IPR PROTECTION AND ABSORPTIVE CAPACITY IN NORTH-SOUTH
TRADEPreliminary Draft
December 2010

Arghya Ghosh
University of New South Wales

Jota Ishikawa
Hitotsubashi University

Abstract. We examine South’s incentive to protect IPR in a North-Southduopoly model where (i) the North firm owns a better technology and has theoption of serving the South market via exports or FDI, and (ii) the South firm
can invest in absorptive capacity to reduce the technology gap. While FDI
by North firm makes absorption easier for South, investment in absorptive
capacity by the South firm might be higher or lower with FDI. For a given
level of trade cost, the North firm prefers FDI to exports if the IPR protection is
sufficiently strong. We find a non-monotone relationship between trade cost
and the degree of IPR protection that maximizes South welfare. Strengthening IPR protection improves South welfare by encouraging North’s FDI forintermediate values of trade cost.

JEL classification numbers: F12, F13, D43
Keywords: imitation, absorptive capacity, intellectual property rights, FDI, international oligopoly

Ghosh: School of Economics,University of New South Wales, Sydney 2052, Australia, E-mail:a.ghosh@unsw.edu.au; Ishikawa: Faculty of Economics, Hitotsubashi University, Kunitachi, Tokyo
186-8601, Japan, E-mail:jota@econ.hit-u.ac.jp.
1

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IPR PROTECTION AND ABSORPTIVE CAPACITY IN NORTH-SOUTH TRADE

1. Introduction
There are many channels through which technology is transferred from developed
countries (North) to developing countries (South). A typical channel of technology
transfers/spillovers is imitation. Superior production technologies in North could
be copied by South firms. It should be emphasized, however, that such copying
is not automatic. Imitation involves active and costly operations. Thus, South’s
capacity to absorb North’s superior technology (i.e., absorptive capacity) is crucial
for imitation. When lacking absorptive capacity, South firms cannot effectively copy
superior technologies.
South’s imitation activities are also importantly affected by the South government
and North firms. In particular, imitation is strongly influenced by the strength ofintellectual property rights (IPR) protection in South. As long as IPR protection
is in force, patented technologies cannot freely be copied. North firm’s location
choice affects South’s imitation as geographical proximity plays an important rolein technology spillovers (e.g., Eaton and Kortum, 1999; Branstetter, 2001, and Keller,
2002). When North firms serve South market, South’s imitation is easier under
foreign direct investment (FDI) than under exports.
In this paper, we examine South’s incentive to protect IPR in a North-Southduopoly model where a low-cost North firm competes with a high-cost South firmin the South market. The extent of effective cost difference between North and South
specifically depends on South’s imitation. As discussed above, South’s imitation
depends on South’s absorptive capacity, South’s IPR protection, and North firm’s
location choice, all of which are endogenously determined in our framework. We
should mention that we deliberately ignore the North innovation which is presumably the source of North firm’s cost advantage and could be affected by South’s IPR
protection. Instead we focus on North firm’s location choice and South firm’s investment
in absorptive capacity and show that incorporating these two features have important
IPR policy implications for South.
To understand these implications better, we present some more details of our
North-South duopoly model. A North firm (firm N), in our framework, has zero
cost of production while a South firm (firm S) starts with unit cost c(> 0). South
government chooses the level of IPR protection α ∈ [0, 1] where α = 0 implies full
protection of IPR while α = 1 implies no protection of IPR. The strength of IPR
protection declines as α increases. Following South government’s choice of α, firm
N decides whether to export to South market or serve it via FDI. If firm N opts toexport to South market it incurs trade cost of t per unit. After the firm N’s location
has been made, firm S chooses the level of investment C(z) in absorptive capacity
which reduces its unit cost from c to c(1 − αz) where z ∈ [0, 1]). As absorption iseasier with FDI, C(z) is lower under FDI.

IPR PROTECTION AND ABSORPTIVE CAPACITY IN NORTH-SOUTH TRADE

3

Location choice and absorptive capacity are critical in determining the firms’
effective unit costs. The former (i.e., the location choice decision) determines firm
N’s effective unit cost of production—0 under FDI and t under exports—, while
investment in absorptive capacity reduces firm S’s unit cost from c to c(1 − αz).
Finally, with IPR policy, location and investment decisions in place, the two firms
compete in quantities.
As Cournot analysis is standard, let us start with the export versus FDI decision. If
firm N chooses FDI, it avoids per unit trade cost. However, FDI makes absorption of
new technology easier for firm S which can partially erode North’s cost advantage.
When IPR protection is weak, the erosion of North’s cost advantage is higher. This
trade-off between trade cost savings and reduction in cost-advantage is key to thelocation choice decision by firm N.
The second and probably more important component of our analysis is endogenous determination of South’s absorptive capacity. Cohen and Levinthal (1990)
argue that a firm’s absorptive capacity is critical to recognize the value of new external information and subsequently assimilate and apply it to commercial ends. Thus,
if South’s absorptive capacity is low, or equivalently its imitation costs are high, thenSouth’s IPR protection policy has little effect.
While a part of firm’s absorptive capacity can be viewed as its innate ability toabsorb new technology—and hence can be treated as exogenous—presumably, thecapacity could be changed via investment. Trade facilitates absorption, but absorption is easier/less costly under FDI as technology transfer/spillover importantly
depends on geographical proximity. Not surprisingly, South has been active inencouraging FDI. Endogenous determination of absorptive capacity provides richinsights and has important policy implications. By locating in South, FDI makes
absorption easier for firm S which encourages investment in absorptive capacity.
However, as firm N saves per unit trade cost, its effective unit cost of production declines with FDI. This reduces firm S’s output and consequently its incentive to invest
in absorptive capacity. We find that absorptive capacity and consequently productivity spillovers—effective cost reduction in our framework—could be higher or lower
with FDI.
The ambiguity might seem surprising as it is often thought that FDI benefits Souththrough technology and knowledge spillover to the local rivals (Keller, 2004). See, forexample, Dimelis and Louri (2002), Griffith et al. (2002), Javorcik (2004), Chakraborty
and Nunnekamp (2008) and Suyanto, Salim and Bloch (2009) for evidence on positive
productivity spillovers. On the other hand, Aitken and Harrison (1999), Djankov
and Hoekman (2000), and Barry, Gorg, and Strobl (2005) found negative relationshipbetween FDI and spillovers. By endogenizing investment in absorptive capacity,
our theoretical analysis offers an explanation for the ambiguous relationship.

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IPR PROTECTION AND ABSORPTIVE CAPACITY IN NORTH-SOUTH TRADE

Finally, we turn to IPR protection. Recall that firm N’s unit cost is exogenously
given. Furthermore, South’s marginal cost declines as South weakens its IPR protection. On both these counts, strengthening IPR protection might seem to reduce
South welfare. Indeed, if location choice is not an issue, this argument holds. For
example, if trade cost is prohibitive, firm N has no choice but to opt for FDI. In
this case, it is optimal for South to offer no protection for IPR. However, if trade
cost is not prohibitive, firm N’s losses under FDI from high spillovers (induced byweak IPR) might outweigh the gains from savings trade cost savings. Thus, weak
IPR might lead firm N to opt for exports. If firm N chooses exports, it might be
bad for South as well. As firm N incurs trade cost under exports, equilibrium priceis higher, which hurts consumers. This negative effect is reinforced if investment
in absorptive capacity is lower under exports. We find that indeed for a range ofparameterizations, it is in South’s interest to strengthen IPR protection just enoughso that firm N opts for FDI.
Interestingly, we find a non-monotone relationship between trade cost and thelevel of IPR protection that maximizes South’s welfare. In particular, we find thatstrengthening IPR protection improves South’s welfare only for moderate values oftrade cost. If the trade cost is too high, IPR protection (to induce FDI) is not necessary
since in that case the North firm opts for FDI anyway. If the trade cost is too low,strengthening IPR protection does not improve welfare either. To understand thelogic, consider the extreme case of zero trade cost. In that case, FDI does notsave trade cost. Furthermore, firm S’s absorptive capacity is higher under FDI.
Hence, irrespective of the strength of IPR protection, firm N always locates in North.
Since firm N’s location choice does not change with a change in the degree of IPR
protection, the South government chooses not to protect IPR at all.
For moderate values of trade cost, where some degree of IPR protection is worthwhile, a decline in trade cost leads to stronger IPR protection. As trade cost declines,
export option becomes more attractive for firm N. This prompts South to tighten the
IPR protection even further. Thus, even if innovation is not affected by the strengthof IPR protection in South, it might still be optimal for South to offer some IPR
protection.
The plan of the paper is as follows. Section 2 describes the relationship between
our analysis and previous IPR literature. Section 3 describes the basic three-stage
game: North firm’s location choice, followed by South firm’s investment in absorptive capacity, and finally Cournot competition between the two firms. Section 4
characterizes the Cournot equilibrium and South’s investment in absorptive capacity. Section 5 analyzes the North firm’s location choice. Section 6 discusses the
optimal IPR policy from South’s perspective taking into account the impact of thedegree of IPR protection on absorptive capacity and location choice. Section 7 offers
concluding remarks.

IPR PROTECTION AND ABSORPTIVE CAPACITY IN NORTH-SOUTH TRADE

5

2. Relation to Previous Literature
Helpman (1993) provided the first general equilibrium analysis of IPR policy in a
North-South product cycle model with innovation, imitation and growth. The earlyworks in this area (Helpman,1993; Glass and Saggi, 2002) find that strengthening IPR
protection in South reduces South welfare and may or may not benefit North. Lai(1998) argues that this finding critically depends on the assumption that imitation is
the sole channel of production transfer from North to South. Instead of imitation,
if FDI is the channel of production transfer then the conclusion no longer holds.
Branstetter and Saggi (2009) push this literature based on North-South product cycle
models further by making both imitation and FDI endogenous. Most papers inthis literature evaluate the welfare consequence of marginal changes in imitation to
analyze the impact of IPR protection. An exception is the paper by Grossman andLai (2004). They explicitly consider both (i) simultaneous choice of IPR protection bytrade partners and (ii) globally efficient regime of IPR protection in a multi-country,
trading world where countries differ in their sizes and innovation capacities.
Despite offering valuable and rich insights, these dynamic North-South generalequilibrium models often do not involve strategic interaction among firms which isoften a key component of analysis in the oligopolistic markets. For detailed microeconomic analysis of firm and government behavior, we adopt a partial equilibrium,
Cournot duopoly framework. This allows us to capture crucial firm level decision,e.g., where to locate, how much to invest, in a detailed fashion.
In a simple North-South duopoly model with Cournot competition, Chin and
Grossman (1990) showed that no protection of IPR is better than the full protectionof IPR for South welfare. Examining the welfare effects of the geographical scope of
patent coverage, Deardorff (1992) reports similar results. Both Chin and Grossman(1990) and Deardorff (1992) consider binary choice regarding protection of IPR: full
protection or no protection. Allowing for various degree of IPR protection as well
as for differences in preference and technology, Diwan and Rodrik (1991) showthat South might benefit from protection of IPR if the differences in preferences aresubstantial. Introducing R&D with spillovers into a North-South duopoly model,
Žigić (1998) shows that the result obtained in Chin and Grossman (1990) is no longer
robust. He specifically regards the intensity of spillover as an indicator of the strengthof the IPR protection. He assumes that if North firm’s cost-reducing R&D decreases
its own marginal cost (MC) by 1, then it also lowers South’s MC by α ∈ [0, 1], whichis the indicator of the strength of the IPR protection.
However, recent empirical evidence shows that the presence of foreign firms does
not automatically leads to technology spillovers. Rather, it depends importantly on
local firms’ investment in R&D related activities (Kathuria, 2000; Kinoshita, 2001;
Griffith, Redding and van Reenen, 2003; Suyanto, Salim and Bloch, 2009). Naghavi

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IPR PROTECTION AND ABSORPTIVE CAPACITY IN NORTH-SOUTH TRADE(2007) extends Žigić (1998) by considering the possibility of FDI and decomposing
the intensity of spillovers into the strength of the IPR protection and the extent ofabsorptive capacity just like αz in our model.1 Naghavi (2007) shows that Southcan always gain from enforcing stringent IPR protection, either by attracting FDI inless R&D-intensive sectors or by stimulating innovation in high-technology sectors.
Yang and Maskus (2009) also have absorptive capacity in their work. They focus on a
scenario where the North firm chooses either exports or technology transfer throughlicensing. They show that by encouraging technology transfer, South’s stronger IPR
protection might improve the ability of South firms to break into export markets andthat South’s welfare depends on its absorptive capacity.
The key difference between our work and Naghavi (2007) and Yang and Maskus(2009) is that we treat absorptive capacity as endogenous by explicitly modelling
South firm’s investment in absorptive capacity. The endogeneity is important in ourframework for two reasons. If the absorptive capacity is exogenous and the sameunder FDI and exports in our model, both location choice decision for North and the
optimal IPR policy become trivial: North always chooses FDI and South offers noprotection of IPR. Alternatively, appealing to common wisdom, one can assume thatabsorptive capacity is higher under FDI than exports. However, that would not be
innocuous as we have discussed earlier (and formally demonstrate in Proposition3), that the absorptive capacity under FDI could be higher or lower than that underexports.
In this regard, our work is related to Grünfeld (2006), as he also explicitly models
the concept of absorptive capacity in an international duopoly model. He considers athree-stage game to explore the relationship between absorptive capacity and firm’s
supplying mode. In his model, the foreign firm decides whether to export to thedomestic country or serve it via FDI. Given this decision, both domestic and foreign
firms engage in cost-reducing R&D, which also determines the R&D spillover rate,
and then in Cournot competition. It should be noted that in Grünfeld (2006), costreducing R&D not only reduces its own marginal cost directly but also facilitates thespillover from its rival. Thus, when each firm determines its R&D level, it explicitly
takes both roles into account. Although our model structure is somewhat similar
to Grünfeld (2006), our focus is completely different from his. We are concernedwith South’s incentive to protect IPR, which is absent in Grünfeld (2006). Moreover,since Grünfeld (2006) assumes two-way spillovers, his model is more appropriate
for the analysis of spillovers between developed countries. In contrast, we deal with
one-way spillovers from North to South, because we focus on South’s imitation of
North.

1

Leahy and Naghavi (2010) introduce joint venture into Naghavi (2007).

IPR PROTECTION AND ABSORPTIVE CAPACITY IN NORTH-SOUTH TRADE

7

3. ModelThere are two countries, North and South, each with one firm denoted by firm Nand firm S respectively. These firms sell a homogenous product in the South. As weare primarily interested in the incentives and welfare consequences of strengthening
IPR protection in South, we assume that all consumers are located in South. The
inverse demand for the product in the South is
P = b − Q,(1)

= b − (qN + qS ));where qi (i = N, S),Q ≡ qN + qS and P respectively denote output of firm i, aggregate
output and market price.
Firm N’s marginal cost of production is assumed to be zero. Concerning location
choice there are two options. Firm N can locate in North and export to South
incurring trade cost t > 0 per unit of qN . Otherwise firm N can opt for FDI in South.
That is, firm N can build a plant in South and serve the South market from that plant.
In that case firm N does not incur the trade cost. For simplicity we assume that there
are no plant-specific fixed costs.
Firm S is located in South. The initial unit cost of production for firm S is a constantc > 0. However, the effective unit cost for firm S is(2)

cS = c(1 − αz);α ∈ [0, 1],z ∈ [0, 1]

where z denotes absorptive capacity of firm S and α captures the degree of IPR
protection in South. If α = 0, intellectual property rights are fully protected while if
α = 1, there is no protection of IPR. As α increases from zero to unity the protection
becomes weaker. Weakening of IPR in South reduces the cost advantage of firm N.
However, even with no IPR protection (i.e., α = 1) firm N enjoys some cost advantage
as long as z < 1.
To attain absorptive capacity level z, firm S has to invest C(z). We assume that
C(0) = 0, C0 (z) > 0 and C00 (z) > 0 for all z > 0. Furthermore, to obtain closed-form
2
solutions, we adopt the standard quadratic specification: C(z) = kz2 , where k = kE if
firm N opts for export and k = kF if firm N opts for FDI. Absorption is easier whenfirms are geographically closer to each other. Accordingly, we assume that kE > kF .
The timing of the events is as follows:Stage 1 [Exports or FDI]: Given α— which we assume to be exogenous until section 4— firm N decides whether to serve the South market via exports or FDI. Let e denotethe binary variable capturing the firm N’s mode of serving South market where 1, if firm N exports to South;e= 0, if firm N serves South by FDI.

8

IPR PROTECTION AND ABSORPTIVE CAPACITY IN NORTH-SOUTH TRADE

Stage 2 [Investment in absorptive capacity]: Given α and e, Firm S chooses the levelof absorptive capacity z.
Stage 3 [Cournot competition]: Given α, e, and z, each firm i chooses qi to maximize
its profit taking rival firm’s output, q j , as given (i, j ∈ {N, S}, i , j).
Before we proceed to analyze the three-stage game described above few remarks
are in order regarding the assumptions of the model. First, the assumption that firm
N’s marginal cost is zero is innocuous. Second, the fact that there are no plant-specificfixed costs simplify the algebra but is not crucial for our results. Introducing a strictly
positive plant-specific fixed cost would make FDI less preferable to exports. Finally,
we have implicitly assumed that the North and the South markets are segmented
and firm S does not sell in North. Introducing the possibility that firm S exports to
the North does not qualitatively change our findings.
4. Analysis
We characterize the unique Subgame Perfect Nash Equilibrium (SPNE) of thegame. To facilitate this characterization we make some simplifying assumptions
regarding the upper and lower bounds of different parameters:
Assumption 1: (i) c < 2b , (ii) t < 2b , and (iii) kF > bc3 .
Assumption 1 implies that the initial marginal cost of firm S is low enough so thatit produces a strictly positive amount of output for all (α, e, z) satisfying α ∈ [0, 1],e ∈ {0, 1} and z ∈ [0, 1]. The bound for t in Assumption 1(ii) ensures that firm N sells
a strictly positive amount in South even when it chooses to export. Assumption
1(iii) ensures that the second-order condition of the stage 2 optimization problem issatisfied and the equilibrium value of z is strictly interior (i.e. lies between zero andunity).
4.1. Cournot equilibrium. First consider the stage 3 game where the two firms
compete in quantities. Prior to this stage, the degree of IPR protection in South(α),
North firm’s mode of entry (e) and the South firm’s absorptive capacity (z) have beenchosen. So, both firms S and N take these variables as given.
For a given (α, e, z), firm S chooses qS to maximize (b − qN − qS − c(1 − α)z)qN whilefirm N chooses qN to maximize (b − qN − qS − et)qN . Routine computation yields:
(3)
(4)

(5)

q̃N (α, e, z) =b − 2c(1 − αz) + dt
b − 2et + c(1 − αz), q̃S (α, e, z) =,33Q̃(α, e, z) ≡ q̃N (α, e, z) + q̃S (α, e, z) =π̃N (α, e, z) =2b − et − c(1 − αz),3(b − 2et + c(1 − αz))2(b − 2c(1 − αz) + et)2, π̃S (α, e, z) =,99

IPR PROTECTION AND ABSORPTIVE CAPACITY IN NORTH-SOUTH TRADE

9where q̃i (α, e, z), and π̃i (α, e, z) denote quantity and profit of firm i(= N, S) in the
Cournot equilibrium. The following lemma records some comparative statics results
for future reference.
Lemma 1. For any given location choice (i.e., e = 0, or e = 1),(i) q̃N (α, e, z) and π̃N (α, e, z) are decreasing in α and z.
(ii) q̃S (α, e, z) and π̃S (α, e, z) are increasing in α and z.
(iii)Q̃(α, e, z) is increasing in α and z.
Both weakening of IPR protection (i.e., an increase in α) and increase in absorptive
capacity (i.e., an increase in z) reduces unit cost of firm S. This in turn increases
firm S’s output and profit. Firm N’s output and profit decline since q̃S (α, de, z)
and q̃N (α, e, z) are strategic substitutes. Part (iii) is a standard result from Cournot
competition: aggregate output increases as unit cost declines (through an increasein α or z in our framework).
4.2. Absorptive Capacity. Consider stage 2 where firm S chooses the level of absorptive capacity z. For a given degree of IPR protection, α, and firm N’s location
choice, e, firm S chooses the z to maximize
k(e)z2π̃S (α, e, z) −≡ πS (α, e, z),2where k(e) ≡ ekE + (1 − e)kF . The marginal cost of investment in z isk(e)z,∂π̃ (α,e,z)

while the marginal benefit from investment in absorptive capacity, given by S∂z
is:2∂q̃S (α, e, z) 2αc(b − 2c(1 − αz) + et)∂π̃S (α, e, z)(6)= 2q̃S (α, e, z)
=
.
9
∂z
∂z
Equating marginal cost with marginal benefit of investment in z gives the Southfirm’s absorptive capacity in stage 2 equilibrium:(7)z=

2αc(b − 2c + et)≡ z(α, e)9k(e) − 4α2 c2where α ∈ [0, 1] and e ∈ {0, 1}.
Observe that that numerator of z(α, e), i.e., 2αc(b − 2c + et), is strictly increasing in
α, while the denominator, 9k(e) − 4α2 c2 is strictly decreasing in α. This observation
leads to our first proposition.
PROPOSITION 1. Absorptive capacity increases as the degree of IPR protection weakens.
dz(α,d)More precisely, for a given e ∈ {0, 1}, dα > 0.
Proof: Immediate from the discussion prior to the proposition.
2

The first equality in (6) follows from differentiating π̃S (α, e, z) ≡ (qS (α, e, z))2 ,10

IPR PROTECTION AND ABSORPTIVE CAPACITY IN NORTH-SOUTH TRADE

To understand Proposition 1, recall the effective cost of production for firm S:
cS = c(1 − αz). As z increases, cS declines which raises firm S’s profit. The weaker the
IPR protection (i.e., the higher the α) the larger is the decline in cS and consequently
the larger the increase in firm S’ profit. Thus the marginal benefit from an investment
in z increases as the degree of IPR protection weakens. This logic, together with thefact that marginal cost of investment, k(e)z, is independent of degree of IPR protection
imply Proposition 1.
Let zF (zE ) denote the equilibrium absorptive capacity of firm S when firm N serves
the South market via FDI(exports). Using (7) we get:(8)

zF ≡ z(α, 0) =(9)zE ≡ z(α, 1) =2αc(b − 2c),
9kF − 4α2 c2

2αc(b − 2c + t).
9kE − 4α2 c2Define qFi ≡ q̃i (α, 0, zF ), πFi ≡ π̃i (α, 0, zF ) and QFi ≡ Q̃i (α, 0, zF ) where i = N, S. Thus
qFi , πFi and QFi respectively denote firm i’s quantity, firm i’s profit and aggregate
output in stage 2 equilibrium when the North firm opts for FDI in stage 1. Similarly
qEi ≡ q̃i (α, 1, zE ), πEi ≡ π̃i (α, 1, zE ) and QEi ≡ Q̃i (α, 1, zE ) respectively are firm i’s output,
firm i’s profit and aggregate output in stage 2 equilibrium when the North firmchooses to export in stage 1. Using Lemma 1 and Proposition 1 we can establish
the following relationships between the equilibrium outcomes in stage 2 and thestrength of IPR protection.
PROPOSITION 2. The North firm’s profit declines while the South firm’s profit andaggregate output increases as the strength of IPR weakens in South. These results hold forboth modes of North entry into the South market— exports as well as FDI. More formally,(i) πFN and πEN are decreasing in α.
(ii) πFS and πES are increasing in α.
(iii)QE and QF are increasing in α.
Proof: See Appendix.
As the strength of IPR protection weakens (i.e., as α increases), South firm’s investment in absorptive capacity (z) increases. Effective unit cost of production forSouth, cS ≡ c(1 − αz), declines. Part (i) follows from the logic that lower cS leads tohigher qS , which in turn imply lower qN and consequently lower πN . Part (iii) is easy
to understand once we recognize that the aggregate output increases as unit costdeclines. To understand part (ii), writedπS ∂πS ∂πS dz
=
+
dα
∂α
∂z dα
S
S
and observe that ∂π= 0 (envelope theorem) and ∂π> 0 (Lemma 1).
∂z∂αIPR PROTECTION AND ABSORPTIVE CAPACITY IN NORTH-SOUTH TRADE

11

Now we turn to the comparison between zF and zE . The comparison for two cases
are immediate—perfect IPR protection, and zero trade costs.
• If IPR protection is perfect, i.e., α = 0, there is no incentive to invest inabsorptive capacity and hence zF = zE = 0.
• If IPR protection is imperfect but there are no trade costs, i.e., t = 0 thenzF > zE .
Except for these two cases the results are less clear-cut. Marginal cost of investment in absorptive capacity, k(e)z, is lower under FDI since k(0)(≡ kF ) < k(1)(≡ kE ).
However, the marginal benefit from investment in z is smaller as well. To understandwhy, note that firm N’s unit cost of production is lower under FDI as it saves trade
cost t per unit. The reduction in firm N’s unit cost leads to higher qN and lower qS .
Lower output (i.e., lower qS ) in turn reduces firm S’s incentive to invest in z.
As both marginal benefit as well as marginal cost of investment in absorptive
capacity are lower under FDI, zF could be higher or lower than zE depending on the
degree of IPR protection (α) and per unit trade cost (t). Proposition 3 compares zF
with zE and relate the comparison to the degree of IPR protection as well as per unit
trade cost.

PROPOSITION 3. Absorptive capacity is strictly higher under FDI if IPR protection is
weak enough. More formally, for all t > 0, there exists a threshold value α̃(t) ∈ [0, 1] suchthat zF > zE holds for all α > α̃(t). Furthermore α̃(t) is increasing in t.
Proof: Using (8) and (9) we get
zF − zE =F

2αc(b − 2c)t(9kF − 4α2 c2 )
E
F
(9(k
−
k
)
−
).
(kE − 4α2 c2 )(9kF − 4α2 c2 )b − 2ct(9kF −4α2 c2 )9tk(i) If 9(kE − kF ) − b−2c
> 0, then 9(kE − kF ) − b−2c
> 0 for all α ∈ [0, 1] and henceFEz ≥ z holds for all α ∈ [0, 1].
t(9kF −4c2 )t(9kF −4α2 c2 )(ii) If 9(kE − kF ) − b−2c < 0, then 9(kE − kF ) − b−2c
< 0 for all α ∈ [0, 1] and henceFEz > z does not hold for any α ∈ [0, 1].
t(9kF −4c2 )9tkF(iii) If 9(kE − kF ) − b−2c
< 0, but 9(kE − kF ) − b−2c > 0, then zF ≥ zE holds for all

α≥

3

q
(b−2c)(kE −kF )
kF −
t
.
2c

q
(b−2c)(kE −kF )9kF −trespectively for cases (i), (ii), and (iii) and the2cDefine α̃(t) = 0, 1, andclaim follows. The last statement of proposition 3 follows from noting that α̃(t) does
not vary with t for (i) and (ii), and is strictly increasing with t for (iii).

We conclude this section by presenting an interesting non-monotonicity result.

12

IPR PROTECTION AND ABSORPTIVE CAPACITY IN NORTH-SOUTH TRADEPROPOSITION 4. (i) Absorptive capacity is non-monotone in firm S’s initial unit cost of
production. That is, for all α ∈ (0, 1] there exists c(α, e) > 0 such thatdz(α, e)> (=, < 0) ⇔ c < (=, >)c(α, e)dc
provided e = 0(FDI), or e = 1(exports) but t is not too large.
(ii) Higher initial unit cost of production does not necessarily imply higher effective unit
cost. More formally, there exists values of c, namely c1 and c2 such that c1 > c2 and yet
c1S ≡ c1 (1 − αz1 ) < c2 (1 − αz2 ) ≡ c2S where z1 and z2 denote absorptive capacities in stage 2
equilibrium corresponding to initial unit costs c1 and c2 respectively.
Proof: See Appendix.
Consider the FDI case (i.e., e = 0). If cost difference is too small to start with, theincremental change in output due to additional investment in z is negligible. More∂q̃ (α,0,z)∂π̃ (α,0,z)
precisely, limc→0 S ∂z
= limc→0 2αc= 0. Consequently, limc→0 S ∂z
= 0. On the3∂π̃ (α,0,z)bother hand, if the cost difference is too large (i.e., c close to 2 ), limc→ b S ∂z
= 02
since limc→ b q̃S (α, 0, z) = 0. Thus, for both extremes — cost differences too large or2
too small — the benefit from an additional unit of investment in z is negligible and∂π̃ (α,0,z)
consequently z ≈ 0. For intermediate values of c however S ∂z is strictly positive
which suggests that the relationship between absorptive capacity z and the initial
unit cost c is non-monotone.
For c > c(α, d), as c increases z declines and hence higher c does imply higher cS .
However, for c < c(α, d), z increases as c increases. This creates the possibility thatc1 > c2 but c1S < c2S where c1S and c2S are effective unit cost of production corresponding
to the initial unit cost c1 and c2 respectively. Proposition 4(ii) says that indeed there
are parameter values for which this holds.

5. Exports versus FDI
Two considerations are important for the firm N’s optimal location choice: trade
cost and absorptive capacity of firm S. FDI lowers firm N’s effective unit cost bysaving per unit trade cost t. However, under FDI, firm S’s unit cost cS ≡ c(1 − αz)might be lower as well if zF > zE . While the former effect favors FDI, the latter one
favors exports. So, when does firm N choose to export (e = 1) and when does itchoose FDI (e = 0)? Assume that in case of indifference between exports and FDI
firm N opts for FDI. Firm 1 opts for FDI in SPNE if and only if πFN − πEN ≥ 0. We havethat
πFN − πEN ≥ 0 ⇔ qFN − qEN ≥ 0(10)⇔ αc(zF − zE ) − 2t ≤ 0.

IPR PROTECTION AND ABSORPTIVE CAPACITY IN NORTH-SOUTH TRADE

13

where the first ⇔ follows from using that πFN = (qFN )2 , πEN = (qEN )2 , and the second ⇔follows from substituting the expression for qFN ≡ q̃N (α, 0, zF ) and qEN ≡ q̃N (α, 0, zE ) in
(10).
First, consider the case α = 0. IPR protection is perfect which implies zF = zE = 0.
Firm N chooses FDI for all t > 0 since αc(zF − zE ) − 2t = −2t < 0. In case of perfect
IPR protection, firm N’s only consideration (while making location choice) is tradecost. By choosing FDI firm N avoids trade cost and hence it prefers FDI to exports.
Now consider the case t = 0. From (8) and (9) we know that zF − zE > 0 which
imply αc(zF − zE ) − 2t > 0. Thus firm N’s optimal choice is to locate in North andexport to South. In case of zero trade costs, firm N’s unit cost is same no matter
where it locates but firm S’s unit cost cS ≡ c(1 − αz) is higher if firm N chooses toexport since zE < zF .
The discussion above casts the trade-off involved in firm N’s location choice interms of trade cost and absorptive capacity. However note that, absorptive capacity
is endogenous variable. The equilibrium value of absorptive capacity depends
on trade cost parameter, t, and the degree of IPR protection, α — see (8) and (9).
Substituting the expression for zF and zE from (8) and (9) in (10) above and analyzing
the inequality further gives the following proposition.
PROPOSITION 5. The North firm prefers FDI to exports if IPR protection is strong
enough and trade cost is not too high. The minimum degree of IPR protection that induces
FDI increases as trade cost declines. More formally, for all t > 0, there exists α(t) ∈ [0, 1]
such that firm N opts for FDI in stage 1 if and only if α ≤ α(t). There exists t̄ such thatα(t) < 1 for t ≤ t̄. Furthermore, α(t) is strictly increasing in t.
Proposition 5 says how the exports versus FDI decision of firm N depends on trade
cost and the strength of IPR protection in South. Even in absence of any protectionof IPR (i.e., α = 1) firm N might locate in South if trade cost is large enough. Thismight suggest that endogenous absorptive capacity and consequently the strengthof IPR protection has little role to play. However, note that if absorptive capacity
were exogenous and same under FDI and exports (i.e., z = zF = zE ), (10) implies thatfirm N would prefer FDI for all t > 0 and not just high t. This observation highlights
the importance of endogenous absorptive capacity in firm N’s choice between FDI
versus exports.
The second part of the Proposition unravels a complementary relationship between trade liberalization and South’s IPR protection. As trade cost declines, theoption of exporting becomes more attractive to North. This imply that the criticallevel of IPR protection needs to be stronger in South so that the North firm prefers
FDI to exports. As we show below, the impact of IPR protection on North’s location
decision play an important role in determining optimal IPR policy for South.

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IPR PROTECTION AND ABSORPTIVE CAPACITY IN NORTH-SOUTH TRADE

6. Intellectual Property Rights
Stronger IPR protection in South leads to higher profit of the North firm (seeProposition 2). Since North welfare consists solely of North firm’s profit in ourframework, α = 0 is optimal for North.
South welfare (WS ) is the sum of consumer surplus (CS) and the South firm’s
profits (πS ). Corresponding to the demand function P = b − Q, consumer surplus
2(CS) is Q2 . Let CSF (CSE ) and W F (W E ) respectively denote the consumer surplus andwelfare when firm N chooses FDI (exports) in stage 1. By definition,
W F = CSF + πFS ;W E = CSE + πES .

Firm N chooses FDI for α ≤ α(t) which imply
W = WFif α ≤ α(t),= WEif α > α(t).
F2South welfare under FDI, W F , increases as α increases since both CSF ≡ Q2 andπFS are increasing in α (Proposition 2). South welfare under exports, W E , increases
with α for analogous reasons. Given the relationship between W E , W F and α it isimmediate that the optimal α for South is either 1 or α(t) (which can be 1 as well forsome parameter values). That is, the degree of IPR protection that maximizes South
welfare is either nil (i.e., α = 1) or just enough (i.e., α = α(t)) so that the North firm
opts for FDI in South. The proposition below provides a sharper characterization.
PROPOSITION 6. Let α∗ (t) denote the level of IPR protection that maximizes South
welfare. There exists t1 and t2 satisfying 0 < t1 < t2 < ∞ such that
1,
if t < t1∗α (t) = α(t) ∈ (0, 1),
if t ∈ [t1 , t2 ]



 1
if t > t2
Proof: See Appendix.
Proposition 6 implies a non-monotone relationship between trade cost and thestrength of IPR protection. If trade cost is too high or too low, South’s welfare is
maximized when it does not offer any IPR protection at all. Else, the optimal degreeof protection is strictly interior. The logic of the result is as follows. Suppose trade
cost is prohibitive. This implies that firm N undertakes FDI anyway. As location
choice is not affected by α, it is optimal to set α∗ (.) = 1 since both CSF and πFS arestrictly increasing in α. Now consider the other extreme, t = 0. Firm N locates inNorth irrespective of α since North cost-advantage is higher if it opts for exports.
Once again, since α does not affect firm N’s location choice, it is optimal to set α∗ (.) = 1
since both CSE and πES are strictly increasing in α. For intermediate values of t, choiceIPR PROTECTION AND ABSORPTIVE CAPACITY IN NORTH-SOUTH TRADE

15

of α affects the location choice of firm N. In particular, there are parameterizations(in particular kE and kF ) such that the South government finds it optimal to chooseα ∈ (0, 1) to attract FDI.
7. Concluding Remarks
We examined South’s incentives to protect IPR in an environment where thestrength of IPR protection in South has no bearing on North firm’s incentives toinnovate. In the presence of (i) endogenous absorptive capacity, and (ii) Northfirm’s location choice—both endogenously determined in our framework—we findthat South can benefit from having a strict IPR protection depending on the level oftrade cost. Interestingly, we find that the relationship between optimal strength of
IPR protection in South and trade cost is non-monotone. If the trade cost is too highor too low then there is no incentive to protect IPR in South. For moderate valuesof trade cost, however it is optimal for South to protect IPR to some extent. In thisrange (of values for trade costs) the IPR protection becomes stronger as the trade
cost declines.
Our analysis also offers an explanation for the ambiguous relationship between
FDI and spillovers often observed in the data. Key to our explanation is the role ofabsorptive capacity. Under FDI, absorption is less costly but the South firm faces
stronger competition since North firm saves trade cost when it opts for FDI. As
a consequence we find that absorptive capacity/spillovers can be higher or lower
under FDI.
Throughout the analysis we have treated trade cost as resource cost instead of tariff.
Except for section 6 (where we consider South welfare) the analysis and the results areinvariant to the particular interpretation of trade cost. Incorporating tariff revenues
in welfare function does not change the main result on non-monotone relationship(Proposition 6) in section 6. Both for zero and prohibitive tariff, tariff revenues do notmatter. For both these cases—which correspond to zero trade cost and prohibitive
trade cost in the previous section—it is optimal for South to offer no IPR protection
at all. However, for intermediate values of t, tariff can impact South’s incentive toprotect IPR in a subtle way. Strengthening IPR protection improves welfare in ourframework when it prompts North to opt FDI. Tariff revenues leads to higher South
welfare under export option while welfare under FDI remains unchanged. This
reduces the relative attractiveness of FDI and weakens South’s incentive to protect
IPR. On the other hand, under exporting option, strengthening IPR protection has
an additional benefit. It increases North output which in turn leads to higher tariff
revenues and consequently higher welfare for South. Thus the range of values forwhich optimal α∗ ∈ (0, 1) as well as the value of α∗ will generally be different when
we treat t as per unit tariff instead of trade cost.

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8. Appendix (to be completed)
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