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

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
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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).

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.

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.

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.

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

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

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.

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.

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

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.

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.
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