Nber Working Paper Series Intellectual Property Rights, Foreign Direct Investment, and Industrial Development

The theoretical model presented in this paper builds upon and extends that presented in Branstetter, Fisman, Foley, and Saggi (2007). We thank Ray Fisman and Fritz Foley for their contributions to that earlier work and for useful comments on this research. All errors remain our own. Views expressed are those of the authors and do not necessarily reflect those of the Bureau of Economic Analysis or the National Bureau of Economic Research. ABSTRACT This paper develops a North-South product model in which Southern imitation and the North-South flow of foreign direct investment (FDI) are endogenously determined. In the model, a strengthening of IPR protection in the South reduces the rate of imitation, which, in turn, increases the flow of FDI. The increase in FDI more than offsets the decline in production undertaken by Southern imitators, so that the South's share of goods produced by the global economy increases. Furthermore, real wages of Southern workers increase even though prices of goods produced by multinationals exceed those of Southern imitators. The preceding results hold when Northern innovation is endogenously determined; in addition, the rate of innovation increases with a strengthening of Southern IPR protection.


Introduction
How does the strengthening of intellectual property rights (IPRs) protection by developing countries impact their industrial development? How does it a¤ect their ability to attract foreign direct investment (FDI)? These and related questions have been at the heart of an ongoing debate that was brought into sharp relief during the negotiations preceding the rati…cation of the WTO's Agreement on Trade Related Aspects of Intellectual Property Rights (TRIPS) in 1995. Opposition to stronger IPR regimes in developing countries rests on two general arguments. First, there is concern that consumer welfare may be adversely impacted by enhancing the monopoly powers of innovators. Second, there is fear that stronger IPR protection in developing countries will hamper their ability to absorb foreign technologies without having any appreciable e¤ect on Northern innovation. 1 On the other side, TRIPS supporters argue that stronger IPRs world-wide will not only increase incentives for innovation but also foster industrial development in developing countries by encouraging multinationals to shift production there. In this paper, we seek to illuminate this important debate by developing a North-South product cycle model in which Southern imitation as well as the North-South ‡ow of FDI respond endogenously to changes in the degree of Southern IPR protection available to Northern …rms. Building on the research tradition established by Grossman and Helpman (1991), the model provides a uni…ed framework for assessing some of the key arguments for and against stronger IPR regimes in developing countries. The theoretical product cycle literature on the e¤ects of Southern IPR protection has been built on two types of growth models analyzed in great detail in Grossman and Helpman (1991) -the variety expansion model and the quality ladders model. Important contributions to this literature were subsequently made by Helpman (1993) and Lai (1998) both of which uti-lized the variety expansion model and Glass and Saggi (2002) who adopted the quality ladders approach. This research established that the e¤ects of increased IPR protection in the South on the Northern rate of innovation depend very much on whether production shifts to the South via imitation of Northern …rms or via North-South FDI. Furthermore, Helpman (1993) forcefully drove home the point that while stronger Southern IPR protection can indeed increase the pace of Northern innovation, such a policy change does not necessarily bene…t the South since it reallocates production in favor of Northern …rms whose prices tend to be higher than those of Southern ones. Thus, international production shifting matters not just for the nature and the extent of innovation but also welfare. Accordingly, we develop a North-South product cycle model with two important features. First, Like Lai (1998), the level of North-South FDI responds endogenously to changes in the degree of Southern IPR protection. Second, like Grossman and Helpman (1991b), imitation is treated as a costly activity and the Southern rate of imitation is endogenously determined. 2 To ease the exposition of our main results and to focus on the e¤ects of Southern IPR protection on activities that occur in the South -i.e. Southern imitation, production by local …rms, and production by Northern multinationals -we …rst analyze a benchmark model in which imitation and FDI are endogenous whereas innovation is exogenously given. The results obtained in this benchmark model are then shown to hold when the rate of Northern innovation is endogenously determined. Apart from tractability, an important advantage of the simpler model is that it allows us to analyze the e¤ects of a strengthening of Southern IPR protection when it does not have any e¤ect on the Northern rate of innovation. This is important because opposition to stronger IPRs in the South is often based on the premise that since Northern innovation is unlikely to respond to changes in the South's IPR regime, the South does not have much to gain from such a policy change. As our analysis below shows, this position is not entirely correct.
Making both imitation and FDI endogenous helps push forward the literature on North-South product cycle models of international trade. Furthermore, since imitation is a costly activity in the real world, analyses that treat it as exogenous fail to capture how changes in the Southern IPR regime alter the allocation of Southern resources among imitation and production. In addition to realism, an important reason for treating imitation as an endogenous activity is that North-South product cycle models with exogenous imitation have yielded remarkably di¤erent conclusions regarding the relationship between imitation and innovation from those that have treated it as endogenous. In a model with endogenous imitation and innovation, Grossman and Helpman (1991b) uncovered a positive relationship between the two activities while Lai (1998) found that a decline in the (exogenously given) rate of imitation leads to an increase in innovation if Northern …rms can undertake FDI in the South. 3 Our model sheds light on the relationship between innovation and imitation when both FDI and imitation are endogenously determined.
In our model, a strengthening of IPR protection in the South reduces the incentive of Southern …rms to imitate Northern multinationals. This decline in imitation makes the South a more attractive location for Northern multinationals. Furthermore, we …nd that the intra-regional reallocation of Southern production (from local imitators to Northern multinationals) that results from a strengthening of Southern IPR protection is dominated by the accompanying inter-regional reallocation of production: in other words, the share of the global basket of goods produced in the South increases with a strengthening of Southern IPR protection.
Our analysis also provides some interesting insights with respect to the e¤ects of Southern IPR protection on prices and wages in the two regions. First, by making the South a more attractive location for production and thereby shifting labor demand from the North to the South, a strengthening of IPR protection by the South lowers the North's relative wage. 4 Second, since Northern multinationals charge lower prices relative to …rms that produce in the North, the increase in FDI helps lower prices. However, this bene…cial e¤ect on prices is partially o¤set by the intra-regional reallocation of Southern production from local imitators to multinationals since a typical imitator charges a lower price than a multinational. Due to the nature of pricing behavior under Dixit-Stiglitz (1977) preferences (prices are mark-ups over marginal costs), these changes in prices and nominal wages translate into clear-cut e¤ects on real wages in the two regions: while Northern real wages decline due to stronger Southern IPR protection, Southern real wages increase. More speci…cally, the purchasing power of Southern workers in terms of Northern goods increases whereas their ability to purchase goods produced by Southern imitators and multinationals remains una¤ected.
As noted earlier, a key argument in favor of weak IPR protection in the South is that Southern imitation lowers prices. Since Southern imitators price below Northern multinationals, this channel is also operative in our model. However, this argument ignores the labor market e¤ects of international production shifting induced by stronger IPR protection in the South. By contrast, in our model, a strengthening of IPR protection by the South raises real wages of its workers. 5 In Section 4 of the paper we show that all of the preceding results regarding wages, prices, and the allocation of production across regions as well as within the South continue to hold when the Northern rate of innovation is endogenously determined. The main additional result that emerges under endogenous innovation is that a tightening of IPR protection in the South raises the rate of innovation. As in Lai (1998), this happens due to two reasons. One, the reduction in imitation risk increases the duration for which Northern multinationals enjoy their pro…t stream and since all Northern …rms are free to become multinationals, the reward to innovation goes up. Second, the reduction in imitation risk implies a greater North-South ‡ow of FDI and this helps move Northern resources from production into innovation.
The relationship between FDI and IPR protection has received significant empirical scrutiny in the literature. 6 As the survey by Park (2008) notes, as far as US data is concerned, there appears to be a clear positive relationship between the degree of IPR enforcement in developing countries and investment by US …rms -see, for example, Lee and Mans…eld (1996) and Nunnenkamp and Spatz (2004). Results derived from non-US data portray a 5 The real wage e¤ects captured by our model would not arise in partial equilibrium models that ignore the labor market e¤ects of IPR reforms. Furthermore, such e¤ects should only be expected to arise when IPR reforms are undertaken on an economy-wide basis as opposed to being focused on a few sectors. 6 For a nuanced and detailed discussion of this literature, see Maskus (2000 7 Given the central role of FDI in our model, it is worth noting that, consistent with a large number of empirical studies discussed in Markusen (1995), we also …nd that an increase in the productivity of Northern R&D leads to an increase in the ‡ow of FDI as well as in the sales of Northern multinationals. Furthermore, we show that the use of FDI incentives by the South in the form of a reduction in the tax rate on the pro…ts earned by multinationals has e¤ects quite like those of IPR reform: it increases North-South FDI, real wages in the South, as well as the Northern rate of innovation. These results not only help clarify the structure of our model but are also quite relevant because incentives toward FDI are widespread in the global economy (UNCTAD, 2003) and a host of recent …rm-level empirical studies document a negative relationship between FDI (particularly by US …rms) and host country tax rates. 8 The rest of the paper is organized as follows. Section 2 presents our benchmark model. Sections 3 describes the e¤ects of a strengthening of Southern 7 Following Feenstra and Rose (2000), they also construct for each reforming country an annual count of "initial export episodes" -the number of 10-digit commodities for which recorded U.S. imports from a given country exceed zero for the …rst time. This serves as a rough indicator of the net rate at which production shifts to the reforming countries, capturing changes in multinational production as well as indigenous imitation. This net rate of production shifting increases sharply after IPR reform, suggesting that any decline in indigenous imitation is more than o¤set by the increase in the range of goods produced by multinational a¢ liates. 8  IPR protection on FDI, Southern production, wages, and prices. Section 4 presents the fully endogenous model and also considers the e¤ects of Southern tax reductions toward Northern multinationals. Section 5 concludes while Section 6 constitutes the appendix.

Model
Consider a world comprised of two regions: North and South. Labor is the only factor of production and region i's labor endowment equals L i , i = N; S. As in Grossman and Helpman (1991b), preferences are identical in the two regions and a representative consumer chooses instantaneous expenditure E( ) to maximize utility at time t: subject to the intertemporal budget constraint where denotes the rate of time preference; r the nominal interest rate; I( ) instantaneous income; and A(t) the current value of assets. The instantaneous utility D( ) is given by where x(j) denotes the consumption of good j; n the number of goods available and 0 < < 1.
As is well known, under the above assumptions, the consumer's optimization problem can be broken down into two stages. First, he chooses how to allocate a given spending level across all available goods. Second, he chooses the optimal time path of spending. The instantaneous utility function D implies that the elasticity of substitution between any two goods is constant and equals " = 1 1 and demand for good j (given expenditure E) is given by where p(j) denotes the price of good j and P a price index such that Furthermore, as is well known, under the two-stage procedure the optimal spending rule is given by i.e. nominal consumption spending grows at a rate equal to the di¤erence between the interest rate and the subjective rate of time preference.

Product market
Three types of …rms produce goods: Northern …rms (N ), Northern multinationals (M ), and Southern imitators (S). Denote …rms by J where J = N; M , or S. Northern …rms can either produce in the North or the South. A …rm needs one worker to produce a unit of output in the North, whereas 1 workers per unit of output are needed in the South. Intuitively, this is due to the costs of coordinating decisions over large distances and operating in unfamiliar foreign environments. Indeed, the theory of the multinational enterprise argues that such …rms rely on 'ownership'advantages derived from technological assets and/or brand names in order to o¤set the disadvantages they face relative to local …rms (see Markusen, 1995).
Given the constant elasticity demand functions, it is straightforward to show that prices of Northern …rms are mark-ups over their marginal costs: Southern …rms can produce only those goods that they have successfully imitated and they need one worker to produce one unit of output. If successful in imitating a multinational, a Southern …rm charges its optimal monopoly price Note that this price can be sustained if and only if it lies below the multinational's marginal cost w S : In what follows, we assume > 1. 9 Let x J denote the output level of …rm J where J = N; M , or S. We know from the demand functions that Using the pricing equations for the three types of products, we have and x Flow pro…t of a Northern producer is given by Similarly, a multinational's ‡ow pro…t equals while that of a Southern …rm equals

FDI and Imitation
Of the n goods that exist, n N are produced in the North, n M are produced in the South by Northern multinationals, and n I are produced by Southern imitators. Let n S n I + n M denote all goods produced in the South. In what follows, we will think of the level of Southern industrial development as roughly corresponding to the Southern share of global manufacturing; i.e., the ratio of goods produced in the South to the number of goods that exist at a point in time. Since this measure of industrial development explicitly 9 When < 1, a Southern imitator limit prices the Northern …rm whose product it has copied by setting its price equal to the Northern …rm's marginal cost w S . includes the activities of a¢ liates of Northern multinationals, the advance of Southern industrial development in our model depends on the rate of FDI.
Let the rate of imitation be de…ned by i.e. denotes the rate of increase of the stock of imitated goods relative to the total number of goods produced by Northern multinationals. Since both multinationals and Southern imitators produce in the South, imitation simply transfers ownership of a good (and the associated ‡ow of pro…ts) from the hands of a multinational to a Southern imitator.
The rate of North-South FDI is de…ned by where n N denotes the number of goods produced in the North. In other words, at each instant, the the total stock of goods produced in the South increases by n N . Note that this measures the in ‡ow of North-South FDI because imitation only targets Northern multinationals and does not, by itself, lead to North-South production shifting. Like Grossman and Helpman (1991b) and Lai (1998), we study a steady state equilibrium in which prices, nominal spending, and all product categories grow at the same rate g: To facilitate exposition, we initially analyze our model under the assumption that the rate of innovation g is exogenously given and then in Section 4 analyze the fully endogenous model. Equations (6), and (14) through (15) imply that in steady state the interest rate equals the sum of the subjective discount rate and the growth rate: r = + g Furthermore, the steady state allocation of products across the two regions satis…es n N n = g g + and n S n N = g Similarly, the ratio of multinationals to their two types of competitors equals The lifetime value of a Northern …rm that opts to produce in the North equals: Note from above that since future products creates competition for existing products, an increase in the rate of innovation (g) reduces the life-time value of a Northern …rm. While it is cheaper to produce in the South (as we show below, the Southern relative wage is lower in equilibrium), shifting production to the South invites the risk of imitation and the value of a Northern multinational …rm equals As is clear, in calculating the value of a multinational …rm, the ‡ow pro…t M is discounted not just by the e¤ective interest rate (which equals + g) but also by the rate of imitation . As in Lai (1998), we assume that imitation targets only Northern multinationals. In other words, the risk faced by Northern …rms that refrain from shifting production to the South has been normalized to zero. In reality, Northern …rms that do not undertake FDI can also have their technologies imitated, but the risk of imitation they face is probably lower than that of multinational …rms that produce in the South. As is known from the work of Mans…eld (1994) and Maskus (2000), multinational …rms indeed internalize the risk of imitation that they face due to weak IPR protection in host countries. 10 Finally, the lifetime value of a Southern producer (i.e. the reward earned by a successful imitator) equals

Relative wage
Since all Northern …rms have the option of becoming multinationals, we must Note immediately from above that if the risk of imitation is positive (i.e. > 0) then we must have M > N . This is intuitive: since any Northern …rm is free to become a multinational, the ‡ow pro…t earned by a multinational must be higher in order to compensate for the risk of imitation faced (only) by multinationals. 11 From the de…nition of pro…t we have The last two equations allow us to write the Northern relative wage (w R ) as a function of the rate of innovation and imitation as well as some of the exogenous parameters of the model: As is clear, the relative wage in the North increases with the production disadvantage faced by Northern multinationals ( ) as well as with the Southern rate of imitation ( ) since both of these factors discourage Northern …rms from relocating production to the South. This reluctance to shift production to the South increases the relative demand for Northern labor and therefore North's relative wage. As we noted earlier, this result di¤ers from that of Grossman and Helpman (1991b) and is line with Lai (1998). Why do these models yield such di¤erent results regarding the determinants of the North-South relative wage? In Grossman and Helpman (1991b), Southern imitation of …rms producing in the North serves as the channel through which international reallocation of production (and therefore labor demand) occurs. By contrast, in our model as well as in Lai (1998) Southern imitation targets multinational …rms and North-South FDI is the channel of international reallocation of production. In our model, by lowering the risk of imitation, a strengthening of Southern IPR protection increases FDI and the demand for Southern labor while it reduces demand for Northern labor. In Grossman and Helpman (1991b), the opposite happens: as imitation declines, more production stays in the North and less of it occurs in the South. Hence the North-South relative wage behaves rather di¤erently across these models.

Imitation incentives and Southern IPR protection
At any given point in time, the unit labor requirement in imitation is given by a I n S . In other words, the unit labor requirement in imitation is assumed to decline with the number of goods produced in the South (n S = n I + n M ). The idea underlying this formulation is that imitation and Northern FDI generate knowledge spillovers for the South that lower the cost of imitation over time. This decline in imitation cost is necessary to sustain imitation in the long run since an ongoing expansion in the number of products in the global economy reduces the pro…tability of imitation over time.
We consider two di¤erent formulations of Southern IPR protection. Under our …rst formulation, the cost function for imitation is given by where k 1 is an index of the degree of IPR protection in the South. The idea underlying this formulation is that as IPR protection is strengthened, imitation becomes a more costly activity for Southern …rms because evading local enforcement of IPRs becomes more di¢ cult. Under our second formulation, the cost function of imitation is given c I = a I w S n S and a Southern imitator's ‡ow pro…t equal Under this formulation, IPR policy is akin to a pro…t tax on imitators: the more stringent is IPR protection, the smaller the rents from imitation. Alternatively, one could view k S as the share of its pro…t stream that an imitator must surrender to local authorities for them to willingly turn a blind eye towards the violation of IPRs of Northern multinationals.
Free entry into imitation implies that the reward from imitation should equal its cost: Substituting from (12) into the above equation and using (8) gives the sales levels of a Southern imitator and a Northern multinational: Furthermore, using we have where The following lemma reports some important properties of the function A( ; g): Lemma 1: A( ; g) < 1 and @A( ;g) @ < 0 < @A( ;g) @g .

General equilibrium
The conditions for general equilibrium are derived from the resource constraints in the two regions. In the North, when the rate of innovation is exogenously given, all labor is allocated to production. Let L i d denote aggregate labor demand in region i where i = N; S. Then L N d n N x N . Substituting from (16) and (26) allows us to write aggregate labor demand in the North as which implies that the Northern labor market equilibrium condition is given by g 1 It is obvious from (27) that aggregate labor demand in the North L N d decreases in . Furthermore, Lemma 1 implies that L N d decreases in . These two properties of L N d imply that in the ( ; ) space, the Northern labor market equilibrium condition, which we will refer to as the N N curve, is downward sloping: increases in while it decreases in and (iii) is unde…ned for = 0. Property (ii) implies that the N N curve is convex in the ( ; ) space whereas property (iii) implies that it does not intersect the vertical axis. From (27) it is straightforward that the N N curve intersects the horizontal axis at 0 > 0. Southern labor is allocated to imitation and production by multinationals and local …rms. Therefore we must have : Substituting into the above resource constraint from equations (16), (17), and (24) gives Observe from (30) that, in steady state, labor demand in the South is independent of the ‡ow of North-South FDI . This implies that in the ( ; ) space, the Southern labor market equilibrium condition (called the SS curve) is a horizontal line at the equilibrium rate of imitation -i.e.
The equilibrium allocation of resources in the global economy is given by the intersection of the N N and SS curves.

E¤ects of Southern IPR protection
In this section, we study the e¤ects of a strengthening of Southern IPR protection when the rate of innovation (g) is exogenously given. We begin by establishing some crucial properties of the North-South ‡ow of FDI. Solving equation (27) for FDI ‡ow in terms of the rate of imitation ( ) gives Observe immediately from (31) that holding constant the numerator of the right hand side increases with g: recall from Lemma 1 that A( ; g) increases with g. Due to the same reason, the ratio =g also increases in g. This implies the following: Remark 1: Holding constant the rate of imitation ( ), the ‡ow of FDI ( ) to the South increases with the rate of Northern innovation: @ @g > 0. Furthermore, the elasticity of the ‡ow of FDI with respect to the rate of innovation is greater than unity: g @ @g > 1.
In this context, it is worth noting that a large number of empirical studies have demonstrated a strong positive correlation between innovation and FDI and, as Markusen (1995) notes, this …nding is so pervasive that it has become a cornerstone of the modern theory of the multinational …rm.
Suppose now that the South increases the degree of IPR protection (k) available to Northern …rms. Note …rst that equation (30) can be written as In other words, from the viewpoint of the South, holding constant the rates of imitation ( ) and innovation (g), an increase in the degree of IPR protection (k) is an e¤ective reduction in the real resources available (i.e. a decline in L S k ) since all three activities that the South is engaged in -imitation, production by multinational …rms, and production by local imitators -would require more resources if k increases and remains unchanged. It is intuitively obvious why an increase in the cost of imitation increases the resources required to sustain a given level of imitation. But why do the two production activities undertaken in the South also become more resource intensive with an increase in the IPR index k? The intuition for this comes from the free entry condition in imitation: as the cost of imitation increases, the sales of a …rm that is successful in imitation also must increase in order to maintain the zero pro…t condition in imitation. Finally, the sales of a multinational (x M ) are proportional to the sales of a Southern imitator (x M ) and if x S increases, so must x M .
Direct calculations yield because " > and < 1. Since aggregate labor demand in the South L S d increases with the rate of imitation and the e¤ective labor supply ( L S k ) falls with the Southern IPR index k, the rate of imitation must fall with k or else the Southern labor market would fail to clear. Now consider how an increase in k e¤ects the N N curve. Since the slope of this curve N ( ; ) is independent of k whereas the horizontal intercept 0 increases with k, the N N curve shifts outward with an increase in k. The decline in the rate of imitation (i.e. the downward shift in the SS curve) along with the outward shift in the N N curve yields: Proposition 1: When the rate of innovation ( g) is exogenously given, a strengthening of Southern IPR protection lowers the rate of Southern imitation ( ) and it increases the rate of North-South FDI ( ): d dk < 0 < d dk .
The logic behind Proposition 1 is easy to see. Recall from Lemma 1 that A( ; g) decreases in . Since decreases in k, it follows then that kA( ; g) increases in k. But with g …xed, equation (27) also implies that the North-South ‡ow of FDI necessarily increases with k or else the Northern labor market cannot clear. Figure 1 illustrates Proposition 1 in the ( ; ) space. 13 With a strengthening of Southern IPR protection, the SS curve shifts down while the N N curve shifts up and the equilibrium of the world economy moves from point A to B, where the rate of Southern imitation is lower whereas the rate of North-South FDI is higher. Since Proposition 1 is our core result from which most other results are derived, it is worth checking whether it holds when Southern IPR protection determines how much rent local imitators collect from their investment in imitation as opposed to making imitation more costly. Let a Southern imitator's ‡ow pro…t from imitation equal S k = (1 k) S = (1 k)(1 )w S x S where k measures the degree of IPR protection and 0 k 1. It is straightforward that in the Northern labor market equilibrium condition (27) we simply need to replace 1=k by (1 k) whereas in the Southern labor market equilibrium condition (30) the same substitution is needed in the second and third terms of the LHS; in the …rst term of the same equation, k needs to be simply replaced by 1. Since an increase in k in our pro…t tax based formulation of IPR protection has analogous e¤ects to an in increase in k under our cost based formulation, Proposition 1 holds under both formulations.

Southern industrial development and FDI
An important objective of this paper is to understand how a strengthening of IPR protection in the South alters the distribution of production across the two regions as well as between Northern multinationals and Southern imitators. How Southern IPR protection a¤ects the global allocation of production depends on its e¤ects on Southern imitation and the North-South ‡ow of FDI. To see the e¤ect of an increase in k on the international allocation of production, …rst note that n S n = +g . Since increases in k and g is exogenously …xed we must have: Corollary 1 (Inter-regional Reallocation of Production): A strengthening of Southern IPR protection increases the South's share of the total basket of goods produced in the global economy ( n S n ): d(n S =n) dk > 0: Given that n I n M = g decreases with k, we can state the following result regarding the allocation of production within the South between multinationals and Southern …rms: Corollary 2 (Intra-regional Reallocation of Production): A strengthening of Southern IPR protection increases the share of Southern production undertaken by Northern multinational …rms ( n M n S ): d(n M =n S ) dk > 0: It is straightforward to show that the total value of multinational sales relative to those of Southern imitators has the following simple expression: Since the the rate of imitation ( ) falls with an increase in the degree of Southern IPR protection, it implies that a strengthening of Southern IPR protection leads to an increase in the aggregate sales of multinational …rms relative to those of Southern imitators.
Now consider a comparison of total multinational sales relative to those of …rms producing in the North: Since n M n N = g+ , equation (33) implies that a typical multinational must have higher relative sales compared to a Northern …rm (i.e. the ratio p M x M =p N x N must exceed 1). Intuitively, since imitation only targets multinational …rms, for a typical multinational to earn the same rate of return as a Northern …rm producing in the North, the multinational must have a higher relative pro…t ‡ow. However, with a decline in the rate of imitation, this relative pro…t ‡ow actually has to shrink in order to ensure multinationals and Northern …rms earn the same rate of return. In other words, a strengthening of Southern IPR protection decreases the sales of a typical multinational …rm relative to those of a Northern …rm.
In this context, one further subtlety that arises from general equilibrium considerations is worth noting: an decrease in the rate of imitation increases the relative Southern wage and therefore the cost of production of multinationals relative to Northern …rms. However, since prices of both types of …rms are mark-ups over their respective marginal costs, this cost increase has a proportional e¤ect on prices of multinationals relative to those of Northern …rms. In other words, by increasing the South's relative wage, IPR reform increases the prices charged by multinationals relative to those of Northern …rms and this translates into lower relative sales for a typical multinational.

Real wages and the aggregate price index
What are the e¤ects of a strengthening of IPR protection in the South on real wages in the two regions? By de…nition, the real wage e¤ects of such a policy change depends upon nominal wages in the two regions and the prices of goods produced by three types of …rm: …rms located in the North, multinationals producing in the South, and Southern imitators. Recall that p N = w N ; p M = w S ; and p S = w S which allows us to write Northern real wages in terms of the three types of goods: In other words, the Northern real wage in terms of goods produced by Northern …rms is una¤ected by Southern IPR protection whereas in terms of the other two goods, it moves in the same direction as the Northern relative wage w R . We already know that Northern relative wage decreases as a result a strengthening of Southern IPR protection since the rate of imitation falls with such a policy change. This decline in the Northern relative wage w R implies that a strengthening of Southern IPR protection decreases real wages in the North.

19
Consider now the e¤ect on Southern real wages. We have In other words, the only e¤ect on Southern real wages of a change in its IPR policy is in terms of goods produced in the North. However, since w R decreases with , it implies that a strengthening of Southern IPR protection increases real wages in the South. The general equilibrium nature of this result deserves emphasis. A common argument in favor of weaker IPR protection in the South is that Southern imitation lowers prices and therefore bene…ts consumers. Since prices of Southern imitators are lower than those of Northern multinationals, this channel is operative in our model as well. However, the story does not end there: international production shifting that results from a reduction in the rate of imitation also has labor market e¤ects. In our model, a strengthening of Southern IPR protection leads to a higher Southern relative wage since the resulting decline in imitation risk makes the South a more attractive location for Northern multinationals. Indeed, changes in prices are dominated by the change in the Southern relative wage so that the purchasing power of Southern workers in terms of goods produced in the North increases whereas there is no change in their ability to purchase goods produced in the South. Despite an increase in real wages, Southern welfare does not necessarily increase because the ‡ow of utility equals the log of real spending (log u = log E log P ) and a reduction in pro…ts of Southern imitators lowers Southern income and can adversely impact Southern spending. While a complete welfare analysis along the lines of Helpman (1993) is beyond the scope of the paper, it is useful to consider how a strengthening of Southern IPR protection a¤ects the aggregate price index P . By de…nition, which can be rewritten as which is the same as While goods produced by multinationals are cheaper than those produced by Northern …rms (p M < p N ), it is the Southern imitators that produce the cheapest goods (p S < p M ). Recall that n I n M = g decreases with the degree of Southern IPR protection (k) since imitation slows down while innovation increases. This implies that n I =n n M =n = g decreases with k, i.e., the share of global production that is in the hands of multinational …rms increases. Furthermore, recall that a strengthening of Southern IPR protection shifts production away from the North and towards the South (inter-regional reallocation). Since p M < p N , the inter-regional reallocation of production from North to the South helps lower the overall price index. However, since p M > p S , the intra-regional reallocation of Southern production in favor of Northern multinationals and away from Southern imitators has the opposite e¤ect. This implies that if the inter-regional reallocation of production is substantial, Southern imitation has the potential to partially bene…t Northern consumers by lowering the aggregate price index P . Indeed, this is the key reason why Helpman (1993) …nds that some amount of imitation is in the interest of the North. However, in our model, since FDI also o¤ers the potential for lowering prices, imitation is not as crucial for welfare purposes. This is worth explaining in some detail. Unlike us, Helpman (1993) assumes that the risk of imitation applies equally to Northern …rms and multinationals. As a result, multinationals and Northern producers can coexist in equilibrium only if the two regions have equal wages. 14 Under such wage equalization, FDI o¤ers no reduction in costs of production and therefore has no price effects. By contrast, in our model, both FDI and imitation imply cost savings and the allocation of production across regions as well as within the South have implications for the aggregate price index.
We next study the e¤ects of a strengthening of Southern IPR protection when innovation is endogenous. 14 Our model would yield the same result if the rate of imitation facing multinationals and Northern producers were the same (i.e. = 0) and multinationals did not face any frictions that hamper their ability to be as e¤ective in production as local Southern …rms (i.e. = 1). 21

The model with endogenous innovation
Note …rst that when the rate of innovation is endogenously determined, the results obtained under the assumption of exogenous innovation (i.e. Proposition 1 and Corollaries 1-2) continue to hold so long as a strengthening of Southern IPR protection does not decrease the Northern rate of innovation g. In what follows, we show that an increase in the Southern IPR protection index k actually increases the rate of innovation (Proposition 2). In addition, we also show that an increase in R&D productivity of the North increases both innovation and North-South FDI (Proposition 3) and that a policy of attracting multinational …rms through a reduction in the pro…t tax imposed on them has e¤ects quite similar to a strengthening of Southern IPR protection.

Costly innovation
When innovation is endogenous and there is free entry into it, the value of a Northern …rm must exactly equal the cost of innovation: where a N is the unit labor requirement in innovation and w N a N n measures the up-front cost of product development. This formulation assumes that the cost of designing new products falls with the number of products (n) that have been invented. In other words, knowledge spillovers from innovation sustain further innovation. This assumption is standard in the literature (see Helpman, 1991a andb, andRomer, 1990) and in its absence growth cannot be sustained in the variety expansion model with …xed resources. This is because the ‡ow pro…t of a successful innovator declines with the number of products invented and incentives for innovation disappear in the long run if the cost of innovation does not also fall with an increase in the number of products.
Substituting from equation (10) into (34) gives the output level of a Northern …rm From equations (34) and (23) we have Utilizing the de…nition of …rm values and pro…ts allows us to rewrite the above equation as Using equations (9) and (21) Substituting from (16) and (17) into the above equation gives us an equilibrium relationship between the three endogenous variables g, , and and the exogenous parameters of the model: Intuitively, this condition follows from the assumption of free entry into imitation and innovation and it ensures that neither activity leads to excess pro…ts for …rms that are successful in such activities. Solving equation (39) for FDI ‡ow in terms of the other two endogenous variables (g and ) gives = g " a N A( ;g)ka I

(40)
Observe immediately from (40) that holding constant the denominator of the right hand side increases with g: this is because =g falls with g whereas A( ; g) increases (Lemma 1). This implies the following result: Remark 2: Holding constant the rate of imitation ( ), factors that increase the North-South ‡ow of FDI ( ) must also increase the rate of Northern innovation ( g).
In this context, it is worth noting that a large number of empirical studies have demonstrated that there is a positive correlation between innovation and FDI; as Markusen (1995) notes, this …nding is so pervasive that it has become a cornerstone of the modern theory of the multinational …rm. Furthermore, since A( ; g) decreases with , we have: Remark 3: Holding constant the rate of innovation ( g), factors that decrease the Southern rate of imitation ( ) must also increase the North-South ‡ow of FDI ( ): An important point to note is that since our model exhibits a negative feedback between FDI and imitation and a positive feedback between FDI and innovation, it necessarily implies a negative feedback between innovation and imitation. This is an important property of the model which di¤erentiates it from the results of Grossman and Helpman (1991b) and aligns it with those of Lai (1998).
Consider now the direct e¤ect of Southern IPR protection on the North-South ‡ow of FDI. From (40) directly observe that the denominator in the formula of ( ; g) decreases with k so that we have: Remark 4: Holding constant the rates of imitation ( ) and innovation ( g), the ‡ow of FDI ( ) to the South increases with a strengthening of Southern IPR protection (i.e. an increase in k).
The intuition for this result comes from equation (38) which requires the rate of return on innovation and imitation to equal each other. Since the right hand side of this equation always equals 1, an increase in the IPR index k must be counterbalanced by an increase in the ratio of production ( n S n = +g ) that occurs in the South for the cost of imitation to not increase relative to the cost of innovation which in turn requires that the ‡ow of FDI increases with the degree of IPR protection k. It is well-known that multinational …rms conduct a large share of global research and development (R&D). Indeed, a generation of empirical studies have documented the positive correlation between FDI ‡ows and R&D investment (Markusen, 1995). Given this, it is worth noting from equation (40) that, holding constant the rate of innovation and imitation, an increase in the R&D productivity of Northern …rms (as measured by an decrease in a N ) implies a faster North-South ‡ow of FDI. We later discuss the general equilibrium response of FDI to an increase in Northern R&D productivity taking into account its e¤ects on the rates of imitation and innovation.

Southern IPR protection under endogenous innovation
Assuming the rate of imitation is exogenously given, Lai (1998) has shown that a decline in this rate increases Northern innovation and the rate of production shifting to the South. 15 A crucial question is whether this important result holds when both imitation and innovation are endogenous and the underlying exogenous variable is the degree of IPR protection (i.e. parameter k). Under endogenous innovation, the Southern labor market equilibrium condition (30) remains unaltered where in the North we now need to account for resources allocated to innovation: Substituting into the above resource constraint from the market measure equations (16), (17), and (35) yields Equations (30), (39), and (42) de…ne the steady state equilibrium of the model in terms of the three endogenous variables: the rate of innovation g, the rate of imitation , and the rate of FDI . All of the e¤ects of increased IPR protection in the South (i.e. an increase in k) are derived from the e¤ects on these endogenous variables. Using the equilibrium ‡ow of FDI and the two resource constraints, we can derive a system of two equations in two unknowns that helps provide a graphical illustration of the consequences of stronger IPR protection in the South.
Recall that the Southern labor market constraint is independent of the ‡ow of FDI . As before, let L S d measure aggregate labor demand in the South (given by the LHS of equation (30)). Recall that @L S d @ > 0 -i.e. 15 In the appendix, we show how our model relates to Lai (1998). holding constant the rate of innovation g, aggregate labor demand in the South increase with the rate of imitation . Similarly, holding constant the rate of imitation, demand for Southern labor increases with the rate of innovation: where we have assumed that > . Thus, the Southern labor market constraint (i.e. the SS curve) is downward sloping in the (g; ) space: In other words, since the South has only a …xed amount of labor resources, an increase in the Southern rate of imitation implies that the rate of innovation g that can be supported by the global economy must be lower. Also, we have i.e. the higher the rate of imitation , the higher the demand for Northern labor. The logic for this is as follows. Since FDI is endogenously determined, a higher rate of imitation makes FDI less attractive to Northern …rms. For a …xed rate of innovation, the demand for Northern workers is inversely related to the ‡ow of FDI. Next consider how an increase in the rate of innovation e¤ects aggregate labor demand in the North. Recall that demand for Northern labor comes from innovation (L N n a N g) and from production (L N p n N x N ). It is obvious that an increase in g raises labor demand in innovation (L N n ). On the production side, labor demand can be written as which immediately implies that if n N n were to increase in g, then it must be that L N p (and therefore aggregate labor demand) in the North increases in g. Further note from above that if were independent of g, it would immediately follow that n N n increases in g. This thought experiment is useful for highlighting the role of the ‡ow of FDI in our model: if the ‡ow of FDI ‡ow were invariant to the rate of innovation, labor demand in the North would necessarily increase with the rate of innovation. However, Remark 2 notes that the ‡ow of FDI and the rate of innovation are positively related. This raises the possibility that n N n might decrease with g. Intuitively, such a situation could arise since the elasticity of the ‡ow of FDI with respect to the rate of innovation exceeds unity. Despite this, we show in the appendix that labor demand in the North necessarily increases with the rate of innovation: As a result, like the Southern labor market constraint, the Northern labor market constraint (i.e. the NN curve) is also downward sloping in the (g; ) space: It is worth emphasizing the role FDI plays in this context: in the absence of FDI, in a variety expansion product cycle model such as Grossman and Helpman (1991b), the Northern market labor constraint is actually upward sloping in the (g; ) space. This is because when imitation is the only channel via which production is reallocated internationally, an increase in the rate of imitation frees up Northern labor for use in innovation thereby generating a positive feedback between imitation and innovation. By contrast, in our model imitation targets production by multinationals and by slowing down FDI, an increase in the rate of imitation actually pulls Northern resources out of innovation and into production.
For a unique steady state equilibrium to exist, the SS curve and the N N curve must have a unique intersection in the (g; ) space. We have already noted that both curves are downward sloping. Neither curve intersects the vertical axis and we show in the appendix that under minor conditions, the horizontal intercept (g s ) of the SS curve is larger than that (g n ) of the N N curve . The latter property means that when the rate of imitation is near zero, the rate of innovation required for the Southern market to be in equilibrium is greater relative to the required rate of innovation for the Southern market to be in equilibrium. This is quite intuitive: when the rate of imitation is zero, Southern resources are utilized only by multinationals for their production activities whereas Northern resources are used up in both innovation and production. As a result, when imitation is non-existent labor market equilibrium in the South calls for a greater rate of innovation than that in the North since the only activity generating labor demand -i.e. FDI -is positively related to the rate of innovation.
Given these properties of the two curves, any intersection of the two curves will be unique if the N N curve is steeper than the SS curve: i.e. r N = S > 1. We can show that r > 1 i¤ a R a N =a I exceeds some threshold a R , where a R is a function of exogenous parameters and the rates of imitation and innovation. Furthermore, as approaches zero, a R can be shown to be decreasing in the rate of imitation . In other words, for close to zero, the required threshold a R is the highest (and therefore the most di¢ cult to meet) at = 0. Next, it can be shown that at = = 0, a R decreases in and at the lowest feasible value of (which is 1= ), the condition a R > a R is necessarily satis…ed for all feasible . Thus, we proceed with the scenario where the N N curve is steeper than the SS curve and the two curves have a unique intersection that pins down the equilibrium of the global economy.
As was already noted, holding constant the rates of imitation ( ) and innovation (g), an increase in the degree of Southern IPR protection (k) increases labor demand in the South in all three activities (i.e. local imitation, production by Southern …rms, and production by multinationals). This is equivalent to an inward shift in the Southern labor market constraint in the (g; ) space. Further note that holding constant g and , an increase in k e¤ects the Northern labor market constraint via its e¤ect on the ‡ow of FDI . Given that the ‡ow of FDI increases in the Southern IPR index k, it follows that labor demand in the North L N ( ; g) (i.e. the left hand side of equation 42) decreases with k. The e¤ect of a strengthening of IPR protection in the South on equilibrium rates of imitation and innovation can now be derived. As IPR protection in the South increases, the Southern labor market constraint (i.e. the SS curve) shifts down while the Northern constraint (i.e. the N N curve) shifts up. These shifts in the two constraints deliver one of our key results: Proposition 2: A strengthening of IPR protection in the South decreases the Southern rate of rate of imitation ( ) while it increases the Northern rate of innovation ( g): d dk < 0 < dg dk . The N N curve illustrates the Northern resource constraint whereas the SS curve denotes the Southern one. In Figure 2, the N N curve is relatively steeper because of the fact that while the rate of innovation is determined primarily by the size of the Northern economy (since only the North innovates), the rate of imitation is determined primarily by the size of the Southern one (since only the South imitates). Of course, the North-South ‡ow of FDI is what links the two resource constraints to each other.
Point A denotes the initial steady state equilibrium. Now suppose that Southern IPR protection is strengthened (i.e. k increases). In Figure 2, this implies an inward shift in the Southern resource constraint and an outward shift in the Northern constraint. Why the Southern constraint shifts has already been explained: all three activities in the South become more resource intensive and this e¤ectively reduces the resource base. The Northern constraint shifts out because of the FDI response: as the ‡ow of North-South FDI increases, more Northern resources become available for innovation. The outward shift in the Northern constraint is relatively smaller because the North is a¤ected via a single, indirect channel (i.e. through the response of North-South ‡ow of FDI) whereas the e¤ect on the South is a more direct one and it occurs via all three activities that take place there. As shown in Figure  2, these shifts in the two resource constraints caused by a strengthening of IPR protection in the South imply that in the new steady state equilibrium B the Southern rate of imitation is signi…cantly lower than that at A while the Northern rate of innovation is higher. 17 Thus, from the perspective of the North, stronger Southern IPR enforcement in our model generates a rather classical trade-o¤ between a static welfare loss and a dynamic welfare gain: the static loss being the decrease in real wages (or in its terms of trade since the relative price of Northern exports is determined by the relative wage) and the dynamic gain being the increase in the rate of innovation. What is noteworthy, however, is that the trade-o¤ in the North results from changes in the IPR policy of the South.
We should emphasize that the properties of the model noted in Remarks 2 and 3 are quite crucial since these establish a positive feedback between FDI and innovation and a negative feedback between these two variables and the rate of imitation. As long as a strengthening of Southern IPR protection discourages imitation, its positive e¤ects on innovation and FDI are implied by Remark 3. For innovation and FDI to be a¤ected negatively by a strengthening of Southern IPR protection, our model would need to have the somewhat strange property that an increase in the resource requirement for imitation (as measured by ka I ) increases the rate of Southern imitation. Due to the complexity of the fully endogenous model, we cannot provide an analytical proof that rules out this unlikely possibility; however, we have not been able to …nd any sets of parameter values under which it arises. Now brie ‡y consider the case where a Southern imitator's ‡ow pro…t from imitation equal S k = (1 k) S = (1 k)( 1)w S x S where k determined the degree of IPR protection and 0 k 1. Under such a formulation, the Northern labor market equilibrium condition is unaltered whereas the other two equilibrium conditions are slightly modi…ed. In equation (39) we simply need to replace 1=k by (1 k) whereas in equation (30) the same substitution is needed in the second and third terms of the LHS; in the …rst term of the same equation, k needs to be simply replaced by 1. It is straightforward to show that results obtained under our cost based formulation of IPR protection continue to hold under thus pro…t-tax formulation.
Finally, we note how an improvement in R&D productivity (i.e. a decrease in a N ) a¤ects the North-South ‡ow of FDI as well as the global allocation of production, once the e¤ects on innovation and imitation are taken into account. First note that a decrease in a N has no direct e¤ect on the SS constraint whereas the e¤ect on the N N constraint is essentially the same as that an increase in the Northern labor supply -i.e. in …gure 1, the N N curve shifts out. This immediately implies that with an increase in Northern R&D productivity, the rate of imitation decreases whereas the rate of innovation increases. Relying on arguments similar to those used to derive the e¤ects of Southern IPR protection, we directly state the following: Proposition 3: With an increase in the R&D productivity of Northern …rms (i.e. a decrease in a N ), the rate of innovation, the North-South ‡ow of FDI, the share of Southern production in the hands of Northern multinationals, and the sales of multinationals relative to other …rms, all increase whereas the rate of imitation decreases.

E¤ects of FDI policies
Many countries implement policies designed to attract FDI, perhaps with the hope of spurring local industrial development (see UNCTAD, 2003). Quite often such policies take the form of …scal incentives under which multinationals that invest locally are o¤ered reduced tax rates. Are such policies justi…able? To address this question, suppose that the South undertakes a policy of o¤ering an incentive to Northern multinationals that lowers the pro…t tax t on Northern multinationals from. What are the consequences of such a policy? First note that when such a pro…t tax is in place, a typical Northern multinational's after-tax pro…t equals It is straightforward to show that when a multinational's pro…t is M t (as opposed to M ), the Northern relative wage equals from where it is immediate that a reduction in the pro…t tax t on multinationals (which is the same as a tax incentive for FDI) increases the Southern relative wage. The intuition is simple: the use of FDI incentives makes the South a more attractive production location and shifts labor demand away from the North in favor of the South.
Under a tax on multinationals, the North-South ‡ow of FDI is given by Since A t ( ; g) decreases in t, it is clear from above that holding constant the rates of innovation (g) and imitation ( ), the North-South ‡ow of FDI ( ) increases with a decrease in the FDI tax rate t. Of course, how the equilibrium ‡ow of FDI responds to the use of an FDI incentive depends on how the rates of innovation (g) and imitation ( ) respond to such a policy. Note that the Southern resource constraint is una¤ected by the FDI tax rate t whereas the Northern constraint is a¤ected via the North-South ‡ow of FDI. But since this ‡ow is inversely related to the tax rate t, it implies that a reduction in t results in an outward shift in the N N curve in …gure 1 without having any a¤ect on the SS curve. This implies that a reduction in the Southern tax rate t on multinationals increases the rate of innovation ( g) and the North-South ‡ow of FDI ( ) whereas it decreases the Southern rate of imitation ( ).
In the presence of the FDI tax, equation (38) (which follows from free entry into innovation and imitation) becomes Since the term in square brackets increases with t, it must be that n S n decreases with t. In other words, a Southern policy of attracting FDI via a reduction in the tax rate t, increases the share of the global basket of goods that is produced in the South. Furthermore, since n I n M = g , such a policy change towards FDI also shifts production in favor of Northern multinationals and away from Southern imitators. Finally, consider the labor market consequences of such a policy. It follows immediately from the formula for the North-South relative wage (see 43) that a reduction in t decreases the South's relative wage (1=w R t ). Furthermore, such a policy change lowers real wages in the North while increasing them in the South.
Corollary 3: A reduction in the Southern tax rate on multinationals increases the South's wage relative to the North as well as the real wages of Southern workers.
Finally, note that the price e¤ects of a reduction in the Southern tax rate on multinationals are quite like those of a strengthening of its IPR protection: both types of policies lower prices of those goods whose production shifts from the North to the South while increasing prices of those goods whose production stays in the hands of multinationals as opposed to Southern imitators.

Conclusion
Opinions regarding the strengthening of IPR regimes in developing countries required under the TRIPS agreement of the WTO vary remarkably across individuals and nations. While the issue is multi-faceted and complex, the following statement broadly captures the disparity in views regarding TRIPs: developing countries have tended to argue that stronger IPR regimes in their markets will have adverse e¤ects on prices without having much of a positive impact on innovation whereas developed countries have stressed that not only innovation, but also FDI ‡ows would respond strongly to such reforms. In principle, an increase in FDI has the potential to o¤er two major sources of welfare gains. One, it can lower prices by shifting production to lower cost locations. Two, FDI has the potential to encourage Southern industrial development by introducing new technologies into the South. In this paper, we have presented a general equilibrium North-South product cycle model with a degree of endogenity that allows us to assess these arguments in a uni…ed framework.
The major results of our core model are as follows. First, we …nd that a strengthening of IPR protection in the South discourages imitation. Second, it increases FDI to a degree that the Southern production base actually expands -i.e. the decline in Southern imitative activity is more than o¤set by the increase in the production activity of Northern multinationals who are drawn to the South because local IPR reform renders it a more attractive production location by reducing the risk of imitation. Third, while prices of those goods that are reallocated from …rms producing in the North to multinationals fall, prices of goods that are reallocated from potential imitators to Northern multinationals increase. In other words, IPR reform in the South has con ‡icting e¤ects on consumer welfare when viewed solely through the price channel. However, what actually matters for consumer welfare is purchasing power. And from this viewpoint, Southern IPR reform bene…ts the South since it increases not only the South's wage relative to the North but also the purchasing power of Southern consumers. By contrast, not only does the Northern relative wage decline, the real income of Northern workers also falters. It is worth emphasizing that only a general equilibrium model such as ours can help assess the full impact of the price changes that result from IPR reforms since these can be o¤set (or dominated) by the accompanying changes in wages. Finally, when innovation is endogenous, a strengthening of IPR protection in the South increases its rate. We should note that while the paper does not provide a full- ‡edged welfare analysis along the lines of Helpman (1993), the clarity with which the various channels that a¤ect welfare emerge in the model does shed new light on a rather complex set of issues.

Appendix
In this appendix, we …rst provide some derivations omitted from the text and then discuss the relationship of our model to Lai (1998).

Rate of imitation with g exogenous
When g is exogenous, the equilibrium rate of imitation solves L S d ( ; ) = L S which is the same as ka I g g + + ka I 1 g( + g) " (g + ) + ka I 1 ( + g) g + = L S Rearranging, we have ka I 1 g( + g) " + ka I g + + ka I ( + g) 1 = L S (g + ) which is the same as B + C = L S (g + ) where 0 < B ka I 1 ( + g) " < C ka I g + ka I ( + g) 1 Solving for yields = g(L S B) C L S It is straightforward to show that increases in L S whereas it decreases in the degree of Southern IPR protection k.

Slope of N N curve
We already noted in the main text that @L N ( ;g) @ > 0. Direct calculations yield @L N ( ; g) @g = " ( + + g)a N a I A( ; g)[ ( + + g) ] ( + + g)(1 ) " From where it follows that a su¢ cient condition for @L N ( ;g) @g > 0 is that a N a I > 1+ " . This is because ( + g)[ " a N a I A( ; g)] > 0 due to the fact that A( ; g) < 1, < 1, a N a I and " > 1. Next note that the condition a N a I > 1+ " is satis…ed for all feasible parameter values: since a N a I , at the lowest feasible value of a N this condition becomes " > 1 + which necessarily holds since > 1= .

Horizontal intercepts of the two curves
It is trivial to observe that neither curve can intersect the vertical axis since labor demand in each country approaches zero as the growth rate approaches zero. The N N curve intersects the horizontal axes at g n where g n " L N (1 ) (a N " a I ) a N " a I Similarly, the SS curve intersects the horizontal axis at g s where g s L S (1 ) " a I a I From where it follows that g s > g n i¤ L S > L S where L S (L N + a N ) a I " a N a I We assume that L S > L S .

Relationship to Lai' s model
Our model di¤ers from Lai's in one key respect: imitation is endogenous in our model whereas it is exogenous in his. Setting = 1 and assuming is exogenous simpli…es our model down to Lai's. In that case, the two endogenous variables (i.e. g and ) must satisfy the following two equations: The following result is proved in Lai (1998): a strengthening of Southern IPR protection (i.e. a decrease in the rate of imitation ) increases the Northern rate of innovation g. The proof proceeds in a straightforward fashion: the implicit function theorem is applied to the above equation to determine the sign of dg d .