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ECONOMICS OF INNO" ATION:
BlACK HOIJE OI~ I)OSl'flVJi: SUM?
Ralph Young
CSIRO Curporate Phllll1ing Office
P~)per
prepared for prcscnlatiol1 to
37th Annual
(~onrercnce
Ausralian Agricultural Economics Societ)'
University uf Sydu(')'
Februnry 1993
ECONOMICS ~)F INNOVATION: BLACK HOLE OR POSITIVE SUM?
Ralph Young
CSIRO Corporate Planning Office
tfA civilisation which ca1lnot burst through its abstractions is
doomed to :.;terility after a very limited period of progress"
A.M. Whitehead l
In recent decades, the dominant theory of macroeconomic growth has been the
neoclassical model based on the work of Solow (1956, 1957) ,md Swan (1956).
Technological change is acknowledged ·'lS the crucial driving force behind economic..
growth, but is treated as an exogenous vari.able. In consequence this -basic
neoclassical model is quite limited in its ability to explain economic growth. 2
Sheehan (1992) suggests this constitutes "something of an admission of defeat for
economic analysis".
TIle view that technical change is endogenous rather than exogenous to economic
growth is not new. Schumpeter J042 and Arrow 1962 hoth emphasised investment in
innovation as central to economic growth. Schumpeter stressed the importance of
economic incentives for entrepreneurs to introduce innovation, and the diffusion
process whilst Arrow focussed on the spillover effects of increased knowledge due to
"leming oy doing". The work of Schumpeter and Arrow fonn the acknowledged
antecedents for lht' new economic growth models.
Disatisfaction with· the haf)ic neoclassica.l model was also a stimulus for the
evolutionary the'ory of innovatiun and growth which built on dw seminal work of
Nelson and Winter 1974. 111is body of literature treats technological change and
innovation as endogenous to the process of economic growth and seeks 10 eliminate
the gap between the basic neoclassical model mld the empirical evidence of the
microecononllc hterature pertaining to the economics of innovation (nasi 1988; Dosi
et a/1988; Freeman 1990).
Similarly the new economic growth models have grown out of dissatification with the
perfoIDlance of the neoclassical model in explaining and predicting economic growth.
l1lis work hat) been pioneered by Rom ~r (1986). Features of these new growth
theories include endogenous teclmical change, investment in human capital andlor
research and innovation as key sources of growth, and increasing returns. Despite the
correspondence of their origins and the overlap of their subject matter, there is
surprisingly little or no cross referencing between the economics of innovation
literature and that of the new economic growth theories. Nevertheless, the l1lpidly
expanding new econom.ic growth literature has been hailed by Sheehan 1992 as
bringing "greater realism to growth theory" and being a contributor to "a fundamental
2
Quoted in Clark 1985.
For recent reviews of the basic neoclassical model and its ltmitntions see BIE
1992, Lucas 1988 and Sheehml 1992.
2
change in. the way economists; and ultimately govemmentandbusiness leaders in
Anglo-Saxon countries think about basic issues of growth and trade and the way they
develop 'policies for industl)' and technology".
TIle aim of this paper is to consider the processes of innovation spedfied futhe new t
growth models and their policy implications, to assess these innovation processes in
the context of the innovation economics literature and to look at possible future
directions for research.
The Processes of Innovation in the New Growtb Models
The literature on the new growth theories has been extensively reviewed p!cently by
BIE~ 1992, Sheehan 1992 and Verspagen 1992, I do not propose to replicate their
work~ but will draw on it to focus on the processes of innovation specified in the new
growtll theories.
A feature of the new growth models is that innovation and growth are endogen0us.
nlis iInplies that these olodels face the problem of accommodating increasing returns.
Followmg Sheehan 1992, two basic approaches have been adopted.
•
treat increasing returns as extemaJities;
•
treat jncreasing returns as monopoJi<;tic competition.
TIlese are Imp0r1ant and novd features of the new growth models and are associated
with the public good aspect: of technjc~il knowledge and the appropriability of
innovation Ie the private ~ood a~pect~.
The different approaches to incorporating extemabilities ,md increasing returns to
scale are summarised in tabular [oml by Verspagen 1992 and are shown in TahJe 1.
In the early papers hy Romer (1986) and Lucas (J988)~ competitive markets are
assumed and increasing returns are based on externalities in production associated
with knowledge accumul~ilion (learning by doing) mId hmmm capital accumulation
via increasing ski111evels.
Romer 1990 acknowledges t.hat the leanling by doing formulation ha~ the advantage
of making the rate of accumulation of nonrival knowledge endogenous but "is
unsatisfaclOfY because it takes the strict proportionality between knowledge and
physical capital or knowledge ,md education as an unexplained and exogenously
given feature of the technology". This fannulation thus ignores the appropriability
issue and "rules out the possibility t.hat finns ma.1ce intentional investments in research
and development".
Later Inodcl~ building on the seminal efforts of Romer 1986 and Lucas 1988 have
attempted to address this issue. Most notable are the papers by Romer 1990 and
Grossman and Hclpman 1989, 1990, 1991. It is on these that we focus our attention,
3
In introducing monopoly powe.r, twoaItemative approaches are adopted ... one
involves innovative products whlchadd to thee:dsting variety; the other involves
inuovation products which are .ofhlgher quality (Sheehan 1992).
Romer 1990 specifies three premises to justify his introduction of monopoly power. •
•
teclmological change - improvement in tbe instructions for mixing together raw
materials - lies at the heart of economic growth
•
technological change arises in large part because of intentional actions taken by
people who respond to market incentives ie endogenous technological cbange
•
instructions for working with raw materials are inherently different from otber
econorruc goods. Once the (fIXed) cost of creating a new set of instructions has
been incurred, the instructions can be repeatedly llsed without additional cost.
To incorporate these premises in his model, Romer specifies two components of
knowledge: human capItal, H, which is flval, and teclmological knowledge, A, which
is non-rival and can grow without bound; three sectors : a research sector which
produces designs for new durables, an intennediate goods sector which uses the
designs to produce durable goods and a final goods sector which uses theintennediate
goods to produce final consunler goods; and four inputs : capital (K), labour (L),
human capital (It) and an index of the level of tedmology (A). K and L are fIXed.
In tbe research sect.or, the accumulation in the stock of designs evolves according to:
where:
8 .- a constant
HA thl' quantity of human capital employed in research
ie HA + Hy ~ Ii and By = the amount of H and devoted to
production.
=
On this basis, the productivity of research vades linearly with the growth in
technological knowledge and the marginal productivity of HA continues to grow in
proportlO11 to A. According to Romer, the cru.cial feature of this specification is that
"knowledge enters into production in two distinct way", A new design enables the
production of a new good Ulat can be used to produce output. A new design also
increase.') the total stock of knowledge and thereby increases the productivity of
u
human capital in the research sector •
'nle intennediate good\) sector is monopolistic with one finn i for each durable good j
t
using a fixed number of units of foregone consumption n to produce each unit of
durable good. 'I11e initial expenditure on the new design is a sunk cost, and hence the
monopolistic firm chooses the level of output (x) to maximise its revenue minus
variable cost at every date. The flow of rental income is p(x) times x and it turns uut
that the monopoly price is a simple mark up over marginal cost.
4
In addition there are two non-convexitiesinthemodel.' One ism fmal out}?ut "" the
existence of monopolistic c;ompetitioltin .theintennediate sectorrneansthat the price
of durable goods to the consumer goods sector will 'be higher than incompetition~
while in theresearchsectof, investment in l~arcb will ignore the impact ofthe:;todt
of designs, A, on the 'productivity of the research sector (Sheehan 1992).
Romer also shows that in the equilibrium steady state, growth occurs ata rate equal to
the rate of endogenous innovation, a rate which is less than the social (command
economy) solution, implying a role forgovenunent to support the accumulation ofA.
ParatleIing the analysis of growth ba.~ed on increasing variety of products, has been
the ancuysis of quality improvement in products. The key contributors are Aghi.on
and Howitt 1990 and Grossman 2nd Helpman 1991.
A major feature underlying the model developed by Grossman and Helpman is the
concept of a qu"liry ladder of a fu(-d range of consumer goods. The highestq!1ality
product enables the producer t~ capture monopoly profits, R&D activities achieve
quality increments and hence with each new innovation builrlingon the previous one,
the productivity/quality of the intennediate/consumer goods is always higher for the
next innovation. 111e research teclmology is similar to the product variety case with
technological spilluvers to all films from prior research and the capturing of
monopoly profits by quality leaders.
luere is also a negalive externality in the model - labelled "creative destruction" Of
"business stealing". it arises because a new innovator destroys the monopoly rents for
the previous iIUlovator.
In these quality models. technological advances ;rre essemjalJy stochastic, with
research succes~ bein:' dependent on the runount of human capital. As a result, this
specificmion cnptures the uncenainty \\'hich characterises the innovation proces~ lU
tht! real world (Verspagen 1992).
In summary the achievement of endogenous technological cbangeis based on the
assumption of a distinction between appropriable and non-appropriable effects in the
production of itmovation~ which in tU01 is required to provide incentives to produce
innovation in the presence of extemabilittes associated with the non-appropriable
effects of innovation. To. achieve appropriabiJity some degree of monopoly power is
a">sumed.
Policy Implications
Sheehan 1992~ following his review of the new growth models, idcnlifies four main
policy related themes which are "often quite at variance with received doctrine
It.
For a discussion ot the reJevance of nonconvexlties for growth~ se~ Romer
1990a Romer concludes that ttnonrival goods exist, that they are important for
3
aggregate growth, and thrt they create nonconvexities that matter for aggregate level
analysis",
5
These are:
•
Suboptimal market solution - the nlaiket growth rate is typically less tbanthe
social optimum, but in the case of modelsincolpOratmgnegative externalities
(Aghion and Howitt 1990, and Grossman and Helpmaa1991),ilie direction·of the,
net effect is ambiguous".
•
policy action will increase growth ie interventions targeted at ale source .ufthe
deviation from the social optimum will increase growth. Examples include
subsidies to R&D, subsidies to investment in human capital and subsidies to
innovation.
•
Generating compamlive advantage .. when growth is driven by innovation or other
extenlalities which are geographically concentrated, mitial conditions can
generate major long tem.1 differences between countries in comparative advantage
and growth potential.
•
Low growth traps - an implication of many of the models is thaI a country which
is specialised in industries which are deficient in relevant respects nmy be trapped
in a low growth situation under free trade. (see also BIE 1992).
Romer 1990 makes the point in relation to input subsidies that Hwhen the decision t.o
invest in physical capital i~ uncoupled from the decision to invest in research, the
effects of a subSIdy to physical capital are quite different from the effects of a
reduction in the mtrket interest rate". Romer concludes that "Although all the
research is embodieo in capital goods, a subsidy to physical capital accumulation may
be a very pOlir substitute for direct subsidies that increase the incentive to undertake
re~earch."
The re~earch sector in the Romer 1990 model is characterised by increasing retuOlS.
such that doubling of both human capital and the stock of knowl.edge leads to an
increase in the marg.inal product of human capit J.1 and a more than proportional
increase in the amount of human cnpiull devoted t.o the research sector - see Figure 1.
Romer considers this result to be consistent with trends observed in the real world.
Romer 1990 also points to the possibility of stagnation occurring if H is too Illw
because of a binding nonnegativity constraint on the amount of human capital in t.he
research sector {HAl. In such a situation growth does not take place - see Figure J.
Romer explains this phenomenon in tenns of all feasible rates of growth for A being
too small relative to the discount rale to justify the sacrifice in current output
necessary for growth to take place, and suggests that this result offers an explanation
for the wide variation in growth rates observed among countries. The proposed
solution for such a country is to engage in trade with other countries which has a large
amount of human capital. The stimulus to growth in India and China resulting from
the (partial) deregulation of trade and investment may provide support for lhis view.
4
At an aggregate economy level, it is not clear that business stealing wiU
reduce consumer surplus since each suc....~edjnb inllov~tion must represent an
improvement over the previous one. At an industry level, however, this may not be
the e,LS<! as Grossman and HeJpman acknowledge.
6
In the contex,tof subsidising researr -: .R01l1er 1990 comments that two ,reasons can be
e4pCCtedto account fQc i4~~ffi.cient hmnancapital devoted to x-esearcb. Oneisthat
research has positive extemal effe:C1S hut because these take the {onn -of
nonexcludable benefits, they are not .reQectW in the market price of the research,
output. Thesecond~asQn is that research produces an input to a sector which
engages in monopoly pricing which "forces a wedge between tbe .marginal social
product of an input used in thlssectorand its market compensation".. Both of these
effects cause human capital to be undercompensated whk,h in tum will cause the
supply to be "too low", Romer proposes that a .govemmeot which cannot affect the
allocation of human capital between different sectors should adopt a second-best
policy of subsidisil1g the production of human capital.
I\·ticroeconomic ASfJt.~lS of the Innovation Process
Auempts in the more recent nlodels of the new growth literature to develop a
microeconomic framework to incorporate various aspects of the innovation process
undoubtedly achieve a greater degree of realism. Inevitably, a significant level of
abstraction is also involved. In this section, the aim is to review the main features of
the innovation process identified in the recent innovation economics literature and to
assess whetllcr any significant gaps still remain to be addressed by the new growth
models.
Features of the innovation process which ate repeatedly strersed in the innovation
economics Iherature are the complex ity of the innovation process, and the significant
differences between sectors (see for exc:unple Dosi 1988, Schererlt)92. Pavitt 1984,
Nelson and \Vinter 1974). 11 is usually taken as read that t.edmoJogical innovation
represents a cruCial factor in the dynamics of economic growth.
Four ba~ic modes of technological advance are identified by Dosi 1988a:
•
fonnalised and economically expensive processes of search eg R&D laboratories
•
illfomlal processes of diffusion eg publicati()ns, techmcal associations
•
learrung by doing and learning by using
~
adoption of innovation developed in other industries and embodied in capital
equipment and intennediate inputs.
Dosi 1988a summarises the innovation process in the foHowing teons ..... t. the process
of innovation in Westem economies embodies complex and varying baJances between
public and proprietary fonns of knowledge, and different combinations between
notional oppo.rtu nj ties of innovation, finn based capabilities to reap these
opportunities and (.~onomic jncentive~ to do so (related to appropriahility
mechansisJns. market conditions, rehttive prices, broat!~r socio-economic conditions
such as industrial relations) .............. technology..specific forms of dynamic increasing
returns t~nd to ~llock-in" the. pro~ses of technical change into particular trajectories,
entailing a mutual ff ,m Jrcement (a positive teedback) between it certain pattern of
7
learning and .a pattern ofalloccuionQf resources into lnnovati\'e .activities where
learning has aXceady occurred in the past"•
Particular aspeCts of the innovation process are highlighted by Dosi 1988 as "stylised
facts"~
•
illnovationinvolves a fundaxnenta! element of uncertainty
•
increasing reliance of major new technological opponunities on advances in
scientific knowledge
•
increasing complexjty of research and innovation militates in favour of fonnal
organisations rather than individual innovators
•
a significant amount of innovations and improvements originate from learning by
doing and learning by using
•
technical ch:wge is a cumulative actIvIty, and the probability of making a
technological advance is ~l function of the tedmoIogical levels already achieved.
TIle mtroduction of stochastic product improvement.f) by Agitjan and Howitt 1990 and
Grossman and Helpman 1991 represents a step towards dealing with lhe uncertainty
issue. Howeyer, Dosi 1988a claims that. innovation search is characterised by strong
uncenamty, which is more th~m the imperfe.ct inlonnation of economic analysis. The
501u11on prcp<,sed by Gold I QRO, and Winter 1986 is to employ the concept of
bounded rationality 1.0 the adaptive and ieanling behaviour of economlC agents subject
to severe Iimitions on the capacity of finns to make ex ollie assessments of future
changes in the environment.
Many of w'! other features of the immvc.uion process identified in the innovation
economic literature including the endogenous nature of the proces:) (see Allen 1988.
Clark and Juma 1988); the cumulative and path dependent nHture of technical change
based on technological paradigms and traject.ories (see Arthur 1988, Freeman 198B;
Dosi 1988. 1988a; Nelson 198~); the interaction of demand ,md supply forces in the
selection process (see Nelson lQi'S~. Dosi 1988; Kline and Rosenberg 1986), and the
distinction betw . . l~n public and private al)pects of knowled!te and the associated
externalities and fh.:.:d tor monopoly power which from the ba.~is of increasing retums
(see Allen 1988; Art.hUf 1988, Freeman 1990, Dos! 1988); appear to have been
incorporated into the Jatest versions of the new growth models (see forex,unple
Romer 19(0).
The most trenchant criticism of the orthodox view relates to the dynrumc tUld
evolutionary nature of the innovation process which is better characterised by
disequilibrium and profit seeking rather than equilibrium and profit maximising.
Nelson and Winter 1974 observe that neochL'isical theory ha') an "explicit or implicit
commitment to the assumptions of faultless maximisation and equilibrium. Very few
of the studies {In a survey b} Kennedy and ~nlirwaIlI ......concemed with the proces~cs
of technical ch,Ulge employ these assumptions. Several.... implicitly deny diem.
However if equilibrium is not Ubed to "close" the modcl~ some ;dtemative is required.
Just a") the Jn2.croeconomic growth theories are evolving to encompass a more
8
sophlsticatedmlcroeconomicfnmlewoIk~the evolutionary theories of growthseern
also to be evolving from the descriptive to a Itu;~:refQnnal modeUingbas;stbuilding on
tbeearly simulation work ofNelsQn 'and Wi~(ter 1974.. One example is the use of the
principle of economic sel~on in a moddlirtg framewotkby Silverberg 1988.
Future Directions
A number of fundamental problems for economicrutaIysis are raised by the new
growth modrls and Sheehan indicates that lht!se wIll foml an important basis for
future resea rch. TIlese are issues which have also been identified intbe innovation
economics iterature referred to earlier.
I
•
Increasing
retulTI}' the nonconvexit.ics associat,ed with increasing returns means
that "standard competitive ru.alysis will not apply" (Sheehan 1992). Sheehan
1992 and HIE 1992 refer to evidence indicating that many modem industries are
characterised by large economies of scale which arise from "massive sunk cost
investment" in plant and equipment. in R&D, and in education and training, from
cumulafive learning by doing benefits llld from complemen.t:nrities and
cooperative linkages. Sheehan argue~ that ~,lese elements are neitherextemal nor
exploited in a Inonopolistic situal n. but are key elements of competitive
strategy. lbe issues of increasing returns and market power are likely to receive
continuing attention ill future research.
•
Multiple Equi •• oria: one example, the Jow gro\'.·
to. Sheehan 1992 identifies four distinct SOUCt
growth m{)de1~ and suggests that this issue wi]
model unalys is
•
ExpectHuons: mo~t of the new growth models are bas(!d on perfect foresight
equHibda. rille a-;sumption of mtional expect ions on the part of economic agenL~
has been criticised in the evolutionary theory literature. Versp:\gen JtJ92 ohserves
that the implicit assumption of f'lltionai technological expe .ltion~ in the ne\v
growth theories combined with the assumption of optimising hell a ,'iour gives
most of these models strong equilibrium characteristics. EmpiricaJ research is
needed to <k:tennine whether the lauer approach. or the disequilibrium process
characterised by cvolutioozU)' theories is more useful.
'ready heen referred
Iple eqiHbria in the new
.;, centre of future growth
Indeed. there is wide agreement (Romer 1990a; BIE 1992, Sheehan 1992, Verspagen
1992) that funher research is required not only to make the new growth models more
useful tor policy guidance but also to give Ulem empirical validation.
In the context of innovation strategy for AustJatia. DIE 1992 concludes that it is foo
early to draw positive conclusions. and that more research is required before the
models can be accepted as provid.ing an adequate exphmatioJl of the growth process.
It seems lih.cJy that t.he contributors to the new growth theories would ,not djsagf'~t!
with such a view.
Nevertheless, to the extent thHt there is agreement that the new growth models
achieve a greater degree of realism. wld it can be assumed that further modelling
9
work is likely to confinn the view that govf.!nunent bas ,a positive role to play, the
question arises as to what fonn this role Inay take. .In a recent analysis of the
Australian innovation system, Gregory questions the demand for adjustment aimed at
increasing productivity and economic gro\\'th. The demand for adjustment is
focussed on increasing private sector R&D, .t:~ geting .government research more.
towards national priorities, increas'vl ~ competition in the research community and
expanding the education system. These measures might have plausibly come straight
from a proponent of tbe new growth theories.
Gregory's concern is based on a number of factors:
•
1110se parts of manufacturing involved is substantial R&D expenditure are
shrinking as a share of tomI employment;
•
The paradox that a country which has never lmd a comparative advantage in high
technology manufacturing is discussing solutions to balance of payments
dificulties in tenns of R&D expenditure to stiInulate high technology
manufacturing; and
•
'llle concentration of R&D within a few finns and industries suggesth R&D policy
will not have sufficient leverage on the economy as a whole.
Greg(uy concludes that t1there ha5 been a significant overselling of 'he economic
benefits of a govenuuent led science and technology push", and tbat it may be best to
think of the National Innovation System in tenns of micro refol1ns, thnt is doing
things better rather than thinking of thl~ syMem as an instrument of mncro policy that
will significmnly cluUlge the structure of l.hc Aust.ralian economy.';
Recent eventh in the Australian economy including the very rapid growth in the
export of ETM's and the emergence of high value-ndded manufactunng fiml'> which
uccounted for $8.3BilIjon in exp0l1s in 1992 nnd .an.~ growing at 13% compound real
per annum (McKinsey & Co. 1992) suggest that there lllay be more prospects for a
demand puH than ,Ul S&T push in relation to Rl~: D and innovation. Rather t.han wait
for events to unfold in the traditional "shetn be right" idiom. there flU), be merit in
giving some urgefl\..) and priority to the fChcarch needed for the empirical iesting of
the new growth models in an Australian context.
10
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[.lI('il<;,
1.\1('<1 ..
lHSR)-I
one ('onSH mi'r
good
(1 H'SH1-1t two consumer
goods
research; interAghion nnd
mediate
Howitt (1990)
goods; con0;\1 mer good
Grossman and
H<.>lpman
(lHf.lH) and
(WOO)
rt'search & inh'rnwdi;:ttc
goods, (,Ollsumer good
HI no-
l'nlrf'U'
procP'" mnovutiOlI thr()u~h
knowl.·{lg(· :wcl1mlllation
t ""
dllTl
tl
Ii : :
&(1 -
('0"('
provements in ' lut';" ints
for interl'Y't'niatf" ':00 Is
intertemporal impr{)V(
ments (positive); htl
rest'arch & con- improvements in qualaty of g(n
suntcr good
eonsum('r good
HOO1('r (1900)
research & In-
fJ.'
i
in con'iumf'r good
sector:
x(;)"
tIlr)
via utility function
knowledge SPl!Jovcrs
research & intcrme
ate sector (positivp)
intertempornl improv.
mf'nts. consumer
51
plus (positive); busi
ness stealing effect
(negative)
termediate
goods; con-
sumer
addition of n(>w lnter-medlatt' goods (Ethlt'r pro-
,\ .,. N(A ... fI ... n)
in consum!'r good
research & interme
L"
ate sector (positive)
duction [unction)
II"L"
~oods
rlll .. "u).unn not "('par lIt·" It\
il
.. !tOllhl
hf' Inft·rpn·tf'tI
:1\
knowledge spillovers
sector:
%(')'-'-. dl
\vHh x(il
:> n
"ElIIIII'S 111
from average humnn
capital (positive)
ness steaHng effect
(negative)
d
+. [f
duction runction)
Pi ~';ut'tivfty stimulus
frmn average human
capital (rr"itlve)
in consumer good
1o;('ctor:
o
rt)
J;";
productivity stimulus
L(('en)
",n onf' (·(lulhtn.·d
!oil'f
lor··
"=
=
T growth in stock of ktlowlcdJ
I = investment in research
L = conventional input eg labou
i ith finn
=
in consum('r good
s{'('tor. F(Ji)
x{i)
GrO'isman nnd
II(-)pman
(}99l)
knowlc·dge spillovers
(p()~ilive)
.n ('OI.'illmf'r good
~('f'tor; F(A. II.
tI)
fi = N(A", /I".
Votaliml
/.',(T,. 1". i.-1 T')
Ii
addition of new ifltermC'diale t!oorls (Ethit'r pro-
gnod
... ('('Inf
human (> .. pitat uc('umlllation II
through learning by
== ou
doing
(',(l) =
ExH!('fW/itil'.S
of itwountion
J>lrurture
III (,otl'iUnH'f
')(lllnth·d
from nhov('
irlll()("
nwdr/
arltm
nwdrl strurtur('
human ratiltal Ilccllmulation II
Ihmllgl. s:lVin~
stochastic (poisson \ im-
/':{frrf\' of
ftl1wnlliot)
0 ror i
H - humnn capital
u - there invested in skill enhunc
A techll ()logy level
=
see above
c = production costs
i intennediate good
=
y =size of innovation
=
=
=
n number of designslblucprinu
A productivity parameter
H human capital
x = intennediate good
=
=
=
g fixed range of consumer goo
J.1 n parameter
j index for highest position on
n =number of designs
A productivity parameter
=
H ~.; human cnpital
x = intenncdiare good
Sflurce: Verspagcn J992
FIGURE 1
o
.. ~ .. ",,, .... Ap
H
... .
AD
..
- G/\T!
hUlllan
-Growth rate and aOlount of human capital in research as a function of total
capital (fOI B = 1).
Source: Romer 1990