contains the largest finns. Nonetheless, it is possible to establishthatthe largestcohortswill be subjectto the low- est rateof exit in the following sense. In each cohort that experiences exit, the firms with the least innovative ex- pertise will exit. Eventually, whole entry cohorts become extinct. This will occur for entry cohort k when sk, the minimum innovation expertise requiredfor survival, ex- ceeds Smax.Based on Lemma 8, sk will exceed Smaxfirstfor the youngest cohorts,which always have the greatestmin- imum product-innovation expertise. Thus, once entry ceases the youngest cohorts, which are also the smallest, will experiencethegreatestratesof exit. This accordswith the findings of numerous studies (for example, David S. Evans, 1987; Timothy Dunne et al., 1989).
VOL 86 NO. 3 KLEPPER:INNOVATIONOVERTHEPRODUCT LIFE CYCLE 575 Proposition5 establishes that over time every firm that remainsin the marketin- creasesits effortonprocessrelativeto prod- uctR&D,whichexplainsthefifthregularity. Intuitively,sincethereturnstoproductR&D areindependentof firmsize whilethereturns to processR&Darea directfunctionof firm size, as firmsgrowtheyincreasetheireffort on processrelativeto productR&D.This is just anextremecase of the generalideathat the returnsto productR&D areless depen- denton the outputof the firm(priorto the R&D) thanthe returnsto processR&D. In this sense processandproductR&D,which areoftencollapsedintoone basedon anap- peal to a Lancasterianattributesframework, aredifferent. Proposition5 appliesto individualfirms. Eventuallythe trendsat the firmlevel must alsobe mirroredatthemarketlevel.Onceen- try ceases, the smallestfirmsare dispropor- tionatelydrivenfromthe marketgiven their costdisadvantage.Thesefirmshavethehigh- est ratioof productto processR&Dbecause they conduct the least amountof process R&D. Thus, as they disproportionatelyexit andincumbentsincreasetheirlevelof process relativetoproductR&D,theratioof totalpro- cess to totalproductR&Dforallfirmsrises.'4 Note,though,thatonce entryceasesthetotal processR&Dof all firmsmightdeclineover time,just at a slowerratethanthedeclinein totalproductR&D.'" The last regularityconcerninginnovation is thatentrantstendto accountfor a dispro- portionateshareof productinnovationsrel- ative to incumbents. Let ik = (i,t(si + g(rdit))/N' denote the expected numberof innovations per firm in period t of firms that entered in period k, where N' is the number of firms in period t that entered in period k and the summation is over these firms. Prop- osition 6 indicates thatik must be greaterthe younger the cohort. PROPOSITION 6: For all periods t, ik < ia fork < 1. PROOF: Since all firms spend the same amount on product R&D, the expected numberof inno- vations per firm, si + g(rdi,), is determined exclusively by si. This implies thaton average the expected number of innovations per firm in each entrycohortwill be determinedby the averageinnovativeexpertiseof firmsin theco- hort.Foreach periodt, Lemma8 indicatesthat the minimuminnovative expertise of cohortk, Sk, is greaterthe younger the cohort (that is, the largerk). Therefore, the average value of si will be greatertheyoungerthecohort,hence ak< il for k < 1. Proposition 6 implies that entrants will be more innovative on average than incum- bents, which explains the last regularity. In- tuitively, the most recent entrantsaresmaller than all other firms and thus earn the least profits from the standard product. The only way they survive given this disadvantage is if they are more innovative on average than incumbents. Thus, it is not necessary to ap- peal to some kind of disadvantage of size in innovation, or to entrants having a greater incentive than incumbents to innovate be- cause they have less to protect (compare Reinganum, 1983, 1985), to explain the greater innovativeness of entrants. Rather, the greater innovativeness of entrants may be attributable to the selection process gov- erning the evolution of the market coupled with an advantage of large firm size in ap- propriatingthe returnsfrom R&D. Indeed, if incumbents either had strategic disincentives to innovate or were less efficient at innova- tion because of their larger size, then oppor- tunities for profitable entry would persist over time, which is not consistent with the first regularity concerning entry eventually becoming small. 4 Priorto entry ceasing, there is a counteractingforce at the level of the marketto the trendin the ratio of firm process to product R&D: smaller, more innovative en- trantsdisplacelarger,less innovativeincumbents.Because theentrantsaresmaller,they havea higherratioof product to process R&D than the incumbents, which contributes toward a higher ratio of product to process R&D at the marketlevel. Thus, it is possible thatpriorto entry ceas- ing, the ratio of process to product R&D at the market level might fall over time. Once entry ceases, however, the ratio must rise. I Whetherthetotalamountof processR&D of all firms declines over time dependson therateat which incumbent firmsexpandtheirprocess R&D relativeto therateof firm exit, which is not determinedwithin the model.
576 THEAMERICANECONOMICREVIEW JUNE 1996 V. Cross-Sectional Implications of the Model In this section it is shown thatthe model can explain various cross-sectional regularitiesre- garding how within industries R&D effort, R&D productivity, cost, and profitabilitydif- fer across firms according to their size. Since the model was not set up to explain these reg- ularities, its ability to explain them can be viewed as supportfor its account of the PLC. A simple cross-sectional implication of the model is thatlargerfirmsshouldperformmore total R&D and also devote a greaterfraction of their R&D to process innovation. PROPOSITION 7: For each period t, the larger the outputof thefirm at the start of the period, Qit- 1,then the greater its total spend- ing on R&D, rdi, + rci,, and the greater the fraction of its total R&D devoted to process innovation,rci,/(rdi, + rci,). PROOF: This follows directlyfromLemmas 1 and3. There have been numerous studies of the relationshipbetween total R&D spending and contemporaneous firm size. It has been re- peatedly found that R&D and contemporane- ous firmsize areclosely related,with firmsize explaining over 50 percent of the variationin firm R&D in more R&D-intensive industries (see Cohen and Klepper [1996b] for a review of these studies). In terms of the composition of firmR&D, F. M. Scherer (1991) analyzes the patentsissued to firmsin theFederalTrade Commission Line of Business Programin the 10-month period from June 1976 to March 1977. Assigning thesepatentsto business units and classifying them according to whether they are process or product patents, Scherer finds that among business units with patents, the fraction of patents that are process in- creases with the sales of the business unit. Based on the assumption that the returns to process R&D aremore closely tied to the size of the firm than the returnsto product R&D, Cohen and Klepper (1996a) develop addi- tional predictions at the level of the industry aboutthe relationshipbetween the fraction of patentsthatareprocess andbusiness unitsales. Using Scherer's data, they find support for Proposition 7 at the level of the industry as well as for theirmore detailed predictions. The intuitionbehindProposition7 is simple: the largerthe firmthen the greaterthe returns fromprocess R&D, hence thegreatertheeffort devoted to R&D in generalandprocess in par- ticular.Alternativelystated,the largerthe firm then the greaterthe output over which it can average the fixed costs of (process) R&D, hence the greaterits R&D effort. This implies that the close relationshipbetween R&D and firmsize is indicative of an advantageof size. In contrast, most studies have interpretedthe close relationshipto indicate no advantageof size. They note thatR&D does not tend to rise morethanproportionallywith firmsize, which implies that increasing the average firm size would not increase total industryR&D spend- ing. This has been widely interpretedto imply there are no advantages of large firm size in R&D (William L. Baldwin andJohnT. Scott, 1987 p. 111). But as Cohen and Klepper (1996b) emphasize, without such an advan- tage it is difficult to explain why there is a close relationship between R&D and firm size.16 In additionto predictionsaboutR&D effort and firmsize, the model has distinctive impli- cations abouthow firmsize andR&D produc- tivity are related. PROPOSITION 8: For each period t, the av- erage product of process R&D, l(rci,)/rci,, and the average product of product R&D, (si + g(rdj,))/rdj,, vary inversely with the size of thefirm,Qj. 6 Note that in the model there is no innate advantage of firmsize in R&D, as Cohen andKlepper(1996b) point out in a related setting. The advantageof large firm size stems from the inability of firms to sell their innovations in disembodied form and the costliness of rapid growth. In the absence of these restrictions,successful innovations could be embodied in the entire industryoutput through the sale of the innovations and/or the expansion of suc- cessful innovators, and the contemporaneoussize of the firm would have no bearing on the firm's incentives to conduct R&D. While many other models assume, either implicitly or explicitly, that innovations cannot be sold and thus link the returnsto innovation to the size of the innovator,few assume any restrictionson firmgrowth.
VOL.86 NO. 3 KLEPPER:INNOVATIONOVERTHE PRODUCT LIFE CYCLE 577 PROOF: Given thatl"(rci,) < 0 for all rci,,the larger rci,then the lower will be l(rcj,)/rcj,. In each periodt, the largerthe firmthen the greaterits spending on process R&D. Therefore, l(rci,)/ rci, will vary inversely with Qt. Regarding productR&D, Proposition6 indicates thatthe expected number of innovations per firm is greaterfor smallerfirms.Since all firmsspend the same amounton productR&D, thisimplies that (si + g(rdj,))/rdj, must be inversely re- lated to the size of the firm, Qit. Proposition8 is consistent with the findings of studies that examine the relationship be- tween totalR&D effort andthe numberof pat- ents and/or innovationsperunitof R&D. John Bound et al. (1984) find that for publicly tradedfirms, the numberof patentsper dollar of R&D is considerably greaterfor firmswith smaller R&D budgets. Examining this rela- tionship within industries using data from a comprehensive census of innovations in 1982 conductedfor the Small Business Administra- tion, Zoltan J. Acs and David B. Audretsch (1991) generally find an inverse relationship across firms between the number of innova- tions perdollarof R&D andtotalR&D spend- ing. If in addition total R&D spending does not rise more than proportionally with firm size within industries, as has generally been found, then Proposition 8 furtherimplies that the total productof R&D will not rise in pro- portion to firm size. Equivalently stated, within industrieslargerfirmswill account for a disproportionatelysmall shareof process and productinnovationsrelative to theirsize. This is consistent with Acs and Audretsch's find- ings (1988, 1991) based on the Small Busi- ness Administrationdata, especially for more R&D intensive industries, with Scherer's (1965) findingsconcerning the rateof patent- ing among large firms, and with the observa- tions of Alice Patricia White (1983) for the select group of dominantfirms she analyzes. This interpretationruns counterto the con- ventionalinterpretationof the inverserelation- ship between R&D productivityand firmsize. This finding has been widely interpretedas a furthersign of the lack of an advantageof firm size in R&D (see, for example, Acs and Audretsch, 1991). Not only do large firmsnot spend disproportionatelymore on R&D than smaller firms, but they appearto get less out of theirR&D spendingthansmallerfirms,sug- gesting they areactually less efficient at R&D than their smaller counterparts.This interpre- tation, though, raises more questions than it answers. If larger firms are less efficient at R&D, why do they conduct more R&D than smallerfirms?Even morefundamentally,how are large firms able to survive and prosperin R&D intensive industriesif they are less effi- cient at R&D than smaller firms? These questions arereadilyansweredby the model. All firmshave the same R&D produc- tivity in the model in the sense that the func- tions g(rdi,) and l(rci,), which calibrate the productivity of product and process R&D re- spectively, are the same for all firms. The lower average productivity of both product andprocess R&D in largerfirmsis a reflection of the competitive advantages conferred by firmsize. By applyingtheir(process) R&D to a larger level of output, larger firms are able to appropriatea greaterfraction of the value of their (process) R&D than smaller firms. This induces them to undertakemore process R&D than smaller firms. Given the diminish- ing returnsto R&D, by undertakingmorepro- cess R&D largerfirmsmarchfurtherdown the marginal-productschedule of process R&D, causing the average product of their process R&D to be lower thanin smaller firms.At the same time, by undertakingmoreprocess R&D and getting a larger returnfrom their process R&Dthansmallerfirms,theyearngreaterprof- its fromprocess R&D thansmallerfirms.This is why they prosperdespite the lower average productivityof their R&D than smaller firms. The greater profits they earn from process R&D also enables them to survive with less average product-innovation expertise than smaller firms, which explains why they gen- erate fewer product innovations per dollar of productR&D than smaller firms.'7 '7 RichardJ. Rosen (1991) recently proposed an alter- native explanationfor why large firms account for a dis- proportionatelysmall shareof innovationsrelativeto their sales which also relies on large size conferringan advan- tage in appropriatingthe returnsfrom R&D. His expla- nation, however, also relies on a stylized depiction of the
578 THEAMERICANECONOMICREVIEW JUNE 1996 Themodelhasfurtherimplicationsregard- ing how the advantagesconferredby size in R&Dwill be reflectedin firmcost andprofit- ability.It predictsthatlargerfirmswill have loweraveragecost. PROPOSITION 9: For each period t, firm average cost c - l(rcj,) varies inversely with Qit. PROOF: Sincerci,variesdirectdywithQitandP'(rci,)> 0 forallrci,,it followsdirectlythatc - l(rci,) variesinverselywithQit. Thispredictionis consistentwiththe find- ingsof RichardE. CavesandDavidR.Barton (1990), who use plantdatafromthe Census of Manufacturerstoestimateproductionfunc- tionsfor4-digitSICmanufacturingindustries. Allowingproductivityto differacrossplants, they findthatfor the averageindustrylarger plantsaremoreproductivethansmallerplants. In lightof thehighcorrelationbetweenplant andbusinesssize,thisfindingis supportiveof Proposition9.ConsistentwiththeroleofR&D inthemodelinimpartingalowercosttolarger firms,CavesandBarton(p. 126) findthere- lationshipbetweenproductivityandplantsize to be strongerin moreR&Dintensiveindus- tries.Proposition9 is also consistentwithE. RalphBiggadike's(1979 pp.65-66) findings aboutentrants.Using detaileddataon new businessunitsof asubsetof firmsinthePIMS dataset,Biggadikefindsthatentrantstendto startwith a pronouncedproduction-costdis- advantagethatdeclinesover time as the en- trantscapturea largershareof themarket. Themodelhasfurtherimplicationsregard- inghowtheadvantagesconferredbyfirmsize in R&D will be reflectedin firmcost and profitability. PROPOSITION 10: The largest and most profitablefirms will comefrom thefirst cohort of entrants. These firms will increase their marketshares over timeand consistentlyearn supernormalprofits. PROOF: Firmsthatenteredin period1withinnova- tive expertiseSmaxwill alwaysbe largerthan all subsequententrantsandwill earngreater profitsthanallotherfirms.Consequently,they will consistentlyearnsupernormalprofitsand will neverexit.SinceAqi,> 0 forall incum- bents,overtimethesefirmswill alsoincrease theirmarketshares. Proposition10 implies that the market sharesof thelargestandmostprofitablefirms intheindustrywillnotdeclineovertime.Fur- thermore,althoughthe profitsof these firms maydeclineovertimeaspricefalls,theywill consistentlyearnsupernormalprofits.These predictions are consistent with Mueller's (1986) findingsconcerningthepersistenceof marketshareandprofitabilityamongthelarg- estmanufacturingfirmsovertheperiod1950- 1972. Muellerfindsthata numberof these firmsmaintainedtheirmarketsharesoverthis 22-yearperiod.Whiletheaverageprofitability of thesefirmsdeclinedovertime,they were still eaming supernormalreturnson invest- mentin 1972.Consistentwiththeroleplayed by R&Din themodelin conferringanadvan- tagetolargerfirms,Muellerfindsthattheper- sistenceof marketshareandprofitabilitywas strongerforfirmsin moreR&D-intensivein- dustries.Proposition10 also predictsthatthe mostsuccessfulandlong-livedfirmswill dis- proportionatelycome fromthe earliestentry cohorts.Thisis consistentwiththefindingsof KlepperandSimons(1993) concerningfour productsthatexperiencedsharpshakeouts:au- tos,tires,televisions,andpenicillin.Theyfind thatthechancesof survivingatleast 10years weresignificantlygreaterfor the earliesten- trants,particularlyin autosandtires,andthat on averagethelargestfirmsenteredearlier. Insummary,thecross-sectionalregularities indicatethatthelargerthefirmthenthegreater its spendingon R&D,thegreaterthefraction of itsR&Ddevotedtoprocessinnovation,the smallerthenumberof patentsandinnovations returnsto risky R&D projects which suggests, counterto the evidence assembled in Mansfield (1981), that large firms will account for a disproportionatelysmall shareof riskier R&D. As the model indicates, as long as R&D is subjectto diminishingreturnsandlargefirmsize provides an advantage in appropriatingthe returnsto R&D, there is little need to resort to other stylizations to account for the disproportionatelysmall number of innovations ac- counted for by largerfirms.
VOL.86 NO. 3 KLEPPER:INNOVATIONOVERTHE PRODUCTLIFE CYCLE 579 it generatesper dollar of R&D, and the lower its averagecosts. Furthermore,earlierentrants tend to grow larger and survive longer. Since all of these patterns are predicted by the model, they provide supportfor it. The extent of the support,though, depends on the degree to which these same patternscan be explained by other theories, particularly theories that can account for various features of the PLC. The most relevant alternativetheories are the dominantdesignview reviewedin the introduc- tion (compare Utterbackand Suairez,1993), which explains many featuresof the PLC, and theories recently advanced in Jovanovic and MacDonald(1994) and Hopenhayn(1993) to explainshakeouts. Each of these theories posits technology- based mechanisms which increase exit and/or make entryharder,contributingto a shakeout. In Utterback and Suairez(1993) the mecha- nism is a dominantdesign, which leads to exit of firms less able to manage the production process for the dominantdesign. In Jovanovic and MacDonald (1994) it is a major (exoge- nous) technological changewhich leads to exit of firmsthatareunable to innovatein the new regime. InHopenhayn(1993) it is a slowdown in productinnovationthatfavors firmsthatin- vest in process innovation, in the manner of the dominantdesign theory.'8 While the theories do not directly address the cross-sectional regularities,they can none- theless be used to speak to them. In each the- ory, the firms that prosper and remain in the industryduringthe shakeoutare the betterin- novators.1t might be expected these firms would spend more on R&D, particularlypro- cess R&D in the UtterbackandSuairez(1993) and Hopenhayn (1993) models, have lower costs, and grow to be larger. This could ex- plain the cross-sectional regularitiesinvolving firmsize and total R&D, the fraction of R&D devoted to process innovation, and average cost. The other two regularities,however, are moredifficultforthe alternativetheoriesto ex- plain.If largerfirmsarebetterinnovators,they mightbe expected to generateatleast as many, if not more, innovations per dollar of R&D thanthe smaller finns. Yet the cross-sectional regularitiesindicatethatthe numberof patents and innovations per dollar of R&D declines with firm size. In terms of the significance of early entry, none of the theories emphasizes the importanceof entrytiming in conditioning the length of survival of firms that entered priorto the shakeout.'9Yet the cross-sectional regularities indicate that among products ex- periencing sharp shakeouts, the date of entry was an importantdeterminantof the length of survival for the preshakeoutentrants.20 Thus, the alternativetheories cannotreadily explain all theregularities.This does notimply that the forces they feature are not operative. Indeed, these forces are largely complemen- taryto the ones featuredin the model. Judging fromthe cross-sectional regularities,however, the model appearsto captureimportantforces that arenot presentin the other theories. VI. ImplicationsandExtensions The notion thatentry,exit, marketstructure, and innovation follow a common patternfor new productshas become partof the folklore of a numberof disciplines, including econom- ics. Although the features of this pattern are based on a limited number of products and much of the evidence is impressionistic, they appear to resonate with our experience. De- spite its popularity, though, there are many skeptics about the PLC, both in terms of its logic and its universality. The principal pur- pose of this paper was to shore up its logical 18Hopenhayn(1993) also posits other,nontechnology- basedmechanismsthatcould triggera shakeout.These are not considered because they cannot address the cross- sectional regularitiesinvolving R&D. '9In eachtheorythe shakeoutis triggeredby events whichchangethe basis for competitionamongincum- bents,whichif anythingmightbeexpectedto undermine thevalueof priorexperience. 20Moreover,itdoesnotappeartobetheshakeoutitself whichaccountsforthiseffect.Klepper(1996)findsthat differencesin survivalratesforthepreshakeoutentrants weremostpronouncedwhentheywereolderandhadsur- viveda numberof yearsof the shakeout.In themodel, thiscanbe explainedby the selectionprocess(compare Klepper,1996).Onaverage,laterentrantsarebetterin- novators.Atyoungages,thiscanoffsetthedisadvantage of lateentryfor firmsurvival,butas firmsage andthe selectionprocesscontinuestooperate,eventuallylateren- trantsmustexperiencehigherhazardrates.
580 THEAMERICANECONOMICREVIEW JUNE 1996 foundations by showing how a simple model could explain all the central features of the PLC. The proposed model groundsthe PLC with two simple forces. One is that the ability to appropriatethe returns to process R&D de- pends centrally on the size of the firm. The other is that firms possess different types of expertise which lead them to pursue different types of product innovations. The advantage of size in process R&D causes firm process R&D to rise over time andeventually puts en- trantsat such a cost disadvantagethatentryis foreclosed. After entry ceases, firms compete on the basis of their size and also their inno- vative prowess. As firmsexit and the number of firmsfalls, the diversity of productR&D is compromised, causing the numberof product innovations and the diversity of competing product variants to decline. The same two forces also explain the relationshipwithin in- dustries between firm size and total R&D spending, relative spending on product and process R&D, the productivity of R&D, av- erage cost, andprofitability.The ability of the model to explain these cross-sectional regu- laritiesin additionto the temporalpatternsthat define the PLCprovides supportfor its expla- nationof the PLC.It also lends credenceto the PLC as a leading case thatcapturesthe salient features of the evolution of technologically progressive industries. A number of stylizations were invoked to highlight the two key forces featured in the model. Perhapsthe most noteworthywere the assumptionsthat average cost was a function of only contemporaneous process R&D, de- cisions were made solely on the basis of short- termprofits,andallinnovationswereultimately embodied in the industry's standardproduct. Although relaxing these assumptions would complicate the model, it need not fundamen- tally alter the ability of the model to explain the PLC. Regarding process innovation, sup- pose process improvements were allowed to cumulate. If all process improvements were assumed to be costlessly imitated one period afterthey were introduced,firmdifferences in average cost would still be a function of only differences in contemporaneousfirmspending on process R&D. Firm average costs would equal c, - I (rci,), where c, reflects the cumu- lative effect on cost of all past process inno- vations by all firms. This change would not fundamentallyaffect the model.2'Even if cost differences across firms were allowed to cu- mulate,it would only reinforcethe advantages of the largest firms. If firms were allowed to be forwardlooking, all firmswould accelerate the growth in their output to take account of the advantages of size in R&D and accord- ingly undertakegreaterprocess R&D in each period(Klepper, 1992). But given the costs of expanding output, firms would still grow by finite ratesin each period andit would still be advantageousto enterearlier.Indeed,the firms that would accelerate the growth in their out- put the most would be those that expected to survive longest, which would be the firmsthat entered earliest with the greatest innovative expertise. Thus, allowing firms to be forward looking would notaltertheadvantagesof early entryandgreaterinnovationexpertiseandthus would not fundamentallyalter the model. Fi- nally, suppose some productinnovationswere not embodied in the standard product but formed the basis for separateproductniches. If all permanent product variants could be costlessly imitated one period afterthey were developed andprocess innovationlowered the average cost of all product variants, then the implications of the model would not change. All firms would produce all product variants andthe incentives for process R&D would de- pend on the total outputof all variants.22 The depiction in the model of how market structureand performance evolve over time for new productsis differentfrom the conven- tional industrial organization paradigm on structureandperformance.Historically,indus- trycharacteristicswere seen as shapingthe na- ture of firm cost functions and barriers to entry, which in turndeterminedstructureand performance. With few exceptions, firm dif- ferences within industrieswere thought to be 2' The only implicationof the model thatwould change is Proposition 3, which would requirefurtherstructuring of the model to establish. 22The only way the model would be fundamentallyal- teredis if eachproductnicherequireditsown processR&D. In this case, each productniche would be analogous to a separateindustry,and the model would no longer be a model of industryevolutionbut of industryfragmentation.
VOL 86 NO. 3 KLEPPER:INNOVATIONOVERTHE PRODUCTLIFE CYCLE 581 irrelevant(Mueller,1986pp.223-24). Inre- cent years,however,it has been recognized thatfirmdifferencesmaybe at the rootof a numberof importantphenomena,suchas the positivecorrelationacrossindustriesbetween industryconcentrationratiosand mean firm profitability(Harold Demsetz, 1973). The modeltakesthis approacha step furtherby embeddingdifferencesin firmcapabilitiesin anevolutionarysettingin whichexpansionin outputat anygiven momentis subjectto in- creasingmarginalcostsandfirmsize imparts an advantagein certaintypes of R&D. The resultis a worldin whichinitialfirmdiffer- encesgetmagnifiedas sizebegetssize,which impartsanadvantageto earlyentryandleads to aneventualdeclinein thenumberof firms andtherateof productinnovation.23 The starknessof the modelprecludesany departuresfromthisevolutionarypattern.This can be remediedby allowing for random eventsthataltertherelativestandingofincum- bentsandpotentialentrants.Forexample,if cohortsdifferin termsof the distributionof theirinnovativeexpertiseor if the innovative expertiseof incumbentsis underminedbycer- taintypesof technologicalchanges,thenlater entrantsmayleapfrogovertheindustryleaders andthefirmsthateventuallydominatethein- dustrymaynotcomefromtheearliestcohort of entrants.24Someproductsaredescribedas eventuallybecomingcommodities,whichcould beaccountedforinthemodelbyallowingtech- nologicalopportunitiesforinnovationeventually to dryup.Incumbentfirmproductandprocess R&Dwouldtheneventuallydeclinetozeroand theadvantagesof earlyentrywouldeventually be eliminated,allowingthenumberof firmsto stabilizebeforethe shakeoutof producershad runitsfullcourse.Themodelcouldalsobegen- eralizedtoincludeotheractivities,suchasmar- ketingandadvertising,thatcouldsubstitutefor processR&D in impartingan advantageto largerfirms (Sutton, 1991).25 While these generalizationswould no doubt enrich the modelandallowittoaccommodatedepartures fromthePLCthathavebeenobservedinsome technologicallyprogressiveindustries(com- pareKlepper,1992), eveninitsstarkformthe modelis ableto addressa widerangeof reg- ularities.Itdemonstratesthatmanyaspectsof industryevolutionand heterogeneitywithin industriesin firmR&Deffortandprofitability canbe explainedby couplingrandomdiffer- ences in firmcapabilitieswith advantagesof firmsize conferredby R&D. REFERENCES Abernathy, William J. The productivity di- lemma.Baltimore:The JohnsHopkins Uni- versity Press, 1978. Abernathy,WilliamJ.;Clark,KimB.andKantrow, AlanM. Industrialrenaissance:Producinga competitivefiture for America. New York: Basic Books, 1983. Abernathy,WilliamJ. and Utterback,JamesM. "Patternsof IndustrialInnovation." Tech- nology Review,June/July 1978, 80, pp. 41- 47. Acs, ZoltanJ. and Audretsch,DavidB. "Inno- vation in Large and Small Firms." Ameri- can Economic Review, September 1988, 78(4), pp. 678-90. . "R&D, Finn Size, and Innovative Activity," in Zoltan J. Acs and David B. Audretsch,eds., Innovationand technolog- ical change: An international comparison. New York:HarvesterWheatseaf, 1991, pp. 39-59. Aitken,HughG.J. Thecontinuouswave: Tech- nology and American radio, 1900-1932. Princeton, NJ: Princeton University Press, 1985. Anderson, Philip and Tushman, Michael L. "Technological Discontinuities and Domi- nant Designs: A Cyclical Model of Tech- nological Change." AdministrativeScience Quarterly, December 1990, 35(4), 604- 33. 23The welfare implications of these and other predic- tions of the model are developed in Klepper(1992). 2 These andothergeneralizationsof the model arean- alyzed in Klepper(1992). 25Indeed,for some industrieseven productR&D could play this role, althoughit would seem as if firmsize plays a more importantrole in conditioning the returmsto pro- cess than product R&D. This issue, and others, such as why firms are limited in their ability to control their in- novation expertise, involve key aspects of the model that merit furtherstudy.
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