Foreign Direct Investment and the Degree of Southern
Penetration∗
Chia-Hui Lu†
Institute of Economics, Academia Sinica
February 18, 2005

Abstract
I develop a dynamic general equilibrium model of North-South trade to investigate towhat extent the South is able to enter international markets through foreign direct
investment (FDI) that serves as a channel for technology transfer. In low- and mediumtech industries, the South catches up and competes with the North on the strength of
its cost advantage. In response, the North abandons the low-tech industries and instead
strengthens its technological lead to escape the South’s competition in medium-tech industries where the North and the South take turns to be the dominant producer in themarket. In high-tech industries, the substantial technological gaps deter the South fromentering. The measures of the three types of industries are endogenously determined.
Countries’ sizes, developmental levels, and openness are linked to the proposed measuresof penetration. The effectiveness of FDI and R&D policies is further assessed.
JEL No: F11, F12, F21, F23
Keywords: Foreign Direct Investment; Market Penetration; Innovation; Product-cycle
Trade.

∗I am grateful to M. Scott Taylor, my advisor, for his encourage and invaluable guidance. I am also

thankful to Robert Staiger, Robert Baldwin, Maria Muniagurria, Jang-Ting Guo, An-chi Tung, and Leonard
K. Cheng for their very helpful comments and suggestions. Any errors are my own.
†
Institute of Economics, Academia Sinica, Nankang, Taipei 115, Taiwan. Tel 886-2-2782-2791 ext. 503.
E-mail: clu@econ.snica.edu.tw

1

Introduction

Over the last 15 years, the share of foreign direct investment (FDI) being channeled to lessdeveloped countries (LDCs) has more than doubled (from 15.3% in 1989 to 30.7% in 2003).1
Through FDI, industries in developed countries (DCs) migrate to the LDCs to exploit their
low production costs, and in the process technologies are also transferred across borders. As aconsequence, LDCs have been absorbing new technologies, expanding their product mix, andbecoming a far larger presence in international markets. In response to the deepening penetration of world markets by LDCs, industries in DCs have either abandoned certain markets
or have intensified their research and development (R&D) in order to further strengthen theirtechnological leads.
This paper develops a dynamic general equilibrium model of North-South trade to analyze the role of international direct investment as a means for the less-developed South tocatch up and compete with the North in the world market. By combining the quality-laddermodel formalized in Grossman and Helpman (1991a, b) (henceforth, the GH model) witha continuum of industries, each of which has a distinct technological sophistication level, I
investigate how far toward the high-tech end of the industry spectrum the South is able topenetrate. It is shown that the North-South technological gaps in high-tech industries are so
wide that the South is deterred from entering. However, in low and medium-tech industries,
the South is seen to catch up with the North by absorbing production technologies embodiedin FDI. As the technological gaps between two countries narrow, the low-wage South is able
to enter the international market and compete with the North. This model predicts thatin response to competition from the South, the North will abandon the market outright in
low-tech industries, but will seek to recapture the market by strengthening its technologicallead in medium-tech industries.2
This model endogenously determines the ranges of the three types of industries, each
1

Source: FDI database, UNCTAD. http://www.unctad.org.
These implications are consistent with the findings of recent empirical studies on North-South FDI and
product-cycle trade. For example, Yeaple (2003) shows that the U.S. outward FDI to less-developed countries
is concentrated mostly in the low- and medium-skilled industries and least of all in the highly-skilled industries.
Schott (2002) examines U.S. product-level trade data during the 1990s and finds that the U.S., facing lowwage competition, has exited the textile goods market in response, but has at the same time engaged inquality-upgrading in the machinery industry.
2

2

of which reveals a different degree of penetration. As illustrated in Figure 1, the marginalindustry that separates the medium-tech group from the high-tech group denoted by z̄ represents the uppermost industrial boundary that the South has ever been able to penetrate.
The marginal industry that separates the low-tech group from the medium-tech group denoted by z represents the uppermost industrial boundary in which the South’s penetration ispermanent–the North has no attempt to recapture the world market after being driven out by
the low-cost South. The set of medium-tech industries ZM ≡ (z, z̄) measures the industrial
range, in which the Southern penetration is temporary. The North and the South take turns
to be the dominate producer in the world market, and product cycle trade prevails. A productcycle starts when a Northern firm shifts production to the South via FDI, and it ends when asuccessful Northern R&D brings production back to the North. From there, FDI intensities
iF (zM ) determine how quickly, on average, an industry moves to the South. The lower the
FDI intensities, the longer it takes for the South to absorb the new technology and replace
the North as the dominant producer in the world market. Thus, iF (z1M ) is adopted to reflect
the period during which the North dominates the production. Similarly, the R&D intensities
iR (zM ) determine how long, on average, it will take for the North to upgrade product quality and recapture the market from the South. The lower the Northern R&D intensities, thelonger it will take for the North to create a better version that will drive the South out of themarket. Therefore, iR (z1M ) is adopted to capture the period during which the South dominates
the production in the industry. This paper features four dimensions {z̄, z, iF (z1M ) , iR (z1M ) }that comprehensively measure the extent of the South’s penetration.
Figure 1: Degrees of Southern Penetration

Temporary

Permanent
z

}|

{z

Never

}|

{z

z

0
Low-tech (ZL )}|z̄Medium-tech (ZM ){1
High-tech (ZH )I relate home and host countries’ sizes, developmental levels, openness as well as the FDI
3

and R&D subsidy policies to these four measures. It is found that the FDI hosting country’s
characteristics and its FDI promoting policies have an inconsistent impact on its ability topenetrate the markets according to measurements based on different perspectives. In otherwords, improving the South’s ability to penetrate in some respects always comes at the expenseof losing in other respects. This implies that the North’s decision regarding which country
among the Southern countries with their different developmental levels, sizes, and policies
should be chosen to receive FDI plays a critical role in shaping the structure of international
production. This study also sheds some light on the impact of FDI on innovation, which serves
as the engine of economic growth. Larger country sizes and an improved developmental level,
whether in the North or the South, increase effective resource endowments and intensify hightech innovations. FDI and R&D subsidy policies, that neither augment the labor endowment
nor improve labor productivity, alter only investment incentives and may lead to a contraction
in high-tech innovation.
In the literature, the chain reaction–FDI affects the home country’s R&D investment,
followed by the firms’ investment decisions concerning FDI and R&D determining the extent
of the Southern penetration that restructures the international production and trade patterns–
is linked for the first time in this paper. Understanding this linkage is essential for economists
and policy-makers concerned with the growth and welfare impacts of FDI. FDI liberalization
changes the pattern of an industry’s evolution and the rate at which new technologies aredeveloped. As R&D is the engine of economic growth, one can move forward to investigate
how the restructuring of the home and host countries’ manufacturing sector affects growth. It
is also quite valuable knowing, based on the status quo, whether adjusting their FDI or R&D
policies in certain ways would be likely to help governments promote growth. This study also
sheds some light on this issue.
The modeling strategies adopted in this paper are to a large extent based on and inspiredby existing studies on product-cycle trade. Vernon’s (1966) product cycle hypothesis firstlinks the dynamic patterns of FDI with those of trade. The early wave of the productcycle literature regards imitation as the only way in which international technology transfer
can take place–see Krugman (1979), Jensen and Thursby (1986), Segerstrom, et al. (1990),
Grossman, and Helpman (1991), and Glass (1997). The imitation rate is exogenously given

4

in Krugman (1979) and Segerstrom, et al. (1990), and is chosen by a social planner inJensen and Thursby (1986). Grossman and Helpman (1991b) endogenize R&D and imitation
processes–the driving forces behind the product-cycle trade–and investigate the impacts ofcountry sizes and subsidies on the innovation and imitation rates. In the same spirit as
Grossman and Helpman, Glass (1997) incorporates heterogeneous preferences and models agradual imitation process to determine the extent of Southern penetration from the verticaldimension–that is, she determines how far the South can penetrate the quality ladder via
imitation. In contrast to and also to supplement the aforementioned studies, Glass and Saggi(2002), Antràs (2003), Cheng, Qiu, and Tan (2004), and Lu (2004) model endogenous FDI
as giving rise to product-cycle trade. However, both Glass and Saggi (2002) and Antràs(2003) consider an economy consisting of a single industry where the discussion is confinedto the speed of technology transfer in that industry and is unable to capture the extent
of the Southern competition throughout the whole of the manufacturing sector that covers
heterogeneous industries. Cheng, Qiu, and Tan (2004) incorporate expatriates, the specificfactor for FDI, into a static continuum Ricardian model to identify the industrial range ofSouthern penetration. My results complement to their. Lu (2004a) serves as a baseline modelfor this study.
This paper is organized as follows. Section 2 describes the model setup regarding consumers’ preferences, the firms’ production, R&D and FDI technologies, as well as the firms’
pricing strategies under Bertrand competition. Section 3 summarizes the equilibrium market
structures. Section 4 describes the steady state equilibrium. In Section 5, the comparative
static analyses are looked at in some detail to examine the implications of the countries’
characteristics, as well as the FDI and R&D subsidies. Section 6 concludes.

2

The Model

Built on the GH model, R&D is product-specific, and it moves a product up its quality
ladder one step at a time. Inspired by Taylor (1993),3 I assume that the extent of quality
improvement with each step up the product ladder is higher in some industries than in others.
I consider a continuum of industries, z ∈ [0, 1]. The inventive step λ(z) shows the rate of3

Taylor (1993) introduces heterogeneous R&D and production technologies across industries.

5

quality improvement for each innovation with which each industry is associated. λ(z) is
exogenously given, λ0 (z) > 0, and λ(0) = 1. Within each industry, there is a continuum ofvarieties, y ∈ [0, 1]. The product space is defined on a unit square, (z, y) ∈ [0, 1] × [0, 1].4
Different versions of each product are indexed by j = 0, 1, 2, ..., which indicates a particular
position along the quality ladder (product line). The quality of good (z, y, j) is denoted byq(z, y, j) = λ(z)j . A successful R&D brings a new version of a product to light, and theblueprint is protected by a worldwide infinitely lived patent.
Labor is the only factor that is not mobile across borders. The North is endowed withskilled labor L that is capable of conducting R&D to bring forth new versions of each productand can engaged in production. The South is endowed with unskilled labor L∗ ( hereafter
an asterisk is adopted to denote Southern variables). Southern labor is employed in two
activities–technology transfer and production. In this paper, FDI refers to the process oftechnology transfer and is distinguished from production. It takes the form of building up
production sites in the South and modifying operating procedures to suit Southern conditions
that requires Southern labor input and is characterized by uncertainty. I assume that the costof transferring the newly invented technology is prohibitively high and only the standardized
technologies can be transferred to and implemented in the South. A production technology issaid to be standardized if it is leapfrogged by that of a newly-invented version of a product.5
After FDI is complete, Southern labor is also used in manufacturing. Northern firms referto those producing in the North, and multinational entrepreneurs (MNEs) refer to thosesucceeding in FDI and producing in the South. An MNE hires Southern workers, retains fullcontrol over production, and remits all profits back to the North. Let J(z, y) and J ∗ (z, y)denote the versions of product (z, y) produced by the Northern (industry) leader and the
MNE leader, respectively, J(z, y) − J ∗ (z, y) ≥ 1.
Supposing that there is no trade friction, the cheaper labor costs in the South is the
only incentive for a firm to undertake costly and risky FDI. This model features endoge4

For example, there are the textile, office machinery, and road vehicle industries. Within the road vehicleindustry, there are different varieties of products, such as sports cars, compact cars, vans, etc.. As I will show
later that each product (z, y) follows a stochastic evolution process in the dynamic equilibrium. By assuming
a continuum of varieties with homogeneous inventive steps within each industry, I am able to apply the lawof large numbers such that the aggregate evolution rates in an industry are non-random and constant.
5
This assumption keeps the technology of the leading-edge version from being transferred to the South. It
is necessary to give rise to a product cycle similar to Vernon’s description.

6

nous cost-seeking FDI and quality-upgrading R&D process that potentially improve firms
competitiveness. The R&D and FDI ventures are financed by Northern Savings.6

2.1

The Consumer’s Problem

Consumers in the North and South face the same prices and share an identical, time separable,
and homothetic utility function. They can save and rent only in the domestic financial market.
The representative Northern consumer’s problem is described first. The expected discounted
value of the infinite lifetime utility U is:
U = E0

·Z ∞
0

¸
−ρt

e

log u(t) dt ,(1)

where E0 is the expectation conditional on the information available at time zero, ρ is therate of time preference (constant and positive), and log u(t) is the utility flow at time t. The
instantaneous utility function is defined as:
log u(t) ≡Z 1Z 100J(z,y,t)log Xq(z, y, j)d(z, y, j, t) dy dz,

(2)

j=0

where q(z, y, j) is the quality of good (z, y, j), d(z, y, j, t) denotes the demand at time t, andJ(z, y, t) represents the leading-edge version of product (z, y) at time t. The representative
consumer maximizes utility, (1), subject to an intertemporal budget constraint:
Z ∞0

e−R(t) E(t) dt ≤ A(0),(3)

where A(0) is the present value of the stream of labor income plus the value of asset holdings
at time 0, and R(t) denotes the cumulative interest factor up to time t. Let r(t) be theinstantaneous interest rate. R(t) =Rt

0 r(s)ds, and Ṙ(t) = r(t).

The consumer’s expenditureE(t) can be expressed as:
Z 1 Z 1 J(z,y,t)X
E(t) =p(z, y, j, t)d(z, y, j, t) dy dz,
0

0

(4)

j=0

where p(z, y, j, t) denotes the price of good (z, y, j) at time t.
A utility-maximizing consumer first chooses to spend equal shares of total expenditure oneach product, and then, within the same product line, only the version that charges the lowest
6

Segerstrom et al. (1990). also make this assumption.

7

quality-adjusted price is purchased. This principle applies to the Southern consumers and theaggregate economy. Let j(z, y, t) denote the version of product (z, y) with the lowest qualityp(z,y,j,t)argminadjusted price at time t, j(z, y, t) =. The world aggregate demand{j=1,...,J(z,y,t)}q(z,y,j)functions are shown as follows: E W (t)/p(z, y, j, t),

if j = j(z, y, t) 0,otherwisedW (z, y, j, t) = ,(5)where E W (t) is the world aggregate expenditure. The Northern consumer’s optimal expenditure profile E(t) is dictated by the following differential equation:Ė(t)/E(t) = Ṙ(t) − ρ = r(t) − ρ.

(6)

The Southern consumer, however, can not buy shares of either Northern firms or MNEs
and spends all wage income on consumption. Let w∗ (t) denote the Southern wage. I normalizew∗ (t) = 1 ∀t, and thus E W (t) = L · E(t) + L∗ .

2.2

The Firm’s Problem

Notice that J(z, y) and J ∗ (z, y) denote the quality levels of the industry leader and the MNE
leader, respectively.7 By an appropriate choice of units, I set the unit labor requirements ofNorthern and Southern labor per unit of output to one, i.e. a(z, y, j) = 1, ∀j ≤ J(z, y), anda∗ (z, y, j) = 1, ∀ j ≤ J ∗ (z, y) that makes the marginal cost of every good equal to the wage
rate of the country where the good is produced.
Firms devote their efforts to R&D. The success of R&D follows a Poisson process, withthe arrival rate depending on the current R&D level. A firm engaging in R&D at intensityiR (z, y) for a length of time dt has probability iR (z, y)dt of success in developing the next
version of product (z, y). Let aR (z, y) = aR denote the unit Northern labor requirement
per unit of R&D intensity and VR (z, y) denote the present market value of each blueprint.
Then, R&D at intensity iR (z, y) requires aR · iR (z, y)dt units of Northern labor that creates
an expected value of VR (z, y)iR (z, y)dt for the investor. Investors act to maximize expectedmaxvalue, i.e. iR (z,y)≥0(VR (z, y) − ωaR )iR (z, y)dt, where ω denotes the relative Northern wage.

An equilibrium with positive and finite R&D investment implies that V R (z, y) = ωaR , and7

Here and henceforth I suppress the time domain when no confusion arises from doing so.

8that iR (z, y) = 0, if V R (z, y) < ωaR . Since the formation of R&D technology implies constantreturns to scale in research efforts together with the assumption of free entry into R&D,
investors are prevented from earning excess returns, i.e. V R (z, y) = ωaR , and the individual
investor is indifferent to the levels of investment intensity.
Analogous to the R&D technology, the success of FDI also follows a Poisson process. Leta∗F (z, y, j) denote the Southern unit labor requirement per unit of FDI intensity. a∗F (z, y, j) =a∗F if j < J(z, y), and a∗F (z, y, j) = ∞ if j = J(z, y). Let V F (z, y, j) be the prize for an FDI
success of good (z, y, j). An equilibrium with positive and finite FDI investment implies that
V F (z, y, j) = a∗F . I further assume that the cost of inventing a new blueprint is higher thanthat of transferring an existing blueprint (a∗F < aR ) that ensures that, in some industries,
followers undertake FDI in an attempt to replace the industry leader.

2.3

The Bertrand Pricing Game

Firms owning patents j ∈ {1, 2, .., J(z, y)} compete as price-setting oligopolists. The one whocharges the lowest quality-adjusted price captures the whole market. If all firms are producing
in the North, they face the same production cost ω, and the industry leader charging a
price a shade below λ(z)ω takes the whole market and earns positive profits. The size ofthe inventive step λ(z) shows the price premium that reflects the consumer’s willingness topay for a superior quality level. An industry leader’s price markup is positively correlatedwith λ(z) which suggests that the quality-advantage stemming from R&D is increasing with
the industry’s technology sophistication level. In the case where some of the followers havetransferred their technologies to the South, faced with the same producing cost w∗ = 1, the
MNE leader J ∗ (z, y) has the highest ability to undercut the industry leader and sets a price∗ωJ(z,y)−J (z,y)
measures the quality gaps between theslightly below λ(z)J(z,y)−J∗ (z,y) , where λ(z)industry leader and the MNE leader. The limit price set by J ∗ (z, y) to undercut the industry
leader cannot be smaller than the production cost and is negatively correlated with λ(z), whichsuggests that the cost-advantage stemming from FDI is more significant in the relatively lowtech industries than in the high-tech industries. In sum, the relative “importance” of a firm’s
quality advantage and a firm’s cost advantage in the price-setting competition is increasing
in z.

9

3

Market Structure

To keep the evolution of each product tractable, I follow Grossman and Helpman (1991a) and
Glass (1997)’s assumption that the industry leader has no advantage in conducting R&D andfaces the same R&D costs (aR ) as the followers do. In the case where the industry leader
currently dominates the production, the producing leader gains only incremental profits if it
succeeds in R&D and becomes a two-step-head industry leader in that its profits are strictly
less than the profits gained by a non-producing firm if it succeed in R&D. Since the supply
of non-producers willing to invest in R&D at the equilibrium interest rate is perfectly elastic,
it follows that the rewards of R&D undertaken by the producing leader do not justify the
research cost, and the producing leader does not engage in R&D.8
In the absence of FDI moving production to the South, all goods are produced in the
North. The evolution of each product is characterized by a process in which the productclimbs stochastically up its quality ladder. The industry leader, upon attaining the mostsuperior quality, wins the pricing game and gains temporary monopoly profits until a better
version in the product line is invented by non-producing followers.
When the North lifts the ban against outward FDI, followers have one more dimension to
improve their competitive edge–the moving-up strategy improves their quality advantages andthe moving-out strategy improves their cost advantages.9 Any investment project is financedin the capital market; only the most profitable projects are funded. Given that the industry
leader currently captures the world market, followers choose between two means–R&D and
FDI–in an attempt to drive off the industry leader. The choice made by the nearest (secondto-top) follower (henceforth N F ) sufficiently reveals the strategy that would be implemented
by other followers. The reason is quiet intuitive. Notice that all followers face the same cost
per unit of FDI intensity (a∗F ). A successful FDI venture, however, brings higher rewards to
N F than it brings to other followers with more obsolete technologies. Since the supply of
N F willing to invest in FDI at the equilibrium interest rate is perfectly elastic, it follows thecosts of capital in equilibrium will be such that followers have blueprints older than N F findthat FDI projects to have negative expected present value. Therefore, within a product line,
89

See Grossman and Helpman (1997, p.93) for the detailed proof.
I assume that there have been at least two versions in each product line prior to time 0, i.e. J(z, y, 0) ≥ 2.

10

followers apart from N F do not engage in FDI. Moreover, all followers face the same costs
per unit of R&D intensity (aR · ω). A successful R&D brings the same profits to followers
regardless of the vintage of their current technologies. If R&D is more profitable than FDI for
N F , it must be true that other followers will also participate in the new round of the patent
race. Instead, if R&D is less profitable than FDI from N F ’s point of view, N F will implement
the moving-out strategy but not the moving-up strategy, and the R&D ventures undertaken
by other followers will not be funded in the capital market at the equilibrium interest rate.
It is prohibitively expensive for the industry leader to engage in FDI. Therefore, N F ’s choice
between the moving-out and moving-up strategies determines the evolution direction of eachproduct.
To make a costly and risky investment venture profitable, regardless of whether it involves
FDI or R&D, two things must be true. First, a successful investment must be able to outrace
the producing firm in the pricing game, and to earn positive profits. Second, the cost of thisventure must not be so high as to make it too expensive.

Assumption 1: λ(0) < ω < λ(1).
Since λ(z) is continuous and increasing in z, Assumption 1 ensures that z 0 exists and is
unique, where λ(z 0 ) = ω, and z 0 ∈ (0, 1). Notice that ω reflects the cost advantage accruing
to MNEs. In any industry z ∈ [z 0 , 1], ω ≤ λ(z), and the improved competitiveness via thecostly FDI venture is not sufficient to beat the industry leader in the Bertrand game (theindustry leader can set a price equal to λ(z) to undercut the MNE leader whose technology
is one step below the leader, and still earn positive profits). Thus N F will implement themoving-up strategy instead of the moving-out strategy. This, however, does not imply thatN F in industry z ∈ [0, z 0 ) with ω > λ(z), will necessarily prefer the moving-out strategy to
the moving-up strategy. Success in both forms of venture will enable the current N F to driveout the current industry leader from the market. Therefore, N F will then have to compare
the rewards and the costs of these two actions and then choose the most profitable one. In
industry z = 0, with λ(0) = 1, the success of the costly R&D does not improve productquality, and N F will undertake the FDI venture for sure. By the property of continuity, there

11exists an industry z̄ ∈ [0, z 0 ) in which N F is indifferent to the moving-up and moving-out
strategies. Since, as shown earlier, the relative importance of a firm’s quality advantage to afirm’s cost advantage in the price-setting competition is increasing in z, the moving-up strategy is strictly preferred in industry z ∈ (z̄, 1], and is strictly dominated by the moving-out
strategy in industry z ∈ [0, z̄).
a∗1
Proposition 1. Let Z̄(z) ≡ aFR (1− λ(z))+ λ(z) where z̄ satisfies Z̄(z̄) = ω. In industry z̄, N F

is indifferent to the moving-up and the moving out strategies given that the industry leader isthe extant producer. (Proof in appendix).

In the situation where N F in industry z ∈ [0, z̄) succeeds in the FDI venture and dominates the production in the South, non-producing firms including the industry leader andother followers have no other choice than to select the moving-up strategy to enhance theircompetitiveness. However, in industries with λ(z)2 < ω, the inventive steps are relatively
small, and the competitiveness gained from R&D accruing to the non-producing firms is not
sufficient to drive out the current MNE leader (the MNE leader can set a price equal toωλ(z)2to undercut the new industry leader who has two-step ahead technology, and still earn

positive profits). Let Z(z) ≡ λ(z)2 and Z(z) = ω. Non-producing firms have no incentive toundertake R&D to recapture the market in industry z ∈ [0, z] but engage in R&D as theyseek to recapture the market from the MNE leader in industry z ∈ (z, z̄).
a∗1
Lemma 1 Suppose Assumption 1 holds. Let Z̄(z) ≡ aFR (1 − λ(z)) + λ(z), and Z(z) ≡ λ(z)2 .

There exists 0 < z < z̄ < 1, where Z̄(z̄) = Z(z) = ω. (Proof in appendix).

Figure 2 shows that two schedules Z̄(z) and Z(z) intersect with ω at z̄ and z, respectively,that together divide the industry spectrum into three groups–from the low-tech end to thehigh-tech end, these being in order, ZL ≡ [0, z] denoting the set of low-tech industries, ZM ≡(z, z̄) denoting the set of medium-tech industries, and ZH ≡ [z̄, 1] denoting the set of hi-techindustries. For high-tech industries, N F (as in the cases of other followers) undertakes R&D
but not FDI in an attempt to outrace the current leader and recapture the world market.

12For any industry below z̄, that is, for the medium-tech and the low-tech industries, FDI ismore profitable than R&D; N F undertakes FDI but not R&D in an attempt to outrace thecurrent leader and recapture the world market. ω and Z intersect at z. This denotes the
cut-off industry below which, when the product is produced in the South, the R&D ventures
undertaken by non-producing firms yield negative profits; outsiders simply exit the market.
For any industry above z, i.e. for any medium-tech industry, non-producing firms engage in
R&D, and race to invent the next generation.
The three industry types reveal different extents of Southern penetration. The Bertrand
equilibrium price of each product, and the firms’ optimal R&D and FDI intensities are summarized in the following subsections.
Hi-tech Industries
For any hi-tech industry zH ∈ ZH , the industry leader undercuts N F by charging price
³

´

E(t)
P̃ (zH ) = λ(zH )ω, and realizes sales X̃(zH ) = λ(z, yielding profits π̃(zH ) = 1 − λ(z1H ) E W .
H )ω

The premium charged, λ(zH ), reflects the consumers’ willingness to pay for a higher-quality
version than N F could produce, and reflects the leader’s ability to mark-up price in the
Bertrand competition. Since Z̄(zH ) > ω, all followers, the non-producing firms, initiate a
new patent race in an attempt to outrace the current leader. The free entry in the R&D
implies that the expected net profit from R&D equals zero in equilibrium, VR (zH ) = ωaR ; theno arbitrage condition in the financial market requires that the stock of any hi-tech product
H)− iR (zH ) = ρ. The hi-techyields a certain return equaling the time preference rate, i.e. Vπ(zR (zH )

R&D intensities are shown in terms of world expenditure, and the North-South relative wage,
as follows:³iR (zH ) =´

1 − λ(z1H ) E W
ωaR

− ρ.

(7)

Ongoing R&D continually moves each high-tech product up its quality ladder; the hi-techindustries never leave the North, and the South never penetrates.

13

Low-tech Industries
In any low-tech industry, zL ∈ ZL , the inventive steps are very small, and ω > λ(zL )2 > λ(zL ).
The cost advantage dominates both the one-step quality advantage and the two-step quality
advantage. N F undertakes FDI in an attempt to take advantage of the lower production costin the South, and to outrace the industry leader in the pricing game. When N F succeeds inthe FDI venture, it becomes an MNE leader, and undercuts the industry leader by charging
W

price P̃ (zL ) = λ(zωL ) , and makes sales X̃(zL ) = λ(zLω)E , yielding positive profits π̃(zL ) =³´

1 − λ(zωL ) E W . The discount charged reflects consumers’ willingness to pay for a lower-quality

version than the industry leader could produce. Since the two-step-ahead quality advantage
λ(zL )2 resulted from further innovation is still dominated by the MNE leader’s cost advantage,
the R&D venture aimed to bring the next version to light is not profitable. No R&D ventures
are undertaken at the the equilibrium interest rate, and iR (zL ) = 0. The MNE leader enjoys
permanent monopoly profits. Each low-tech product permanently stagnates in the South once
production is moved to the South via FDI.
Medium-tech Industries
In any medium-tech industry, zM ∈ ZM , each product repeatedly experiences a two-stage
life cycle. A product cycle starts when a Northern firm shifts production to the South via
FDI, and it ends when a successful Northern R&D brings production back to the North.
Let ZM 1 and ZM 2 denote the sets of products shifting in Stage 1, and Stage 2, respectively,
where ZM 1

S

ZM 2 = ZM . In Stage 1, the cost advantage dominates the one-step quality

advantage, ω > λ(zM 1 ), the MNE leader undercuts the industry leader by charging priceWP̃ (zM 1 ) = λ(zωM 1 ) , and realizes sales X̃(zM 1 ) = λ(zMω1 )E , yielding positive profits π̃(zM 1 ) =³´

1 − λ(zωM 1 ) E W . Since λ(zM )2 > ω, the two-step-ahead quality advantage λ(zL )2 resulted

from further innovation will dominate the MNE leader’s cost advantage. Non-producing
firms race to bring a higher version to light in an attempt to recapture the market. The
M1)
no arbitrage condition, Vπ(z− iR (zM 1 ) = ρ, together with the free entry in the FDI, i.e.
F (zM 1 )VF (zM 1 ) = a∗F solve the equilibrium medium-tech R&D intensities:´³

iR (zM 1 ) =1 − λ(zωM 1 ) E W
a∗F
14

− ρ.

(8)

The MNE leader produced in the South gains temporary monopoly profits until a higherquality version is brought to light by non-producing firms, and the duration of Southerndominance ends. The product cycle then transforms into Stage 2 that is denoted by ZM 2 . In
Stage 2, the industry leader charges price P̃ (zM 2 ) = λ(zM 2 )2 , and realizes sales X̃(zM 2 ) =EW, yielding profits π̃(zM 2 ) =λ(zM 2 )2³´

ω
E W . The premium charged reflects consumers’
1 − λ(zM22)

willingness to pay for the superior quality of the product than the MNE leader could produce.
M2)
The no arbitrage condition implies that Vπ(z− iF (zM 2 ) = ρ, and free entry in the R&D
R (zM 2 )implies that VR (zM 2 ) = ωaR . The equilibrium FDI intensities are shown:³

iF (zM 2 ) =´ω
1 − λ(zM
EW
2
2)

ωaR

− ρ.

(9)

The current industry leader produced in the North captures the world market until N F(the previous industry leader) succeeds in FDI. Once again, the South penetrates this industry
and becomes the dominator in the world market. The product shifts to Stage 1, and renews
its life cycle.
The North and the South take turns to be the dominate producer in the world market.
Two variables iF (zM ) and iR (zM ) are used to measure how fast the production of industryzM is moved to the South and moved back to the North. An FDI venture at intensity iF (zM )for a time length of dt has a probability iF (zM )dt of succeeding in transferring the technology
to the South. The inverse of the probability denotes the expected waiting time for the event(the success of FDI) to occur.10 The higher the FDI intensities are, the sooner, on average,
the South absorbs the new technology, and replaces the industry leaders. Therefore, FDI
intensity iF (z1M ) is adopted to capture the duration when the North dominate the production.
Similarly, the higher the Northern R&D intensities are, the sooner the North recaptures themarket from the South, and the shorter the Southern dominance period is.

1
iR (zM )is thusadopted to measure the time length during which the South dominates the production in a
medium-tech industry.
10

One of the notable properties of the Poisson process.

15

4

The Steady StateI consider the balanced growth steady state in which the instantaneous interest rate is constant and equals the time preference rate, r(t) = r = ρ. Allocations of resources to the various
activities remain fixed through time, which requires that the rate of each medium-tech industry moving out equals the rate of moving up, and the measures of each industry type areconstant.
Definition 1: Let nH , nL , nM , nM 1 , and nM 2 be the measures of ZH , ZL , ZM , ZM 1 , andZM 2 , respectively.
By definition 1, nH = 1 − z̄, nL = z, and nM = z̄ − z are constant as E W and ω areconstant in the steady state. Within each medium-tech industry, the measures of products
produced in the South and the North are also constant if:iR (zM 1 ) · nM 1 (zM ) = iF (zM 2 )nM 2 (zM ).

(10)

The right-hand side denotes the aggregate products moving to the South; the left-handside denotes the aggregate products moving back to the North. The net product flow in eachRz̄

medium-tech industry is zero, and nM 1 = nM 1 (zM )dzM , and nM 2 = z̄ −z −nM 1 are constant.
z

The steady-state conditions are simplified into the forms of the Southern and the Northernlabor clearing conditions as shown in (11) and (12):

z(ω)
Z
∗

L =
0

|

z̄(ω)
Z

EW

z̄(ω)
Z

EW

iF (zM )a∗F (1 − nM 1 (zM ))dzM .
ω dzL +
ω nM 1 (zM )dzM +λ(zL )z(ω) λ(zM )
z(ω)
{z

}

Labor Employment in Production

|

{z

(11)

}

Labor Employment in FDI

The left-hand side represents the aggregate Southern labor supply. On the right-handside, the first brace denotes the aggregate Southern labor employed in production in the lowtech and medium-tech industries; the second brace represents the aggregate Southern labor
employed in transferring Northern technology in medium-tech industries.
z̄(ω)
Z

L=
z(ω)

|

1

Z
EW
EW
(1
−
n
(z
))dz
+
dzH
M1 M
M
λ(zM )2λ(zH )ω
{zz̄(ω)

Labor Employed In Production16}z̄(ω)Z

Z1iR (zM 1 )aR nM 1 (zM )dzM +

+
z(ω)

|

{z

iR (zH )aR dzH .
z̄(ω)

(12)

}

Labor Employed In R&D
The left-hand side denotes the Northern labor supply. The right-hand side represents theaggregate Northern labor employed in manufacturing and in innovation. Let SS and N N
schedules depict the combinations of E W and ω that satisfy (11) and (12) that can be further
simplified as:
z(ω)

SS :

EW Z
L =
λ(zL )dz + (E W − ρa∗F ) · nP 1 (ω, E W ),
ω
∗

0

and
Ã

NN :

L=

!

EW
− ρaR · (1 − z(ω) − nP 1 (ω, E W )),ωwhere nP 1 (ω, E W ) is the aggregate measure of the medium-tech industries produced in theSouth. The N N schedule is upward sloping. Under Assumption 2,
1
Assumption 2: 2λ(z)< λ0 (z) < 12 , ∀z ∈ (0, 1)

the SS schedule is downward sloping that ensures the uniqueness of the steady state as
illustrated in Figure 3. The intersection of N N and SS that is labeled A represents thesteady state world expenditure E W and relative wage rate ω which together with Z̄(z) andZ pin down the margin industries of product cycle industries, z and z̄. Iteratively, the hitech innovation rate (7) the medium-tech moving-up rate (8) and the medium-tech moving-out
rate (9) are solved, which provide us sufficient information to assess the degree of Southern
penetration from different perspectives.

5

Comparative Statics Analysis

The paper features four measures {z̄, z, iF (z1M ) , iR (z1M ) } that comprehensively capture theextent of the South’s penetration.
In this section, I analyze how the initial steady state equilibrium, point A, is disturbed
by expansion in the Northern labor force L̂ > 0, by expansion in the Southern labor forceL̂∗ > 0, by an R&D subsidy sR > 0, and by an FDI subsidy sF > 0. One interpretation of17

L̂ > 0 is that the North improves its effective labor force through greater education. I discuss
which Northern policy–improving domestic labor productivity in production and innovationor altering the incentive for R&D–is more effective in deterring Southern competition. Similarly, I compare which Southern policy–improving domestic labor productivity in production
and absorbing new technology or altering the incentive for FDI–is more effective in strengthening Southern competition. The expansion of the Southern size can also be interpreted as aresult of another Southern country which is initially-closed and now integrates into the world
economy via trade and FDI liberalization. This exercise provides predictions about how thestructure of international production is affected as the less developed Southern countries (forexample, China) increase their involvement in the world economy. It also provides predictions about among a group of potential FDI hosting countries, how the degree of Southern
penetration varies with their labor endowments or FDI policies. This study alone considers the heterogeneous industry inventive steps and have much riche implications than the
single-industry model.

The Northern Labor Resource Expansion
The N N schedule captures the Northern labor market clearing condition, and it shifts to theright with L̂ > 0. The SS schedule remains in place. Point B in Figure 3 represents the newsteady-state equilibrium in which the relative wage has decreased while the world expenditure
has increased.
The Northern expansion weakens the MNEs’ cost advantages. In industry z̄, the movingup strategy now becomes more profitable than the moving-out strategy. Therefore, the setdz̄
of hi-tech industries expands, dL< 0. In industry z, initially, the North exits the market

when the South enters, now the North has incentive to undertake the next round of R&D,
since the two-step quality advantage dominates the Southern cost advantage. The measuredz
of low-tech industries shrinks, dL< 0. The range of medium-tech industries shrinks and ispushed toward the low-tech end of the industry spectrum.
In the new steady state, the weakened cost advantage deters competition from the Southin terms of the shrinkage in both the temporary and permanent Southern penetration ranges.
Within each medium-tech industry, the speed of industry moving out, however, is increased.

18

The intuition behind this is that the increased world expenditure increases sales, and thedecreased relative Northern wage decreases the Northern production cost, and these factors
together increase the instantaneous profits of the active industry leader; the profit rate of theactive industry leader is higher than the real effective interest rate (the real interest rate plus
the risk of losing earnings). The no arbitrage condition implies that an upward adjustment of
the leader’s risk of losing its monopoly position is needed in the new steady state, and thus
the FDI intensities undertaken by the non-producing firms in an attempt to drive out theindustry leader from the market increase as well. The impact on the duration of the Southerndominance further hinges on the magnitudes of the industry inventive steps. Specifically, theperiod during which the South dominates the production in the market is prolonged if andonly if the inventively step is relatively big, i.e. λ(zM ) > ΛL , where ΛL ≡ω

W dω dLdL dE W

1− Eω. From(7), it is trivial that the high-tech innovation is intensified by the increased profit rates. Notice that if λ(z̄) < ΛL , the innovation rate in each medium-tech industry increases. Together
with the reinforced high-tech innovation, the long-run growth rate is boosted.11 Proposition
2 summarizes the impacts of the Northern size expansion:

Proposition 2: The expansion of the North’s size (i) weakens the Southern cost advantage,
dω
dL

dz
< 0, (ii) shrinks the set of low-tech industries, dL< 0, (iii) expands the set of high-

(zH )
dz̄
tech industries, dL< 0, and (iv) raises high-tech innovation, diRdL> 0. (v) The set of< 0, and is pushed toward the low-tech end. For
medium-tech industries shrinks, d(z̄−z)dL(zP )each medium-tech industry zP , (vi) it accelerates
industry moving out, diFdL> 0 ; (vii) it³´

shortens the South’s dominant duration,d1iR (zP )dL< 0 , if and only if λ(zM ) < ΛL . (Proof in

Appendix).

The Southern Labor Resource Expansion
The SS schedule captures the Southern labor market clearing condition, and it shifts to theright with L̂∗ > 0. The N N schedule remains in place. Point C in Figure 4 represents the newsteady-state equilibrium in which the Northern relative wage increases, and world expenditure
11

Similar to G&H(1991a), innovation propels growth, and the growth rate is defined as the rate of increasein the consumption index.

19

also increases.
The Southern labor resource expansion improves the cost advantages of MNEs. In industryz̄, the moving-out strategy now is more profitable than the moving-up strategy. The set ofdz̄
the high-tech industries shrinks, dL∗ > 0. In industry z + ², ² > 0, in which, initially, theNorth launches a new round of R&D investment immediately after the South takes over theworld market, but now the North exits the market in response, since the two-step quality leadis not sufficient to make the new leader earn a positive profit as it competes with the MNE
dzleader. The set of the low-tech industries expands, dL∗ > 0. The range of the medium-techindustries also expands, and is pushed toward the high-tech end of the industry spectrum.
In the new steady state, the improved Southern cost advantage strengthens the South’s
competition in terms of expanding both the temporary and permanent penetration ranges.
Within each medium-tech industry, the duration of the South dominance, however, is shortened. By (8), the increased world expenditure and the lowered Southern relative wage together
increase the instantaneous profits of the active MNE. The returns of the stock of MNE leader
are now higher than the real effective interest rate. By the no arbitrage condition, an adjustment of a higher risk of losing monopoly position faced by the MNE leader is needed, andthus the medium-tech innovation rates increase in response.
The speed of industry moving out increases if only if λ(zM ) > ΛL∗ , where ΛL∗ ≡

r
W

1− Eω

ω

dω dL∗dL∗ dE W

The high-tech innovation is intensified by the expanded market size, even though the Northern relative wage is increased. Proposition 3 summarizes the long-run impacts of Southernsize expansion.

Proposition 3: The expansion of the South’s size, L̂∗ > 0, (i) improves the South’s costdzdω
advantage, dL∗ > 0, (ii) expands the set of low-tech industries, dL∗ > 0, (iii) shrinks the setdiR (zH )dz̄
of high-tech industries, dL> 0.
∗ > 0, and (iv) raises the high-tech innovation ratesdL∗(v) The set of medium-tech industries expands d(z̄−z)> 0, and is pushed toward the high-techdL∗
end. For each medium-techindustryzP , (vi) it shortens the duration that the South domi´³nates the production,d1iR (zP )dL∗< 0 ; (vii) and it slows down the speed of industry moving

F (zP )
out, didL< 0 , if and only if λ(zM ) < ΛL∗ . (Proof in Appendix).
∗

20

.

Although the innovation rates in the high-tech and medium-tech industries are reinforced,
the growth rate is not necessarily boosted due to the shrinkage of high-tech industries, and the
expansion of low-tech industries. This experiment suggests that the South’s size is positively
correlated with range that it is able to penetrate and negatively correlated with the period
in which the South maintains its dominant position. Among Southern countries that are
identical except for their sizes, the bigger Southern country will penetrate farther, but on
average, will dominate for a shorter period of time in each of the medium-tech industries.

FDI Subsidy
I discuss the effectiveness of the FDI subsidy in an attempt to promote technology transfer
here. Suppose that the Southern government bears a fraction sF of the cost of FDI uniformly
across industries, which is financed by lump-sum taxation; the unit labor requirement perunit of FDI intensity becomes (1 − sF )a∗F , with sF > 0. A uniform FDI subsidy alters thecosts of FDI, and shifts the Z̄ schedule downward to Z̄(sF > 0) as shown in Figure 5.
At the initial steady state wage rates, in industry z̄, the moving-out strategy is now more
profitable than the moving-up strategy. Non-producing firms stop engaging in the R&D
ventures, and get involved in the FDI ventures in an attempt to outrace the current leader.
The upper bound of the medium-tech industries expands toward the high-tech end, from z̄
0to z̄ which is the direct effect of the South’s FDI subsidy. The Southern labor market faces
excess labor demand, and the Northern labor market encounters excess labor supply which
creates a pressure to drive down the Northern relative wage. The SS schedule shifts to theleft to S 0 S 0 (sF > 0), and the N N schedule shifts to the right to N 0 N 0 (sF > 0) in response.
The decreased Northern wage weakens the Southern cost advantage, and triggers an indirect
effect which offsets part of the FDI incentive created by the subsidy policy. I assume thatthe direct effect is stronger than the indirect effect. At the new steady state equilibrium,dω< 0, and the upper bound of the set of
Point D, the relative Northern wage decreases dsF

the medium-tech industries expands into the high-tech end, moving from z̄ to the right to z̄d ;and the set of hi-tech industries shrinks. The upper bound of the set of low-tech industries,
however, shrinks due to the weakened Southern cost advantage, moving from z to the rightto z d ; in industries (z d , z), a further widening quality gap is now sufficient for the North to21

outrace the MNEs in the pricing game, and the North starts to undertake R&D. The set of
medium-tech industries expands and is extended toward both ends.
The Southern FDI subsidy policy lowers the world expenditure level. Equation (8) and (9)show that the impacts of FDI subsidy policy on the industry innovation rate and moving-outWWF ) dErate hinge on the magnitude of dE. Henceforth, I discuss the case in which (1−s
< −1.
dsF
EW
dsF

This case occurs if in the initial steady state, the North dominates a great majority of theindustries in world markets i.e. z + nP 1 << 1 − z − nP 1 . I argue that, in this situation,
the South is most likely to seek to implement a subsidy policy to strengthen its penetration.
Proposition 4 summarizes the long-run impacts of the FDI subsidy policy.

Proposition 4: The Southern FDI subsidy (sF > 0) (i) shrinks the set of high-tech industries,dz̄
dsF> 0,; however, (ii) this occurs at the expense of shrinking the set of low-tech industries,dz
dsF< 0, due to the deteriorating cost advantage. (iii) The set of medium-tech industries isaugmented, d(z̄−z)> 0, and is expanded toward both ends. The FDI subsidy contracts thedsFWF ) dE< −1, (iv) it is effective in prolonging the South’s
world expenditure level. If (1−s
EW
dsF

³

duration of dominance,d´

1iR (zP )dsF> 0, (v) the moving-out speed increases in industries withsmall inventive steps if and only if λ(zM ) < ΛsF , where ΛsF ≡

r
W

1− Eω

ω
dsF dω
dE W dsF; howeverR (zH )
(vi) it contracts innovation investments in the high-tech industries, dids
< 0 . (Proof inF

Appendix).

R&D Subsidy
The Northern government might hope to deter competition from the South by subsidizing
R&D investment. Suppose that the Northern government bears a fraction sR of the cost of
R&D uniformly across industries, which is financed by lump-sum taxation; the unit labor
requirement per unit of R&D intensity becomes (1 − sR )aR , with sR > 0. The R&D subsidy
alters the relative incentive of R&D to FDI, and shifts the Z̄ schedule upward to Z̄(sR > 0),
as shown in Figure 6.
At the initial steady state wage rates, in industry z̄, the moving-out strategy is now
less profitable than the moving-up strategy. Non-producing firms stop engaging in the FDI
ventures and start getting involved in the R&D ventures in an attempt to outrace the current
22leader in the pricing game. The upper bound of the medium-tech industries is deterred, and0

is pushed back toward the low-tech end of the industry spectrum, from z̄ to z̄ which is the
direct effect of the R&D subsidy. The Northern labor market thus faces excess labor demand,and the Southern labor market encounters excess labor supply, all of which creates a pressure
to raise the Northern relative wage. The N N schedule shifts to the left to N 0 N 0 (sR > 0), andthe SS schedule shifts to the right to S 0 S 0 (sR > 0) in response. The increased Northern wage
strengthens the South’s cost advantage and triggers an indirect effect which offsets part of
the R&D incentive created by the Northern subsidy policy. I assume that the direct effect isstronger than the indirect effect. At the new steady-state equilibrium, Point E, the relative
Northern wage goes up. The upper boundary of medium-tech industries is pushed away fromthe high-tech end in the new equilibrium, moving from z̄ to the right to z̄e ; and the set of hightech industries expands. The upper boundary of low-tech industries, however, is extended,moving from z to the left to z e , due to the improved Southern cost advantage; in industries(z, z e ), the further widening quality gap is not sufficient for the North to outrace the MNE
leader in the pricing game, and the Northern firms permanently exit these industries. The
range of the medium-tech industries shrinks and is contracted from both ends.
The impact of the Northern R&D subsidy on world expenditure is ambiguous. I restrictWR ) dE< −1. This situation occurs
my discussion by focusing only on the case in which (1−sEWdsR

if in the initial steady state, the South dominates a great majority of industries in world
markets, i.e. 1 − z − nP 1 << z + nP 1 . This is the situation in which the North is most likely
to implement a subsidy policy to deter Southern competition. Proposition 5 summarizes thelong-run impacts of the R&D subsidy policy.

Proposition 5: The Northern R&D subsidy (sR > 0) (i) expands the set of high-tech indz̄
dustries, ds< 0; however, (ii) it does so at the expense of expanding the set of low-techRdz
industries, ds> 0, due to the improved South’s cost advantage. (iii) The range of mediumRWR ) dE
tech industries shrinks, d(z̄−z)< 0, and is contracted from both ends. If (1−s< −1, (iv)
dsR
EW
dsR

the North’s R&D subsidy policy is effective in slowing down the speed at which each mediumF (zP )tech industry moves out from the North to the South, dids
< 0; (v) it shortens the South’sRduration of dominance in industries if and only if λ(zM ) > ΛsR , where ΛsR ≡

23

W

1− Eω

ω
dsR dω
dE W dsR

R (zH ). (v) However, it contracts R&D investments in high-tech industries, dids
< 0. (Proof inR

Appendix).

It is found that the FDI and R&D subsidy policies have a positive effect on local labor
returns. The South, by subsiding FDI, expands its temporary penetration range, but at theexpense of contracting its permanent penetration range; the North, by subsiding R&D, deters
temporary Southern penetration, but at the expense of permanently losing the market inmore industries. I show that the impacts of R&D and FDI subsidies on the speed of industry
moving out and the innovation rates hinge on the effects of the policy on the world expenditurelevel, and the industry characteristic–the size of the inventive steps.

6

Conclusions

Foreign direct investment is considered to be an important channel through which technology
transfer takes place across borders. This paper shows that the extent of Southern penetration (competition) via FDI varies across industries with different technological sophisticationlevels and is dictated by the relative strengths of FDI and R&D intensities on the part ofoligopolistic firms competing within a product line. Three types of industries are endogenously grouped. The first is the high-tech group, in which ongoing R&D deters the potential
low-cost competition, and the South never enters. In the medium-tech group, the South enters the world market through MNEs that transfer the Northern technologies to the Southvia FDI and dominate the production until the North further improves its own production
technology and recaptures the market. In the low-tech group, FDI moves production to theSouth, and the North permanently exits the industry. The FDI and R&D intensities serveas two natural measures that capture the degree of Southern penetration in the medium-techindustries. The former reflects the speed at which an industry is moved to (penetrated by)
the South and later reflects the period during which the South dominates the production inthat industry.
The extent of Southern penetration is linked to the countries’ characteristics and the effectiveness of FDI- and R&D-subsidy policies is also assessed. I show that expanding the sizeof the South results in the expansion of the low-tech and medium-tech groups, but it also
24

shortens the period during which the South is in a dominant position in each medium-techindustry. Conversely, expanding the North’s size mitigates the Southern penetration in termsof the shrinkages of the low-tech and medium-tech groups, but it accelerates the speed atwhich each medium-tech industry moves to the South. The South, by awarding FDI subsidies, effectively expands the medium-tech group, but it is faced with the expense of shrinking
the low-tech group due to the weakened Southern cost advantage. The North, however, by
subsidizing R&D, effectively expands the high-tech group, but it faces the expense of expanding the low-tech group and having to permanently exit the markets in a growing number ofindustries. Augmenting the countries’ sizes leads to an increase in high-tech innovation, but
R&D and FDI subsidies may cause high-tech innovation to contract.
This study shows that countries’ characteristics and policies have critical and inconsistentimpacts on the extent of Southern penetration, which implies that the North’s decision about
whom to choose to receive FDI among a group of low-cost Southern countries essentiallydetermines the distribution of R&D investments across industries as well as the structure ofinternational production, both of which together directly determine long-run growth.
In this era of increasingly liberalized international investment, the question as to what are
the impacts of FDI on the home and host countries’ growth and welfare is very much a concernof policy-makers and economists. Based on the general-equilibrium framework developed inthis paper, we can address and answer this question. Some preliminary results are found inLu (2004). Moreover, trade policies, such as import tariffs or export subsidies and production
subsidies can be regarded as alternative means for promoting or discouraging FDI, or deterringor intensifying Southern penetration. Comparing the effectiveness of different potential policy
instruments is also of much practical and theoretical interest.

25

Appendices
Proof of Proposition 1
In any momentary equilibrium, the values of various types of firms are dictated by the noarbitrage conditions–the sums of the profit rates and the expected rates of capital gain (orloss) equal to the opportunity cost of funds (the normal rates) in the capital market are shownas follows:πV̇+ − i = r,VV
where Vπ denotes the dividend rates, V̇V denotes the capital gains, and i denotes the probability
that the extant producer is replaced by either a new industry leader or an MNE leader andforfeits its future profit stream. Since the R&D and FDI technologies are characterized byconstant returns to scale, the supply of non-producing firms willing to invest in an attempt toreplace the extant producer at the equilibrium interest rate is perfectly elastic. It follows thatin each industry only the most profitable venture is funded in the capital market. Suppose
in industry z̄ that the nearest follower (N F ) is indifferent to the moving-up and moving-out
strategies given that the industry leader is the extant producer. If N F succeeds in an FDI
venture and becomes the MNE leader J ∗ , it undercuts the industry leader by charging a priceω> 1 and gains instantaneous profits πJ ∗ (z̄) = (1 − λ(z̄))E W . The MNE, however,equal to λ(z̄)ω

faces a probability of iR of displacement from the market by a new industry leader. Instead, if
N F undertakes R&D and becomes the industry’s new leader J, it gains instantaneous profits1
πJ (z̄) = (1 − λ(z̄))E W and faces a probability of iR of displacement from the market by a new

industry leader.12 Based on the assumption of free-entry, the stock market value of J ∗ and J
are VJ ∗ (z̄) = a∗F . VJ (z̄) = aR ω that are constant in the steady state (V̇ = 0). Together with
the no-arbitrage conditions, we have:1(1 − λ(z̄))(1 − λ(z̄)
)
ω
=
.
a∗F
aR ω

Multiplying both sides of the above equation by a∗F ω and then adding λ(z̄), it follows thatZ̄(z̄) = ω.
12

Suppose N F chooses to undertake R&D venture to outrace the extant producer between these two
indifferent strategies.

26

Proof of Lemma 1a∗1Both Z(z) ≡ λ(z)2 and Z̄(z) ≡ aFR (1 − λ(z)) + λ(z) are increasing in z given λ0 (z) > 0. Sincea∗λ(0) = 1, λ(z) > 1, ∀ z ∈ (0, 1], and aFR < 1, it follows that λ(z) < Z̄(z) < Z(z) ∀z ∈(0, 1], and λ(0) = Z̄(0) = Z(0). By definition ω = Z̄(z̄) = Z(z), if Assumption 1 holds,
Z̄(0) < Z̄(z̄) < Z̄(1), and Z(0) < Z(z) < Z(1) which implies that 0 < z̄ < 1 and 0 < z < 1.
Moreover, Z(z) > Z̄(z) ∀z ∈ (0, 1] which implies that Z(z) = Z̄(z̄) if and only if z < z̄.
Therefore, 0 < z < z̄ < 1 exists.

Proof of Proposition 2–Expanding the Northern SizeI calculate the magnitude of the horizontal shifts in the SS and N N schedules in response to
an increase in L, and find that¯

dE W ¯¯¯= 0,dL ¯SS¯

dE W ¯¯
ω
> 0.
¯
=
¯
dL N N
1 − z(ω) − nP 1 (ω)

The SS schedule remains in the same position, and the N N schedule shifts to the right.
Wdω> 0, and dL< 0. Moreover,
Therefore, dEdLdz̄
dz̄ dω
== ³ a∗
F
dL
dω dL

1

1
+1
aR λ(z̄)2´dω
λ0 (z̄) dL

< 0,

dz dω
1
dω
dz
=
=
< 0.
0
dL
dω dL
2λ(z)λ (z) dL
The range of temporary South penetration shrinks; so does the range of permanent Southdω
penetration. Since dL< 0, and by Assumption 2,

³ ∗

aF 1
+1
aR λ(z̄)2´

λ0 (z̄) < 1 < 2λ(z)λ0 (z) , therange of medium-tech industries
also
shrinks, d(z̄−z)< 0, and is pushed toward the low-techdL³´
end. Recall that iF (zP ) =1−ωλ(zM )2

EW

aR ω

³

− ρ. Taking the total derivative,´

1 − λ(zωM )2 dE W
E W dω
diF (zP )
=
− 2
> 0,
dL
aR ω
dL
ω aR dL
which impliesthat³´ the speed of industry moving out is accelerated. Moreover, recall thatiR (zP ) =1−

λ(zM )
ωa∗F

EW− ρ. Taking the total derivative,"Ã

1 dE WE W dω dLdiR (zP )
= ∗
1− 1−
dL
aF dL
ω dL dE W
27!

#λ(zM ).
ω

³

An expanded Northern size shortens the duration of Southern dominance, i.e.
0, if and only if λ(zM ) <

ω

d

´
1
iR (zP )dL<. On the other hand, the duration of Southern dominanceW dω dLdL dE W1− Eωcould be prolonged, if industries’ inventive steps were relatively large.
Finally,
I show that³´
the high-tech innovation rate is reinforced. Recall that iR (zH ) =1− λ(z1

H)

EW− ρ. TakingaR ω

the total derivative,
´

³

"

#

1 − λ(z1H ) E W
diR (zH )1 dE W1 dω
=−> 0. Q.E.D.
W
dL
aR ω
E
dL
ω dL

Proof of Proposition 3–Expanding the Southern SizeI calculate the magnitude of the horizontal shifts in the SS and N N schedules in response to
an increase in L∗ , and find that¯

dE W ¯¯1> 0,¯= z(ω)∗¯dL SS
R λ(z)
dz + nP 1 (ω)
ω
¯
dE ¯
¯
dL∗ ¯

0

W¯

= 0.
NN

The SS schedule shifts to the right, and the N N schedule remains in the same place.
Wdω> 0, and dL
Therefore, dE∗ > 0. Moreover,dL∗dz̄dz̄ dω
== ³ a∗∗FdL
dω dL∗1

1+1aR λ(z̄)2

´

dω
> 0,
λ0 (z̄) dL∗

dz
dz dω
1
dω
=
=
> 0.
∗
∗
0
dL
dω dL
2λ(z)λ (z) dL∗
The range of temporary Southern penetration expands; so does the range of permanentdωSouthern penetration. Since dL∗ > 0, and by Assumption 2,

³ ∗

aF 1
+1
aR λ(z̄)2´

λ0 (z̄) < 1 <> 0, and is pushed
2λ(z)λ0 (z), the range of medium-tech industries also expands, d(z̄−z)dL∗
toward the high-tech end. Recall that iR (zP ) =
³

´

(1−

λ(zM ))E Wω
∗aF− ρ. Taking the total derivative,

1 − λ(zωM ) dE W
diR (zP )λ(zM )E W dω
=
+
> 0,
dL∗
a∗F
dL∗
ω 2 a∗F dL∗³

which implies that the duration of Southern dominance is shortened, i.e.
Recall that iF (zP ) =

(1−

ω
)E W
λ(zM )2aR ω− ρ. Taking the total derivative,

E W dω
diF (zP )=dL∗
aR ω 2 dL∗

"Ã

ω
1−
λ(zM )228!

#

ω dE W dL∗−1 .
E W dL∗ dωd´1iR (zM )dL∗< 0.

F (zP )The expanded Southern size accelerates the speed of industry moving out, i.e. didL
> 0,∗

if and only if λ(zM )2 >

W

1− Eω

ω

dω dL∗dL∗ dE W. On the other hand, the speed of industry moving out

could be slowed down, if industries’ inventive steps were relatively small.
Finally,
I show that³´
the high-tech innovation rate is reinforced. Recall that iR (zH ) =1− λ(z1

H)

EW

aR ω

− ρ. Taking

the total derivative,
´

³

"

#

1 − λ(z1H ) dE W
diR (zH )E W dL∗ dω
=
1−
> 0,
dL∗
aR ω
dL∗
ω dE W dL∗
∗

W

dL dω
since 0 < Eω dE
W dL∗ =

(1−z−nP 1 )< 1. Q.E.D.
∂nP 1∂z(1−z−nP 1 )+ω( ∂ω + ∂ω)Proof of Proposition 4–FDI Subsidy sF > 0
The simplified forms of the Southern and Northern labor market clearing conditions become:
z(ω)

EW Z
sF E W
SS : L =λ(z)dz + (E W − ρa∗F )nP 1 (ω, sF ) +ω
1 − sF ω0z̄(ω,s
Z F)

∗

0

Ã
0

NN : L =(ω − λ(z))nP 1 (z)dz,
z(ω)

!

EW
− ρaR · (1 − z(ω) − nP 1 (ω, sF )).
ω

I calculate the magnitude of the horizontal shifts in the SS and N N schedules in responseto an increase in sF from 0, and find that³¯
dE W ¯¯¯dsF ¯E W − ρa∗F

´

=−

W
∂nP 1 (ω,sF )
+ Eω
∂sF

z(ω)
R

SS 0 ,sF =0

0

¯
dE ¯
¯
dsF ¯

³

W¯

=

E W − ρaR ω´(ω − λ(z))dz

z(ω)

< 0,

λ(z)
dz + nP 1 (ω)ω∂nP 1 (ω,sF )∂sF

1 − z − nP 1 (ω)

0

N N ,sF =0

z̄(ω)
R

> 0,

1 (ω,sF )³´P 1 (z̄) > 0. The SS schedule shifts to the left, and the N N
since ∂nP∂s= λ(z̄)(λ(z̄)−1)na λ(z̄)2F

1+ Ra∗

λ0 (z̄)Fdωschedule shifts to the right. In the new steady state, ds< 0. Moreover,
F





dz̄
=³
dsF

 a∗
 F

0 (z̄)  aR+
1
λ
2aR λ(z̄)
|

1

a∗F

´

Ã

!

1−
{z

1
+
λ(z̄)

Direct Effect

29

}

dω
dsF

| {z }
Indirect Effect
 > 0,


dz
1
dω
=
< 0.
0
dsF
2λ(z)λ (z) dsF
The range of temporary Southern penetration expands; the range of permanent Southern
penetration shrinks. Moreover, d(z̄−z)> 0; the range of medium-tech industries expands
dsF
toward both ends.
By using similar techniques, I can show the vertical shifts in both schedules:

³
¯
dω ¯¯
¯
dsF ¯

¯
dω ¯¯
¯
dsF ¯

=−
0

Ã
EW
ω

SS ,sF =0

E W − ρa∗F
−

z(ω)
R
0

´

W
∂nP 1 (ω,sF )
+ Eω
∂sF

!
λ(z)
∂z
dz + ∂ωλ(z)ω³
N N 0 ,sF =0= − EWz̄(ω)
R(ω − λ(z))dz

z(ω)

< 0,

+ (E W − ρa∗F ) ∂nP∂ω1 (ω)

E W − ρaR ω´∂nP 1 (ω,sF )∂sF(1 − z(ω) − nP 1 (ω)) + (E W − ρωaR )
ω

³

∂z(ω)
+ ∂nP∂ω1 (ω)
∂ω

´ <0

W

Since the SS schedule shifts down more than the N N schedule does, dE< 0. I discuss
dsFWF ) dE< −1. Recall that iR (zP ) =only the case in which (1−s
EW
dsF

λ(z

)

(1− ωM )E W
(1−sF )a∗F

− ρ. Taking thetotal derivative,³

diR (zP )=dsF´

1 − λ(zωM ) E W"(1 − sF )2 a∗F(1 − sF ) dE W
(1 − sF )λ(zM ) 1 dω
1+
+
W
E
dsF
(ω − λ(zM )) ω dsF

#

< 0.
³

The FDI subsidy policy is effective in prolonging the South-dominant duration, i.e.
³

0. Recall that iF (zM ) =´

1− ω 2λ(zM )

EW

ωaR

d

´
1
iR (zM )dsF− ρ. Taking the total derivative, and valuing the equa-tion at point sF = 0, I obtain³

diF (zP )=dsF´

1 − λ(zωM )2 E W
ωaR





1 dE W1
1 dω 

−
.
ω
W
E dsF
1 − λ(z )2 ω dsF
M

However, whether or not the FDI subsidy is effective in accelerating industry moving out
F (zP )
further depends on industry-specific inventive steps. Specifically, dids
> 0, if and only ifF

λ(zM ) <
13

r

W

1− Eω

ω
dsF dω
dE W dsF.13dω
By assuming that the direct effect dominates the indirect effect, we know that −1 < ω1 ds< 0. Moreover,FWsince −1 < −(1 − sF ) < E1

dsF
dE W

W

< 0, we have 0 < Eω

30

dsF dω
dE W dsF< 1.

>

Finally,³ the high-techinnovation rate is shown to decrease in response. Recall that´iR (zH ) =1− λ(z1

H)

EW− ρ. Taking the total derivative,

ωaR

³

´

"

1 − λ(z1H ) dE W
diR (zH )E W dsF dω
=
1−
dsF
ωaR
dsF
ω dE W dsF

#

< 0.

The FDI subsidy policy slows down the hi-tech innovation rates.

Proof of Proposition 5–R&D Subsidy sR > 0
The simplified forms of the Southern and the Northern labor market clearing conditions
become:z(ω)

EW Z
SS : L =λ(z)dz + (E W − ρa∗F )nP 1 (ω, sR ),
ω
00

∗

0

Ã
00

NN : L =!

EWsR E W− ρaR · (1 − z(ω) − nP 1 (ω, sR )) +
ω
1 − sR ωz̄(ω,sZ R )Ã

z(ω)

!

ω
1−
nP 1 (z)dz.
λ(z)2

I calculate the magnitude of the horizontal shifts in the SS and N N schedules in responseto an increase in sR from 0, and find that¯

1 (ω,sR )−(E W − ρa∗F ) ∂nP∂s
dE W ¯¯
R
> 0,
¯
=
z(ω)
dsR ¯SS 00 ,sR =0
R λ(z)
dz + nP 1 (ω)ω

0¯
dE W ¯¯¯dsR ¯1 (ω,sR )+ EW−(E W − ρaR ω) ∂nP∂s
R

=−

z̄(ω)
R ³
z(ω)

´

ω
1 − λ(z)nP 1 (z)dz
2< 0,

1 − z(ω) − nP 1 (ω)

N N 00 ,sR =0

1 (ω,sR )1 (ω,sF )since ∂nP∂s= − ∂nP∂s< 0. The SS schedule shifts to the right, and the N N schedule
R
F
00

00

dω
shifts to the left. In the new steady state, ds> 0. Moreover,
R





dz̄
=³
dsR

 a∗

F
−
a∗F

0
a
+ 1 λ (z̄) | RaR λ(z̄)2

1

´

Ã

!

1−
{z

1
+
λ(z̄)

Direct Effect

1
dz
dω
=
> 0.
0
dsR
2λ(z)λ (z) dsR
31

}

dω
ds
| {zR}
Indirect Effect < 0,


The range of temporary Southern penetration shrinks; the range of permanent Southern
penetration expands. Furthermore, d(z̄−z)< 0; the range of medium-tech industries shrinks
dsR
from both ends. The vertical shifts in both schedules are
¯

dω ¯¯
Ã
¯
=
dsR ¯SS 00 ,sR =0
W
E
ω

¯
dω ¯¯
¯
dsR ¯

1 (ω,sR )−(E W − ρa∗F ) ∂nP∂s
R

−

z(ω)
R
0

+ (E W − ρa∗F ) ∂nP∂ω1 (ω)

1 (ω,sR )−(E W − ρaR ω) ∂nP∂s
+ EW
R
00

N N ,sR =0

> 0,

!

λ(z)
∂z
dz + ∂ω
λ(z)
ω

= EW

(1 − z(ω) − nP 1
ω

z̄(ω)
R ³
z(ω)

´

ω
1 − λ(z)nP 1 (z)dz2(ω)) + (E W − ρωa

R)

³

∂z(ω)
+ ∂nP∂ω1 (ω)
∂ω

´ >0

W

Both the SS and N N schedules shift upwards, but the sign of dE
is ambiguous. I restrictdsRWR ) dE
my discussion to the case in which (1−s
< −1.
EW
dsR

Recall that iR (zP ) =(1−

λ(zM ))E Wω
∗aF− ρ. Taking the total derivative,"ÃdiR (zP )1 dE WE W dω dsR
= ∗
1− 1−
dsR
aF dsRω dsR dE W!

#

λ(zM ).
ωThe effectiveness of the R&D subsidy in shortening the South-dominance duration furR (zP )> 0 if and only ifther depends on the industry-specific inventive step. Specifically, dids
R
W

1− Eω

ω
dsR dω
dE W dsR< λ(zM ).14 On the other hand, if the inventive steps are relative small, the R&D³

subsidy might prolong the South-dominance duration! Recall that iF (zM ) =´1−ωλ(zM )2EW(1−sR )ωaR

−ρ.

Taking the total derivative,
³



´



1 − λ(zωM )2 E W 
diF (zP )(1 − sR ) dE W
(1 − sR ) 1 dω 
´
=
1
+
−³

 < 0.
2W
dsR(1 − sR ) ωaR
EdsR
1 − ω 2 ω dsR
λ(zM )The R&D subsidy policy is effective in³ slowing´ down the speed of industry moving out
1− λ(z1H)

diF (zP )< 0. Finally, recall that iR (zH ) =dsR³

diR (zH )=dsR´

1 − λ(z1H ) E W(1 − sR )2 ωaR

EW(1−sR )ωaR"

− ρ. Taking the total derivative,#(1 − sR ) dE W
(1 − sR ) dω
1+
−
< 0.
W
E
dsR
ω
dsR

The high-tech innovation rate is slowed down even when the R&D is subsidized.
14

W

W

1 dω
E
Notice that E1W dE
dsR < 0, and ω dsR > 0, thus ωW
dsR dω
dsR dω
< 0, and 1 < 1 − Eω dE
W ds .
dE W dsRR

32

References[1] Antràs, P., “Incomplete Contracts and the Product Cycle,” (2003), Harvard University
and NBER.
[2] Cheng, L. K., L. D. Qiu, and G. Tan, “Foreign Direct Investment and International
Trade in a Continuum Ricardian Trade Model,” working paper (2004).
[3] Glass, A. J., “Product Cycles, and Market Penetration,” International Economic Review, (1997), 38, 865-891.
[4] Glass, A. J., and K. Saggi, “Intellectual Property Rights and Foreign Direct Investment,” Journal of International Economics, (2002), 56, 387-410.
[5] Grossman, G. M., and E. Helpman, “Quality Ladders in the Thoery of Growth,”
Review of Economic Studies, (1991a), 58, 43-61.
[6] Grossman, G. M., and E. Helpman, “Quality Ladders and Product Cycles,” Quarterly Journal of Economics, (1991b), 106, 557-86.
[7] Krugman, P., “A Model of Innovation, Technology Transfer, and the World Distribution of Income,” Journal of Political Economy, (1979), 87, 253-266.
[8] Lu, C., “Moving Up or Moving Out? A Unified Theory of R&D, FDI, and Trade,”(2004) Academia Sinica, submitted.
[9] Lu, C., “Growth Reducing FDI,” (2004) Academia Sinica, Mimio.
[10] Segerstrom, P. S., T. C. A. Anant and E. Dinopoulos, “A Schumpeterian Modelof the Product Life Cycle,” American Economic Review, (1990), 80(5), 1077-91.
[11] Schott, P.K., 2002. “Moving Up and Moving Out: U.S. Product-Level Exports andCompetition from Low Wage Countries,” mimeo, Yale School of Management.
[12] Taylor, M.S., “‘Quality ladders’ and Ricardian trade,” Journal of International Economics, (1993), 34, 225-43.

33

[13] Vernon, R., “International Investment and International Trade in Product Cycle,”
Quarterly Journal of Economics, (1966), 80(2), 190-207.
[14] Yeaple, S., “The Role of Skill Endowment in the Structure of U.S. Outward Foreign
Direct Investment,” Review of Economics and Statistics, (2003) 85, 726-734.

34

Figure 2: A Continuum of Industries is Endogenously Divided into Low, Medium and
Hi-tech Groups
6

Z(z)

Z̄(z)

1

0

..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.
.
Low-tech .. Medium-tech ....
..
..
..
..
.
.
z
z̄
ZL
ZM

35

w
ω ≡ w∗

Hi-tech
.
ZH

-

1

z

Figure 3: Comparative Statics Analysis–L̂ > 0
ω
6

Z(z)

S

N

N 0 (L̂ > 0)Z̄(z)A.........................................................ω.........................................
...
..
?
..
..
..
..
ωb
..
..
..
..
N
..
..
..
..
..
..
N0
.
.
0
zb
z̄b z
z̄
EW
-

z ¾

B
S

- EW
EbW

-

Figure 4: Comparative Statics Analysis–L̂∗ > 0
ω
6

Z(z)

S

S 0 (L̂∗ > 0)

N

Z̄(z)

z ¾
z̄c
¾

C
ωc
A
6
..........................................................ω...........................................
..
..
..
..
..
..
..
..
..
..
N
..
..
..
..
..
..
0
W
zc
z
z̄
E W Ec
¾
-

36

S0
S

- EW

Figure 5: Comparative Statics Analysis–FDI Subsidy sF > 0
ω
6

Z

S
0

S (sF > 0)
N

N0

Z̄
Z̄(sF > 0)
¾Direct Effect

z ¾
z̄

z̄d
-¾

0

A
................................................ω.................................................
..
..
..
..
S
?
..
..
..
..
ωd
..
..
N
D
..
..
S0
..
..
N 0 (sF > 0)
..
..
..
..
..
..
- EW
.
.
0
W
zd
z
Ed
z̄
EW
¾

Indirect EffectFigure 6: Comparative Statics Analysis–R&D Subsidy sR > 0
ω
6

Z

S0

N 0 (sR > 0)SN0Z̄ (sR > 0)

Z̄

z ¾

..Direct Effect
..
..
..
..
..
..
..
.
z̄

z̄e
-¾

E
ωe
6
N0
-..................................................................................
..
ω
..
A
..
..
..
N
..
..
.
z̄

0

ze
¾

0

z

W
Ee

¾

Indirect Effect37

EW

S 0 (sR > 0)S
- EW