Finite Lifetimes, Patentsʹ Length and Breadth, and Growth

Transcription

1 Auburn University Department of Economics Workin Paper Series Finite Lifetimes, Patentsʹ Lenth and Breadth, and Growth Bharat Diwakar and Gilad Sorek Auburn University AUWP This paper can be downloaded without chare from:

2 Finite Lifetimes, Patents Lenth and Breadth, and Growth Bharat Diwakar and Gilad Sorek July 06 Abstract We study the implications of patents breadth and duration (lenth to rowth and welfare, in an overlappin enerations economy of finitely livin aents. This demoraphic structure ives room to inter-enerational trade in old patents and life-cycle savin motive, which prove to be relevant to the implications of different patent-policy dimensions. Patent breadth protection affects life-cycle savin and thereby areate investment, and the allocation investment between patents and physical capital. Patents duration affects also the stock of, and trade in, old patents. We show that, these unique characteristics of the OLG economy provide a case for incomplete patent breadth protection and finite patent duration, which are both rowth and welfare enhancin. Furthermore, we show that the implications of patent policy to rowth depend on whether the differentiated inputs are intermediate oods or investment oods. Our results contrast with the ones derived in previous studies that employed the same technoloies and preferences in model economies of infinitely livin aents. Hence, this work hihlihts the importance of the assumed demoraphic structure to the implications of patent policy. JEL Classification: : L6, O-30 Key-words: IPR, Patent lenth, Patent Breadth, Growth, OLG Economics department, Auburn university, Auburn Alabama. s: ms004@auburn.edu, bzd003@auburn.edu.

3 Introduction There is, by now, a lare literature on the role of patent policy in modern rowth theory, namely, the effects of patents strenth on R&D-based rowth and welfare. This literature, however, was almost exclusively written in model-economies with infinitely livin aents. This study contributes a comparative analysis on the implications of patent policy to rowth and welfare, for the alternative workhorse framework for macroeconomic modelin - the overlappin enerations (OLG economy of finitely livin aents. We hihliht two unique implications of the OLG demoraphic structure to patent policy, in a variety expansion model (i.e. horizontal differentiation. First, we show that in the OLG economy patent breadth and patent duration (lenth have uneven effects on rowth. Secondly, we show that the effect of patent policy on rowth depends on whether the differentiated inputs are defined as intermediate oods (see for example Kwan and Lai 003, Barro and Sala-i-Martin 004, Cysne and Turchick 0 and Zen et al. 03, or as investment oods - i.e. physical capital, or "machines" (see for example Rivera-Batiz and Romer 99, Strulik et al. 03, and Prettner 04. These two types of inputs differ in their formation timin: the intermediate oods are formed in the same period they are bein used, whereas the investment oods must be formed one period ahead of utilization. The demoraphic structure of the OLG implies that, if patent duration exceeds the lifetime of patent holders, inter-enerational trade in old patent prevails. This trade in old patents crowds out investment in new innovative R&D. Moreover, in the OLG economy areate savins rely on labor income of youn workers. When the differentiated inputs are intermediate oods, all savins out of labor income are invested in old and new patents. Hence shortenin patent lenth enhances innovation, and thereby rowth, by reducin the investment in the (smaller stock of old patents. However, the effect of patent breadth rowth is positive because it s overall effect on output, and thereby labor income and savin and rowth, is positive. Hence, we show that when the differentiated inputs are intermediate oods, rowth is maximized with minimal patent lenth and maximal patent breadth protection. The above result contrasts with the those obtained by Kwan and Lai (003, Cysne and Turchick (0 and Zen et al. (03, who studied the same variety expansion rowth model we employ here with infinitely livin aents. These three studies differ only in their modellin approach of patent policy. The first two studies model patent policy throuh constant imitation rate, followin Helpman (993. This modelin approach can be interpreted as stochastic patent duration, as will be explained below. The third paper models patent policy alon two (more natural dimensions: deterministic patent duration alon with price reulation which is equivalent to our modelin of patent breadth. All three studies conclude that rowth is maximized under complete patent protection. That is, the same innovation and production technoloies, and instantaneous preferences. Cysne and Turchick (0 corrected Kwan and Lai s (003 early analysis and modified their results accordinly. The same modelin approach and conclusions are presented in Barro and Sala-I-Martin s (004 textbook (Ch. 6.

4 Chou and Shy (993 where the first to identify the crowdin-out effect of lon patent-duration due to trade in old patent, which hinders innovation and rowth. With technoloies and instantaneous preferences that differ from the ones we employ here, they also find that one period patent duration yields hiher rowth rate than infinite patent duration. In their model, differentiated consumption oods are produced with labor and the time of utilization, hence it corresponds to production with intermediate oods. However, they did not consider patent breadth protection. Sorek (0 studies the effect of patent breadth and patent lenth protection on quality rowth (i.e. vertical differentiation in an OLG economy, where differentiated consumption oods are also produced with labor. In his setup the effect of patent policy depends solely on the elasticity of inter-temporal substitution (throuh the effect of the interest rate life-cycle savin in the OLG model, unlike in the present work. Next, we study the counterpart model economy that produces with differentiated investment oods, that are formed one period ahead of use. Here, the differentiated machines compete with patents over the allocation of savin as an alternative form of investment. As a result, weakenin patent breadth protection induces contradictin effects on rowth. Weakenin patent breadth protection lowers the price of patented machines, which in turn increases demand for machines. With more machines bein utilized output and labor income are hiher, and therefore areate savin an investment is increasin 3. This is the positive static effect of loosenin patent breadth protection on rowth. However, on the other hand, hiher demand for machine shifts investment away from patents towards physical capital. This is the neative dynamic effect of weakenin patent breadth protection on rowth. Shortenin patent duration induces the same trade-off throuh lowerin the averae price of machine varieties, plus additional positive effect on rowth due to decreasin the investment in old patent (i.e. the crowdin-out effect. We will show that when differentiated inputs are investment oods rowth is always maximized with incomplete patent breadth protection or intermediate patent lenth (but not always with minimal patent lenth, and that incomplete patent breadth protection is always welfare maximizin. By contrast, in the counterpart models of infinitely livin aents (cited above the implications of patent policy does not depend on the timin of differentiated-inputs formation. There, the effect of patent policy on rowth works solely throuh the effect of patent protection on the rate of return (which is definitely positive there as well as in our OLG economy, which in turn determines the rowth rate throuh the standard Euler equation. As mentioned above, this study finds that rowth is always maximized with complete protection but welfare may be maximized with incomplete protection. The paper proceeds as follows: Section presents the model. Section 3 studies the implications of patent policy to rowth for differentiated intermediate oods, and Section 4 studies it implications to rowth and welfare for differentiated investment oods. Section 5 concludes this study. 3 This is in line with Jones and Manuelli (99 who showed that in neoclassical economy of finitely livin aents, rowth is bounded by the ability of the youn eneration to purchase capital held by the old. One of the remedies they consider to support sustained rowth in such economy is direct income transfers from old to youn. Similarly, Uhli and Yanaawa (996 showed that reliance on capital-income taxation can enhance rowth. 3

5 Model The model presented below is identical to the one employed by Kwan and Lai (003, Cysne and Turchick (0 and Zen et al. (03 and Barro and Sala-I-Martin (004, Ch. 6, except for its demoraphic structure that follows Diamond s (965 canonical OLG framework: a population of constant size composes two overlappin enerations, of measure L, in each and every period - "youn" and "old". Each aent is endowed with one unit of labor to be supplied inelastically when youn. Old aents retire to consume their savin. We present the model here under the assumption of full patent protection - i.e. infinite patent duration and complete patent breadth protection that implies innovator can chare unconstraint monopolistic price. We study the implications of incomplete patent protection in Section 3.. Differentiated inputs as intermediate oods The final ood Y is produced by perfectly competitive firms with labor and differentiated intermediate oods, to which we refer as "machines" Y t = AL t N t 0 K i,t di (0, ( where A is a productivity factor, L is the constant labor supply, K i,t is the utilization level of machine-variety i in period t, respectively, and N t measures the number of available machinevarieties 4. In the benchmark case, once invented, each machines variety is eternally patented. Machines fully depreciate after one usae period, and the final ood price is normalized to one. Under symmetric equilibrium, utilization level for all machines is the same, i.e. K i,t = K t i, and thus total output is Y t = AN t K t L The labor market is perfectly competitive, and therefore the equilibrium wae and areate labor income are w t = A( N t K t L and w t L = A( N t K t L, respectively. The profit for the final ood producer is π i,t = AL t N t N t Ki,t di p i,t K i,t di w t L t,i 0 i= where p i,t is the price of intermediate ood i in period t, and L i,t is labor input employed in the production of this ood. Profit maximization yields the demand for each machine: Ki,t d ( = A L p i,t. Given this demand, the periodic surplus for the patented machine i is P S i,t = (p i,t Ki,t d, which is maximized by the standard monopolistic price p i,t = i, t. Pluin this price into Ki,t d yields Kd i,t = A L i, t. Then, pluin the latter expression back into (a 4 The elasticity of substitution between different varieties is. (a 4

6 yields the followin expression for total output Y t = A Nt L (b Followin (b, output rowth rate (which coincides with per-capita output rowth 5, denoted Y Y t+ Y t, coincides with the rate of machine-varieties expansion, denoted N,t+ N t+ N t, i.e. Y = N. Innovation technoloy follows lab-equipment specification, so the cost of a new blue print is. New and old varieties play equivalent role in production as reflected by their symmetric presentation in (. Therefore, the market value of old varieties equals the cost of inventin a new one -. When machine-varieties are patented forever, all old patents are bein traded, as the youn saver buy patents from the old retirees. Hence the return on patent ownership - over old and new technoloies is + r t+ = P S i,t++. Pluin the explicit expressions for the surplus and the innovation cost we obtain the stationary interest rate + r = ( K d + = ( A L + (. Preferences Lifetime utility of the representative aent, who was born in period t, is derived from consumption over two periods based on the loarithmic instantaneous-utility specification 6 U t = ln c,t + ρ ln c,t (3 where ρ (0, is the subjective discount factor. Youn aents allocate their labor income between consumption and savin, denoted s. The solution for the standard optimal savin problem is s t = wt. Hence, areate savin is S +ρ t = wtl, which after substitutin the explicit expressions +ρ for w t becomes S t = N t( A L [ ( + ρ ( ] (4 3 Patent Policy and Growth We first solve for the stationary rowth rate under the assumed complete patent protection. In each and every period, areate savin is allocated to investment in old patents and investment in new patents (i.e. invention of new machine varieties 5 As both total population and the labor force are constant. 6 It is well known that under the assumed demoraphic structure, the loarithmic instantaneous utility implies that savin (and investment level is independent of the interest rate. In section (5 we will consider the implications of the eneral CRRA preference form. 5

7 I t = N t+ (5 Imposin the equilibrium condition S = I, we equalize (4 and (5, to derive the stationary rate of variety expansion (and output rowth + y = N t+ N t L ( A = ( + ρ [ ( ( ] Equation (6 implies that rowth is subject to stron scale effect, i.e. it increases in labor force size. It increases also in total productivity factor, labor income share, and the discount factor, and decreases in innovation cost. 3. Patent breadth We model patent breadth protection with the parameter λ, which limits the ability of patent holders to chare the unconstraint optimal monopolistic price: p (λ = λp = λ where λ (,, and thus p (λ (,. One can think of p (λ as the maximal price a patent holder can set and still deter competition by imitators. Weaker breadth protection lowers the cost of imitation, thereby imposin a lower deterrence price on patent holders 7. When λ =, patent breadth protection is complete and patent holders can chare the unconstraint monopolistic price p =. With zero protection λ =, patent holders are losin their market power completely, therefore sellin at marinal cost price. Note that as patent breadth protection is weakened machines price is reduced and therefore demand for each machine-variety is increasin. However, loosenin patent breadth protection does not affect directly the inter-enerational trade in old patents. Pluin p (λ = λ in (4 and (5, and imposin S = I, we obtain the explicit rowth rate as a function of patent breadth protection + y = N t+ N t L ( A = ( + ρ [ ( λ ( λ ] Proposition Under production with intermediate oods, rowth is maximized with maximal patent breadth protection, i.e. λ =. Proof. Differentiatin the riht hand side of (7 for λ reveals that rowth rate is increasin in patent breadth protection, that is λ (, : λ > 0. (6 (7 3. Patent lenth 3.. Deterministic Patent Lenth Here we consider deterministic patents duration, which is a discrete number of periods denoted T, and derive analytical results for the case of one-period duration T =. Under one-period patent 7 Our modelin approach is equivalent to the explicit price (ceilin reulation considered by Zen et al.(03. 6

8 duration, there is no inter-enerational trade in old patents, and only new technoloies are sold at the monopolistic price p m =. All old varieties are sold under perfect competition at marinal cost price p c =. Hence, demand for machines in each competitive industry is Ki,t d = A L. The share of monopolistic industries, denoted µ, depends on the (stationary rowth rate: µ = Hence total output that was iven in (a modifies to +. [ Y t = A Nt L ( + ( ] (8 + + The savin and investment expressions, from equations (4-(5 also modify accordinly S t = [ ( + ρ N ta L I t = N t+ ( + + ( + ( ] (9 + and the equilibrium condition S t = I t yields an implicit expression for the stationary rowth rate + = ( A + ρ L [ ( + ( ] (0 Proposition For production with intermediate oods, rowth rate under one period patent duration is always positive and hiher than under infinite patent duration. Proof. The left hand side of (0 is increasin linearly in. Its riht hand side is decreasin monotonically in from infinity, for = 0, to a positive finite value, for. Hence, by the fix-point theorem, there exists unique solution for (0 with > 0. For, the riht hand side of (0 approaches ( (, which is, by (6, the rowth rate under infinite A L +ρ patent duration. Hence, the stationary rowth rate defined by (0 for one-period patent duration is necessarily hiher than the one defined in (6 for infinite patent duration. Proposition contrasts with the result obtain by Zen et al. (03, who find that infinite patent duration maximizes rowth the counterpart economy with infinitely livin aents. It alins, however, with the result obtained in Chou and Shy (993, for OLG economy that produces with differentiated intermediate oods, thouh with labor as sole production input. Under any intermediate patent lenth protection T, patented technoloies are bein traded at different prices- accordin to their remainin life time, subject to the followin no-arbitrae condition: + r = ( λ K d m + v = ( λ Km d ( + v λ =... = K d ( m + v λ T = Km d v v T v T where v denotes the market value of each technoloy invented in period 0, when sold in period, and v is the market value of those technoloies in period, and so on and forth. At period 7

9 T, which is one period before the patent expires, the value of the technoloy oes down to the present value of the surplus, as it will not be sold aain in the next period. Loner patent duration increases the equilibrium interest rate. An equivalent (positive effect of patent duration on the interest rate enerates the positive relation between patent duration and rowth (throuh the standard Euler equation in Zen et al. (03, for infinitely livin aents economy. The averae market value of all traded technoloies, denoted v is increasin with patent lenth protection. For a iven patent lenth protection, T, the stationary rowth rate is iven by the implicit expression 8 ( A + = + ρ v(t L [ ( [ ( ( + T λ ( λ ] ( ] + ( + T (0a Where v(t is the averae value of all existin technoloies: v(t = + + v (+ + v ( v (+ T + T. However, we find the analysis of this expression non-tractable. We could not also derive a comparison between the stationary rowth rates under incomplete patent breadth and finite patent duration, presented in equations (7 and ( Stochastic patent lenth Here, we follow the patent-policy modelin of Kwan and Lai (003 and Rubens and Turchick (0, assumin that each period a fraction π of the existin patents expire 9. Accordinly, only the fraction π of new-technoloies is effectively patented in the first period of utilization. This means that actual patent-protection lenth, denoted T, is stochastic, with the expected value E(T = π π for all new and old patented technoloies. Under this specification the stationary fraction of patented industries, µ, is µ = π + π µ = ( + ( π + π Demand for machines in each competitive industry is K d i,t = A L and thus, total output that was iven in (a modifies to [ Y t = A Nt L π + π ( ( ( + ( π + ( ] ( + π Areate savin and investment from (6 and (7, also modify accordinly: S t = [ ( + ρ A Nt L π + π ( ( + ( π + ( ] (3 + π 8 Note that for T = the expression in (0a coincides with (0 and for T it coincides with (6. 9 Or, as in their oriinal interpretation, a fraction π of the patented technoloies is bein imitated due to lack of patent-protection enforcement. 8

10 ( I t = N t+ N t + ( π + π N t = + π N t+ (3a Equalizin areate savin from (3 and areate investment (3a yields the followin implicit function of the stationary rowth rate + = ( + ρ A L [ π ( ( + ( π + ( ] (4 Proposition 3 The rowth maximizin stochastic patent duration is zero. Proof. Differentiatin the riht hand side of (4 for π, yields the followin first order condition for π < 0 : < (+. This condition necessarily holds if <. The latter condition can be written as <, which holds for any (0, as demonstrated in fiure. + Fiure : Provin Proposition 3 The horizontal axis in fiure one take values of, from zero to one. The blue curve is the function + and the red one is. 9

11 4 Differentiated inputs as investment oods Considerin the differentiated inputs as physical-capital (i.e. "specialized machines", implies that they should be formed one period ahead of utilization, as part of investment uses. We still assume that the formation of one specialized machine takes one unit of input. Therefore the usae cost of each machine, in current value terms, equals the (ross interest rate + r t paid at period t 0. The current value of the periodic surplus from rentin each patented machine, modifies accordinly to P S i,t = [p i,t ( + r t ] Ki,t d, and under complete patent protection this surplus is maximized by the standard monopolistic price p i,t = ( + r t i. Pluin this price into Ki,t d yields Kd i,t ( = A L +r t i, t. Under infinite patent duration, the rate of return on investment in patents is iven by + r t = P S+. Pluin the explicit term of the surplus yields an implicit expression for the equilibrium interest, which equalizes the return on investment in patents and investment in physical capital: t : + r t = [p i,t ( + r t ] K d i,t + = ( + r t ( ( λ A L λ + Lemma There exists a stationary interest rate that is increasin with patent breadth protection Proof. The left hand side of (5 is increasin linearly in r, from one (for r = 0 to infinity. The riht hand side of (5 is decreasin in r from ( λ A L ( λ + r. Hence, by the fix point theorem there exists positive stationary interest (5 > (for r = 0 to zero (for rate r that solves (5. Differentiatin the riht hand side for λ yields a positive derivative for λ <. Hence the value of r, which solves (5, is increasin with patent breadth protection λ. Lemma implies that the expression λ [ + r(λ] in (5 is also increasin in the strenth of patent breadth protection λ. Under one period patent duration there is no inter-enerational trade in old patents, implyin + r t = P S. Therefore, under one period patent duration, with complete equation (5 modifies to t : ( + r t = ( + r t ( ( λ A L λ [( ( + r t = A ] L (5a Clearly, for a iven patent breadth protection, the interest rate under one period patent duration in (5a is lower than under infinite patent duration, as iven in (5. 4. Patent Breadth Here we consider the effect of patent breadth protection on rowth, under infinite patent protection. Hence, relevant interest rate is the one defined in (5. Pluin K d i,t = A L ( +r 0 Similar modelin approach was taken by Strulik et al (03 and Prettner (04. back into 0

12 (a yields the followin expression for total output The savin and investment equations modify to ( Y t = A Nt L λ ( + r (6 S t = I t = N t+ [ ( ( A Nt L λ(+r + ρ (7 ( + A L λ ( + r Equalizin areate savin and areate investment yields the stationary rowth rate ] (8 + = + ρ A ( L λ(+r + A L ( λ(+r (9 We define ψ λ(+r and pluin it into (9 to re-write the rowth equation + = ψ + ρ A L + ψ (0 Proposition 4 For production with diff erentiated physical capital, the rowth maximizin patent breadth is always incomplete Proof. Differentiatin (0 for ψ reveals that the rowth rate is increasin with ψ, if ψ, that is A L > ( λ(+r A L. Hence, under this condition the rowth rate is decreasin in λ. We evaluate the latter condition, for λ =, by pluin into it the interest rate for one-period patent duration, iven in (5a. For this interest rate the latter inequality, does not hold, but rather it turns to equality. Hence, because the interest rate under infinite patent duration that is iven in (5 is hiher, the latter inequality always holds. 4. Patent lenth We focus here on the effect of patent duration on rowth iven that patent breadth protection is complete, λ =. The discussion in subsection 3.. suests that Proposition 4 implies also that rowth is always maximized with less than infinite patent duration: the effect of marinal shortenin of patent duration on ψ, is equivalent to the effect of marinal decrease in λ. addition shortenin patent duration decreases the averae fix-cost per variety, denoted v(t in the discussion above, which by itself works to enhance rowth. Nevertheless, a formal proof of this As both decrease the averae price of machines and the interest rate. > In

13 conjecture turns out to be intractable. Hence, we will focus here on comparin rowth under oneperiod patent duration and under infinite patent duration, for λ =. Under one period patent lenth, the relevant interest rate is the one defined in equation (5a, and the rowth equation modifies to the followin implicit equation + = + ρ ( + A L ( +r ( +r + ( +r + ( +r Elaboratin ( yields the xplicit expression for the rowth rate under one period duration + = ( L ( + ρ A = + r + ρ ( (a Proposition 5 For production with diff erentiated investment oods, one period patent duration yields lower rowth rate than infinite duration if A L is suffi ciently low. Proof. The proof derives from comparin the rowth rate under one period patent duration iven in (a with the rowth rate under infinite patent duration iven in (0, for complete patent breadth, i.e. λ =. For suffi ciently low A L, the rowth rate in (0 approaches +ρ +r, which is reater than the one in (a; recall that the interest rate in (0 is hiher. It can be also shown that under one period patent duration rowth is maximized with full patent breadth protection. 4.3 Welfare Our welfare analysis focuses on the effect of patent breadth protection in rowth under production with physical capital and infinite patent duration. Welfare is defined as the present value of the life time utility for the livin eneration and all future enerations, under the private discount rate: W ρ t U t ( t=0 Where U t is the life utility of the representative consumer who was born in period t, iven in equation (3. To maintain tractability we confine to patent breadth protection. Pluin in the explicit expressions for c and c in the lifetime utility function (3 yields the followin indirect utility function ( ( N t A λ(+r U t = ln + ρ ln + ρ ( ρ( N t A λ(+r + ρ ( + r (3 Pluin (6 into (5, and elaboratin the resultin eometric sequence, yields the followin

14 expression for the present value of the life-time utility for the current and all future enerations, iven the initial variety span N 0 : W = U 0 ρ ( + ρ ln( + + ρ ρ (4 Proposition 6 Incomplete patent breadth protection is always welfare improvin Proof. By Proposition 4, rowth rate is always maximized under incomplete breadth protection. Hence, by (5, a suffi cient condition for incomplete breadth protection to maximize welfare is havin U 0 λ by (+ρ λ < 0 when evaluated at λ =. The sin of the derivative of (4, iven N 0, is iven + (+r λ +r [ρ( ]. Lemma states that the expression increasin (+r λ is zero < 0 when evaluated at λ =, that is marinal when evaluated at λ = 0. Hence, the sin of U 0 λ loosenin of patent breadth is welfare improvin. 4.4 CRRA Utility Finally, we turn now to consider the implication of the eneral CRRA instantaneous utility to our previous result, considerin the followin lifetime utility form: U = c θ t θ + ρ c θ t+ θ where θ is the elasticity of inter-temporal substitution, and for θ = (6 falls back to the loarithmic form (3. The modified solution for the standard optimal savin problem is s t = Hence, areate savin now is S t = w tl +ρ θ (+r θ θ (5 w t. +ρ θ (+r θ θ.substitutin the explicit expressions for w t into S t and equalizin to areate investment iven in (8 yields the rowth equation + = + ρ ( + r θ ( A L λ(+r + A L ( λ(+r (6 As it is well known, in the standard OLG framework the effect of interest rate on savin depends on the inter-temporal elasticity of substitution: it is positive (neative if θ < (θ >. Hence, because the interest rate is increasin with patent protection, the positive impact of decreasin patent breadth on rowth is diminishin with the inter-temporal elasticity of substitution. More specifically, for θ < all our results remain (and will hold for a larer set of parameters as a decrease in the interest rate by itself stimulates savin and investment (this is an additional effect was not induced under the loarithmic utility form. However, as θ increases beyond one, the decrease in the interest rate due to loosenin patent breadth protection will work to hinder rowth, 3

15 counterin the positive effects that were defined in Propositions -3. For suffi ciently hih value of θ this direct interest effect may entirely dominate the over all impact of loosenin patent protection on innovation and rowth. Nevertheless, the empirical literature commonly suests that θ is lower than one, and thus supportin the relevance of our main findins. The welfare analysis for θ turns out bein intractable. 5 Conclusions This work contributes to the literature on patent policy and economic rowth by analyzin the rowth and welfare implication of patent lenth and breadth in the overlappin enerations framework of finitely livin aents. The OLG demoraphic structure ives room to inter-enerational trade in patents and life-cycle savin. These elements, which are proved to be relevant to patent policy are abstracted in lare by the current literature on patents and rowth, which is written for infinitely livin aents. Our comparative analysis implies that these two elements provide a case for incomplete patent protection that is both rowth and welfare enhancin, in contrast with the results obtained in the analyzes of infinitely livin aents. Compared with the few previous studies on patent policy written in the OLG framework, our contribution is twofold: (a hihlihtin the dependency of patent policy implications on the assumed nature of the differentiated oods, whether they are consumption or intermediate oods or investment oods (b explorin the uneven effect of patent breadth and duration on rowth. References [] Barro R.J., Sala-i-Martin, X., 004. Economic rowth, Second Edition. MIT Press. Cambride. MA [] Chou, C., Shy, O., 993. The crowdin-out effects of lon duration of patents. RAND Journal of Economics 4, [3] Cysne R., Turchick D., 0. Intellectual property rihts protection and endoenous economic rowth revisited. Journal of Econonomic Dynamics & Control 36, [4] Diamond P., 965. National debt in a neoclassical rowth model. American Economic Review 55, 6 50 [5] Diwakar B., Sorek G., 05. Economic development and state-dependent IPR. Auburn University Workin Peprer-AUWP 05-6 See for example Hall (988, Beaudry and Wincoop (996, Oaki and Reinhart (998, Enelhardt and Kumar (009. 4

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