THE SOUTH AS AN INNOVATOR TOO: FACTOR ENDOWMENTS, NORTH-SOUTH
TRADE, AND ENDOGENOUS GROWTH
by
Basant K. Kapur
Department of Economics
National University of Singapore
July 2009
Abstract: Southern countries have increasingly become innovators, and not simply
imitators. We study this phenomenon here. Our model synthesizes elements from
endogenous growth (profit-motivated R&D under monopolistic competition), earlier
trade theory (the roles of factor endowments and intensities, but with each country’s
skilled-labour endowment required for R&D as well), and the North-South literature
(differential inter- and intra- national spillover effects from sectoral production to
R&D). In equilibrium, South conducts R&D in the less skill-intensive product. An
increase in North’s skilled-labour endowment could either increase or decrease the
skilled-labour wage: it increases South’s innovation rate too. Other unexpected results
are that trade might make North worse off, and an increase in South’s skilled-labour
endowment might reduce world innovation and well-being. The latter will not occur in
the social planner allocation, which, further, varies significantly with consumer demand
patterns.
I Introduction
An extensive literature on North-South trade, growth, and R&D has arisen over the past two
decades (see, for example, papers cited by Gancia and Bonfiglioli (2008)).
This growth
literature, without exception,1 treats the South (S) as at most an imitator: it does not originate
new products, varieties, or processes, but usually at some cost learns to imitate what has been
developed in the North (N). This paradigm is rapidly becoming dated. As discussed in more
detail in Section II, with globalization and the vast improvements in information and
communications technologies (ICT), countries such as South Korea, Taiwan, China, India, and
Brazil have developed significant, and growing, innovational capabilities, which have resulted in
a wide and increasing range of product and process innovations.2 Innovations have been both
horizontal – the development of new final products and varieties – and vertical – the
development of improved production components or processes, often associated with vertical
production chains operated by multinational enterprises (MNE’s).
It is thus timely to initiate the construction of growth models which feature an innovational
role for S, and this article marks a first attempt in this direction. We focus on horizontal
innovations, leaving the study of vertical innovations to subsequent research.
Our model
synthesizes elements from endogenous growth models (profit-motivated R&D under monopolistic
competition), earlier trade theory (the roles of factor endowments and intensities, but with part of
each country’s skilled-labour endowment required for R&D), and the North-South literature
(differential inter- and intra- national spillover effects from sectoral production to sectoral R&D):
the resulting complexity produces valuable insights, but unfortunately, for reasons of tractability,
permits only a local analysis, as explained further below.
In Section II, we discuss the empirical trends which motivate the present analysis, and briefly
review the related literature. Section III sets up the model, and characterizes its equilibrium
1
Chen and Puttitanun (2005) develop a short-run partial-equilibrium model with two innovating
firms, one in the North and one in the South, and two imitating Southern firms, and study how
the optimal degree of intellectual property rights protection in the South varies with its
technological ability.
2
South Korea and Taiwan are usually categorized as newly industrializing economies, but one
may define the South broadly to include all non-North economies – a convention that is widely
followed in writings on North-South trade, e.g. Dinopoulos and Segerstrom (2004) and Falvey
et. al. (2006).
1
properties. In Section IV various comparative-dynamic experiments are conducted, and in
Section V the Social Planner’s optimum is characterized. Finally, Section VI concludes.
II Recent Developments
Horizontal innovative activities in S have often arisen after the companies and industries
concerned have developed capabilities in intermediate-goods production and R&D. Perhaps the
most noteworthy example is Korea’s Samsung Group: ‘Within a decade of launching its first
memory chip [in the mid-1980’s], Korea’s Samsung had become the world leader in flash and
memory chip production. This company and LG Electronics have capitalized on their lead in
digital technology to become forces in the markets for flat-panel displays and digital mobile
telephones’ (Yusuf (2003), p. 327). Samsung now innovates in and produces a remarkably wide
range of consumer products – mobile phones, LCD and plasma TV sets, home theatre systems,
MP3 players, digital cameras and camcorders, monochrome and colour laser printers, and home
appliances (refrigerators, washers and dryers, cooking ranges, airconditioners, and other items).
Underpinning this wide product range is a strong commitment to R&D, both basic and
applied. Samsung Electronics alone has 42 R&D Centres with around 26,000 employees (UK in
Korea (2009)), and each year it invests at least 9% of its sales revenues in R&D. According to a
company website, it registered over 17,000 patents in 2006, and its over-2400 patents in the US
were the second-most of any company. The quality of its products is widely-appreciated: a
market research company observes, ‘Targeting the mid-range and high-end segments (of the
mobile phone market), Samsung's strategy of small-volume production of numerous models has
created high profit margins, and built up a strong brand’ (MIC (2006)). ‘Some results of Korea
research have been world leading in their business implementation. Samsung and LG are now
world leading mobile phone and flat screen TV manufacturers’ (UK in Korea (2009)), and, for
Korea as a whole, ‘the ratio of R&D investment is among the highest in the world, hitting nearly
3% of GDP last year’ (ibid.).
A similar pattern is observed in Taiwan, in the computer industry in particular. R&D played a
major role in the development of Taiwan’s semiconductor industry, with the impetus coming
initially from government research laboratories: ‘(t)hat baton has now clearly been passed to
R&D facilities within the leading firms themselves’ (Keller and Pauly (2003), p. 149). This in
2
turn has been a major factor propelling the growth of its computer industry, with chipset design
playing a key intermediary role (Chen (2008)). In recent years, Taiwanese companies accounted
for over 80% of world laptop production (Reuters (2008)), although increasingly the actual
production is occurring in China, owing to the cost advantage. While much of Taiwan’s desktop
and notebook production occurs under contract for companies such as HP, Dell, and Apple, its
homegrown companies such as Acer and Asus also enjoy significant market shares: in 2005,
‘Acer successfully became the world’s fourth largest branded computer maker’ (EMSNow
(2006)). In recent years, major US and Japanese firms such as Intel, Microsoft, HP, and Sony
Computer Entertainment have opened R&D centers in Taiwan to take advantage of its talent
pool, research infrastructure, and proximity to customers, producers and suppliers.
In an interesting study of innovation globally, including a ranking of countries, the Economist
Intelligence Unit (EIU, 2007) reports, ‘China is breaking out of its position as a member, along
with India, of the underdeveloped world…the huge sums of money it is pouring into R&D and
education will ensure that it climbs steadily up the rankings’ (p. 14). Currently, China’s R&D
momentum is significantly MNC-driven: ‘Much of China’s inbound investment will continue to
target innovation-rich sectors such as mobile and fixed communications, aviation, vehicle
manufacturing, pharmaceuticals and foodstuffs…Multinational companies are opening research
centres in China, lured by the fact that local scientists are paid only about 20% as much as
Western scientists. To exploit this situation, more than 300 foreign companies, including major
life science firms, have established R&D centres in China.’ At the same time, difficulties
remain: ‘Problems include the rampant theft of intellectual property, academic fraud, weak
financial markets, and political meddling in science and research. At the corporate level, Chinese
innovation remains weak. Top-down government plans for fostering innovation do not
automatically lead to a strong innovation performance’ (ibid., p. 15).
Earlier known mainly as an outsourcing destination for low-cost business services, India too
has been rapidly moving up the value chain, towards significantly greater emphasis on R&D.
‘(I)t may come as a surprise that $1 billion, or about a quarter of Wipro's (a leading Indian outsourcer’s)
revenue last year, was generated through R&D services -- including designing semiconductors,
automobile parts, and a variety of electronic devices’ (McGee (2008)).
Although much of Indian
innovation is directed towards developing improved processes in manufacturing and improved production
3
components, there is a growing focus on final product and service development as well. ‘India seems to
be excelling in innovation in certain industries like automotive (Mahindra and Mahindra Scorpio 4-wheel
drive was awarded…the “Best Car of the Year” by BBC on Wheels, developed the electric car, the lowcost car, etc) or software (with Tata Consulting Services or Infosys as world players in the provision of
software services)’ (Chaminade and Vang (2008)). Other innovative areas include pharmaceuticals,
biotechnology, and new textile products and designs. As with China and Taiwan, many MNC’s have
located R&D centers in India: with vast improvements in ICT, ‘(c)ollaboration tools and disciplined
design techniques make it conceivable for people who are not in the same building to work together as if
they are neighbors…Once this "distributed development" becomes a reality, it is natural for portions of
such work to migrate to locations where large numbers of talented scientists and engineers are more
readily available. India, for example, graduates more than 100,000 English-speaking engineers each year’
(Bagla and Goel (2009)). A further noteworthy feature, in both China and India, is the conduct of R&D
activities ‘by external vendors on behalf of European and North American clients’ (ibid.).3
The foregoing review suggests three broad, partially overlapping motivations for the growth
of R&D and innovative activity in S: (a) leveraging on the know-how and experience gained from
production activities in the same or related industries; (b) the lower cost of R&D, owing to the availability
of a large pool of scientific and technical manpower (or a large patient base, as in the case of drug trials);
and (c) proximity to markets in S, especially to large markets such as in China and India, and the
development and customization of products to best suit customer tastes in these markets. Our analysis in
this paper will focus on the first two of these, leaving (c) to future research.
As pointed out earlier, the extant literature on North-South trade and growth, including Gancia and
Bonfiglioli (2008), views S as an imitator, and a related significant concern is the implications
for trade and growth patterns of imperfect intellectual property rights protection in S. Our review
of empirical developments clearly indicates, however, that some Southern nations are actively
advancing the technological frontier in certain industries or sectors, in which they have gained
valuable production experience.
With production patterns being generally influenced by a
country’s resource endowments, connexions may be discerned between these endowments,
patterns of specialization in open economies, and innovational capabilities – which this article
3
Developing countries outside Asia are also active in R&D, although they appear to have had a
slower start: for example, in 2006 Brazil’s Science and Technology Ministry launched a scheme
to support R&D in fields relating to HIV/AIDS, hepatitis, semiconductors and software,
nanotechnology, biotechnology, biomass or renewable energy, and aerospace (Ramalho (2006)).
4
explores. The Southern nations concerned are also actively engaged in seeking patent protection,
both domestically and abroad, for their innovations, and for convenience we assume that both
Northern and Southern firms enjoy the same degree of patent protection for their innovations.
III The Model
Overview
We consider a world comprising two countries (or regions), N and S. Both produce two sets
of differentiated goods in two monopolistically competitive industries, A and B: the production
functions for goods in each industry are identical, but differ across industries. Each production
function is linear homogeneous and Cobb-Douglas in skilled labour H and unskilled (or lessskilled) labour Z, and the same across countries; capital is abstracted from in the model. A is Hintensive relative to B. R&D in each industry requires only H, and serves to increase the
measure of goods available in that industry over time. Consumer tastes are identical across
countries, and the instantaneous utility function is logarithmic in Dixit-Stiglitz aggregates of the
goods sold by each industry. There is no population growth. Lastly we will consider both openeconomy and autarchic equilibria of the model, and in the open-economy case we assume free
trade in goods as well as free mobility of investible funds across countries. We now specify the
model in detail, commencing with the open-economy case.
Production and Unit Costs
Slightly abusing notation, the production function for a typical good j in each industry is:
θ
1−θ
,
(1) ykAj = JH kAj
Z kAj
θ ∈ (0,1) , k = N, S
β
1− β
Z kBj
,
(2) ykBj = LH kBj
β ∈ (0,1) , k = N, S
where y denotes output, J and L are constants, and θ > β as assumed.
Firms are price-takers in input markets, and by suitable choice of J and L, we have the
following unit cost functions uc, with wkH, wkZ denoting the wage rates for H, Z in country k:
(3) uckAj = wθkH w1kZ−θ ,
k = N, S
5
β
w1kZ− β ,
(4) uckBj = wkH
k = N, S .
Consumption, Output Prices
With identical and homothetic tastes, a representative consumer (assumed infinitely-lived) in
each country may be defined, who maximizes lifetime utility U:
(5) Uk =
∫
∞
0
e − ρt [ln C kAt + τ ln C kBt ]dt , τ > 0 , k = N, S,
where t denotes time, ρ > 0 the rate of time preference, and CkA, CkB are CES aggregates of the
continua of individual consumption items c purchased from each industry:
αA
(6) CkA = [ ∫0n A c kAj
dj ]1 / α A , α A ∈ (0,1) ,
(7)
αB
CkB = [ ∫0nB c kBj
dj ]1 / α B , α B ∈ (0,1) ,
k = N , S,
k = N, S .
The measures nA, nB of goods available at any time are given by
(8) nA = nNA + nSA,
(9) nB = nNB + nSB,
where nkl denotes the measure of varieties of output of industry l produced in k (l = A, B; k = N,
S). Thus, N-consumers will wish to consume varieties of both goods produced in both countries
(assumed non-overlapping across countries), and likewise for S-consumers.
Tariffs and transport costs are assumed to be absent, so each good sells at the same price
across countries. Price-taking consumers face prices {pAj, pBj} for all goods in the two groups,
and as is well-known (Grossman and Helpman (1991)), consumer optimization can be
represented by a two-stage procedure. In the first stage they choose amounts of all goods to
minimize the cost of achieving given levels of CkA and CkB, leading to the following ‘derived
demand’ functions for individual goods:
−ε A ε A
(10) cNAj + cSAj = (C NA + C SA ) p Aj
PA ,
j ∈ [0, n NA ] ∪ [0, n SA ]
−ε B ε B
(11) cNBj + cSBj = (C NB + C SB ) p Bj
PB ,
j ∈ [0, n NB ] ∪ [0, n SB ] ,
6
where ε A = 1/(1 − α A ) is the price-elasticity of demand for good j in industry A, and analogously
for ε B , and the imputed price indices are:
−α A /(1−α A )
−α A /(1−α A )
(12) PA = [ ∫0nNA p Aj
dj + ∫0nSA p Aj
dj ] − (1−α A ) / α A ,
(13)
−α B /(1−α B )
−α B /(1−α B )
PB = [ ∫0nNB p Bj
dj + ∫0nSB p Bj
dj ] − (1−α B ) / α B .
Each producer of individual good j is assumed to be monopolistically competitive, and the
profit-maximizing prices are
(14) pklj =
ucklj / α l , k = N, S, l = A, B,
j ∈ [0, n Nl ] ∪ [0, n Sl ] ,
while, from Shephard’s Lemma, the input demands are
(15) Hkj = θ ( wkH / wkZ )θ −1 y kAj + β ( wkH / wkZ ) β −1 y kBj , k = N, S, j ∈ [0, nkA ] ∪ [0, nkB ]
(16) Zkj = (1 − θ )( wkH / wkZ )θ y kAj + (1 − β )( wkH / wkZ ) β y kBj , k = N, S, j ∈ [0, nkA ] ∪ [0, nkB ].
The numeraire of the model is introduced below, as also is the second stage of consumer
optimization (which, as is well-known, does not affect the optimal prices given in (14)).
R&D
Both N and S can undertake (variety-expanding) R&D, assuming for convenience no overlap
in the varieties each country develops. Knowledge spillovers from existing to the development
of new varieties in each industry are assumed, and we also assume that cross-national spillovers
are less knowledge-enhancing than intra-national.4 Thus,
R
/(n NA + λ A nSA ) ,
(17) H NAR / a = n& NA
λ A ∈ [0,1)
R
/(nSA + λ A n NA ) ,
(18) H SAR / a = n& SA
4
Grossman and Helpman (Chapters 6-9) develop a series of models with either one or two
primary factors of production, and spillovers that either flow completely freely across national
boundaries or are solely national in scope: all their models have only a single differentiatedproduct, innovating, industry (either by itself or juxtaposed with a traditional non-innovating
industry), and so their analyses are quite different from ours.
7
R
/(n NB + λ B nSB ) ,
(19) H NBR / a = n& NB
λ B ∈ [0,1)
R
(20) H SBR / a = n& SB
/(n SB + λ B n NB ) .
In the above, HklR is the amount of k skilled labour employed in R&D in industry l, (k = N,S, l =
A, B), a > 0 (assumed common to all) inversely parameterizes the productivity of labour in R&D,
λ A and λ B are cross-national spillover coefficients, dots denote time derivatives, and n& klR denotes
the rate of creation of new l-varieties by k researchers. As will be seen below, in the presence of
foreign direct investment (FDI), n& klR need not equal n& kl , which denotes the rate of expansion of lvarieties produced in k.
It is assumed that the inventor of each differentiated product enjoys a perpetual monopoly
right over its production and sale – he may either, as assumed here, also be its producer, or
equivalently charge a royalty for the use of his invention to competitive producers of the good
(Barro and Sala-i-Martin (2004, p. 216)). Within each country and industry group firms are as
usual assumed to be symmetric.
R&D is financed by issuing equity, the value of which
(dropping the j subscript here) for each firm in group ‘kl’ is denoted by vkl (equal to the
discounted value of the firm’s future profits). The no-arbitrage condition holds:
(21) v&kl = rvkl – π kl ,
k = N, S, l = A, B
where r is the interest rate (to be determined, bonds and equities being perfect substitutes under
certainty), and profits π kl are
(22) π kl = (pkl – uckl)ykl,
k = N, S, l = A, B.
Free entry is also assumed, so that if n& klR is positive,
(23) vkl n& klR = wkH HklR,
k = N, S, l = A, B
which implies, from (17)-(20)
(24) vkl[nkl + λl nk 'l ]
= wkH a,
k, k’ = N, S, k ≠ k ' , l = A, B.
If the left side of (24) is less than the right, it is easily shown that that particular n& klR must equal 0,
which will turn out to be a consideration of some significance in our analysis.
8
Market-Clearing Conditions, Budget Constraint
The market-clearing conditions for goods and labour are
(25) yNlj = cNlj + cSlj,
l = A, B,
(26) ySlj = cNlj + cSlj, l = A, B,
j ∈ [0, nlN ]
j ∈ [0, nlS ]
(27) H k = ∫0nkA H kAj dj + ∫0nkB H kBj dj + HkAR + HkBR,
(28) Z k = ∫0nkA Z kAj dj + ∫0nkB Z kBj dj ,
k = N, S
k = N, S
where H k , Z k are the exogenously fixed supplies of skilled and unskilled labour in k (k = N, S).
Since tastes are identical and homothetic across countries, we can aggregate the country
representative consumers into a global representative consumer. Equities are the only asset in
positive net supply in each country. To anticipate the subsequent discussion, we will only be
considering situations in which factor prices are equalized across countries, and hence so will be
the prices of differentiated products in each industry. As such, by symmetry the value of total
firm equity in industry l (l = A, B) is vl(nNl + nSl), so that the total wealth V of the global
consumer is
(29) V =
vA(nNA + nSA) + vB(nNB + nSB),
and his budget constraint is
(30) V&
= rV + w H ∑ k H k + wZ ∑ k Z k – ( PAC A + PB C B ),
where Cl = CNl + CSl denotes global consumption of good l (l = A, B). This completes the
specification of the model, and by Walras’ Law one equation is not independent: one can in fact
derive (30) from the other equations of the model.
9
Solving the Model
We first consider some important preliminary issues. As mentioned, we will, for tractability,
only consider equilibria in which wH is the same across countries, and so is wZ.5 In a purely
competitive Heckscher-Ohlin world, factor-price-equalization (FPE) is assured under certain
conditions, notably that both countries continue to produce both goods, and there is free trade, so
that goods prices are equalized across countries. In our model, under free trade both countries
may well continue to produce A- and B- goods, but differentiated varieties of each of these,
whose prices could differ.
Hence, Heckscher-Ohlin arguments for FPE are not directly
applicable here.6
We thus adopt the following approach. We begin by studying the steady-state equilibrium
that results when factor endowments in both countries are identical. FPE will certainly obtain
here, notwithstanding that the two countries produce non-overlapping varieties of the two goods
(in equal measures, and quantities). We then consider how the steady-state equilibrium changes
when there is a marginal increase in N’s endowment of H.
We show that a determinate
equilibrium results under such an increase, maintaining the condition that FPE holds,7 and study
its features.
We are thus constrained to study only local variations from a symmetric
5
As usual, this need not be taken literally. If one N-worker is, say, twice as efficient as one Sworker, and provided, as we shall assume, that this differential is the same across both A and B,
we need simply to adjust labour supplies and inputs in either of the two countries by this
differential. Henceforth, we shall implicitly deal with such efficiency-adjusted labour quantities.
6
One alternative is to assume that both countries produce the entire ranges of varieties of both
goods, but (with differing factor endowments) possibly in differing quantities. This may be ruled
out if we assume, as appears plausible, that the producer, who is also the inventor, of a particular
differentiated product incurs a nonzero ‘coordination cost’ of organizing and carrying out its
production in two different locations. (Licensing its production to a competitive fringe of
producers in the foreign country could well involve communication costs, with similar
consequences.) Under FPE he would then only produce in one location. We adopt this assumption here. If indeed coordination costs are absent, so that production occurs in both locations, it
would appear logical to assume that the knowledge spillover effect depends not only on the
measure, but also on the quantities, of goods produced in each location: this would significantly
complicate the analysis, but one might expect that it would not change the results qualitatively.
7
This does not rule out the possibility that there might exist other equilibria in which FPE does
not hold, but intuition suggests that a marginal change in a single endowment would not
precipitate this. In any event, as we show by construction, an equilibrium with FPE certainly
exists. A related issue is whether, with identical factor endowments, there can exist an
asymmetric equilibrium in which each country specializes in only one industry: we show in
Section V below (fns. 22,21) that this is not possible.
10
equilibrium, although the qualitative results are likely to hold for larger variations, as long as
FPE prevails.8 As with various (but not all) endogenous growth models, the model has no
transitional dynamics, and so the steady-state equilibria fully characterize the model’s solutions
under differing parameter configurations. We proceed now to study the model along these lines.
For the second stage of consumer optimization, the Hamiltonian for the global consumer is
(31) Ht = ln C At + τ ln C Bt + ψ t [ rtVt + wHt ∑k H k + wZt ∑k Z k – ( PAt C At + PBt C Bt )],
ψ t being the co-state variable. Necessary conditions for optimality are
(32)
∂H t
∂C At
= C At−1 – ψ t PAt = 0,
(33)
∂H t
∂C Bt
= τC Bt−1 – ψ t PBt = 0,
(34) ψ& t = ( ρ − rt )ψ t ,
and we also have the transversality condition
(35) Limt →∞ e − ρtψ tVt = 0.
The Mangasarian sufficiency conditions for a maximum (Chiang (1992)) are satisfied, and we
assume for now the existence of a growth path satisfying the necessary and sufficient conditions:
conditions for existence are presented below. From (32), nominal spending on A, EAt, is
(32′) EAt = PAtCAt = 1 /ψ t
Analogously to Grossman-Helpman, we adopt the following normalization (numeraire):
(36) EAt
≡
1 for all t.
From (32′) this implies
(37) ψ t = 1, all t,
which from (34) and (33) yield
(38) rt = ρ , all t,
(39) PBt CBt = τ .
8
Unfortunately, given the complexity of the model, determining the precise range of
endowments over which FPE holds is analytically impossible, and would require a numerical
treatment.
11
Since our primary focus is on the relationship between factor endowments, factor intensities,
and production and R&D patterns, we impose symmetry in other respects by assuming henceforth that λ A = λ B = λ , α A = α B = α , and, as mentioned, Z N = Z S . We also assume initially
that H N = H S and τ = 1 : these will be relaxed subsequently. Lastly, we assume that FDI is
freely possible, so that varieties of either good that have been developed in one country can if
desired be produced in the other country, helping to ensure that FPE is maintained over time.9
With FDI and complete symmetry, the precise allocation of industry R&D activities across
the two countries is indeterminate, although the aggregate amounts of R&D activities in the two
industries, and across industries in each country, are determinate. To facilitate comparison with
the subsequent analyses when H N and τ are varied, we arbitrarily assign all R&D in A to N,
and all R&D in B to S. As such, (24) holds for the country-industry combinations ‘NA’ and ‘SB’.
In a steady-state equilibrium, as a result of FDI the production ratios n Sl / n Nl , l = A, B will be
constant, and logarithmically differentiating (24) for ‘NA’ and ‘SB’ with respect to t we have
(40)
v& NA n& NA
+
v NA n NA
=
w& H
wH
=
v& SB n& SB
+
v SB n SB
From earlier equations, one obtains, for any variety of each good, produced in either country,
(41) π A = (1 − α ) / n A
(42) π B = τ (1 − α ) / n B .
(We continue to exhibit the τ term, despite its being set equal to 1 here, to facilitate subsequent
comparisons.) Using these, we may determine v& NA / v NA , v& SB / v SB from (21). Next, let rA and rB
denote n NA /(n NA + n SA ) (=1/(1+ n SA / n NA )) and n NB /( n NB + n SB ) respectively: these are to be
determined, but will as mentioned be fixed in a steady state. It should also be noted that as a
R
result of immediate FDI n& NA
= n& NA + n& SA at any t, and likewise for ‘SB’: the left side refers to the
9
As often occurs in such models, identification of exactly which varieties are produced in each
country is not possible, but the measure of varieties of each good produced in each country is
determinate. FDI could entail the re-location of production of existing varieties, or the
immediate production abroad of newly-developed varieties, or even the transfer abroad of
individual divisions of multi-divisional organizations, as long as the divisions operate quite
independently of each other.
12
innovation rate, and the right to the induced expansion of production in both countries. From the
labour-market clearing equations (27) and other terms we may then obtain
(43)
n& NA
n NA
=
R
n& NA
n NA + n SA
= [λ + (1 − λ )rA ][
(44)
n& SB
nSB
=
R
n& SB
n NB + n SB
= [1 − (1 − λ )rB ][
H N θαrA τβαrB
−
−
]
a
awH
awH
H S θα (1 − rA ) τβα (1 − rB )
−
−
].
a
awH
awH
Using either of these equations, say the former, and correspondingly the expression for
v& NA / v NA , as well as (40) and manipulating terms we obtain
(45)
w& H
wH
= ρ + [λ + (1 − λ )rA ][
H N θαrA τβαrB (1 − α )
−
−
−
].
a
awH
awH
awH
With rA, rB fixed in steady state it is easily seen that the only stable solution10 for wH (note that
this is the skilled labour wage in terms of the numeraire, total consumption spending on A) is the
constant one, namely
(46) wH =
[θαrA + τβαrB + (1 − α )]
H N + aρ [λ + (1 − λ )rA ]−1
.
This should be substituted in (43)-(44). We also have a further relationship between n& NA / n NA
and n& SB / n SB , namely (40), and using this, (43)-(44), and our solutions for v& NA / v NA , v& SB / v SB ,
we finally arrive at a relationship between rA and rB only:
(47) [λ + (1 − λ )rA ][1 − (1 − λ )rB ]{H N [τ (1 − α ) + θα (1 − rA ) + τβα (1 − rB )] − H S [(1 − α ) +
θαrA + τβαrB ]} – aρ{[λ + (1 − λ )rA ][(1 − α ) + θαrA + τβαrB ] − [1 − (1 − λ )rB ][τ (1 − α ) +
θα (1 − rA ) + τβα (1 − rB )]} = 0
10
More completely, wH is a determinant of v NA n NA , from (24), which is a constituent of V, and
when wH is unstable V will change at a rate that eventually violates the transversality condition.
13
We also have a second relationship between rA and rB, obtained by first adding the country
labour-market-clearing conditions for Z to determine wZ:
(48) wZ = α [(1 − θ ) + τ (1 − β )] /( Z N + Z S ) ,
and substituting this back into either country’s, say N’s, Z-market-clearing condition to yield:
(49) rB = [τ (1 − β )]−1{0.5[(1 − θ ) + τ (1 − β )] − (1 − θ )rA }.
With H N = H S and τ = 1 it is then easily verified that rA = 0.5 = rB is the solution of the model.
From (43)-(44) we then also have, initially,
(50)
n& NA
n&
[ H k (1 − α ) − aρα (θ + β )(1 + λ ) −1 ]
= SB = (1 + λ )
,
n NA
nSB
a[α (θ + β ) + 2(1 − α )]
where ‘k’ denotes N or S, as applicable. Thus, the condition for existence of an initial growth
equilibrium is that the above numerator, in square brackets, be strictly positive. This completes
the characterization of the initial equilibrium.
The Autarchy Case
To provide one basis of comparison with open-economy scenarios, we provide the results for
the autarchy case, focusing illustratively on N (for S only the superscripts and subscripts need to
be changed). We also employ the superscript ‘a’ where necessary to indicate the autarchy
values. Assuming that τ is sufficiently close to 1 that n& NlRa is positive for both l = A, B, and with
no international knowledge spillovers the analogue of (24) is
a
a
a
= w NH
(51) v Nl
n Nl
a,
l = A, B.
Logarithmically differentiating this with respect to t we obtain an equation of the same form as
(40), but between ‘NA’ and ‘NB’. Consumer optimization for the N-consumer is analogous to
a
a
that conducted earlier, and choosing PNA
as the numeraire here, we still obtain rt = ρ . By
C NA
a
,
following analogous steps to those earlier, we obtain the stable solution for w NH
a
(52) w NH
= [θα + τβα + (1 − α ) + τ (1 − α )][ H N + 2aρ ] −1 ,
14
a
and the market-clearing solution for w NZ
,
a
(53) wNZ
= α [(1 − θ ) + τ (1 − β )] / Z N .
Using (52) and setting τ = 1 our solution for the initial equilibrium innovation rates is
(54)
n& NA
n& NB
[ H N (1 − α ) − aρα (θ + β )]
=
=
,
a[α (θ + β ) + 2(1 − α )]
n NA
n NB
and the existence condition for an initial growth equilibrium is that the above numerator be
positive.
Comparing (50) and (54), the open economies will grow faster than the closed ones if λ > 0 ,
but not if λ = 0 .11 In the latter case, twice as many skilled workers will be engaged in R&D in
the open economies than in either closed economy, but this advantage is exactly offset by the
fact that, since rA = 0.5 = rB, half of the goods developed in, say, N will be produced abroad via
FDI, and will not generate spillover benefits to further innovation in N, and likewise for goods
developed in S. However, if λ > 0 some spillover benefits to each country from production in
the same industry in the other country will be generated, providing a further boost to innovation
and growth. As is well-known, even if λ = 0 open-economy consumers will gain from the
increased variety of both sets of goods that they can consume. We thus have
Proposition 1. The open economies will grow faster than the closed ones if λ > 0, and at
the same rate if λ = 0. In either case consumers will be better off in the open economies.12
11
As an aside, the Dixit-Norman integrated-world-equilibrium construct employed by Grossman
and Helpman in their Chapter 7 (in which λ = 1) to facilitate their characterization of the trade
equilibrium cannot be directly applied here, since we assume λ < 1 .
12
One might argue that the results here depend on the existence of ‘scale effects’, which have
been questioned in the literature. It is certainly reasonable, though, to suppose that two
economies can have a higher combined R&D input than either economy alone. On scale effects
more generally, increasing difficulty of research over time, as argued for example by Segerstrom
(1998) and Jones (2009), has been used to account for stagnant research performance in the face
of increasing numbers of scientists and engineers. In order not to further complicate our already
complex analysis, we do not model these issues explicitly (especially since H k (k = N, S) are
not growing in our model) but, if desired can proxy them (particularly if we allow the H k ’s to
grow) by suitably adjusting the parameter a (equations (17)-(20)) over time.
15
IV Comparative Dynamics
(A) Increase in H N : With the open economies initially in the above-described equilibrium, we
consider first the effects of a marginal increase in H N . Differentiating (47), using (49), and
defining
(55) Δ =
(1 − α ) + 0.5α (θ + β )
we obtain
(56)
drA
dH N
=
(1 − β )
0.5(1 + λ ) 2 Δ
, >0
.
(θ − β ) (1 + λ ) 2 αH N + 2aρ{(1 − λ )Δ + α (1 + λ )}
This equation, and succeeding ones in this sub-section, only hold at τ = 1, which has accordingly
been explicitly substituted in. Positiveness of drA / dH N , and correspondingly negativeness of
drB / dH N , has major implications: with H N slightly above H S , and rA and rB slightly above
and below 0.5 respectively, it must from equation (24) be the case that innovation in A can now
only be profitable in N, and in B only in S. Specialization in R&D is now dictated by economic
incentives, specifically the effect of the higher spillover benefit in each of these industry/country
combinations relative to the alternative, rather than being an arbitrary assignment as was the case
when H N = H S .
Stated more broadly, the relationship between factor endowments, factor
intensities, and production patterns has determinate consequences for the international
distribution of R&D activities as well.13
13
Actually, it turns out that there is another possible, less economically appealing, equilibrium,
even under FPE. Suppose we had initially left the country allocation of R&D unspecified, only
keeping the total world amount of R&D in each industry determinate. Then, when H N increases
marginally, it is possible for rA and rB to remain at 0.5 each, and for all of the increase in H N to
be devoted to R&D in the two goods in some (within limits) arbitrary proportions, again keeping
the world amounts of R&D determinate. We ignore this equilibrium for three reasons: (a) it is
empirically counterfactual: there are clear North-South differences in production patterns,
associated with differing factor endowments; (b) it need not occur if we assume that H
production workers and researchers in the same industry have an arbitrarily small preference for
congregating in the same country (perhaps because they enjoy exchanging views about industry
experiences), in which case even a small positive shock to production and R&D activity in N in A
could induce a movement to the equilibrium described in the text (the reverse specialization,
16
The economy will transition to the new steady state immediately: upon the small instantaneous shift in H N , country production and R&D patterns, forward-looking asset prices, and
consumption levels will also adjust instantaneously, so that there are no transitional dynamics.
From (48), wZ is unaffected by the increase in H N , while the effect on wH is more
complicated. Differentiating (46) with respect to H N and using (56) we have
(57)
dw H
dH N
=
(1 + λ ) 2 αH N
0. 5Δ
(1 + λ ) 2
times:
.
+ 2aρ{(1 − λ )Δ + α (1 + λ )} (θ − β ){0.5(1 + λ ) H N + aρ }2
aρ (1 − λ )(1 − θ ) Δ − 0.25(1 + λ )α (θ − β )[(1 + λ ) H N + 2aρ ]
The final two expressions above are of opposing sign, so the net effect is indeterminate a priori.
To appreciate the logic behind this, it is useful to consider two cases:
(a) if λ is close to 1, and θ is not too close to β , the net effect is negative. In this situation, the
gain in spillover benefits from locating more of A-production in N is small, leading to a smaller
increase in the induced demand for H to work in R&D, which tends not to offset the negative
effect on wH of the increase in H N . With θ not too close to β the fall in wH will fairly
significantly reduce the relative price of A to B, increasing the demand for A, which will induce
an increase in demand for H – in N, since proportionally more of A is now being produced in N –
to help equilibriate with the increased supply of such labour.
(b) if λ is not too close to 1, and θ is close to β , the net effect is positive. Now, there is a
larger increase in the induced demand for H in R&D, tending to induce an increase in wH. This
increased demand is not significantly dampened by the induced increase in the relative price of A
to B since with θ close to β the relative price increase will be small (moreover, there is a
with rA and rB being respectively less and more than 0.5, and N specializing in B-innovation,
cannot be an equilibrium when H N marginally increases, since B is less H-intensive); and (c)
welfare-wise, it can be shown that the combined steady-state innovation in A and B – which we
show below to be a determinant of lifetime well-being – is lower in this equilibrium than that
studied in the text (except for a limiting situation, also discussed below, where they are equal).
This is perhaps not surprising, since maintaining rA and rB at 0.5 each deprives the world
economy of the ‘boost’ to R&D from some degree of country specialization in production.
17
reallocation of production in S towards B, so again more of the demand for A will have to be met
from N).
The relationship between trade-related production patterns and sectoral R&D levels thus
produces interesting and important differences from the analyses in static or exogenous-growth
open-economy models, which focus on only the former of these considerations (Acemoglu
(2002) however has a similar result regarding wH in a different endogenous growth model,
focusing mainly on closed economies).
We examine next the effect on innovation rates.
Substituting from (46) into (43), differentiating, using (56), and re-arranging terms we obtain
d (n& NA / n NA )
(58)
dH
N
=
=
∂ (n& NA / n NA )
∂H
N
+
∂ (n& NA / n NA ) drA
∂rA
dH N
θ − β drA
(1 − α )(1 + λ ) (1 − α )
1+ λ N
+
H + aρ ]α
}
{H N (1 − λ )Δ − [
2
2 aΔ
2
1 − β dH N
aΔ
= (1 − α )(1 + λ ) /( 2aΔ ){(1 + λ ) 2 αH N + 2 aρ [(1 − λ ) Δ + α (1 + λ )]} times:{0.5(1 + λ ) 2 αH N + aρ [ 2(1 − λ ) Δ + (1 + λ )α ]} + (1 − β )(θ − β ) −1 (1 − λ )(1 + λ ) H N Δ ,
>0
Increased availability of H N affects n& NA / n NA both directly (and positively) and indirectly,
through the induced increase in rA. Unexpectedly, the latter effect is ambiguous in sign: on the
one hand, it generates higher spillover benefits to innovation, but on the other, since A is
relatively H-intensive, it draws more H into production. The higher the spillover benefit from
the increase in rA (the lower is λ ) and the smaller the difference in factor-intensity between the
two industries (the smaller is θ − β ) the more likely that the indirect effect is positive, and vice
versa. Overall, however, n& NA / n NA unambiguously increases.
Next we have
(59)
d (n& SB / n SB )
dH N
= (1 − λ )
1 − θ H S α (θ + β ) drA
+
−
[
]
1− β a
2aw H dH N
[(1 + λ )α (θ + β )(1 − λ )(1 − θ ) aρ ] / 4a (θ − β ){(1 + λ ) 2 αH N + 2aρ [(1 − λ ) Δ + α (1 + λ )]} +
18
[0.5(1 + λ ) H N + aρ ]α (1 + λ ) 2 (1 − α ) / 2a{(1 + λ ) 2 αH N + 2aρ [(1 − λ ) Δ + α (1 + λ )]}Δ
The first right-hand term is zero or positive as the initial value of n& SB / nSB is zero or positive,
and the other terms are positive, so an increase in H N also raises the innovation rate in S! The
increase in H N induces as mentioned an increase in rA and decrease in rB, the latter implying an
increased relative production of B-varieties in S. This has a twofold effect: it enhances the
productivity of R&D in B in S, and the production shift from A to B in S releases some H for
work in R&D. A third possible, derivative effect works in the opposite direction: if wH declines,
the skill-intensity of production (in both countries) rises but our formal analysis shows that the
second effect dominates this (an analogous, muted effect also operates in N on n& NA / n NA ). In a
closely but not fully integrated world economy, an increase in input supply in one country thus
has far-reaching consequences beyond that country’s borders – again, through generalequilibrium effects involving production and input demand changes.
To compare the changes in country innovation rates, we express (40) more explicitly as
( 40' )
n& SB / n SB – n& NA / n NA = {[1 − (1 − λ )rB ]τ (1 − α ) − [λ + (1 − λ )rA ](1 − α )} / awH
Differentiating this with respect to H N and noting that term in braces on the right equals 0
initially, it is easily shown that the derivative is negative: n& SB / nSB will go up by less than
n& NA / n NA . In (49), the coefficient of rA is absolutely smaller than 1. When, ceteris paribus,
some A-production is ‘transferred’ from S to N, relatively more H than Z is released in S, so that
B-production in S, as a fraction of the total measure of B-varieties, rises by less than Aproduction, as a fraction of the total measure of A-varieties, is reduced: this difference is also not
affected by any induced changes in relative factor prices, since both A and B production
functions are Cobb-Douglas. As a consequence, the spillover benefit to the productivity of R&D
in S rises by less than that in N, which affects the innovation rates accordingly.
Since N will now be producing and exporting more A- and fewer B- varieties, and PA will now
decline faster than PB (equations (12)-(13)), N’s terms of trade with S will commence
deteriorating. Unlike conventional trade models, however, this need not entail ‘immiserizing
growth’ (Bhagwati (1958)), or, as in the Stolper-Samuelson theorem, lower real rewards to the
19
factor used intensively in A, since in our model the price changes are an outcome of faster
induced innovation rates. Not only might wH, as discussed, therefore increase relative to wZ, but
both H and Z will benefit from the faster, continuing decline in goods price indices. (At the same
time, if wH increases, Z will initially be worse off since wZ is unchanged, and the higher wH
implies higher unit production costs and hence higher prices initially.) These considerations
apply to workers in both N and S. Of course, to the extent that the increase in H N is not simply
quantitative, but reflects also a productivity increase (raising the efficiency-adjusted amount of H
in N), there will be a further benefit to individual Northern skilled workers. Summarizing,
Proposition 2. A small increase in H N above H S (a) raises rA above, and reduces rB
below, ½; (b) induces a determinate specialization of R&D in N in A, and in S in B; (c)
could cause wH to either increase or decrease, leaving wZ unchanged; (d) raises the
innovation rate in both N and S, in N more than in S; and (e) will impose initial losses on
skilled (if wH decreases) or on unskilled (if wH increases) workers, which will subsequently
be reversed as goods price indices continually decline, faster than previously.
(B) Increase in H N , and (independently) decrease in τ : Here, τ is not restricted to be 1
throughout. This is a case of some interest, since a lower τ implies a lower share of consumer
spending on B, and hence ceteris paribus a lower profitability of R&D in B, relative to A.
At the same time, care has to be exercised in studying such a reduction, since its effects when
H N is not increased above H S are fundamentally different from when it is increased. In the
former case, one could not simply differentiate (47) with respect to τ , since (47) has been
derived assuming that N specializes in R&D in A and S in R&D in B. While this assumption is
innocuous (and, as earlier mentioned, arbitrary) when H N = H S and τ = 1 , it is not so when
H N = H S and τ < 1. When factor endowments are equal in N and S, it must be the case that rA
= ½ = rB: as such, neither country has an advantage in A (or B) R&D, so at a lower τ both
countries will continue to engage in R&D in both A and B, but will devote more resources to
R&D in A than in B.14 However, when H N > H S and rA and rB rise above and fall below ½
When H N = H S and τ < 1 it cannot be an equilibrium for, say, N to specialize in R&D in A
and S in R&D in B: the latter is less remunerative, so S will have some H ‘left over’.
14
20
respectively, specialization in R&D occurs, and will continue to occur when, within limits to be
described subsequently, τ is reduced below 1.
Formally, we differentiate (47) with respect to H N , under the additional condition that
dτ / dH N = − φ , say, where φ can take on any (fixed) positive value up to an upper bound that
is imposed subsequently, and evaluate it at H N = H S , τ = 1 , to obtain the right-hand derivative
(indicated with a ‘+’ superscript):
(60)
drA +
dH N
(1 − β ) 0.5(1 + λ ) 2 Δ − (1 + λ )φ (1 − α )[0.5(1 + λ ) H N + aρ ]
.
.
(θ − β )
(1 + λ ) 2 αH N + 2aρ [(1 − λ ) Δ + α (1 + λ )]
=
H N = H S ,τ =1
Comparing (60) with (56), the change in rA will be less in the present case, but, for low φ , still
positive. The lower remunerativeness of R&D in B at a lower τ results in less H being drawn
into it than would otherwise occur, resulting in more H being available for production in S,
retarding the increase in rA. It would be a mistake, however, to extrapolate from this to conclude
+
that for a higher φ drA / dH N would be negative. The highest possible value of φ for this
+
pattern of cross-country R&D specialization to occur is that at which drA / dH N → 0 : once this
limit is attained, and rA and rB both equal ½, N loses its productivity advantage in A R&D, and at
that and lower values of τ there occurs a switch to a regime in which both countries engage in
R&D in both goods (but in differing total amounts, since H N > H S ), with rA and rB remaining
at ½. Essentially, as B R&D becomes increasingly less remunerative, a point is reached beyond
which it is no longer worthwhile for S to engage solely in such R&D, but attainment of this point
also requires that production patterns concurrently adjust so that rA and rB each equal ½.
A decrease in τ works against the earlier-discussed positive effect of an increase in H N on
S’s innovation rate both directly and by retarding the increase in rA and associated decrease in rB.
To illustrate the relative strength of these effects, we consider the extreme case of φ indeed
+
being large enough that drA / dH N → 0 , which from (60) occurs as φ tends to
(61) φˆ = (1 + λ ) Δ{(1 − α )[(1 + λ ) H N + 2aρ ]}−1 .
21
Differentiating (44) with respect to H N and evaluating it at dτ / dH N = − φˆ , H N = H S , τ = 1 ,
we obtain
(62)
d (n& SB / n SB )
dH
+
= −
N
H = H ,τ =1, dτ / dH = −φˆ
N
S
N
θα (1 + λ )
4 aΔ
, < 0.
A sufficiently large value of φ can thus indeed reverse the positive effect of a higher H N on
n& SB / nSB .
It can be shown, however, that n& NA / nNA will still increase when φ = φˆ .
The
implications of differing innovation rates in the two industries are examined below.
Proposition 3. If H N > H S , and τ is progressively reduced below 1 (down to a particular
limiting extent), rA will progressively decline towards ½. n& SB / n SB , which rose when only
H N increased above H S , will decline with τ , and in the limit as rA converges to ½ will
decline to a level lower than when H N = H S and τ = 1. However, n& NA / n NA will still be
higher than when H N = H S and τ = 1.
We consider next the welfare implications of concurrent variations in H N and τ , for both
open and closed economies, and for this we first examine the agent’s lifetime utility function
(equation (5)).
CAt and CBt (which, depending on the context, will refer to either the
representative global consumer’s consumption in open economies, or a representative country
consumer’s consumption under autarchy) are given by (32' ) , (36) and (39), with, from (12) and
(13), PAt equal to PA0 e −[(1−α ) / α ] g At , and correspondingly for PBt. Here, PA0 denotes the initial
value of PA (which changes upon opening-up, as more varieties immediately become available)
and gA is the equilibrium growth rate n& A / n A , which of course also changes upon opening-up.
Substituting into (5), integrating some terms by parts, and re-arranging, we obtain
(63) U = ( ρ 2α ) −1 (1 − α )( g A + τg B ) + ρ −1 [τ ln τ − (ln PA0 + τ ln PB 0 )] .
Earlier, from (50) and (54), open-economy innovation rates were seen to discretely exceed
closed-economy rates if λ > 0. Coupled with the higher variety that consumers in the former
enjoy, they are clearly better off than closed-economy consumers, and by continuity open22
economy innovation rates would continue to exceed autarchic rates even for a small increase in
H N and decrease in τ . On the other hand, in the extreme case that λ = 0, open- and closed-
economy innovation rates are equal when H N = H S and τ = 1 , and which economies will be
better off when H N and τ are varied is not evident. We thus study this next, assuming also that
in both open and closed cases the decrease in τ is given by the same absolute magnitude,
converging to φ = φˆ .
Setting λ = 0 and the limiting φ to φˆ generates outcomes most
unfavourable to the open-economy case, and it is of interest to examine whether in this setting
trade can be welfare-reducing.
Considering to begin with the first right-hand expression of (63), we have to compare
d ( g A + g B ) + / dH N
d ( g A + g B ) / dH N
O
H = H ,φ =φˆ ,τ =1
N
S
C ,S
H N = H S ,φ =φˆ ,τ =1
with
d ( g A + g B ) / dH N
C,N
H N = H S ,φ =φˆ ,τ =1
and
, where ‘O’, ‘C,N’ and ‘C,S’ refer to open economies, the closed
N economy, and the closed S economy respectively.15 (Examining (63), the remaining term in
the differentiation of ( g A + τg B ) with respect to H N , g B dτ / dH N , will be the same in open
and closed economies at the initial point, and can hence be ignored.) After differentiation and
manipulating terms we obtain
(64)
d ( g A + g B ) + / dH N
(65)
d ( g A + g B ) / dH N
(66) d ( g A + g B ) / dH N
O
H N = H S ,φ =φˆ ,τ =1
C,N
H N = H S ,φ =φˆ ,τ =1
C ,S
H N = H S ,φ =φˆ ,τ =1
= [ 2(1 − α ) − α (θ − β )] / 4aΔ ,
= [ 4(1 − α ) − α (θ − β )] / 4aΔ ,
= − α (θ − β ) / 4aΔ.
By continuity, the rankings of these derivatives will remain the same even for small discrete
variations in H N and τ . Thus, since at the ‘benchmark’ steady state (at H N = H S , τ = 1 )
15
In the C,S case the change in H N has no direct effect, so d ( g A + g B ) / dH N
C ,S
H N = H S ,φ =φˆ ,τ =1
simply constitutes the effect of a differential change in τ of limiting magnitude φˆ, to facilitate
comparison with the other cases.
23
closed and open-economy innovation rates are equal, in the new steady state the innovation rate
will be lowest in ‘C,S’, followed by ‘O’, with the highest innovation rate in ‘C,N’. Also, from
(12)-(13), and normalizing the initial closed-economy price indices to unity, the squarebracketed second right-hand term in (63) will be higher in the open economies by the amount
[(1 − α ) / α ](1 + τ ) ln 2 , on account of the increased consumption variety immediately made
available by trade. S is thus clearly better off in the trade equilibrium, while whether N is better
or worse off depends on whether the effect on lifetime wellbeing of the initial gain due to
increased variety dominates or is dominated by the lower ( g A + g B ) under trade, whose effect
on wellbeing accrues over time: as (63) shows, this depends also on ρ , in the usual manner.16
What accounts for the lower ( g A + g B ) under trade for N? As may perhaps be expected from
the discussion after (54), if the increase in H N were accompanied by an equal increase in H S ,
then ( g A + g B ) would change equally in the closed and open economies. (In this case, the open
economies would for τ < 1 remain at rA = ½ = rB, but with both countries innovating in both
products.) Clearly, then, an increase only in H N and with φ = φˆ implies a less favourable
outcome for N under trade than when closed. The reason essentially is that with higher H N N
innovates more, but part of what is or has been innovated is sent for production abroad via FDI
in the open-economy case, so that its spillover benefit to further innovation in N is lost, and this
is not offset by either significant changes in rA, rB or by a higher H S . When N is closed,
however, the more quickly developed products following on the increase in H N remain entirely
within the economy, and continue to generate spillover benefits to further innovation.
Proposition 4. When λ > 0 all individuals in both countries are better off under trade than
under autarchy, even when there are small increases in H N and decreases in τ . However,
It can also be shown that the increase in H N has the same welfare effects in the open-economy
case as in the case of the other open-economy equilibrium described in fn. 13, which is perhaps
not surprising since with φ = φˆ the limiting values of rA and rB underlying equation (64) are, as
mentioned, ½. The same result, obviously, holds for higher values of φ (as discussed
immediately after (60)), while for lower values of φ , inducing departures of rA and rB from ½ in
16
the equilibrium we have been focusing on in the text, it can be shown that an increase in H N has
more favourable welfare effects than in the case of the equilibrium in fn. 13.
24
when λ = 0 and there are small increases in H N and decreases in τ it is possible for
Northern individuals to become worse off under trade.
Unlike some earlier studies, such as Grossman and Helpman (Chapter 8), Young (1991),
Acemoglu et. al. (2006), and Galor and Mountford (2008) which identify, in various models in
which S does not innovate,17 possible dynamic losses to S from trade, our model identifies a
possible loss to N instead. While a theoretical possibility, the empirical likelihood of this is
slight: the strong assumptions necessary for it, in particular that λ = 0 and drA+ / dH N → 0 , are
unlikely to hold empirically. Trade-induced changes in innovation and production patterns are
much more likely to be welfare-enhancing for all participating countries. However, to the extent
that policy-makers and special interests in N inadvertently or deliberately underestimate the
values of λ and drA+ / dH N , protectionist pressures in N can arise.
(C) Increase in H N and smaller increase in H S : Although ostensibly straightforward, this
case generates some unexpected results. Formally we set dH S / dH N = ω , where ω ∈ (0,1) , and
we consider first the case in which τ is fixed at 1, after which τ is concurrently reduced.
(a) Differentiating (47), the effect of the increases in H N and H S on rA is simply equal to the
right side of (56) multiplied by 1 − ω. As expected, therefore, the rise in rA is mitigated by the
concurrent increase in H S . Using (58) and differentiating ( 40' ) we obtain
(67)
d (g A + g B )
dH
N
O
= (1 − α )(aΔ2 ) −1 times:-
H = H ,dH / dH =ω
N
S
S
(1 + λ )Δ + {H N (1 − λ )Δ[1 +
N
1−θ
1 − λ drA
θ −β
H N (1 + λ )
]− 2
[α (
+ aρ ) + aρΔ
]}
1− β
1− β
2
1 + λ dH N
Since the increase in H S only enters the above through the induced reduction in drA / dH N , it
will actually reduce g A + g B if the coefficient of drA / dH N is positive. This will occur if λ is
17
Grossman-Helpman’s Chapter 8 sets up a model with a single primary factor, a traditional noninnovating sector, and a single, differentiated-product sector, in which the less advanced country
will develop new varieties under autarchy but not under trade.
25
fairly low – implying a reduction in rA below what it would otherwise be fairly considerably
reduces spillover benefits – and θ is fairly close to β , as discussed after (58) (the additional
effect discussed after ( 40' ) is also weaker if θ is close to β ). Since we are comparing across
open economies, and nA and nB are state variables, the changes in H N , H S will not affect the
initial measures of varieties of both goods available to consumers, and so, if the coefficient of
drA / dH N is positive, the concurrent increase in H S is welfare-reducing!
Although surprising, this result can be rationalized. As is well-known, expanding-productvariety models are characterized by the market failure that in undertaking R&D entrepreneurs do
not internalize the spillover benefit to future R&D activities, as a result of which a sub-optimal
amount of R&D is undertaken. In our open-economy model, the increase in H S , by reducing
drA / dH N , effectively compounds this underlying market failure when the coefficient of
drA / dH N is positive, hence reducing growth and well-being. In turn, this suggests that if
optimal R&D subsidies were in place, such a reduction in well-being will not occur. We
examine this in the next Section.
(b)
In this case, the term 0.5(1 + λ ) 2 Δ on the right side of equation (60) has simply to be
multiplied by 1 − ω , and the resulting equation (60) only applies when its right side is nonnegative. We then obtain the following interesting insight: suppose S has a policy objective of
being as competitive as N in the production of, and R&D in, A, and to this end invests in raising
the effective skill level of its skilled workers. Then, our equation shows that, if φ is positive, it
is not necessary for S to raise H S all the way to equal H N to achieve this objective: H S only
has to be raised ( ω has to be chosen) so that the right side of the revised equation (60) falls to 0.
Essentially, if φ > 0 then industry B is reduced in attractiveness relative to A, and so part of the
adjustment to equal competitiveness of S as N in A is accomplished through market forces.
There will now be an additional right-hand term in (67) to reflect the direct effect of a change
in τ on ( g A + g B ) (in addition to the indirect effect through rA), but it is still the case that the
increase in H S can be welfare-reducing. Summarizing, we have:
26
Proposition 5. An increase in H S that is concurrent with, and smaller than, an increase in
H N will reduce innovation and welfare if λ is fairly low and θ is fairly close to β , on
account of the reduced country specialization in production, and hence reduced spillover
benefit to innovation. If at the same time τ is reduced then, in addition to this innovation
and welfare result, there is the further consequence that H S need not increase as much as
H N for S to become as competitive as N in production and innovation in industry A.
V The Social Planner Economy
We consider first the situation of a ‘global’ social planner (SP), who seeks to maximize the
well-being of the representative consumer through globally optimal production and R&D
allocations. However, we confine ourselves to allocations that satisfy the requirement of static
productive efficiency at each point of time: the marginal rate of technical substitution between H
and Z in industry A has to equal that in B in each country, and the marginal rate of transformation
(MRT) between A- and B- production in N has to equal that in S. We do this for two reasons.
First, these conditions are satisfied in the market economies studied above, and it would be of
interest to examine whether, with these conditions holding, the SP allocation still differs from the
private.
Second, under the current WTO regime, production or input subsidies that
‘demonstrably distort trade’ (Noland and Pack (2003), p. 89) are deemed to be ‘actionable’,
whereas ‘subsidies of up to 75 percent for certain costs of industrial research and up to 50
percent of precompetitive development activity’ are explicitly permitted (ibid.). Our focus will
thus be on whether an SP allocation that implicitly requires R&D subsidies, which do not distort
static allocative efficiency and thence trade patterns, can make a positive dynamic contribution to
the economies we study.18
Since each A-good enters symmetrically into CA, and similarly for B-goods, efficiency
requires that the amounts of each good produced in industry A be the same in and across the two
18
We do, however, admit one other subsidy, which is not trade-distorting and does not interfere
with static efficiency but rather enhances it: namely, an across-the-board consumption subsidy at
rate (1 − α ) , which, as is well-known, is required to offset the distortion due to monopolistic
pricing of consumer goods. For convenience, we assume that all subsidies are financed by lumpsum taxes, assumed feasible.
27
countries (when produced in both countries), and likewise for B. We then have, with global
consumption demand for each good equal to global output, and dropping the time subscript,
(68) CA = [ ∫0n A y αAjA dj ]1 / α A
= n (A1−α ) / α JH θA Z 1A−θ
(69) CB = [ ∫0nB y αBjA dj ]1 / α A
= n B(1−α ) / α LH Bβ Z 1B− β ,
where nA, nB are given by equations (8), (9), so that the foregoing integrations are over the
amounts produced in both countries, HA = HNA + HSA represents the total H devoted to Aproduction in the two countries, and likewise for HB, ZA, and ZB.
Next, equality of marginal rates of technical substitution across industries implies
(70) hkA = ΦhkB , k = N, S,
where hkj denotes the skilled-unskilled labour ratio in country k, industry j, and
Φ = θ (1 − β ) /[ β (1 − θ )] (> 1), while equality of MRT’s between A and B across countries can be
easily shown to imply
(71) hNA = hSA, hNB = hSB.
Also, letting fA = nSA/nNA and fB = nSB/nNB, equality of the amounts produced of each good in each
industry across countries implies HSj = fjHNj (j = A, B), and likewise for the Zkj’s. Combining
these with (70)-(71), the market-clearing conditions for Z (equations (28)), and the assumption
that Z N = Z S yields after some manipulation a relationship between fA, fB, and other terms:
(72) fB = 1 + (1 − f A ) /[ΦH NB / H NA ] ,
as well as an expression for ZNA (which helps to determine all other Zkj’s):
(73) ZNA = Z N /[1 + ΦH NB / H NA ] .
28
As the analysis below will show, with τ initially set equal to 1, each country will optimally
specialize in R&D in one good, and (in particular for H N > H S ) we suppose that N specializes in
R&D in A, and S in B. Instead of working with rA, rB, it is notationally convenient to work with
fA, fB, which are constant in each steady state. Given our specification about R&D specialization
R
R
n& NA
and n& SB
in equations (17) and (20) will simply equal n& A and n& B , and after manipulation
these equations may be expressed as
(74) n& A = n A (1 + λf A ) H NAR / a(1 + f A )
(75) n& B = n B (λ + f B ) H SBR / a(1 + f B )
The SP will thus seek to maximize consumer well-being subject to the foregoing equations.
The state variables are nA, nB, and for convenience we specify his control variables as HNA, HNB/
HNA, and fA, with fB being from (72) a function of HNB/ HNA and fA. To conserve space, we do not
reproduce his Hamiltonian H tSP here, but proceed directly to the necessary conditions for an
optimum (ψ At , ψ Bt are the co-state variables associated with (74) and (75)):
(76)
H
H
ψ n λ + fB
θ + τβ ψ A n A 1 + λf A
∂H SP
−
(1 + NB ) − B B
( f A + f B NB ) ≤ 019
=
H NA
a 1+ f A
H NA
a 1+ fB
H NA
∂H NA
(77)
∂H SP
− Φ[(1 − θ ) + τ (1 − β )]
τ
=
+
−
∂ ( H NB / H NA )
1 + ΦH NB / H NA
H NB / H NA
τ (1 − f A )
(1 + f B )Φ ( H NB / H NA )
2
−
ψ A n A 1 + λf A
a
1+ fA
H NA −
ψ B nB λ + f B
a
1+ fB
ψ B n B (1 − λ )(1 − f A )[ H S − f A H NA − f B ( H NB / H NA ) H NA ]
a
(78)
Φ( H NB / H NA ) 2 (1 + f B ) 2
H NA −
≤ 0
ψ n λ + fB
ψ n λ + fB
1
∂H SP
τ
=
H NA / Φ − B B
H NA −
−
+ B B
a 1+ fB
a 1+ fB
∂f A
1 + f A (1 + f B )ΦH NB / H NA
19
The weak inequalities here and below serve to take boundary conditions into account. There
are other boundary conditions, which do not bind at the optimum and are hence ignored.
29
ψ A n A (1 − λ )[ H N − H NA (1 + ( H NB / H NA ))]
(1 + f A ) 2
a
−
ψ B n B (1 − λ )[ H S − f A H NA − f B ( H NB / H NA ) H NA ]
[ΦH NB / H NA ](1 + f B ) 2
a
(79) ψ& A = ρψ A − {(
(80) ψ& B
1
α
= ρψ B − {τ (
1
α
≤ 0
− 1)
1 ψ A 1 + λf A
[ H N − H NA (1 + ( H NB / H NA ))]}
+
nA
a 1+ f A
− 1)
1 ψ B λ + fB
[ H S − f A H NA − f B ( H NB / H NA ) H NA ]}
+
nB
a 1+ fB
(81) Limt →∞ e − ρtψ it ni t = 0, i = A, B,
as well as (72) and (74)-(75). Our approach to solving this optimization problem is constructive:
from inspection, we identify a possible candidate solution, and then examine whether it satisfies
the existence, necessary, and sufficient conditions for an optimum. First, with a logarithmic
utility function it is reasonable to hypothesize that the ψ i ni ’s (i = A, B) are constant: from (74)(75), (79)-(80), and τ = 1 initially these occur at the following value:
(82) ψ i ni = (1 − α ) / αρ , i = A, B.
Next, let us suppose that at the optimum fA = 0 = HNB/HNA, while HNA > 0: in other words, we are
examining a candidate solution in which each country specializes not only in R&D but also in
*
, then is
production of each good.20 With (76) as an equality, the solution for HNA, H NA
*
= (θ + β )αaρ /(1 − α )[1 + Φ −1 ]
(83) H NA
Since this is independent of H N , we may simply set H N larger than this, and a corresponding
condition for H S , to ensure existence of a solution with positive innovation rates. Next, under
our candidate solution, the first two right-hand terms in (78) are jointly 0, the next two are jointly
20
This is not inconsistent with the assumed equality of MRT’s between A and B across the two
countries, since it simply implies that the two economies are exactly at the margin between
specialization and non-specialization. The rationale for this treatment is provided below.
30
negative (since θ > β ), and the last two are negative, so the assumed corner value of f A* is
certainly admissible. Further, after some manipulation (77) becomes, at the candidate solution
(84)
(θ + β )[Φ − 1] (1 − α )
∂H SP
*
=
−
(1 − λ )[ H S − H NA
Φ −1 ]
−1
α
a
ρ
∂ ( H NB / H NA )
[1 + Φ ]
The first right-hand expression is not likely to be significantly positive, since Φ is unlikely to
significantly exceed 1. In the second expression, the square-bracketed term is positive given that
a solution exists, and so for λ < 1 and ρ fairly small (a small value of ρ is also necessary to
*
< H N ) the entire right-hand term will be negative, implying that our candidate
ensure H NA
solution indeed satisfies the necessary conditions for optimality. As pointed out, existence of a
feasible solution can also be assured, and it is also easily shown that the Arrow sufficiency
condition (Chiang, op. cit.) is satisfied, so our proposed solution is indeed optimal.
The key assumption is λ < 1 , owing to which the SP optimally concentrates production of
each good in a single country. This is achieved without production subsidies, as shown below:
subsidization of R&D affects the amount of H devoted to it in each country, hence the amount of
H available for production, and hence, under equality of MRT’s across N and S, the amounts
produced of the two goods in each country.21
From (70) and Z N = Z S we obtain
*
*
H SB
= H NA
/ Φ , and so if H N = H S more H will optimally be devoted to R&D in S than in N,
since A-production requires relatively more H. As H N rises above H S , of course, the H
allocation to R&D in N will at some point exceed that in S. The market allocation cannot
achieve the optimal outcome, owing firstly to the non-internalization of future spillover benefits
characteristic of expanding-product-variety models, and secondly to the fact that no individual
researcher can change the aggregate amount of R&D the country conducts.22
21
It can be shown that, once each country is fully specialized, the SP would ideally like to
subsidize R&D further: however, this would ‘break’ the equality of MRT’s in such a way that
production subsidies would also be required, to maintain complete specialization, and hence we
ignore this, particularly as it does not affect our findings qualitatively.
22
Formally, ( 40' ) holds in the market economies, and so if H N = H S (implying rA = ½ = rB)
and τ =1, innovation rates in S and N have to be equal, which is not the socially optimal pattern.
Higher subsidization of R&D in S than in N is required to achieve the optimal allocation.
31
Digressing slightly, further calculations reveal that the optimal R&D subsidy rates in the
*
*
in N (so that b NA
decentralized economies would be 1 − b NA
w NH is the after-subsidy wage cost
*
incurred in R&D in N) and 1 − bSB
in S, where with τ = 1,
*
(85) b NA
= (1 − α )(θ + β )aρ /{θ (1 − α )( H N + aρ )[1 + Φ −1 ] − θα (θ + β )aρ }
and
*
= (1 − α )(θ + β )aρ /{β (1 − α )( H S + aρ )[1 + Φ ] − βα (θ + β )aρ } .
(86) bSB
It is easily shown that if H N (and H S , assumed for comparison purposes to equal H N ) exceeds or
*
*
*
*
*
, then (a) b NA
equals H NA
, bSB
> 0, (b) bSB
< b NA
, so R&D in S is more highly subsidized (fn.
*
*
22), and (c) if H N equals or only slightly exceeds H NA
, then b NA
will exceed 1, implying a tax
on R&D in N (again, because it has to be discouraged relative to R&D in S). Notwithstanding
the equality of MRT’s across countries, the wage rates under complete research and production
specialization will differ, being θ (1 − α )[1 + Φ −1 ] / (θ + β )αaρ for wNH, β (1 − α )[1 + Φ ] /(θ + β ).
αaρ for wSH, (1 − θ ) / Z N for wNZ, and (1 − β ) / Z S for wSZ. Thus the higher Z-intensity of B induces,
at τ = 1 , a higher Z wage in S than N, while the higher R&D subsidy in S exceeds the effect of
the higher H-intensity of A to also, from the above expressions, induce a higher H wage in S than
N. Lastly, with the consumption subsidy and the more rapid rates of innovation, one would
expect that each labour group, and not only the representative global consumer, is better off
under the SP allocation, and some indicative calculations we have performed accord with this.
At the global optimum, an increase in H N or H S will increase the amount of R&D
conducted in the country concerned, which will be welfare-enhancing: the possibility that arose
in the market economies of an increase in H S being welfare-reducing cannot arise here, since
*
(equation
each country remains fully specialized in production as a result of adjustment of bSB
(86)). Next, we note that at the global optimum neither country has an incentive to unilaterally
deviate, since, for example, subsidizing R&D in A in S is ineffective when it produces no A,
whilst its consumers enjoy the full benefit of the R&D in A conducted by N. Our result thus
differs from Spencer and Brander (1983), who focus on cost-reducing R&D.
Third, by
32
continuity the foregoing SP allocation pattern remains optimal even if τ is slightly below 1:
although S would then be producing and innovating in a slightly less desired product, full
specialization remains optimal when λ < 1 since it leads to highest research productivity.
Proposition 6. At the social optimum (and maintaining static productive efficiency within
and across countries), with τ equal or close to 1, each country will be at the margin of
specialization, producing and innovating in only one good.
subsidies will be required to achieve this optimum.
Consumption and R&D
An increase in either country’s
endowment of skilled labour, combined with an adjustment in its R&D subsidy rate, is
unambiguously welfare-improving.
Do our results imply that Southern countries’ endeavours to develop increasingly ‘high-tech’
industries are a mistake? A critical assumption underlying the foregoing analysis is that τ is
equal to or only slightly below 1. As τ is progressively reduced, a trade-off increasingly arises
between the benefit to research productivity from each country’s specializing in production and
the loss arising from the fact that under the foregoing allocation S is constrained to produce and
innovate in only the less-demanded product, namely B. One might then conjecture that for lower
values of τ a switch to a non-specialization regime, with both countries producing, and having
the option to conduct R&D in, both goods would be optimal. We next investigate this formally,
but, in the interests of space, briefly: full details are available upon request.
If both countries are to have the option to conduct R&D in both goods, we must have nNA =
nSA and nNB = nSB, irrespective of whether H N is equal to or slightly above H S : otherwise one
country will have an efficiency advantage over the other in conducting R&D in the good in
which the equality does not hold. Total H input into R&D in each good is the sum of each
country’s input, with each country’s input enjoying intra- and inter-country spillover benefits
from that good’s production. (With nNA = nSA and nNB = nSB, the amounts of these combined
spillover benefits for each good are the same across countries.) The SP’s optimization problem
can then be set up in a manner very similar to that above, the main differences being that (a) fA
(and fB) are no longer choice variables, each being equal to 1, and (b) a new choice variable is
introduced, namely the sum of the two countries’ H input into R&D in, say, A, with the sum of
33
the inputs into B R&D then determined residually from the two countries’ combined H-marketclearing condition. With τ < 1 we also have a non-negativity constraint on total B R&D input.
Carrying out the optimization, we discover interestingly that this non-negativity constraint is
binding: with τ < 1 both countries will optimally conduct R&D only in A. In order to simplify
further mathematical calculations, and to focus directly on the trade-off described earlier, we
now assume identical factor intensities ( θ = β ). The total H input into production in either
country will then equal 1 + τ times the input into A-production, and we obtain
ns*
(87) (1 + τ ) H kA = θ (1 + τ )αaρ /(1 + λ )(1 − α ) , k = N, S,
the superscript ‘ns’ denoting ‘non-specialized’ (in production). The existence condition is thus
that this be less than or equal to each country’s H endowment.
In our earlier complete
specialization case, with θ = β the optimal H input into A-production in N (the only good that N
produces) equals the optimal H input into B-production in S, and (83) specializes to
*
(83' ) H NA
= θαaρ /(1 − α ).
Comparing this to (87), which economy devotes more H to production, and hence less to R&D,
depends on τ relative to λ . At the initial date, 0, when the levels of nA (= nNA + nSA) and nB are
the same in the fully specialized (fs) and ns economies, the economy which devotes more
resources to production will enjoy higher Cj’s and lower Pj’s (j = A, B), but will innovate less
rapidly. Using (63), the utility levels enjoyed in these economies are determined to be:
(88) U
fs
(1 − α )(1 + τ ) H N + τH S θaρα 1 1 − α
1−α
−
−
[
]− [
ln n A0 − ln J + θ (1 + τ ) ln
=
2
ρ α
θαaρ
1+τ
1−α
αaρ
(1 + τ )(1 − θ ) ln Z N ] −
(89) Uns =
(1 + τ )[θ ln
τ 1−α
[
ln nB0 − ln L]
ρ α
(1 − α ) (1 + λ )(H N + H S ) θaρα (1 + τ ) τ lnτ 1 1 − α
[
−
]+
− {
ln n A0 − ln J +
ρ
ρ α
2
1−α
αaρ 2
1−α
τ 1−α
+ (1 − θ ) ln(1 + τ ) − ln 2 + θ ln(1 + λ ) − (1 − θ ) ln Z N ]} − [
ln n B 0 − ln L].
θαaρ
ρ α
34
Some special cases serve to illustrate the possible outcomes (for convenience, we set H N =
H S , factor endowments being of lesser significance when factor intensities are identical). First,
let τ = 1: the fs economies will devote more resources to R&D and will grow faster, but the ns
economies will have higher initial consumption levels.23 Which have higher lifetime utility then
depends on ρ : however, ρ is bounded above by the existence conditions for equilibrium
growth paths in the fs and ns economies, that for ns being more restrictive, and it can be shown
that for all values of ρ at or below this upper bound Ufs exceeds Uns. This validates our earlier
claim that complete specialization is optimal when τ is equal to or slightly below 1.
Second, suppose instead that τ = λ : it is then readily shown that Uns > U fs. Although the fs
economies enjoy higher spillover benefits from complete specialization, this is dominated by the
fact that S is constrained to produce, and conduct R&D in, only the less desired product, B.
Lastly, as τ falls close to 0, Uns still exceeds U fs. In general, then, for a range of lower values of
τ non-specialization appears advantageous, although unfortunately whether this occurs
uniformly for all values of τ in this range cannot be established without numerical simulations.
The foregoing results also hold for H N slightly in excess of H S , provided λ is not too close
to 1, and we have
Proposition 7. If τ is significantly below unity, then a switch to a regime in which both
economies produce equal amounts of A and of B goods, and conduct R&D only in industry
A, can be optimal.
Returning to the question posed just after Proposition 6, Southern countries may indeed wish
to pursue the development of high-tech industries if τ is appreciably below 1, since such
industries have higher ‘market potential’. If real-world complexities which our two-sector model
does not fully encompass are taken into account, further considerations arise. Within each broad
sector there may well exist niches in which there is asymmetric market demand in N and S.
Biotechnology geared to developing treatments for diseases more prevalent in certain areas is
With τ literally equal to 1, the allocation of R&D resources between A and B in the ns case
becomes indeterminate, since both goods are equally desirable, although the total R&D resource
allocation is determinate: however, by continuity the result reported in the text for τ = 1 remains
valid for τ slightly below 1, in which case the ns economies specialize completely in A R&D.
23
35
one example: consumer tastes in a variety of products, such as automobiles and mobile phones,
may also be highly differentiated. Entrepreneurs and innovators with better information on
domestic demands may thus find it worthwhile to first cater to these demands before venturing
abroad. Productive and R&D efficiencies may also differ across countries and products. All
these imply that both N and S may find sub-sectors, in both A and B, worth producing and
innovating in. Finally, new industries are continually arising, which may attract N resources
from existing ones, which S researchers and producers may then move into.
VI Conclusion
As a natural progression, Southern countries such as South Korea, Taiwan, China, India, and
Brazil have evolved from the production of increasingly sophisticated goods and services to the
conduct of R&D in the same or related product lines, aimed at developing new varieties of
products or improved production components and processes. This paper is to our knowledge the
first that seeks to dynamically model (horizontal) innovative, and not simply imitative, activity
by S firms, and endogenous growth models which incorporate feedback between existing
production varieties and the development of new varieties are an excellent point of departure for
this purpose. For a more inclusive treatment of production patterns, our expanding-productvariety model is complemented with a ‘Heckscher-Ohlin’ structure with two countries, two
monopolistically competitive sectors both engaging in production and R&D (R&D and
monopolistic competition are of course absent from the Heckscher-Ohlin model), and two inputs,
H and Z, of which only the former is required for R&D. As well, we assume that cross-national
spillovers of production-related R&D know-how are less potent than intra-national.
Taste
patterns also play a significant role. The resulting interrelationships between factor endowments,
factor intensities, tastes, production patterns, and sectoral R&D produce a complicated but rich
analysis. For tractability, unfortunately, we are constrained to conduct only local analyses,
although it is likely that our results apply over a wider range.
Being Z-abundant, S specializes in R&D in the Z-intensive product (if it is equally demanded
by consumers). Other results are more unexpected. wH may either increase or decrease when
H N is increased. An increase in H N increases the innovation rate in S too, on account of the
induced re-allocation of production patterns across countries. If cross-national spillovers are
weak or non-existent, and the Z-intensive product is less attractive to consumers than the other
36
(so that S produces more of the H-intensive product under trade than it otherwise would, even
though it does not innovate in it), it is possible that the North becomes worse off under trade than
under autarchy. Again, if cross-national spillovers are weak or non-existent, an increase in H S
(by less than H N ) can actually reduce world innovation and well-being, by inducing less
production specialization across countries, and hence weaker intra-national spillovers from
production to R&D. When τ is equal or close to 1 the achievement of constrained social
optimality (allowing for R&D and consumption subsidies, but not production or input subsidies)
requires that each country specialize completely in production and R&D in one industry, so as to
maximize the spillover benefit to R&D (and in this case an increase in H S definitely enhances
innovation and welfare). For lower values of τ , however, a production-non-specialization
regime, in which both countries produce equal amounts of both goods, but conduct R&D only in
A, can be optimal. Less formally, we have suggested that asymmetries in customer demands and
other factors across countries could lead both N and S to find niches in each broad sector or
industry to specialize in, all the while continuing to exploit the ‘leverage’ to R&D from enhanced
production specialization that has been a major focus of our analysis.
In sum, our analysis suggests that a dynamic-general-equilibrium model, which focuses on
the interrelationships between production patterns, R&D and consumer tastes across countries,
with the first-mentioned of these influenced by relative factor endowments and factor intensities,
is capable of yielding interesting and valuable new insights. Further research, along the lines
suggested at the end of Section V as well as studying vertical R&D, will lead to even better
understanding of the fascinating, evolving dynamics of North-South trade and innovation.
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