Intellectual property rights, southern innovation and foreign direct investment

Transcription

1 Intellectual property rights, southern innovation and foreign direct investment Anuj J. Mathew University of avarra, Pamplona, pain and Arijit Mukherjee University of ottingham and The Leverhulme Centre for Research in Globalisation and Economic Policy, UK August 008 Abstract: In a orth-outh trade model, we analyze the effect of a er outhern patent system on the orthern firm s incentive for foreign direct investment (). A er outhern patent regime increases the outhern firm s incentive for innovation. For a given outhern patent system, the incentive for innovation by the outhern firm is lower under than under exporting by the orthern firm. The effect of a er patent regime on the incentive for depends on the innovative capability of the outhern firm, on the degree of product differentiation and on the transportation cost. If the outhern firm does innovation either irrespective of the outhern patent regime (which occurs for sufficiently low cost of innovation) or only under a outhern patent protection (which occurs for a moderate cost of innovation), a er patent protection may reduce the orthern firm s incentive for. Key Words: Foreign direct investment; Innovation; Patent protection JEL Classifications: F1, F13, O3, O34 Correspondence to: Arijit Mukherjee, chool of Economics, University of ottingham, University park, ottingham, G7 RD, UK arijit.mukherjee@nottingham.ac.uk Fax:

2 Intellectual property rights, southern innovation and foreign direct investment 1. Introduction A fascinating development in recent decades is the dominance of foreign direct investment () over international trade (UCTAD, 006), which has generated a vast theoretical and empirical literature on. 1 A factor which is often considered to be an important determinant of is the protection of intellectual property rights. ince the developed-country firms make use of their intellectual-property related assets under, a common concern of those firms is about the patent protection in the developing countries. ince the inception of the Uruguay round of the General Agreement on Tariffs and Trade, developing countries are increasingly urged to strengthen their patent systems in order to standardize the patent regime across the world, thus trying to protect the intellectual properties of the developed-country firms. The empirical evidence is mixed on patent protection and. While the empirical studies by Lee and Mansfield (1996), Maskus (1998) and marzynska (004) provide support for the positive relationship between patent protection and, other works show that there is either a negative (see, Yang and Maskus, 001, Pfister and Deffains, 005) or an insignificant (see, eyoum, 1996 and Fosfuri, 004) relationship between these two. The availability of technology licensing is identified as the reason for lower in the presence of a er outhern patent system. unnenkump and patz (004) show that industry as well as the host-country characteristics play important roles in determining the relationship between and patent. 1 ee, aggi (00) for a recent survey on. 1

3 We develop a simple orth-outh model of international oligopoly in the presence of product innovation by the outhern firm. A er patent protection in the outh increases the incentive for outhern innovation. Further, for a given outhern patent system, the incentive for innovation by the outhern firm is lower under than under exporting by the orthern firm. This is in line with the empirical evidence (Veugelers and Houte, 1990 and Goto and Odagiri, 003). However, whether a er patent protection in the outh increases the incentive for by the orthern firm depends on the innovative capability of the outhern firm, on the degree of product differentiation and on the transportation cost. If the outhern firm innovates either irrespective of the outhern patent regime (which occurs for sufficiently low cost of innovation) or only under outhern patent protection (which occurs for a moderate cost of innovation), the orthern firm s incentive for may be higher under the outhern patent protection depending on the degree of product differentiation and the transportation cost. In a theoretical work, Glass and aggi (00) show that a er patent protection in the outh absorbs more outhern resources for imitation, thus crowding out, which, in turn, moves resources in the orth from innovation to production and reducing orthern innovation. Higher cost if imitation in the outh and lower orthern innovation are responsible for the reducing effect of a er outhern patent regime in Glass and aggi (00). In contrast, our results are due to a new factor, viz., the innovative activity of the outhern firm, which has so far been ignored in the literature. In our analysis, imitation is costless and a er patent protection in the outh reduces imitation exogenously (as in Helpman, 1993 and Lai, 1998). The switch from the process patent regime to product patent regime in many developing countries such as in India may justify this assumption. While process patent allows the imitator to produce a product similar to that of the innovator by using a different production process, product patent completely prevents the imitator to produce the product of the innovator. Hence, in our analysis, the

4 Thus, we abstract our analysis from the resource effect considered in Glass and aggi (00), and show the implications of outhern innovation in determining the effects of the outhern patent system on by the orthern firm. In a orth-outh framework, Helpman (1993) and Lai (1998) also consider the effects of the patent system on. However, unlike our paper, both these works ignore innovation by the outhern firms and assume that the outhern firms are only capable of doing imitation. While imitation is prominent in the outhern countries, empirical evidence shows considerable innovative activities by the outhern firms. It is particularly important to consider innovation by the outhern firms when considering in newly industrialized countries or in relatively technologically advanced developing countries. Many Asian countries such as outh Korea, India and Taiwan are inventing new products those are competing with the existing products of the developed countries firms. In an earlier study, Correa (1990) presents the main characteristics of the software market and industry in Latin America while discussing development and commercialization of software in many Latin American countries. ignificant R&D efforts are also evidenced in Indian pharmaceutical industry. 3 Tsai and Wang (004) provide evidence of significant R&D efforts in Taiwan s electronics industry. In different contexts, the importance of innovation in the less developed countries is acknowledged in Muniagurria and ingh (1997) and Zhou et al. (00). Hence, onesize-does not fit all, and we may need to consider outhern innovation while analyzing the effects of outhern patent regimes on by orthern firms. er patent protection can be viewed as an approximation for the product patent regime, while the er patent system can be viewed as an approximation for the process patent regime. 3 Rajesh Unnikrishnan reports, Domestic giant Ranbaxy Laboratories tops the list of companies from developing nations in filing patents. The company has filed patents for 40 products. According to the Patent Cooperation Treaty (PCT) database, Indian drug companies have filed around 4,00 applications. Of these, 55% are for pharmaceutical innovations (The Financial Express, December 13, 004). 3

5 Our paper is related to the vast theoretical literature analyzing the effects of the patent system in the orth-outh trading environment (see, e.g., Chin and Grossman, 1990, egerstrom et al., 1990, Diwan and Rodrik, 1991, Grossman and Helpman, 1991, Deardorff, 199, Taylor, 1994, Vishwasrao, 1994, Fosfuri, 000, Markusen, 001 and inha, 006). However, a common feature of those works is to ignore by the orthern firms and innovation by the outhern firms, which are the ingredients of our analysis. The remainder of the paper is organized as follows. ection describes the model. ection 3 determines the profits of the firms conditional on the R&D decision of the outhern firm and the decision of the orthern firm. ection 4 determines the equilibrium R&D decision of the outhern firm. ection 5 shows the effects of the outhern patent system on the decision of the orthern firm. ection 6 concludes. Proofs are relegated to the appendix.. The Model Consider two countries, called orth and outh. Assume that there is a firm in each of orth and outh and call the firms as and respectively. For simplicity, we assume that at the beginning of the game neither firm has any technology to produce a good. The firms can invest in R&D to invent new technologies. Let firm targets to invent product x, while firm targets to invent product y. We consider that the products x and y are imperfect substitutes. 4 We assume that each firm can invent a single product at one point of time, which implies a restriction on 4 The assumption of imperfect substitutes can be consistent with a patent if we consider that the degree of substitutability depends on the tastes and preferences of the consumers. For example, even if the manual typewriter is different from the electronic typewriter or computer, these products may be imperfect substitutes depending on the tastes and preferences of the consumers. Evidences can also be found from the pharmaceutical industry where two different drugs can solve some common problems. For example, both Zantac and Gaviscon solve the problem of acidity, and become substitutes. 4

6 the R&D capacity of the firms. 5 ince x and y are imperfect substitutes, each firm would prefer to invent the technology which is different from its competitor. 6 Assume that firm is more capable in doing innovation and requires lower investment for R&D. We assume that the R&D investment of firm is R 0 and firm needs to spend R amount more than firm, where R > 0. The cost of R&D to firm is R R R. This is consistent with the previous works where the firms in + the developed countries do R&D at a lower cost, which reflect their higher capabilities in R&D, and are more prone to innovation (see, e.g., Muniagurria and ingh, 1997, and Zhou et al., 00). To economize on the notation, we normalize the cost of R&D of firm to 0. This simplification will not affect our analysis as long as firm always does innovation in equilibrium. Assume that a firm can imitate the technology invented by the other firm, if the patent law permits. We will consider two types of patent regimes in the outh: patent protection and patent protection. Under patent protection in the outh, only the patent holder of the product can sell its product in the outhern market, thus eliminating imitation. However, under patent protection in the outh, along with innovation, both firms are allowed to do non-infringing imitation of the competitor s technology and can sell the same product in the outh. As already mentioned in footnote, the and patent regimes in our analysis can approximate the product and process patents respectively. Where product patent prevents the imitator to produce the product of the innovator, process patent allows 5 In real world, we don t find one firm is investing in all the products. This may be due to strategic reasons, or may be due to physical or financial constraints on R&D. We assume the latter and consider that each firm can invent a single product at any point of time. 6 There may be a coordination problem in the R&D stage, i.e., which firm will invent which technology. However, the flow of information at the R&D stage and slight early investment of one firm may solve this coordination problem. We assume away this coordination problem by considering a predetermined choice of technology development, since the coordination problem does not add anything to the main purpose of this paper. 5

7 the imitator to produce the product of the innovator with a non-infringing production process. We assume that both firms are symmetric with respect to imitation and, for simplicity, we assume that the cost of imitation is 0. Our assumption of zero imitation cost is not crucial for our result as long as the cost of imitation is exogenous and generates imitation as the equilibrium outcome whenever the patent law permits noninfringing imitation. Assume that the firms compete in the outhern market, and the representative consumer s utility depends on the consumption of x, y and a numeraire good m, and it is given by x y U ( x, y) + m with U(x, y) a( x + y) γxy, where γ shows the degree of product differentiation. 9 The products are perfect substitutes for γ 0, and they are isolated for γ 1. ince we consider the goods x and y as different, we concentrate on γ [0,1). Given the utility function, the inverse market demand functions for x and y are respectively P x P y a x γy, (1a) a y γx, (1b) where P x and P y are the prices of x and y. For simplicity, we normalize the constant average costs of production for both x and y to zero. We assume that firm may either relocate its production to the southern country (called ), or produce in the orth and export to the south. requires a 9 This utility function is due to Bowley (194), and is typical in the literature (see, e.g., ingh and Vives, 1984). ote that x x + x ( y y + y ), and x and x ( y and y ) are the outputs of x ( y ) by firms and respectively. 6

8 fixed investment, F, 10 while exporting by firm involves a transportation cost, t. In order to avoid corner solutions, we assume that t is low enough to always ensure positive output by firm. For our analysis, it means a t <. () We consider the following four-stage game. At stage 1, firm decides whether to export or to undertake. At stage, the firms take their decision on R&D to invent technology for a new product. Given our assumption that the R&D cost of firm is 0, firm will always do R&D. Therefore, the R&D decision is effectively for firm only. At stage 3, imitation occurs if the patent law permits. At stage 4, the firms compete in the product market like Cournot duopolists. We solve the game through backward induction. 3. Profits of the firms 3.1. o innovation by the outhern firm Let us first consider the situation where the firm doesn t do innovation. However, firm can imitate the product of firm under patent in the outh trong patent protection in the outh Under patent protection in the outh, imitation is not an option to the firms, and only firm sells its product as a monopolist. The outputs of firm under export and under are a t and a respectively. The profits of firm under export and under are respectively: 10 F captures all the start-up costs of a new plant, including the adjustment cost of learning to operate in a new institutional and financial environment. 7

9 (I) E a t Π (3) Π ( I F ) a F. (4) Weak patent protection in the outh Weak patent protection in the outh allows non-infringing imitation, and firm imitates the technology of firm. We assume that imitation allows the imitator to produce a perfect substitute of the innovator s product. 11 ote that we have assumed that imitation occurs irrespective of export and by firm. Though a more general approach would perhaps consider that imitation would be more effective under than under export, might be because of the distance between the firms, it must be clear that this situation would make more likely under a outhern patent protection by reducing imitation under. However, we assume away this bias on imitation under export and. Under If firm exports, firms and maximize the following expressions respectively to determine their outputs: Max( a x x t) x (5) x Max( a x x ) x. (6) x 11 It is possible that even if imitation helps the firms to use similar production technologies, the products may be differentiated due to the factors such as brand names, after sales service, etc. However, it is reasonable to assume that if the firms invent different technologies for different products, these products are supposed to be more differentiated than the products produced by the imitated technologies. While both technological and non-technological factors are responsible to make the products differentiated under the former, only the non-technological factors are responsible for product differentiation under the latter. To keep the matter as simple as possible without loosing the main insights, we assume that the firms produce homogeneous products under imitation, while their products are differentiated if they use technologies for different products. 8

10 The equilibrium outputs can be found as ( I E ) a t x 3 and ( I E ) a + t x 3. (7) The equilibrium profits of the firms are (I) E a t Π and 3 E ( I ) a + t Π. (8) 3 Under If firm undertakes, firms and maximize the following expressions respectively to determine their outputs: Max( a x x ) x F (9) x Max( a x x ) x. (10) x The equilibrium outputs can be found as ( I F ) a x 3 and ( I F ) a x 3. (11) The equilibrium profits of the firms are Π ( I F ) a 3 F and F ( I ) a Π. (1) Innovation by the outhern firm Let us now consider the situation where firm innovates at stage. In this situation, both the firms can imitate under patent protection in the outh. 9

11 3..1. trong patent protection in the outh Under patent protection in the outh, imitation is not a feasible option, and therefore, firms and produce respectively products x and y. Under If firm exports, firms and maximize the following expressions to determine their outputs: Max( a x γ y t) x, (13) x Max( a y γx ) y. (14) y The equilibrium outputs can be found as ( I ) a( γ ) E t x and ( 4 γ ) E + γt y. (15) ( I ) a( γ ) ( 4 γ ) The equilibrium profits of the firms are ( γ ) (I) E a t Π ( 4 ) and γ Π (I) E a ( γ ) ( 4 γ ) + γt R. (16) Under If firm undertakes, firms and maximize the following expressions to determine their outputs: Max( a x γ y ) x F (17) x Max( a y γx ) y. (18) y The equilibrium outputs can be found as ( I F ) a x and + γ ( ) ( I F ) a y. (19) + γ ( ) The equilibrium profits of the firms are 10

12 Π (I) F a ( + γ ) F and Π (I) F a ( + γ ) R. (0) 3... Weak patent protection in the outh If there is innovation by the outhern firm and there is patent protection in the outh, firm (firm ) imitates the product of firm (firm ). Hence, each firm sells two goods (own innovated good and the imitated good of the rival). Under If firm exports, firms and maximize the following expressions to determine their outputs: Max( a x x, y x γ y γy t) x + ( a y y γx γx t) y (1) Max( a x x γy γy ) x + ( a y y γx γx ) y () x, y Differentiating (1) with respect to x, y and solving for x, y we get the profit maximizing outputs as ( 1 γ ) t( 1 γ ) x ( 1 γ ) 1 a x & ( 1+ γ )( 1 γ ) ( 1 γ ) t( 1 γ ) y ( 1 γ ) 1 a y. (3) ( 1+ γ )( 1 γ ) imilarly Differentiating () with respect to x, y and simultaneously solving for x, y we get the profit maximizing outputs as ( 1 γ ) x ( 1 γ ) 1 a 1 a 1 γ y 1 γ x and y. (4) 1+ γ 1 γ ( 1+ γ )( 1 γ ) ubstituting (3) into (4), and solving for x, x, ( + γ ) ( ) ( ) y and ( )( ) y, we get ( I ) a t x E ( I ) a + t and x E (5) γ ( ) 11

13 ( I ) a t y E and 3 1 ( + γ ) ( I ) a + t y E. (6) 3 1 ( + γ ) The equilibrium profits of the firms are ( I ) ( a t) 9( 1+ γ ) E Π (7) Π E ( I ) ( a + t) 9( 1+ γ ) R. (8) Under If firm undertakes, firms and maximize the following expressions to determine their outputs: Max( a x x γ y γy ) x + ( a y y γx γx ) y F (9) x, y Max( a x x γy γy ) x + ( a y y γx γx ) y. (30) x, y Differentiating (9) with respect to x, y and solving for x, y we get the profit maximizing outputs as ( 1 γ ) x ( 1 γ ) 1 a x and ( 1+ γ )( 1 γ ) ( 1 γ ) y ( 1 γ ) 1 a y. (31) ( 1+ γ )( 1 γ ) imilarly differentiating (30) with respect to x, y and solving for x, y we get the profit maximizing outputs as ( 1 γ ) x ( 1 γ ) 1 a x and ( 1+ γ )( 1 γ ) ( 1 γ ) y ( 1 γ ) 1 a y. (3) ( 1+ γ )( 1 γ ) ubstituting (3) into (31), and solving for x, x, y and y, we get ( I ) 1 a x F and 3 ( 1+ γ ) ( I ) 1 a y F and 3 ( 1+ γ ) ( I ) 1 a x F (33) 3 ( 1+ γ ) ( I ) 1 a y F. (34) 3 ( 1+ γ ) 1

14 The equilibrium profits of the firms are ( I ) a F Π weal F (35) 9 1 ( + γ ) ( I F ) a Π R. (36) 9 1 ( + γ ) 4. R&D decision ow we are in position to determine the R&D decision of firm. Recall that, since we are interested in equilibrium where firm always does innovation, we have normalized the R&D cost of firm to 0. Therefore, the R&D decision is effectively taken by firm only Weak patent protection in the outh Conditional on by firm, the comparison of the profits of firm under patent protection in the outh (see (1) and (1)) gives us that, firm does innovation if R < 9 a ( 1+ γ ) a 9 R. (37) imilarly, comparing (8) and (8), we get that, conditional on export by firm, firm does innovation under patent protection in the outh if R < 9 ( a + t) ( 1+ γ ) a + t 3 R. (38) 4.. trong patent protection in the outh Conditional on by firm, the comparison of the profits of firm under patent protection in the outh (see (0)) shows that firm does innovation if 13

15 a R < ( γ ) ( 4 γ ) R. (39) imilarly, conditional on export by firm, the comparison of the profits of firm under patent protection in the outh (see (16)) shows that firm does innovation if a R < ( γ ) ( 4 γ ) + γt R. (40) The comparison of (37), (38), (39) and (40) gives the following result immediately. Lemma 1: We have R < R < R < R. Proof: ee Appendix A for the proof. Lemma 1 shows that the outhern firm has lower incentive for innovation under patent protection than under patent protection. There are two ways that a patent protection helps to increase the incentive for R&D by firm. On one hand, paten protection increases the profit of firm under innovation by protecting its product from imitation. This is similar to the usual R&D inducing effect of a patent protection. On the other hand, patent protection reduces the profit of firm under no innovation by eliminating imitation, thus increasing the gain of firm from innovation. Lemma 1 also shows that, for a given outhern patent system, the incentive for innovation by firm is always higher under export by firm. ince exporting by the orthern firm involves a transportation cost, the output of firm is higher under exporting than under by firm, which, in turn, increases the outhern firm s gain from innovation under exporting compared to by firm. This result is in 14

16 line with the empirical evidence (Veugelers and Houte, 1990 and Goto and Odagiri, 003), and questions whether is always conducive in fostering the domestic R&D. 5. or? Let us now determine the equilibrium production strategy of firm. ince the production strategy of firm affects the R&D decision of firm, the R&D decision of firm may play an important role in determining the equilibrium production strategy of firm. Firm prefers to export if Π > Π. F E 5.1. If R < R Let us first consider the case where the cost of R&D is very small so that firm does innovation irrespective of the outhern patent system and the mode of production of firm. Under patent protection in the outh, the comparison of the profits of firm under export and under, shown in (7) and (35) respectively, gives the following result. Lemma : If R < R and there is patent protection in the outh, firm prefers to exporting if and only if ( + ) ( a t) 9( 1 ) () I a F < F γ + γ Under patent protection in the outh, the comparison of the profits of firm under export and under, shown in (16) and (0) respectively, gives the following result: 15

17 Lemma 3: If R < R and there is patent protection in the outh, firm prefers to exporting if and only if () I a a( γ ) t F < F. + γ 4 γ The following proposition compares firm s incentive for under and under patent protection in the outh when firm always innovates. Proposition 1: If the R&D cost of innovation is small enough (i.e., R < R ), firm s incentive for is higher under patent protection in the outh if 4 ˆ a(14 9γ 7γ + γ ) t > t and γ > γˆ Otherwise, firm s incentive for 4 3 9γ 16γ + γ is higher under patent protection in the outh. Proof: ee Appendix B for the proof. Thus, we see that the incentive of firm is higher under patent protection in the outh if either product differentiation is sufficiently large (i.e., γ is sufficiently small) or the transportation cost is sufficiently small (i.e., t is sufficiently small). This result may be explained as follows. For any γ [0,1), the profit of firm is higher under patent protection in the outh compared to patent protection in the outh, irrespective of exporting and by firm. Further, while the profit under is independent of t, the profit of firm under export reduces with t for two reasons. First, given the outputs, a higher t reduces the per-unit profit of firm. econd, given the per-unit profit of firm, a higher t reduces its output and profit. 16

18 If t 0, the output of firm is almost the same under exporting and, for both and patent protection. In this situation, the output effect of a higher t becomes the important factor, and the loss of market share under export due to a rise in t is more under patent protection compared to patent protection. As a result, if t 0, firm s relative benefit from over export is higher under patent protection compared to patent protection, thus creating higher incentive for under patent protection for γ [0,1) and t 0. If a t, the output and profit of firm under export tend to zero if there is patent protection in the outh, while they are positive under patent protection, for any γ [0,1). In this situation, the profit gain of firm under export due to a lower t is negligible under patent protection, while it is significant under patent protection. However, if γ 0, firm s gain in profit due to the patent protection is higher under export than under. While negligible competition due to a large product differentiation increases firm s profit significantly under patent protection for both and exporting, it only increases firm s profit under significantly for patent protection. As a result, firm s profit difference between and exporting is higher under patent protection than under patent protection. If γ 1, competition between the products are severe and the profits of firm are very much similar under and patent protection for and for exporting. However, in this situation, firm s profit difference between and exporting is higher under patent protection than under patent protection. 17

19 5.. If R < R < R Let us now consider the case where the cost of R&D is such that firm does not innovate under patent protection if firm undertakes. Otherwise, firm innovates always. Under patent protection in the outh, the comparison of the profits of firm under export and under, shown in (7) and (1) respectively, gives the following result. Lemma 4: If R < R < R and there is patent protection in the outh, firm prefers to exporting if and only if ( I) a ( a t) 3 9( 1+ γ ) F < F3. Under patent protection in the outh, the comparison of the profits of firm under export and under, shown in (16) and (0) respectively, gives the following result: Lemma 5: If R < R < R and there is patent protection in the south, firm prefers to exporting if and only if () I a a( γ ) t F < F4. + γ 4 γ The following proposition compares firm s incentive for under and under patent protection in the outh when firm does not innovate under patent protection if firm undertakes. 18

20 Proposition : If the cost of innovation is such that R < R < R, firm s incentive for is higher under patent protection in the outh. Proof: ee Appendix C for the proof. The intuition for the above result is as follows. Consider patent protection in the outh. If the cost of innovation is such that firm does not innovate under by firm, the profit of firm under reduces compared to the situation where firm innovates under by firm. This is because, in the latter situation, firm gets the opportunity to produce the product of firm, while no innovation by firm eliminates that possibility. As a result, if firm does not innovate when firm undertakes and there is patent protection in the outh, patent protection in the outh always increases firm s incentive for If R < R < R Let us now consider the situation where the cost of innovation is such that firm innovates only under patent protection in the outh, irrespective of exporting or by firm. Under patent protection in the outh, the comparison of the profits of firm under export and under, shown in (8) and (1), gives the following result: Lemma 6: If R < R < R and there is patent protection in the outh, firm prefers to exporting if and only if ( I) a ( a t) F < F

21 Under patent protection in the outh, the comparison of the profits of firm under export and under, shown in (16) and (0) respectively, gives the following result: Lemma 7: If R < R < R and there is patent protection in the outh, firm prefers to exporting if and only if F < F 6 ( I ) a a( γ ) + γ t 4 γ. The following proposition compares firm s incentive for under and under patent protection in the outh when firm innovates only under patent protection in the outh. Proposition 3: If the cost of innovation is such that R < R < R, firm s incentive for is higher under patent protection in the outh if either γ < or γ > and ~ a( + 9γ 8γ + γ ) t > t γ + γ Proof: ee Appendix D for the proof. Proposition 3 can be explained as follows. trong patent protection in the outh eliminates imitation but encourages innovation by the outhern firm. Hence, the patent protection helps to increase the profit of firm under both export and, since the product differentiation is higher under outhern innovation than under imitation. If the products are sufficiently differentiated, the profit gain for firm under patent protection (compared to patent protection) is higher under 0

22 compared to exporting, since the trade cost creates the distortion under exporting. However, if the products are not very much differentiated, firm s profit gain under patent protection is higher under compared to exporting provided exporting creates significant distortion, which happens for sufficiently high transportation cost. Therefore, if the products are not very differentiated and the transportation cost is sufficiently small, firm s profit gain under patent protection is higher under exporting compared to, thus creating higher incentive under patent protection in this situation If R < R < R Let us now consider the case where firm innovates only when firm exports and there is patent protection in the outh. Under patent protection in the outh, the comparison of the profits of firm under export and under, shown in (8) and (1) respectively, gives the following result: Lemma 8: If R < R < R and there is patent protection in the outh, firm prefers to exporting if and only if ( I) a ( a t) F < F Under patent protection in the outh, the comparison of the profits of firm under export and under, shown in (16) and (4) respectively, gives the following result: 1

23 Lemma 9: If R < R < R and there is patent protection in the outh, firm prefers to exporting if and only if ( I) a a( γ ) t F < F8. 4 γ The following proposition compares firm s incentive for under and under patent protection in the outh when firm innovates only when firm exports and there is patent protection in the outh. Proposition 4: If the cost of innovation is such that R < R < R, firm s incentive for is higher under patent protection in the outh for all feasible values of t and γ. Proof: ee Appendix E for the proof. Intuitively, the above result can be explained as follows. As usual, patent protection helps to protect the product of firm, which creates an incentive for. Moreover, since firm innovates only if there is patent protection and firm exports, by firm under patent protection eliminates product market competition by deterring outhern innovation, thus encouraging firm to undertake under patent protection If R > R Finally, consider the situation where firm does not do innovation irrespective of the patent system in the outh and the production strategy of firm. This case corresponds to the previous works where the outhern firm can only imitate the product of the orthern firm.

24 Under patent protection in the outh, the comparison of the profits of firm under export and under, shown in (8) and (1) respectively, gives the following result: Lemma 10: If R > R and there is patent protection in the outh, firm prefers to exporting if and only if ( I) a ( a t) F < F Under patent protection in the outh, the comparison of the profits of firm under export and under, shown in (16) and (4) respectively, gives the following result: Lemma 11: If R > R and there is patent protection system in the outh, firm prefers to exporting if and only if ( I) a a t F < F10. The following proposition compares firm s incentive for under and under patent protection in the outh when firm never innovates irrespective of the outhern patent system and the production strategy of firm. Proposition 5: If the cost of innovation is such that R > R, firm s incentive for is higher under patent protection in the outh for all feasible values of t and γ. Proof: ee Appendix F for the proof. 3

25 The above result is due to the standard argument for a patent protection in the outh. If firm never innovates, patent protection helps to protect the product of firm, thus creating higher incentive for under patent protection. The following table summarizes the findings on section 5: R F - F > 0 for 4 R < R ˆ a(14 9γ 7γ + γ ) t > t and γ > γ 16γ + γ R < R < R t > 0, γ > 0 R < R < R γ < or ~ a( + 9γ 8γ + γ ) t > t and γ > 4 7 8γ + γ 13 3 R < R < R t > 0, γ > 0 R < R > 0 t, γ > 0 6. Conclusion Though evidence suggests that patent protection in the host country has significant impact on the incentive for, the existing theoretical literature did not pay enough attention to this issue. We take up this issue in this paper and show how the patent regimes in the host country affect the incentive of a multinational. In a orth-outh model, we show that innovation in the outh plays an important role in determining the effect of the outhern patent system on the incentive for by the orthern firm. A er patent protection in the outh increases the incentive for innovation by the outhern firm, irrespective of or export by the orthern firm. Further, for a given outhern patent system, the incentive for innovation by the outhern firm is lower under than under exporting by the 4

26 orthern firm. However, the effect of the outhern patent system on the incentive for by the orthern firm depends on the innovative capability of the outhern firm, on the degree of product differentiation and on the transportation cost. If the outhern firm innovates either irrespective of the outhern patent regime or only under patent protection in the outh, the orthern firm s incentive for may be higher under patent protection in the outh depending on the degree of product differentiation and the transportation cost. Hence, an important policy implication resulting from our paper is that the outhern countries may need to consider a trade off between and domestic innovation while designing their patent policies. There are situations where a patent protection may deter, yet increasing domestic innovation. While our framework of an international duopoly helps us to present a simplified analysis keeping the central points in focus, the implications of more firms are easy to see. If there are multiple firms in the outh, given the other specifications of the model, the market will be more competitive. If the cost of innovation is very low so that all the firms in the outh innovate, the orthern firm may have higher incentive under patent protection, since it could have more profits by imitating the outhern goods and also avoiding the transportation cost. However, when the cost of innovation increases, which reduces the possibility of new product development in the outh, the incentive for by the orthern firm under patent protection increases, since patent protection helps to protect the product of the orthern firm. It is important to note that we have considered the incentive for inward by the orthern firm. However, in the present economic scenario where the outhern firms are increasingly prominent in international trade and capital flows, it is 5

27 important to identify the effects of the patent regimes under two-way where the outhern firms can also undertake. In this respect, it would be interesting to see the implications of orthern demand and also to focus on patent harmonization. We intend to take up these issues in our future research. 6

28 Appendix A Proof of Lemma 1 ( R R ) (1 γ )( a + t) We get from (39) and (38) that < 0. Hence, t 9(1 + γ ) R reaches minimum at R a t, and the minimum value of R R 1 a γ 4 3γ + γ + 4 ( γ + 1)( γ + ) > 0, which proves that R >. R Comparing R and R from (39) and (40), we get that R R tγ ( + γ )( γ ) > 0, which proves that R >. R Comparing R and R from (37) and (38), we get that R R t(1 γ )(a + t) > 0, which proves that 9(1 + γ ) R >. R Taken together, we get that R < R < R < R. Q.E.D. Process Process Product Product B Proof of Proposition 1 The comparison of 1 ( I) F and ( I) F shows that () I ( I ) F > F 1 4 if ˆ a(14 9γ 7γ + γ ) a t > t. However, tˆ < t 4 max ifγ > γˆ Therefore, 3 9γ 16γ + γ firm s incentive for is higher under patent protection in the outh if t > tˆ andγ > Otherwise, firm s incentive for is higher under patent protection in the outh. Q.E.D. C Proof of Proposition ( I ) ( I ) etting F F, we get the following two roots of t : 4 3 7

29 a(14 + 5γ γ a(14a + 5γ γ 3 γ 3 γ ( + γ ) (3 + 14γ γ + ( + γ ) (3 + 14γ γ 43 64γ 7γ 3 γ ) 43 64γ 7γ 3 γ ) 3 + 6γ 3 + 6γ γ γ 5 + γ ) 5 + γ ) ince 43 64γ 7γ + 6γ + 14γ + γ < 0 for γ [0,1], neither of these roots is real, irrespective of the value of γ. Therefore, there is no real value of t such that F F. ( I ) 4 ( I ) 3 Let us now take a value of γ, say γ 0. We get that F > F if ( I ) 4 ( I ) 3 γ 0. Hence, for any a, t and γ, we get F > F, which implies that ( I ) 4 ( I ) 3 firm s incentive for is higher under patent protection. Q.E.D. D Proof of Proposition 3 The comparison of 5 ( I) F and F ( I ) 6 shows that F a ( + γ ) ( a( γ ) t) (4 γ ) a ( a t) ( I ) ( I ) 6 F5 > 0 4 if ~ a( + 9γ 8γ + γ ) t > t. We get 4 7 8γ + γ ~ a t < tmax. However, ~ t > 0 provided γ > Therefore, firm s incentive for is higher under patent protection if either 13 3 γ < so that t > 0 is always greater than ~ t, or 13 3 γ > and t > ~ t. Q.E.D. 8

30 E Proof of Proposition 4 We get that F > as 8 F10 a t a ( γ ) t 4 γ 0 for γ [0,1), where F 10 is shown in Lemma 11. Further, we get that F >, where 10 F9 F7 F 9 is shown in Lemma 10. Hence, it proves that F >. Q.E.D. 8 F7 F Proof of Proposition 5 As already shown in Proposition 4, F F9 10 >, which proves the result. Q.E.D. 9

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