National Treatment in International Agreements on. Intellectual Property

Transcription

1 ational Treatment in International Agreements on Intellectual Property Yasukazu Ichino Faculty of Economics, Konan University June 27, 2010 Abstract ational treatment (T), a practice of governments granting the same patent protection to any inventors regardless of their national origin, has been a main feature of international agreements on intellectual property rights (IPR). In this paper we look for some economic rationale for national treatment in international agreements on IPR. By comparing the equilibrium of the noncooperative patent policy game under non-t regime and that under T regime, we found that under certain conditions national treatment in IPR protection never enhances the global welfare and actually reduces it. We suggest that a role of national treatment may be enhancing fairness among the countries. Key Words: Intellectual Property Rights, ational Treatment JEL Classi cation umbers: F13, O34 *Address: Okamoto, Higashinada-ku Kobe , Japan. yichino@center.konan-u.ac.jp Phone: Fax:

2 1 Introduction ince the enactment of TRIPs (Trade-Related Aspects of Intellectual Property Rights) agreement with the start of WTO, there have been several theoretical researches on international protection of intellectual property rights (IPR). Examples are McCalman (2002), Lai and Qiu (2003), Grossman and Lai (2004), and cotchmer (2004), among others. 1 In those studies, the interests are in the issue of harmonization, which is a new main feature of international IPR protection brought by the TRIPs agreement. However, there is another, rather old feature in international agreements on IPR. That is national treatment (T). Here, let us clarify the terms. ational treatment of IPR protection means that governments should treat all investors alike, regardless of their national origin. Although national treatment requires whatever protections granted to local inventors should be granted to foreign inventors as well, it does not specify each government what to protect, how long to protect, or how strong to protect. On the other hand, harmonization of IPR protection requires all the signatory countries to provide protections with the same coverage, the same length, or the same strength. In the studies mentioned above, national treatment is just taken for granted. That is, national treatment is not analyzed but simply assumed. This is partly because, as stated above, their focus is on the issue of harmonization in the TRIPs agreement, and partly because national treatment is a practice that has been exercised even before the TRIPs agreement. In fact, national treatment was established in the earliest international agreements on IPR, such as the Paris Convention of 1883 on patents and other industrial property, and the Berne Convention of 1886 for literary and artistic works. In spite of such a long history of national treatment, as far as I know, there has been no formal analysis examining economic rationale for national treatment in IPR protection. 2 In the GATT, the importance of national treatment is easily understood. Without national treatment, a trade agreement to lower tari s would be completely undone by the 1 One of the precursors of these studies is Chin and Grossman (1990). 2 cotchmer (2004) makes some comments on the incentive of the governments to grant national treatment, but her discussion goes verbally, without a formal model. 2

3 adjustment of discriminatory internal taxes. 3 However, in agreements of IPR protection, it is not obvious why national treatment is necessary, or how it bene ts the member countries of an agreement. Therefore, in this paper, we are going to analyze the e ect of national treatment on the patent protection policies and on welfare, and look for some economic rationale for national treatment. That is, our main questions are: (1) Can national treatment stimulate innovation globally? (2) Can national treatment be global welfare enhancing? (3) How is each country in uenced by national treatment? To answer these questions, we use a simpli ed version of the orth-outh model developed by Grossman and Lai (2004), where the two governments play the game of choosing their patent policies. By comparing the equilibrium of the game under non-t regime with the equilibrium of the game under T regime, we found that national treatment has a perverse e ect that stimulates innovation of less innovative rms and dampens innovation of more innovative rms. This leads us to our main nding that national treatment never enhances the global welfare and actually reduces it under certain conditions. The rest of the paper is organized as follows. In the next section, we describe the two-country model of ongoing innovation. Then, we analyze the noncooperative game in which two governments set their patent policy without national treatment (ection 3) and with national treatment (ection 4). In ection 3, without national treatment, the governments are free to choose di erent strength of patent protection for inventors in di erent countries, while in ection 4, with national treatment, the governments are forced to provide the same strength of protection to all inventors. In ection 5 we compare the results derived in ection 3 and 4, to see the e ect of national treatment on the policy outcome and on the welfare of the countries. In the last section, we make several remarks and discussions on our ndings. 3 ee a recent study by Horn (2006). 3

4 2 A Model Our aim in this paper is to study policy choices of the governments on patent protection. For this aim, we use a simpli ed version of the Grossman-Lai s (2004) model of ongoing innovation. In the model, there are two countries, named the orth and the outh. We take the orth as a developed country, and the outh as a developing country. 2.1 Technology In each country, there are two types of products: one is a homogeneous product which is the numeraire, and the other is a variety of di erentiated product. A new kind of di erentiated product is invented from private R&D activities. We suppose that R&D activities employ human capital H and labor L, with assuming that the amount of human capital is xed exogenously. peci cally, the number of new varieties invented in a given period in country j (j = ; ) takes the following CE form: n j = n j (L j ; H j ) = b j L j j + (1 b j ) H 1 j j j. Here, notice that we model that two countries have di erent innovation-generating technologies. Also, we allow the two countries have di erent amount of human capital. upposing that the orth is a developed and the outh is a developing country, we assume that the orth has a larger amount of human capital than the outh: H H. In addition, on this CE function, we assume j 1=2. This restriction is su cient for the patent policy choices of the governments satisfying the rst-order conditions also satisfy the second order conditions. For simplicity, we consider that each of newly invented product have the same life length, which is equal to one. That is, in every period, all of the varieties are developed at the beginning of the period, and become obsolete at the end of the period. In the next period, a whole new set of varieties are developed. Although innovation-generating technologies can be di erent, the manufacturing process is assumed the same in the orth and in the outh. Once invented, one unit of a dif- 4

5 ferentiated product is produced from one unit of labor only. imilarly, one unit of the homogeneous good is produced from one unit of labor only. Thus, with the assumption of a competitive market for the homogeneous product, in each country labor demand for production of the homogeneous product is perfectly elastic at w = 1, where w is the wage rate. Therefore, by assuming su ciently large supply of labor, we have w = 1 as the equilibrium wage in each country. 2.2 Preferences Consumers in the two countries have identical preferences. There are M consumers in the orth and M consumers in the outh. As in Grossman-Lai, here we interpret M and M not the population of each country but the scale of demand for di erentiated product in each country. With this interpretation, we assume M M, that is, the orth has larger demand for di erentiated products than the outh. With free trade in di erentiated products, the representative consumer in each country derives utility from consuming the homogeneous good, and consuming all varieties of di erentiated product. That is, the utility function is given by n X+n u = y + k=1 h (x k ), where y is consumption of the homogeneous good and x k is consumption of the ith variety of di erentiated product. The subutility function h () is increasing and concave function, with h 0 (0) = 1, and xh 00 (x) =h 0 (x) < 1 for any x. The former condition is to make sure that there is a positive demand for any nite price. The latter assumption is for any rms producing a di erentiated product to charge a nite price. The utility maximization of the representative consumer gives the demand for a differentiated product h 0 (x k (p k )) = p k, where p k is the price of the kth variety. After the consumer chooses his optimal consumption, the demand for homogeneous product is derived as the di erence between his income and what he spends for all kinds of di erentiated product. 5

6 2.3 Patent protection In this paper, we take patent length as a policy choice of the governments to protect intellectual property rights. ince the life length of a new variety is assumed one in our model, the patent length, 0 1, is a fraction of a period during which only the original inventor of a di erentiated product is allowed to produce and to sell its invention. Therefore, for period, the rm granted a patent is able to behave as a monopoly rm. Given the inverse demand curve p = h 0 (x), the monopoly price satis es the condition (p w) =p = xh 00 (x) =h 0 (x). We let denote the monopoly pro t per consumer when the rm sets the monopoly price. Then, the total monopoly pro t earned from country j is M j. On the other hand, in a remaining fraction of the period 1, the patent gets expired and competitors can imitate the product costlessly. The price goes down to the competitive level p = w, thus the inventor gets no pro t for 1 period. Let us now look at the international IPR protection policy in detail. As we have mentioned in Introduction, in this paper we do not assume national treatment, since examining it is our objective. We suppose that the orth government gives a patent length to orthern inventors and to outhern inventors. imilarly, the outh government provides patent length to orthern inventors and to outhern inventors (For these s, the rst subscript stands for the country of the government, and the second subscript stands for the country of the rms). By this setting, we can let each government treat local rms and foreign rms di erently. We call this the regime of nonnational treatment (non-t). On the other hand, when each government is committed to provide the same protection to all rms, i.e., the orth government sets = and the outh government sets =, we call that the two governments are practicing reciprocal national treatment (T). In the model, we assume that parallel imports are prohibited: even when a patent is expired in one country, as long as it is protected in the other country, a rm can earn the monopoly pro t in the country where its patent is still alive. 6

7 2.4 Pro t maximization of inventing rms Here we are going to describe the pro t maximization of a typical inventing rm. For a rm in the orth, its R&D activity is stimulated by the patent length set by the orth government and set by the outh government. When a orth rm comes up with a new invention, it earns monopoly pro t M in the orth country for period, and it earns M in the outh country for period. Therefore the total pro t this typical orthern rm earns is (M + M ) per invention. To simplify the notation, we let Q = M + M. This is a measure of the overall patent protection given to orthern rms. In other words, Q is the innovation incentive given to orthern rms. imilarly, per-invention pro t of a typical outhern rm is denoted by Q where Q = M + M. Given the patent lengths, each inventing rm decides how much workers and human capital to employ to conduct R&D. ince human capital H is used only in the R&D sector and its amount is xed exogenously, and since the innovation-generating function n j (L j ; H j ) exhibits constant returns to scale, we can put the pro t-maximization problem of inventing rms in country j as follows: max L j Q j n j (L j ; H j ) wl j, where Q j = M j + M j. The rst-order condition Q j (L j ; H j j = w (1) gives the labor demand of R&D activities. By di erentiating (1) with respect to j and j, we can derive the e ect of patent policies on the labor demand by j j = M Q j M Q j 2 n j 2 j 2 n j 2 j > 0, (2a) > 0. (2b) 7

8 2.5 Welfare ow we are able to derive welfare of each country. Let C m = h (x (p m )) p m x (p m ) be the consumer surplus from a product with live patent, and C c = h (x (p c )) p c x (p c ) is the consumer surplus from a product with expired patent, where p m and p c are the monopoly price and the competitive price respectively. ince p m > p c, it follows that C m < C c. oting that the national income is the sum of labor income and the humancapital income, the welfare in the orth is given by W = w L L + (M + M ) n (3) +M [n ( C m + (1 ) C c ) + n ( C m + (1 ) C c )]. In (3), the rst term is the labor income from the manufacturing sector; the second term is the pro t of R&D sector, a part of which goes to the workers and the rest goes to human capital owner. The last term is the orthern consumers surplus from di erentiated products. imilarly, the welfare in the outh is given by W = w L L + (M + M ) n (4) +M [n ( C m + (1 ) C c ) + n ( C m + (1 ) C c )]. 3 oncooperative Patent Protection under the non-t Regime In this section we consider the two governments choosing their patent policy noncooperatively without national treatment. The orth government chooses and to maximize the welfare function (3). The rst-order conditions (FOCs) for and are respectively M ( C m + (1 M ( C m + (1 ) C ) C @L = M (C c C m ) = M (C c C m ) n. 8

9 The interpretation of these rst-order conditions are quite straightforward: in equation (5) and (6), the left-hand side is the increased consumers surplus from larger varieties of products due to stronger patent protection, and the right-hand side is consumers loss due to stronger patent protection. An increase in is to stimulate inventions of orthern rms, while an increase in to stimulate inventions of outhern rms. The loss due to stronger patent protection is smaller for than for. This is because the loss in the consumers surplus is partly o set by the pro t to orthern rms for an increase in, but there is no such an o set for an increase in since the pro t goes to outhern rms. Using the expression (2a) and (2b), we rewrite the rst-order conditions (5) and (6) as follows: M ( C m + (1 ) C c ) (Q ) Q = C c C m (7a) M ( C m + (1 ) C c ) (Q ) Q = C c C m (7b) where (Q ) = (Q ) = (@n =@L ) 2 n =@L 2 > 0 (@n =@L ) 2 n =@L 2 > 0. n n otice that (Q ) and (Q ) are @L respectively: that is, they measure how much the number of varieties is increased slight increase in patent lengths. 4 We refer j as the responsiveness of innovation-generating technology in country j to the changes in patent lengths. imilarly, the rst-order conditions of maximizing the outh welfare (4) with respect 4 When explicitly written, j (Q j) = b j j. 1 1 j (Q jb j) j b j 9

10 to and are: M ( C m + (1 ) C c ) (Q ) Q = C c C m (8a) M ( C m + (1 ) C c ) (Q ) Q = C c C m. (8b) The equilibrium patent policies to stimulate the orthern invention, and, are found by solving equation (7a) and (8a) simultaneously, while the equilibrium policies to stimulate the outhern invention, and, are determined by (7b) and (8b). By inspecting these four equations, we can make the following comments on the equilibrium patent lengths. The rst comment is on the comparisons of patent lengths granted to the same rm by di erent governments: i.e., the comparisons of with, and of with. From (7a) and (8a), we see that the marginal bene t of lengthening is larger than that of lengthening since M > M. On the other hand, the marginal cost of lengthening is smaller than that of lengthening because C c C m < C c C m. Therefore, due to the larger marginal bene t and the smaller marginal cost, it results in that >. In words, orthern rms are receiving stronger patent protection from its domestic government than from the foreign government. Although this result looks trivial, the similar result may not hold for outhern rms. Let us look at equation (7b) and (8b). If M = M, then it immediately follows that > since the marginal cost of lengthening is smaller than that of lengthening. However, if M is large enough compared to M, then it may happen that > : the orth government may grant outhern rms a stronger patent protection than the outh government does, because of the large consumers surplus of the orth. econd, let us compare the patent lengths granted by the same government to rms of di erent national origin: namely, compare with and with. Counterintuitively, it could happen that a government may give longer patent protection to the foreign rms than to its local rms. Of course, it is true that each government has a tendency to give longer protection to its local rms than the foreign rms, since it 10

11 cares about the pro t of the local rms but does not care about the pro t of the foreign rms. However, which rms, the locals or the foreigners, a government is to give a longer protection depends also on, the responsiveness of R&D activities to patent policies. If, for example, the innovation generation of the orth is far more responsive to a change in patent protection than that of the outh, then the outh government may grant a longer patent protection to orthern rms than to outhern rms. Finally, it is interesting to notice that the comparisons made above are independent of the amount of human capital. In fact, the equilibrium patent lengths do not depend on the amount of human capital at all. What matters for the government to choose patent lengths is not the size of innovation capabilities but the responsiveness of innovation activities. 4 oncooperative Patent Protection under the T regime In the noncooperative patent protection without national treatment, the one we have analyzed in the previous section, there is always some global ine ciency. This is not hard to see. For example, take the decisions of by the orth government. When it decides, it takes account of the marginal cost of strengthening patent protection. Also, it takes correctly into consideration the marginal bene t to the orthern consumers due to the increased varieties of the orthern products. However, the increased varieties of the orthern products bene t the outh consumers as well, but the orth government does not take it into account when choosing. amely, the choice of by the orth government is too small from the global standpoint. In fact, the similar argument applies to the decision of the other patent policy variables,,, and as well. They are, too, too small to maximize the global welfare. In this section and the following section, we would like to examine whether such an ine ciency under the non-t regime could be reduced when the two governments adopt reciprocal national treatment (T), by mutually restricting their latitude of policy choices. In the T regime, the orth government gives the same patent length,, to orthern 11

12 rms and outhern rms. The outh government grants the same patent length to orthern rms and outhern rms. For inventing rms, under the T regime, they faces the same overall patent protection regardless of their national origin. That is, the per-invention pro t a typical rm earns internationally is (M + M ), which is the same for orthern and outhern rms. Here, we let Q = M +M. Then, under the T, the labor demand of the innovation sector in country j, denoted by L T j, is determined by j(l T j ; H j j = w. ow, let us look at the welfare. The welfare of the orth under the T regime is given by = w L L T + (M + M ) n T (9) +M n T ( C m + (1 ) C c ) + n T ( C m + (1 ) C c ) W T where n T = n (L T ; H ) and n T = n (L T ; H ) are the number of new varieties invented under the T regime. The rst-order condition with respect to is given by M ( C m + (1 ) C c ) nt (Q) + n T (Q) n T = C c C m Q n T + nt n T + nt. (10) The rst-order condition (10) is essentially a weighted average of the rst-order conditions (7a) and (7b). This is because the patent policy in the T regime in uences inventions of the outh as well as that of the orth. imilarly, the welfare of the outh under the T regime is = w L L T + (M + M ) n T W T +M n T ( C m + (1 ) C c ) + n T ( C m + (1 ) C c ), 12

13 and the rst-order condition with respect to is M ( C m + (1 ) C c ) nt (Q) + n T (Q) n T = C c C m Q n T + nt n T + nt (11) The simultaneous solutions of equation (10) and (11) gives the equilibrium patent policies under the T regime, and. 5 Comparing the T regime and the non-t regime 5.1 When the innovation-generating functions are the same Here, we suppose that the innovation-generating function of the orth and that of the outh have the same functional form: n () = n (). In terms of parameters this means that = and b = b. We let and b denote the common value of these parameters. First, we derive the following result about the overall patent protections. Proposition 1 If the innovation-generating function of the orth and that of the outh are the same, then Q = Q = Q. Proof. When the innovation-generating functions are the same, then () = (). Let () denote this common function. ow, summing the FOCs in the T case, equation (10) and (11), we have (M + M ) C c Q (C c C m ) (Q) = 2 (C c C m ). (12) For the non-t case, summing the FOC of maximizing W with respect to (equation (7a)) and the FOC of maximizing W with respect to (equation (8a)) gives (M + M ) C c (C c C m ) (Q ) = 2 (C c C m ), (13) Q 13

14 and summing the FOC of maximizing W with respect to (equation (7b)) and the FOC of maximizing W with respect to (equation (8b)) gives (M + M ) C c (C c C m ) (Q ) = 2 (C c C m ). (14) Q The right-hand sides of equations (12), (13) and (14) are the same and independent of Q s. The left-hand sides of them have the same functional form in terms of Q s. If the left-hand side of equation (12) is a monotonic function of Q, then there is unique Q that satis es (12), and thus Q = Q = Q is proven. In Appendix A, we show that the left-hand side of (12) is in fact a decreasing function of Q. Therefore, when the R&D sectors in the two countries have the same technology (and thus have the same responsiveness to patent protection policies), then the equilibrium patent policies result in giving the same size of overall protection to the orthern inventing rms and to the outhern inventing rms (i.e., Q = Q ), and it is just equal to the overall patent protection granted under the national treatment regime (i.e., Q = Q = Q ). This result may not be as straightforward as it looks. First, notice that this result is independent of the market size and the amount of human capital. Even when these size variables are di erent between the orth and the outh, if the innovation-generating technology is identical, then this result follows. econd, recall that Q = M + M and Q = M + M. Here, what the orth government chooses is not Q but and. That is, the orth government does not have entire control over the determination of Q. imilarly, the outh government does not have entire control over the determination of Q. Thus, it is interesting to see that the two governments end up with granting the the same overall protection to all rms in equilibrium, even though the marginal incentive they face when choosing,,, and are all di erent. ow, in the proposition below, we compare the equilibrium patent policies. Proposition 2 If the innovation-generating function of the orth and that of the outh 14

15 are the same, then > >, and > >. Proof. Compare equation (7a), (7b) and (10). ince C c C m < C c C m n n + n < C c C m, it follows that M ( C m + (1 ) C c ) (Q ) < M ( C m + (1 ) C c ) (Q) Q Q < M ( C m + (1 ) C c ) (Q ) Q. Because Q = Q = Q, it turns out that C m + (1 ) C c < C m + (1 ) C c < C m + (1 ) C c. Therefore, > > since C m < C c. In a similar fashion, it can be shown that > >. This result is quite intuitive. When the innovation-generating functions are the same, each government grants longer patent length to its local rms than to the foreign rms under the non-t regime. Then, when each government is forced to set the same length of protection for all rms, then it chooses something in between. Thus, under the T regime, patent protection granted to the local rms are weakened while the one granted to the foreign rms are strengthened in the both countries. This helps us to understand the welfare e ect of national treatment. As we have explained at the beginning of the previous section, the ine ciency is present under the non-t regime because all of the policy variables,,,, and, are too small to maximize the global welfare. When national treatment is introduced, then the ine ciency caused by and being too small is alleviated since > and >. However, the ine ciency caused by and being too small is worsened since < and <. Therefore, national treatment has a mixed e ect on 15

16 the global welfare, and thus just examining the equilibrium policy choices is not enough to see whether reciprocal national treatment enhances the global welfare. o, now we shall compare the welfare. From equation (9) and (3), the welfare di erence of the orth between the T regime and the non-t regime is calculated as follows: W = L T ; H H (L ; H ) +M ( C m + (1 ) C c ) n T n + n T n W T + (n ( ) n ( )) M (C c C m ) Using this expression, we can present the following proposition. Proposition 3 If the orth and the outh have the same innovation-generating technology, then W T = W and W T = W. Proof. ince Q = Q, the labor demand in R&D sector in the T regime is the same as that in the non-t regime. Then, the number of varieties produced under the T regime is the same as that under the non-t regime. Thus, the rst and the second line of (15) are zero. ow, we show that the third line is also equal to zero by proving that ( ) ( ) = n n. (16) ubtracting equation (7a) from (10) to get M ( ) (C c C m ) Q = n n + n, (17) and subtracting equation (10) from (7b) to get M ( ) (C c C m ) Q = n n + n. (18) Dividing (17) by (18) gives (16). This proves W T shown that W T = W. = W. By a similar way, it can be 16

17 Therefore, as long as the two countries have the same innovation-generating technology, reciprocal national treatment does not change at all the welfare of each country. Although the T and the non-t regimes give the same welfare, this does not mean that each government is indi erent between providing and not providing national treatment. Because for each government national treatment is a restriction on its policy choices, a government can be made better o by lifting its national-treatment restriction if the other government is committed to national treatment. imilarly, if the other government is not practicing national treatment, one government has no incentive to provide national treatment unilaterally. Therefore, if we consider the game where each government chooses independently whether to provide national treatment or not, both not providing national treatment will be the dominant strategy equilibrium of the game. 5.2 When the innovation-generating functions are di erent ow in this section we explore how the T regime changes the global welfare when the two countries have di erent innovation-generating technology. First, we are going to compare the overall patent protections given to the orthern rm and to the outhern rms: i.e., compare Q, Q, and Q. For the T case, summing the FOCs (equation (10) and (11)) gives (M + M ) C c Q n T (C c C m ) (Q) + n T (Q) n T + nt = 2 (C c C m ). (19) For the non-t case, summing the FOC of maximizing W with respect to (equation (7a)) and the FOC of maximizing W with respect to (equation (8a)) gives (M + M ) C c (C c C m ) Q (Q ) = 2 (C c C m ). (20) In addition, for the non-t case, summing the FOC of maximizing W with respect to (equation (7b)) and the FOC of maximizing W with respect to (equation (8b)) 17

18 gives (M + M ) C c (C c C m ) Q (Q ) = 2 (C c C m ). (21) Using these equations, we can present the following proposition. Proposition 4 uppose that 0 () 0. 5 If () (), then Q Q Q. Proof. uppose Q > Q. Then, from equation (20) and (21), it would be (M +M )C c Q (C c C m ) > (M +M )C c Q (C c C m ), which implies (Q ) < (Q ). On the other hand, however, (Q ) (Q ) (Q ) since 0 0. Therefore, Q Q. ow, uppose Q > Q. Then, from equation (20) and (19), it would be (M +M )C c Q (C c C m ) < (M +M )C c Q (C c C m ), which implies nt However, since () (), we have nt is a contradiction. (Q)+nT (Q) n T +nt (Q)+nT (Q) n T +nt > (Q ). (Q) (Q ). This Finally, suppose Q < Q. Then, from equation (19) and (21), it would be (M +M )C c Q (C c C m ) > (M +M )C c Q (C c C m ), which implies nt However, since () (), we have nt a contradiction. Hence, Q Q Q. (Q)+nT (Q) n T +nt (Q)+nT (Q) n T +nt < (Q ). (Q) (Q ). This is If the innovation-generating technologies are di erent between the two countries, which rms are to be granted a larger overall protection under the non-t regime? Proposition 4 answers this question. The rms granted a larger overall protection is the rms whose innovation technology is more responsive to patent protection policy. In addition, Proposition 4 suggests that the T regime cannot give stronger protection to the rms of the both countries. For example, if, then reciprocal national treatment would be stimulating outhern invention (Q > Q ), but dampening orthern invention (Q < Q ). Casually speaking, means that the orthern rms are more innovative than the outhern rms. Then, Proposition 4 can be interpreted that reciprocal national treatment discourages innovation of the more innovative rms and encourages innovation of the less innovative rms. 5 Here, the condition 0 0 is equivalent to 0, which implies that elasticity of substitution between labor and human capital is less than one. 18

19 ext, we would like to see if the global welfare is increased by national treatment. To make our analysis easier, hereafter we restrict our attention to the case of Cobb-Douglas technology. That is, we assume n j (L j ; H j ) = L b j j H1 b j j. Then, = b =(1 b ) and = b =(1 b ). The di erence of the innovation technology between the orth and the outh is now solely from the di erence between b and b. Moreover, as we assume the Cobb-Douglas function, we can derive algebraic expressions for the equilibrium policies and overall protections. We present those expressions in Appendix B. We now rewrite the welfare di erence of the orth country between under the T regime and under the non-t regime as follows: W T W = (1 b ) Qn T +M C c n T Q n n + n T n (22) M (C c C m ) n T n + n T n. ow, suppose >. Then Q < Q and thus n T < n. Therefore, the rst line, which is the change in the human capital income, is negative. The second line represents the consumers surplus generated by new inventions in the world. but n T ince n T < n > n, it is not certain that the total number of new invention is increasing or decreasing. Hence the second line can be positive or negative. The third line is the consumers loss due to the strengthened patent protection, or consumers gain due to the weakened patent protection. This line also can be positive or negative, since < < as long as and are close enough, and since n T < n and n T > n. Therefore, the overall change in the orth welfare when the regime is changed from the non-t to the T is not determined by a simple inspection of equation (22). We need a more detailed analysis. 19

20 imilarly, the welfare di erence of the outh country between the T and non-t is W T W = (1 b ) Qn T +M C c n T Q n n + n T M (C c C m ) n T n n + n T n (23) We can give a similar interpretation to equation (23) line by line, as we did for equation (22). When >, the rst line in equation (23) is positive, the second line and the third line can be positive or negative. Thus, we are not able to determine which is larger, W T or W, without scrutiny. umming equation (22) and (23), we derive the global welfare di erence between under the T regime and under the non-t regime: W T + W T (W + W ) = ((C c C m ) (1 b ) ) Q n Qn T ((C c C m ) (1 b ) ) Qn T Q n + (M + M ) C c n T n + n T n (24) Here, again, it is not certain whether the global welfare under T regime, W T + W T, is larger than the global welfare under the non-t regime, W + W. When >, the rst line of equation (24) is positive while the second line is negative, and the third line can be positive or negative. Calculating equation (24) with substituting in the corresponding expressions for Q s and n s would be very cumbersome. o, we follow another strategy. We take W T + W T (W + W ) as a function of b, and evaluate the derivative with respect to b at b = b. By doing this, we can see whether b and b close enough. W T + W T is larger than (W + W ) at least for Proposition 5 uppose that innovation-generating technologies are in Cobb-Douglas form: n j (L j ; H j ) = L b j j H1 b j j. Then, at b = b, W T + W T (W + W ) reaches a local maximum of zero. 20

21 Proof. ee Appendix C. Proposition 5 seems quite striking, although it is derived under a quite restrictive setting. It says that reciprocal national treatment never enhances the global welfare, as long as two countries have similar innovation-generating technologies. Why does reciprocal national treatment lowers global welfare? As we have seen in Proposition 4, reciprocal national treatment encourages innovation of the less innovative rms while it discourages innovation of the more innovative rms. Intuitively, this is a main cause of a reduction in the global welfare. Our last question is how the welfare of each country is a ected by reciprocal national treatment. We examine this in Proposition 6. Proposition 6 uppose that innovation-generating technologies are in Cobb-Douglas form: n j (L j ; H j ) = L b j j H1 j b j. Then, at b = b, W T W is decreasing in b and W T W is increasing in b. Proof. ee Appendix D. Therefore, if b > b and they are close enough, then W T < W and W T > W. By national treatment, the country having a larger cost share of labor is made worse o, and the country having a smaller cost share of labor is made better o. 6 Concluding remarks In this paper, we look for some economic rationale of national treatment in international agreements on IPR. However, we have not found any e ciency reason for national treatment. When the orth and the outh have the same innovation-generating technology, reciprocal national treatment does not change at all the welfare of each country (Proposition 3). Moreover, when the two countries having not identical but similar technology, at least in the Cobb-Douglas case, reciprocal national treatment lowers global welfare (Proposition 5). 21

22 One may argue that national treatment may work not in the noncooperative policy setting, like we studied in this paper, but in some cooperative setting. However, if full international cooperation were possible, then national treatment would be only reducing the global welfare, since what national treatment does is to tie the hands of the policy makers to maximize the global welfare. Or, we may nd a reason of national treatment in a transaction-cost argument. For example, practicing national treatment saves management cost of the patent o ce, since it does not have to discriminate patent applicants. Although this argument is certainly persuasive, it cannot be the sole reason of national treatment. This is because it does not explain why reciprocity of national treatment is required by international agreements. Another area to look for the reason of national treatment is fairness. For example, national treatment may be helpful to reduce international inequality. In fact, Proposition 6 can be interpreted that national treatment is enhancing the fairness, since it increases the welfare of the country whose innovating technology is less responsive to the policies. However, we cannot be certain that the country with less responsive innovation technology is always a poor country. If a poor country uses labor intensively in R&D sector, and thus has a larger cost share of labor, then, according to Proposition 6 it is the poor county who loses by national treatment. o, we have to be careful to interpret Proposition 6 as a fairness argument for national treatment. Appendix Appendix A. Taking a derivative of the left-hand side of equation (12), = d (M + M ) C c (C c C m ) (Q) dq Q (M + M ) C c (C c C m ) 0 (Q) + Q (M + M ) C c Q 2 (Q) 22

23 ince (Q) = b (1 1, ) 1 (Qb) 1 b this derivative is rewritten as 1 h (Qb) Qb 1 b b + 2 (Qb) 1 2b b i (C c C m ) ince (Qb) 1 b b < 2 (Qb) 1 2b b, the expression above is negative if 2 (Qb) 1 2b b is nonpositive. We calculate 2 (Qb) 1 2b b = b 2 (Qb) 1 b (1 ) 2b (1 ) (Qb) (Qb) 1 b 1 b 2 (Qb) = (1 2) b (1 ) (Qb) 1 b 1 b 0 because 1=2. Appendix B When the innovation-generating technology is in the Cobb-Douglas form, we have n j (L j ; H j ) = L b j j H1 j b j. Then, the following algebraic expressions are derived. The equilibrium patent policies under the T regime are = M ((1 + g) (C c C m ) ) M ((C c C m ) ) ((g + 2) (C c C m ) ) (C c C m ) M C c = M ((1 + g) (C c C m ) ) M ((C c C m ) ) ((g + 2) (C c C m ) ) (C c C m ) M C c, and the equilibrium policies under the non-t regime are = (1 + ) (C c C m ) M (C c C m ) M ((2 + ) (C c C m ) ) (C c C m ) M C c = ((1 + ) (C c C m ) ) M (C c C m ) M ((2 + ) (C c C m ) ) (C c C m ) M C c = (1 + ) (C c C m ) M (C c C m ) M ((2 + ) (C c C m ) ) (C c C m ) M C c = ((1 + ) (C c C m ) ) M (C c C m ) M ((2 + ) (C c C m ) ) (C c C m ) M C c, 23

24 b j where j =, g = n + n, and 1 b j = j n T + nt The equilibrium overall protections are n T n T j + nt. Q = Q = Q = C c g (M + M ) (g + 2) (C c C m ) C c (M + M ) ( + 2) (C c C m ) C c (M + M ) (2 + ) (C c C m ). The equilibrium numbers of varieties are n T = (Qb ) H n T = (Qb ) H n = (Q b ) H n = (Q b ) H. Appendix C. The di erence in the global welfare is W T + W T (W + W ) = ((C c C m ) (1 b ) ) Q n Qn T ((C c C m ) (1 b ) ) Qn T Q n n + (M + M ) C c n T n n T ow taking the rst derivative with respect to b and evaluating it at b = b, we 24

25 have d W T + W T (W + W ) b db =b dq dq = ((C c C m ) (1 b) ) n (n + n ) db db dn T + (M + M ) C c + dnt dn nt db db db dn + Q db dn T db + dnt db dq dn T db where all derivatives are evaluated at b = b. Using the expressions presented in Appen- dix B, we can calculate that dq db n db (n + n ) = 0 and dn db + dnt db = 0 at b = b. Therefore, the rst derivative of W T + W T (W + W ) with respect to b evaluated at b = b is zero. have Then, taking the second derivative with respect to b and evaluated at b = b, we d 2 db 2 (W + W ) b =b d 2 Q d 2 Q = ((C c C m ) (1 b) ) W T + W T db 2 n d 2 n + ((C c C m ) (1 b) ) Q db 2 dq +2 ((C c C m ) (1 b) ) dq +2 db n + Q dq db (M + M ) C c + d2 n nt db 2 dn db db dn db 2 db d 2 n T db 2 (n + n ) d 2 n T db 2 + d2 n T db 2 dq dn T db db dn T db + d2 n T db 2 + dnt db where all derivatives are evaluated at b = b (and we call it b). After a lengthy algebra, we nd that the sign of the expression above is the same as the sign of the following expression: 2 [(C c C m ) (1 b) ] (2 + ) (C c C m ) (1 2b) 2 (25) where = b=(1 b). This is negative for b 1=2. For b > 1=2, we rewrite the expression 25

26 (25) as [(2 ( b) + 5) (C c C m ) + (1 + 2b + 2b) ] (C c C m ) (2b 1) (C c C m ) 2 2, which is negative for b > 1=2. Therefore, the second derivative of W T + W T (W + W ) with respect to b evaluated at b = b is negative. Appendix D. The welfare di erence of the orth country is given by W T W = (1 b ) Qn T +M C c n T n Q n M (C c C m ) n T n n T n n n T Taking the derivative with respect to b and evaluating at b = b (and calling it b), we have d W T W b db =b dq dq dn T dn = (1 b) n + Q db db db db dn T dn dn T d dn T +M C c M (C c C m ) n + db db db db db d d dn dn T +M (C c C m ) n + db db db db where all derivatives are evaluated at b = b. Using the expressions presented in Appendix B, the expression above is reduced to d db W T W b =b = n M (C c C m ) 2 ( ) (1 b) 2 (( + 2) (C c C m ) ) < 0. Therefore, W T W is decreasing in b at b = b. ince W T + W T (W + W ) 26

27 is neither increasing nor decreasing in b at b = b, it follows that W T W is increasing in b at b = b. This implies that when b > b and they are close enough, W T < W and W T > W. 27

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