Welfare Impacts of Cross-Country Spillovers in Agricultural Research

Transcription

1 Welfare Imacts of Cross-Country illovers in Agricultural Research ergio H. Lence and Dermot J. Hayes Working Paer 07-WP 446 Aril 2007 Center for Agricultural and Rural Develoment Iowa tate University Ames, Iowa ergio Lence is a rofessor of economics and Marlin Cole Chair of International Agricultural Economics at Iowa tate University. Dermot Hayes is Pioneer Hi-Bred International Chair in Agribusiness and a rofessor of economics and of finance at Iowa tate University. This aer is available online on the CARD Web site: Aroriate attribution should be given to the authors of this aer for any use, uotation, or excerts of this material. Questions or comments about the contents of this aer should be directed to ergio Lence, 260 Heady Hall, Iowa tate University, Ames, IA ; Ph: (55) ; Fax: (55) ; shlence@iastate.edu. Iowa tate University does not discriminate on the basis of race, color, age, religion, national origin, sexual orientation, gender identity, sex, marital status, disability, or status as a U.. veteran. Inuiries can be directed to the Director of Eual Oortunity and Diversity, 3680 Beardshear Hall, (55)

2 Abstract The welfare imlications of intellectual roerty rotection (IPP) for rivate sector agricultural research are analyzed, focusing on the realistic cases in which countries rovide different IPP levels, technology sills over across countries, and the ublic sector is involved in research. A model is develoed to determine who benefits from, and who should ay for, the associated research. The aer contains some interesting results on the imlications of a harmonization of IPP olicies through multilateral agreements or via technology that allows research firms to revent the coying of lants and animals that exress traits that have emerged from their research. Keywords: biotechnology, GURTs, intellectual roerty, research sillover, welfare analysis. JEL Classification: F3, L, O3, O34, Q6, Q7.

3 WELFARE IMPACT OF CRO-COUNTRY PILLOVER IN AGRICULTURAL REEARCH Advances in rivate sector lant and animal genetics often have alicability outside the country where the research was conducted. Historically, firms that conducted successful research and develoment (R&D) have catured some of the international benefits by charging a remium for the resulting seedstock. For examle, rents associated with imroved erformance of hybrid breeds and varieties can be catured by charging a remium rice for these seeds, and this remium can be maintained for many generations by controlling access to the urebred arental lines. This remium ricing solution has had less relevance in breeds and varieties where the commercial traits are assed on in retained seeds and in the offsring of commercial farm animals. Until relatively recently, the only way to cature any benefits associated with these breeds and varieties has been to charge a remium for the first generation knowing that the roducer will relicate this imrovement in future generations. Governments have attemted to stimulate rivate sector agricultural R&D by roviding legal rotection for intellectual roerty in both domestic and international markets. However, the ability of countries to imose intellectual roerty rights on farmers in other countries has not been universally acceted (WG-FAO 200). In some instances, the rivate sector has been willing to conduct R&D even when little intellectual roerty rotection (IPP) was afforded in one or two major markets. For examle, work on Roundu Ready soybeans rogressed desite the relative lack of IPP for this technology in some major soybean growing countries (i.e., Brazil and Argentina), because legal IPP was available in the U.. domestic market. In the resent article we focus on the welfare imlications of legal IPP in agriculture when the associated R&D has commercial alication in more than one country. Agricultural markets tend to be uniue in that the customer is a farmer who sells the resulting cro or livestock roduct into cometitive domestic and international markets. The farmer further may have the otion of using unimroved genetics, or ossibly the newly develoed technology from

4 cros and animals grown in revious years. The resent study develos a model that allows olicy makers and those who design domestic and international mechanisms to rotect intellectual roerty to determine who benefits from, and who should ay for, the associated R&D. Recent develoments have generated ublic interest in this toic. First, there has been a large reduction in ublic research caacity in develoing countries due in large art to a decline in international funding for this research. This suggests that these countries will rely more and more on research sillovers from more develoed countries to remain cometitive. econd, the recent develoment of genetic use restriction technologies (GURTs), oularly known as the terminator gene, can be viewed as an extreme form of IPP, and this technology has received criticism from some less develoed countries. Third, the develoment of Roundu Ready soybean seed by Monsanto introduced a new form of IPP in the U.. marketlace. To access this technology, U.. soybean roducers must ay a technology fee of about $7.50 er 50-ound bag of Roundu Ready lanting seed and must agree not to kee the harvested beans for future lanting or for re-selling to other farmers (chnef 2003). The disarity in the alication of this technology fee has become controversial because U.. roducers feel that they are aying for research that hels their foreign cometitors (American oybean Association 2003). Finally, cross-country rotection of intellectual roerty rights in agriculture continues to stimulate discussion and controversy at international bodies such as the World Trade Organization via the 994 Agreement on Trade-Related Asects of Intellectual Proerty Rights (WTO 994). Related Research The framework develoed for the resent study is based on a model by Lence et al. (2005), which in turn is based on studies by Loury (979), Lee and Wilde (980), Dixit (988), and rinivasan and Thirtle (2002). The single-country model by Lence et al. (2005) is nested within the model roosed here and their results can be relicated within the resent model by restricting the number of countries to one and by eliminating the ublic sector. 2

5 Related work includes Moschini and Laan (997), but they do not consider the incentive structure for R&D firms, the welfare imacts that occur after the exiration of the innovator s atent, the uncertainties associated with R&D, sillovers, or the ublic sector. Other recent relevant studies are Alston and Venner (2002) and Tongeren and Eaton (2002), who incororate the incentives for the R&D firms but do not include sillovers, the market for the cro, the welfare of those who roduce the cro, or the ublic sector. illovers in the context of IPP and North-outh trade are addressed by Žigić (998, 2000). Among other imortant differences with our model, Žigić euates the intensity of sillovers to the strength of IPP and focuses on economy-wide sillovers rather than the agricultural research sillovers that are our main interest. wanson and Goeschl (2000) and Goeschl and wanson (2002) oint out that GURTs are a way for innovators to rotect their intellectual roerty, and they recognize that this will enhance R&D. They also attemt to uantify the otential imact of GURTs on cro yields in develoing countries by extraolating the exerience with hybrid seeds. Harhoff, Régibeau, and Rockett (200) discuss GURTs as a means by which innovators can exert market ower and conclude that GURTs may be beneficial because they imrove market erformance. The structure of our model reuires simultaneous euilibrium in three markets in each country. The seedstock industry must in euilibrium conduct an amount of R&D that can be justified by the exected earnings from that research, and each seedstock industry articiant must resond to incentives and to cometition from other comanies in an otimal way. The market for seeds and breeding stock must also be in euilibrium, and the farmers who urchase the imroved roduct should do so only if the remium charged is less than the additional rofits they can exect. Finally, the domestic and international markets for the final roduct must be in euilibrium, and changes in costs and farm roductivity must eventually imact market rices. We arameterize the model and simulate the imact of changes in these three factors on consumer, roducer, and R&D industry welfare in both countries. 3

6 The model is designed so that, to the extent ossible, the inuts reuired for calibration are readily available. To the best of our knowledge, the main difficulty regarding data reuirements for the roosed model concerns the arameterization of the R&D hazard rate, as little emirical research has been erformed on this toic. However, this limitation is overcome by means of sensitivity analysis using alternative arameterizations. Imortantly, the roosed model is helful not only because it can be used to erform emirical analysis when roerly calibrated but also because it allows otential users to concetualize the various critical issues involved in the evaluation and determination of otimal IPP systems for agriculture. We begin with the rivate sector model and extend it to include a ublic sector that also conducts research. A Multi-Country Model of Private Investment in Agricultural R&D The strength of the IPP regime is embedded in a arameter μ,ipp μ,right + μ cost 0, which measures the maximum marku over the marginal cost of roducing x (c ) that the develoer of an imroved farm inut would be allowed to charge for it in country. The legal IPP level μ,right 0 is increasing with the extent u to which the develoer is granted IPP rights on the innovation in country, and with the level of enforcement of such IPP rights in. Parameter μ cost 0, on the other hand, reflects the marku advantage enjoyed by the innovator over its cometitors arising from the costs of transferring or coying the outut-enhancing innovation. At time 0, R&D firms invest resources to comete in a race to develo x, a more roductive version of an existing farm inut (e.g., seed, or breed) x 0. A successful outcome (x ) of the develoment rocess is random and the R&D cometition ends at time t, when x is first obtained. The first develoer of x is granted legal IPP for T eriods, so the successful innovator could legally charge a rice w, = ( + μ,right + μ cost ) c over the interval [t, t + T] if it found it otimal to do so and firms in the industry had no other source of market ower. The legal IPP level is reduced to zero once the IPP rights exire at time t + T, (i.e., μ,right = 0), so the innovator s maximum allowable marku falls to its cost advantage μ cost only. 4

7 The revious discussion highlights the need to address the various comonents affecting the R&D investment decision at time 0. uch comonents include the derived demand for the imroved farm inut x which in turn involves the end-demand for farm outut, the innovator s ricing decision w,, the nature of the R&D rocess, and the determination of euilibrium in the R&D market at time 0. Each of these comonents is the object of the following subsections. Farm Production Let f (x 0, z ) and g (x, z ) denote the roduction functions of country under x 0 and x, resectively, where z is a vector of other variable inuts. Assuming for concreteness that x is a Hicks-neutral imrovement in x 0, the R&D imrovement is reresented by g (x, z ) = ( + α ) f (x, z ), with imrovement factor α and function f ( ) assumed to satisfy standard regularity conditions. The imrovement factor α will tyically differ across countries and may even be negative for some countries. However, α =j > 0 if the new inut was secifically develoed to enhance outut in country j. In this instance, s j α j /α =j rovides a measure of the new technology sillover to country j. For examle, s j < 0 means that the new technology designed for country j actually reduces outut if emloyed in country j. At the other extreme, s j > indicates that, even though the new technology was designed for country j, it leads to an even greater imrovement on the roduction function of country j. Given rices, w 0, w, and r associated with farm outut y and farm inuts x 0, x, and z, resectively, country s farm rofit functions dual to the traditional and new technologies are () and (2), resectively: () π 0 ( (2) π (, w 0, r ), w \, r ) max max x z [ 0, f (x 0, z ) w 0 x 0 r z ], x z [, g (x, z ) w x r z ]. If farmers can choose either technology, the unrestricted farmers rofit function is (3): (3) π (, w 0, w, r ) max[π 0 (, w 0, r ), π (, w, r )]. 5

8 Profit functions () through (3) are used below to analyze euilibrium in the outut and inut markets. Farmers are assumed to behave as erfect cometitors in all markets. In other words, the model assumes that individual farmers do not internalize the effects of their own actions on the markets, either for the final cro or for either tye of inut. Euilibrium in the Market for Farm Outut Using Hotelling s lemma, country s farm suly y * y (, w 0, w, r ) is given by (4): (4) y * = π 0(, w 0, r ) / if π 0(, w 0, r ) > π (, w, r ), π (, w, r ) / if π 0(, w 0, r ) < π (, w, r ), and a convex combination of π 0( ) / and π ( ) / otherwise. uly function (4) is increasing in increasing and convex in. as long as π 0 (, w 0, r ) and π (, w, r ) are Conditional on inut rices w 0 [w 0,, w Q0 ], w [w,, w Q ], r [r,, r Q ], euilibrium in the world market for farm outut reuires consumer and roducer rices to euate aggregate cro consumtion with aggregate cro outut: Q (5) = Q D D ( * ) = = y ( *, w 0, w, r ), where D ( ) denotes the Marshallian demand function for the cro in country, and D is the consumer rice for the cro in country. In addition, euilibrium consumer and roducer rices for the cro and net exorts must also satisfy condition (6) for all countries and j to rule out arbitrage oortunities: D D (6) * * ξ j 0, υ j 0, ( * * ζ j ) υ j = 0. j j In (6), ξ j reresents the wedge between the consumer rice in country and the roducer rice in country j, and υ j is the cro consumtion in country sulied by cro roducers in country j. The term ξ j catures not only transortation costs but also other 6

9 7 frictions such as imort tariffs. Further, ξ > (<) 0 reresents a tax (subsidy) on domestic consumtion met by domestic roducers. Conditions (5) and (6) define the vectors of euilibrium consumer and roducer rices for farm outut D * [ * D,, * D Q ] and * [ *,, * Q ], resectively, where * D ( D w 0, w, r, ξ), * ( w 0, w, r, ξ), ξ [ξ,, ξ Q ], and ξ [ξ,, ξ Q ]. The Innovation ulier s Pricing Decision and Inut Market Euilibrium Alication of Hotelling s lemma yields country s derived demands for standard farm inut x 0 * = x 0 (, w 0, w, r ) and imroved farm inut x * = x (, w 0, w, r ): (7) x 0 * = < > otherwise. ) /,, ( 0 and convex combination of and a ),,, ( ),, ( 0 if ),,, ( ),, ( if ) /,, ( w r w r w r w r w r w w r w π π π π π π (8) x * = > < otherwise. ) /,, ( 0 and convex combination of and a ),,, ( ),, ( 0 if ),,, ( ),, ( if ) /,, ( w r w r w r w r w r w w r w π π π π π π It is clear from (5) through (8) that the rices of farm inuts x 0 and x determine cro outut and consumtion, as well as inut usage. This imlies that simultaneous euilibrium in the cro and inut markets reuires the secification of the technology used to roduce inuts x 0 and x, as well as the cometitive behavior of the suliers of such inuts. In the interest of sace, attention will be restricted to scenarios where the x industry is erfectly cometitive excet for the market ower conferred by the legal IPP and the innovator s cost advantage. 2 Also for simlicity, it will be assumed that x 0 is roduced at constant marginal cost c 0, and that x is roduced by the innovator at constant marginal cost c. 3 Under erfect cometition and constant marginal costs c 0, the rice of the standard farm inut x 0 is w 0 = c 0 for all countries. Hence, if the innovator behaved as a monooly in each country, it would set w = ( m w c 0, c, r, ξ) to maximize rofits. That is:

10 (9) m w = Q argmax w { ( w = c ) x [ ( c 0, w, r, ξ), c 0, w, r ]}. Embedded in (9) is the ricing constraint imosed by the cometition from the traditional inut being sulied at rice c 0. Exression (9) also assumes that otential arbitrageurs are not allowed to trade the new inut across countries to take advantage of rice differentials. In contestable markets (Baumol, Panzar, and Willig 982), however, the otimal rices charged by the innovator for the imroved farm inut will be (0) instead of (9): Q (0) w * = argmax w { ( w c ) x [ ( c 0, w, r, ξ), c 0, w, r ]}. = subject to: w ( + μ,ipp ) c, =,, Q. In (0), μ,ipp μ,right + μ cost is the innovator s effective IPP level in country. According to (0), the extent to which the innovator aroriates the rents from the imroved inut in country deends on the extra marginal cost incurred by otential cometitors to roduce x (μ,ipp ). This extra cost arises from two sources, namely, cometitors technological disadvantage (μ cost ) and legal liability (μ,right ). For examle, in the instance of a seed innovation, μ cost would reresent the additional costs (in units of c ) associated with transferring the trait without access to the original arent lines. 4 This cost would obviously be greater for hybrid lines than for oen ollinated varieties. Further, if the seed innovation has a utility atent, the legal liability cost (μ,right ) faced by those violating the atent would be determined by the robability of being sued and found guilty, and by the enalty imosed on them if convicted. In summary, given roduction costs c 0 and c, the innovator s degree of market ower μ IPP = [μ,ipp,, μ Q,IPP ], and the values of exogenous variables (r and ζ), (0) yields the innovator s otimal rices for inut x across countries w *. In turn, w * determines euilibrium consumer ( D *) and roducer ( *) rices for the cro from (5) and (6), total farm outut y* = Σ y * from (4), and the amount of the new inut bought by farmers x * = Σ x * from (8). 8

11 A Firm s Decision to Invest in R&D If the imroved inut x is first obtained at time t and the innovator is granted an effective level of IPP rights μ,right through the next T eriods, the innovator s IPP levels will be μ,ipp = μ,right + μ cost over the interval (t, t + T) and μ,ipp = μ cost afterward. Hence, at time t the resent value of the rents extracted by the successful innovator are given by (): t + T Q () v(c 0, c, r, ξ, μ right, μ cost, T, i) = t = {[ w ( ) c ] x ( )} μ μ ex( i τ) dτ, IPP = μ, right + cost Q + t+ T = {[ w ( ) c ] x ( )} μ μ ex( i τ) dτ, Q, IPP = cost = i [ ex( i T)] {[ w ( ) c ] x ( )} μ, IPP = μ, right + μ = Q + i ex( i T) {[ w ( ) c] x ( )}, IPP = μ = cost μ, cost where i is the continuously-comounded interest rate er unit of time and τ is a variable of integration. The terms Σ {[w ( ) c ] x ( )} reresent the rents er unit of time accruing to the innovating firm. The resent value of each eriod s rents is obtained by discounting them at the aroriate discount rate i by means of ex( i τ). Finally, the resent value of the discounted rents over the entire eriod is obtained by integrating with resect to time. R&D firms must decide whether to attemt to develo x and obtain the associated IPP before x exists. Here, such a decision is reresented by means of the standard model of R&D cometition advanced by Loury (979) and Lee and Wilde (980). This model ostulates that there are N identical R&D firms. To articiate in the cometition to develo the imroved farm inut x, firm n must make a lum-sum R&D investment (e.g., hysical caital) k n and then incur a recurrent cost (e.g., labor) l n. R&D sunk cost k n and recurrent cost l n jointly determine the firm s hazard rate h n = h(k n, l n ), where h( ) is concave, twice continuously differentiable, strictly 9

12 increasing, and satisfies h(0, 0) = lim k h ( ) = lim l h 2 ( ) = 0. The firm s hazard rate h n is the conditional robability that it will succeed in develoing the imroved x in the next small unit of time, given that no firm has succeeded so far. Individual firms hazard rates are thus functions of the resective lum-sum investments and recurrent costs, but are indeendent of the length of time elased since the R&D cometition started. 5 The aggregate hazard rate for the R&D industry (H) is obtained by adding u the individual hazard rates: (2) H = h( k n, l n ). N n= Given that H is the hazard rate for the R&D industry, the robability that no firm has won the race by time t is ex( H t). Further, if no firm has won the race, the robability that firm n (who invested k n at the starting time 0) will win the R&D race in the next infinitesimally small interval (t + dt) is h n dt. Hence, the unconditional robability that such a firm wins the R&D race over the interval (t, t + dt) is ex( H t) h n dt, and the resent value of the exected rents associated with such a victory euals v( ) ex( i t) ex( H t) h n dt. As of time 0, the resent value of the exected rents to firm n from winning the R&D race is the sum of the latter exression over all future infinitesimal time intervals. That is: (3) v ( ) ex( i τ) ex( H τ) h n dτ = v( ) h n /(i + H). 0 In addition to the lum-sum k n invested at time 0, R&D firm n will incur the recurrent cost l n until the race is over. The exected resent value of the recurrent costs is (4): τ (4) l n ex( iτ 0 ) dτ 0 ex( H τ ) H dτ = l n [ ex ( iτ )] i ex( H τ ) H dτ, = l n /(i + H). 0

13 The inner integral on the left-hand side of (4) reresents the resent value of the recurrent costs if the race finished at time τ, whereas the term [ex( H τ ) H dτ ] denotes the robability of such an event. The outer integral accounts for the fact that the race may finish at any time after the lum-sum investment is made. With exected returns and exected recurrent costs given by (3) and (4), resectively, firm n s exected rofits from investing k n at time 0 to articiate in the R&D race are: (5) V(k n, l n, H ( n) ; ) = v( ) h(k n, l n )/[i + h(k n, l n ) + H ( n) ] k n l n /[i + h(k n, l n ) + H ( n) ], where H ( n) Σ j n h(k j, l j ). The decision roblem for exected-rofit-maximizing R&D firm n consists of choosing the rest of the industry. Otimal values * k n and l * n so as to maximize V(k n, l n, H ( n) ; ), given the hazard rate H ( n) for first-order necessary conditions for the maximization of (5). * k n = k * (H ( n) ; ) and l * n = l * (H ( n) ; ) are obtained from the Euilibrium in the R&D Market Otimal lum-sum investment and recurrent costs for each of the R&D entrants are obtained as indicated in the receding subsection. Because firms are identical, euilibrium in the R&D industry is ostulated to be the symmetric Nash euilibrium. That is, the euilibrium otimal caital and labor levels for each of the N R&D firms must satisfy conditions (6) and (7): (6) k e = k * [(N ) h(k e, l e ); ], (7) l e = l * [(N ) h(k e, l e ); ]. Therefore, the euilibrium aggregate lum-sum investment and recurrent costs are given by K e = N k e and L e = N l e, resectively. Further, from (2), (6) and (7), the euilibrium aggregate hazard rate for the R&D industry is: (8) H e = N h(k e, l e ).

14 The euilibrium industry hazard rate H e reresents the euilibrium robability that the innovation will occur in the next unit of time. Alternatively, uantity /H e is the euilibrium average time that it takes to obtain the innovation. Given K e, L e, and H e, the resent value of the aggregate total exected R&D costs in euilibrium is K e + L e /(i + H e ). Welfare Analysis Let π e 0 ( ), e π ( ), and e μ, IPP = μ, right + μ π cost ( ) μ, IPP = μ denote farmers euilibrium rofits in cost country before the innovation, after the innovation but under IPP rights, and after exiration of IPP rights, resectively. Then, if the innovation occurred at time τ, the country s e e roducer surlus er unit of time would be zero u to time τ, [ ( ) π ( )] π + μ μ, IPP = μ, right e e from time τ until time τ + T, and [ ( ) π ( )] afterward. Discounting such π = μ μ, IPP changes u to time zero and adding them u yields the resent value of the roducer surlus if the innovation haened at time τ, which is the term within curly brackets in (9): τ + T cost 0 e e (9) ΔP = { [ π ( ) μ = + ( )], IPP μ, right μ π cost 0 ex( i τ 0 ) dτ 0 0 τ + τ + T e = μ π 0 ( )] ( cost 0 e [ π ( ) ex iτ ) dτ } ex( H e τ ) H e dτ, μ, IPP cost 0 0 = H i ( i + e H e ) e { π ) μ, IPP = μ, right + μcost ( [ ex( i T)] e + π ) μ, IPP = μcost e ( ex( i T) π ( )}. 0 The resent value of the exected country s roducer surlus due to the introduction of the imroved inut x (ΔP ) is comuted as in (9) because [ex( H e τ ) H e ] is the robability of the innovation occurring during the interval (τ, τ + dτ ). The exected country s consumer surlus due to the innovation (ΔC ) can be measured in a similar way. That is, define De 0 ( ), De ( ), and De μ IPP = μ right + μ cost () μ IPP = μ cost,,, 2

15 as country s euilibrium consumer rices for the cro before the innovation, after the innovation but under IPP rights, and after exiration of IPP rights, resectively. Then, if the innovation occurred at time τ, the consumer surlus er unit of time would be zero until time τ, De 0 ( ) De ( ) μ, IPP = μ, right + μcost D ( ζ ) dζ from time τ until time τ + T, and De 0 ( ) De ( ) μ, IPP = μcost D ( ζ ) dζ after time τ + T. Discounting and adding u such values yields the consumer surlus if the innovation occurred at time τ, shown as the term within curly brackets in (20): τ + T (20) ΔC = 0 τ = Q De 0 De ( ) ( ) μ, IPP = μ, right + μcost D ( ζ ) dζ ex( i τ 0 ) dτ 0 + Q τ + T = De 0 De ( ) ( ) μ, IPP = μcost D ( ζ ) dζ ex( iτ 0) dτ 0 ex( H e τ ) H e dτ, = H i ( i + e H e ) {[ ex( i T)] Q De 0 ( ) De ( ) μ, IPP = μ, right + μcost D ( ζ ) dζ Q + ex( i T) = De 0 ( ) De ( ) μ, IPP = μcost D ( ζ ) dζ }. Exression (20) takes into account the robabilities associated with the innovation taking lace at different times in the future. till another welfare measure is the euilibrium aggregate resent value of exected rofits for the R&D industry (RD). This can be comuted from (2): (2) RD = N V(k e, l e, (N ) h(k e, l e ); ]. That is, RD is calculated by aggregating (5) across the N R&D firms. 3

16 Public Investment in Agricultural R&D The R&D model discussed so far has ignored the imortance of ublic sector R&D, imlicitly considering rivate sector R&D as searable and additive to ublic R&D. However, there are reasons to be cautious about this assumtion. The ublic sector is often seen as a viable substitute for rivate sector research, and domestic governments and international organizations often fund ublic sector research on yield imrovements. In articular, the Consultative Grou on International Agricultural Research (CGIAR) suorts fifteen centers located throughout the world with a mission to foster agricultural growth through the rovision of ublic goods (see htt:// The uestion as to whether rivate research substitutes for, or comlements ublic research has been controversial. For examle, Wright and Pardey (2006) have shown that the bulk of ublic sector work on transgenic cros in develoing countries involve traits develoed in the U.. They also reort on a survey of stakeholders with interest in lant breeding in develoing countries indicating that U.. atents adversely affected their research. Graff et al. (2004) reort that inefficiencies in accessing intellectual roerty (e.g., legal costs and uncertain ownershi rights) aear to be hindering ublic sector research on some horticultural cros, an argument that can easily be extended to orhan cros in develoing countries. Another roblem that has received attention is the ossible reduction in the ublic sector s freedom to oerate due to existing atents on the research tools themselves (see, e.g., Binenbaum et al. 2003). The interaction between rivate and ublic sector R&D is imortant because, as ointed out by Evenson and Gollin (2003), many historically imortant genetic imrovement rojects in the develoing world were based on roductive lant tyes develoed in the North and then bred for location-secific traits in the outh. The literature discussed above suggests that rivate sector IPP when imroerly designed can hamer valuable ublic sector R&D, and in this case the additional value created by stronger rivate sector IPP will be offset by reduced effectiveness of ublic sector research. 4

17 The model introduced in the revious section can be modified to incororate ublic R&D investment. However, such an exercise reuires the secification not only of the ublic sector s R&D technology but also the ublic sector s objective function. Here, we assume that the ublic sector s technology is identical to the one used by the rivate sector, thus imlying that ublic R&D directly cometes with rivate R&D. As er the ublic sector s objective function, it is assumed that the ublic sector is exogenously mandated to use a roortion B of the total labor and caital used by the rivate sector in R&D, and (if successful in its R&D endeavor) to sell the innovation x at marginal cost. There are other ways of secifying the interaction between the ublic and rivate sectors, but these involve strategic interactions that would needlessly comlicate the model. The way we have aroached the issue is to assume that the ublic sector conducts R&D based on the same criteria as the rivate sector. For examle, both sectors will focus more on economically imortant cros that are secific to economically imortant growing areas. This assumtion sets u the ublic sector as a substitute for the rivate sector. We do not exlore the situation where the ublic sector is a comlement to the rivate one, as would be the case where the former does basic research and the latter alies such research. This comlementary research relationshi does not aear to be controversial. To incororate the ublic sector, the euations resented in the revious section that reuire modifications are re-secified below using the same numbers as before, but with an aostrohe. o for examle, the exected rofits to firm n from investing the lum-sum k n at time 0 in the resence of ublic R&D is reresented by euation (5 ) instead of (5): (5 ) V(k n, l n, K ( n), L ( n), H ( n) ; ) = v( ) h(k n, l n )/[i + h(k n, l n ) + H ( n) + h B ] k n l n /[i + h(k n, l n ) + H ( n) + h B ], where K ( n) Σ j n k j, L ( n) Σ j n l j, H ( n) Σ j n h(k j, l j ), and h B h[b (k n + K ( n) ), B (l n + L ( n) )] is the ublic sector s hazard rate. 5

18 Otimal values * k n = k * (K ( n), L ( n), H ( n) ; ) and l * n = l * (K ( n), L ( n), H ( n) ; ) are obtained from the first-order necessary conditions for the maximization of (5 ). In euilibrium, the otimal lum-sum investment and recurrent costs for each individual firm are given by (6 ) and (7 ), resectively, whereas the aggregate hazard rate is given by (8 ): (6 ) k e = k * [(N ) k e, (N ) l e, (N ) h(k e, l e ); ], (7 ) l e = l * [(N ) k e, (N ) l e, (N ) h(k e, l e ); ], (8 ) H e = N h(k e, l e ) + h(b N k e, B N l e ). Therefore, euilibrium aggregate lum-sum investment and recurrent costs can be calculated as K e = ( + B) N k e and L e = ( + B) N l e, resectively. The introduction of ublic-sector R&D affects the welfare analysis both directly and indirectly. The indirect imact stems from the changes in euilibrium lum-sum investments, recurrent costs, and aggregate hazard rate induced by the ublic-sector R&D, as given by (6 ) through (8 ) instead of (6) through (8), resectively. In essence, the ublic sector s indirect effect is due to the the exected time until innovation. In contrast, the ublic sector s direct imact arises from the zero-marku marginal-cost ricing of x when the ublic sector is the successful innovator. To see this, note that the unconditional exected country s roducer and consumer surluses can be exressed as (9 ) and (20 ), resectively: e e Nh ( k, l ) (9 ) ΔP = e H ΔP ( ) uccess=priv + e e h ( BNk, BNl ) H e ΔP ( ) uccess=pub, e e Nh ( k, l ) (20 ) ΔC = e H ΔC ( ) uccess=priv + e e h ( BNk, BNl ) H e ΔC ( ) uccess=pub. The terms ΔP ( ) uccess=priv and ΔP ( ) uccess=pub (ΔC ( ) uccess=priv and ΔC ( ) uccess=pub ) are the exected changes in country s roducer (consumer) surluses conditional on the successful innovator being resectively a rivate firm and the ublic sector, whereas the terms N h(k e, l e )/H e 6

19 and h(b N k e, B N l e )/H e are the corresonding robabilities. The exressions for ΔP ( ) uccess=priv and ΔC ( ) uccess=priv are like (9) and (20), resectively, excet for the aggregate hazard rate being given by (8 ) instead of (8). In contrast, the ublic sector s marginal cost ricing of x means that ΔP ( ) uccess=pub and ΔC ( ) uccess=pub must be comuted as (22) and (23), resectively: e (22) ΔP ( ) uccess=pub = { [ π ( ) 0 τ e μ = 0 π 0( )] ex( iτ 0) dτ } ex( H e τ IPP ) H e dτ,, 0 = H i ( i + e H e ) e [ ( ) μ = 0 e π π ( )],, IPP 0 (23) ΔC ( ) uccess=pub = 0 τ Q = De 0 De ( ) ( ) μ, IPP = 0 D ( ζ ) dζ ex( iτ 0) dτ 0 e( H e τ ) H e dτ, = e Q H e i ( i + H ) = De 0 ( ) De ( ) μ, IPP = 0 D ( ζ ) dζ, where the euilibrium aggregate hazard rate is defined by (8 ). To calculate exected changes in societal welfare, the introduction of ublic-sector R&D reuires consideration of the exected the surlus of the ublic R&D sector. Under the stated assumtions, the latter surlus consists simly of the (negative of the) sum of the ublicsector s lum-sum investment and the resent value of the ublic sector s recurrent costs until the innovation is obtained. In euilibrium, the ublic R&D sector s exected surlus is calculated as: (24) PU = B N [k e + l e /(i + H e )], where k e, l e, and H e are given by (6 ), (7 ), and (8 ), resectively. 7

20 imulation ecification and Parameterization We resort to simulations to analyze the imlications of technological sillovers and ublic research on euilibrium welfare and R&D. The simulations reuire secifying functional forms for each country s cro roduction and demand, and for the hazard rates of the individual R&D firms. Cro roduction functions under the traditional inut are ostulated to exhibit constant elasticity of substitution between inuts and decreasing returns to scale (so as to yield uwardsloing cro suly curves): (25) f (x 0, z ) = F {[ a / σ ( σ ) /σ x x 0 + ( σ ) / σ σ /( σ ) η /(+ η ) z ] }, where F > 0 is a scaling arameter, σ 0 is the elasticity of substitution between inuts x 0 and z, and η > 0 is the constant elasticity of cro suly. Parameter a x > 0 determines the share of total costs due to inut x 0, as the cost share euals a x The farm rofit function associated with (25) is: 0 /(a x w σ w σ 0 + r σ ). η (26) π 0 (, w 0, r ) η ( + η (+ η ) ) + + η F η (a x w σ 0 + σ r η /( σ ) ). Technology and rofits under the imroved inut (g (x, z ) and π (, w, r ), resectively) are straightforward to obtain from (25) and (26) by noting that g (x, z ) = ( + α ) f (x, z ). Cro demand is assumed to be isoelastic for each country, so that D ( ) = D ε, where D > 0 is a scaling arameter and ε > 0 is country elasticity of demand for the cro. Finally, the hazard rate function of each individual R&D firm is reresented by the decreasing returns to scale Cobb-Douglas technology h(k, l) = A K k κ L l κ, where A is a scaling arameter, and κ K > 0 and κ L > 0 are constants such that κ K + κ L <. Given the ostulated functional forms, simulating the model for Q countries entails secifying values for 2 Q demand arameters (ε and D ), 6 Q suly arameters and exogenous variables (η, σ, a x, F, α, r ), Q legal IPP arameters (μ,right ), and Q 2 transaction cost arameters (ζ j ). In addition, values must also be secified for the length of time during which 8

21 IPP rights are enforced (T), the interest rate (i), the cometitive disadvantage cost (μ cost ), the cost of roducing old seed (c 0 ) and new seed (c ), the roductivity of labor and caital in the R&D rocess (κ L and κ K ), the number of R&D firms (N), and the relative size of the ublic R&D sector (B). Therefore, to simlify matters, we restrict attention to simulations involving just Q = 2 countries with frictionless cro transactions (ζ j = 0) and identical arameters excet for imrovement factors (α ) and legal IPP arameters (μ,right ). Home denotes the country for which the new inut is develoed and Rest-of-the World (ROW) denotes the country receiving the technological sillover. Because of the frictionless transactions, in euilibrium consumer rices eual roducer rices for the cro. The arameterizations we use are based on those in Lence et al. (2005). The conclusions reached hold for a wide range of arameter values. For the urose of reorting results, the benchmark scenario with no ublic R&D (i.e., B = 0) was arameterized with η =.5, ε = 0.5, σ = 0.3, cost share = 0 ercent, T = 20 years, i = 0 ercent er year, μ cost = 0, κ K = κ L = 0.4, N = 5 firms. Other arameters of the model are normalized to unity; these are the rice of other inuts (r), and the cost of roducing old seed (c 0 ) and new seed (c ). imulations were conducted by fixing the home country s imrovement factor at α Home = 0 ercent and allowing for sillover levels from the home country to ROW (s ROW α ROW /α Home ) to vary between s ROW = 0 (i.e., no sillover) and s ROW = (i.e., full sillover). To exlore the effects of legal IPP, simulations were erformed for a large range of feasible legal IPP values in the home country (μ Home,right ), and ROW was assumed to either have no legal IPP (i.e., μ ROW,right = 0) or to have the same level of legal IPP as the domestic country (μ ROW,right = μ Home,right ) (i.e., the latter scenario reresents harmonized legal IPP). The effect of ublic R&D was examined by running simulations with B ranging from 0 to (note that B = means that ublic lum-sum investment and recurrent costs in R&D are eual to the aggregate of the analogous rivate R&D exenditures). 6 In the reorted simulations, the home country and ROW were assumed to have identical market shares in cro roduction and consumtion. 7 Comrehensive sensitivity analyses of alternative arameterizations were erformed, in articular regarding market shares and 9

22 elasticities. The results were ualitatively very similar to those that are shown in the figures below, aart from some obvious differences in scaling. Results and Discussion The main results from the simulations are summarized ictorially in figures through 8, which reort exected welfare changes for a range of sillovers and legal IPP levels in the home country. Panels A and B of figures through 4 show resectively results for the scenarios without and with ublic R&D (i.e., B = 0 and B = ). Figures -8, 3, 5, and 6 corresond to the base scenario with no legal IPP in ROW, whereas figures 9-2, 4, 7, and 8 reresent the base scenario under harmonization (i.e., where the legal IPP in ROW is the same as in the home country). These two alternative scenarios are discussed next. No Legal IPP in ROW Figure.A shows the resent value of the exected consumer surlus in the home country, under a range of legal IPP levels in the home country and sillover coefficients from the home country to ROW. The grah shows that home consumers always benefit from strictly ositive aroriability (μ Home,IPP > 0). When there is no sillover (s ROW = 0), the welfare of the home consumers increases with additional aroriability u to a value of about μ Home,IPP =.4. This increase in consumer welfare occurs because increased legal IPP encourages R&D, and R&D reduces the cro rice as the new technology enhances the outut of farmers in the home country. The reduction in consumer welfare change after this maximum oint occurs because the owner of the new technology catures more and more of the benefits associated with it, leaving less room for a reduction in cro rices. However, at even higher legal IPP levels (μ Home,IPP 2.), rent extraction by the owner of the new technology is restricted by the ossibility of home farmers reverting to the old technology. Hence, the welfare increase of home consumers reaches a lateau. 20

23 As the sillover level is increased from s ROW = 0 to s ROW =, the level of aroriability that maximizes the consumer welfare increases as well. The logic behind this result is that full sillover allows ROW farmers to take full advantage of the new technology, but the absence of any legal IPP in ROW means that the owner of the technology cannot cature any benefit from its use by ROW farmers. In this situation, the leakage of rents associated with the sillover reduces the ability of R&D firms to cature the benefits associated with the new technology from all of those who use it. This means that less R&D is done than is otimal from the consumers standoint. This rent leakage can be artly offset by increasing the legal IPP level in the home country. Consumer welfare in the home country increases monotonically with the level of sillover. Consumers gain from additional cro outut and when R&D conducted in the home country leads to additional outut from ROW, consumers benefit regardless of their location. The welfare resonse surface of ROW consumers is not shown because it is identical to the one shown for the home country. This is true because consumers in the home country and ROW are assumed to have the same share of world consumtion (50 ercent share for each country) in the baseline scenario, and all consumers are assumed to face the same rices regardless of where they live. In general, consumer welfare is greatest whenever sillover is highest and for aroriability μ ROW,IPP 2. From the consumers ersective, a large amount of sillover increases the case for high legal IPP in the home country. This is true because higher aroriability in the home country encourages R&D, and this enhances not only the roduction caability of home farmers but also that of farmers in ROW. As ROW has no legal IPP, ROW farmers do not have to ay any rents to the innovator. In turn, this allows ROW farmers to offer their outut to all consumers at a lower rice. Figure 2.A shows the R&D industry s welfare surface. This surface is from the same set of simulations used to generate the consumer surface described above, and again the shae of this surface is insensitive to alternative arameterizations. tarting with a sillover of s ROW = 0, the welfare of R&D firms increases in the home country s level of aroriability, but this 2

24 resonse flattens when the level of legal IPP exceeds μ Home,IPP = 2.. This flattening occurs because farmers in the home country always have the choice of reverting to the unimroved breed or variety, and this otion limits the monooly ricing ower of the successful R&D firm. The welfare of the R&D industry falls as sillover grows. By assumtion, the successful R&D firm cannot cature any rent from ROW roducers. illovers allow ROW farmers to cature market share from home roducers, because home farmers must ay a remium for the imroved seed that is not charged in ROW. As this the cometitiveness of home farmers decreases the relative size of their cro, it reduces the ability of R&D firms to cature rents from them. In other simulations that are not reorted here, the degree to which the welfare of R&D firms falls with resect to the sillover coefficient increases as the elasticity of suly increases, and as demand becomes more inelastic. However, the degree to which the welfare of R&D firms falls with resect to the sillover is not monotonic in the outut share of ROW; the fall is largest when ROW s baseline outut share is 50 ercent. Figure 3.A shows the welfare change surface for roducers in the home country under the same arameters as the consumer and R&D surluses described above. tarting with a sillover of s ROW = 0, we see that roducers in the home country benefit slightly from increased legal IPP u to the oint μ Home,IPP =.3. This increase in roducer welfare is surrising because we assume an inelastic demand (ε = 0.5). One would normally exect roducers to lose from outward shifts in the suly curve when demand is inelastic. The result comes about because aroriability increases R&D that enhances the technology available to farmers in the home country, but has no direct imact on the technology available to ROW roducers. Therefore, such R&D allows farmers in the home country to cature market share from roducers in ROW. However, when we introduce even small amounts of sillovers (e.g., s ROW 0.2), the ositive link between legal IPP and the welfare of roducers in the home country is broken. Producers in the home country are generally worse off when aroriability is high and sillovers are greatest. The welfare 22

25 change surface of ROW roducers (see figure 4.A) looks like a mirror image of the welfare change surface for roducers in the home country. Figures 5.A and 6.A show the changes in roducer welfare with a much higher demand elasticity (ε =.5), and all other arameters at the levels used for figures 3.A and 4.A. These results are very similar to those shown in figure 3.A and 4.A, resectively, desite the large the demand elasticity. This result suggests that under a wide range of arameters, roducers in the home country lose from legal IPP when sillover is ositive. Figure 7.A shows the total surlus for the home country under the same set of arameters as used in figures.a through 3.A. Total welfare in the home country increases with the legal IPP level u to a oint, and eventually flattens out as R&D firms are allowed to cature rents. Total welfare in the home country achieves its maximum when aroriability euals μ Home,IPP =.6 and sillover is s ROW = 0. However, the total welfare of the home country is relatively insensitive to the level of sillover. This is true because losses to home farmers and R&D firms caused by large sillovers are offset by gains to home consumers. The socially otimal level of legal IPP in the home country is slightly larger as the level of sillover increases. The aggregate welfare change surface for roducers, consumers and R&D firms in both countries are deicted in figure 8.A. World welfare rises monotonically with sillovers. Further, excet for small sillovers (s ROW 0.3), world welfare also rises monotonically with the level of aroriability in the home country u to the oint where the ability of R&D firms to cature the benefits of the research is limited by the ability of the home farmers to revert to the unimroved technology. The results resented above suggest that as sillovers increase, the welfare of both roducers and R&D firms in the country with strong legal IPP falls. This clearly acts as a disincentive for roducers to suort stronger IPP and encourages both R&D firms and roducers to work to reduce sillovers. This is unfortunate because world welfare increases with sillovers and it also increases in legal IPP u to a oint. An obvious uestion is whether 23

26 harmonizing legal IPP levels across countries yields a more desirable outcome. Harmonization might occur via multilateral agreement or by usage of GURTs. It is imortant to note, however, that the resent analysis imlicitly assumes that sillovers are indeendent of IPP in the two countries. This may not be the case, esecially in ROW. As Zilberman et al. (2004) show, lower IPP may lead to less effort to introduce traits of various local varieties, thus reducing the gain from the new technology. This may be interreted as a reduction of the sillover, suggesting that only some areas of the sillover-ipp sace are realistic and thus rovide useful information. Harmonized Legal IPP When we conduct welfare comarisons under harmonized legal IPP, the R&D industry benefits from both sillovers and aroriability under all arametric assumtions. This result makes sense. R&D firms benefit when they are allowed to collect rents in both countries, and the rents they obtain from ROW roducers deends on the relevance of the research (i.e., the sillover) to them. Under harmonized IPP the R&D firms have a much greater incentive to conduct research relevant to ROW roducers and, as a result, world welfare and ROW welfare under harmonized IPP are greater than when ROW does not rovide legal IPP. Figures 9.A and 0.A show roducer surlus in the home country under inelastic and elastic demand, resectively. Unlike the scenario without legal IPP in ROW, home roducers now benefit from both legal IPP and sillovers (u to a oint that deends on the demand elasticity). The welfare maximizing outcome for home roducers occurs when legal IPP is μ Home,IPP = and sillover euals s ROW = 0.5 for the inelastic demand case. For the scenario with elastic demand (not shown), maximum home roducer surlus is achieved for μ Home,IPP =.4 and s ROW = 0.7. Producer surlus in ROW for inelastic and elastic demand is deicted in figures.a and 2.A, resectively. These grahs are crucially different from the ones corresonding to no IPP in ROW, in that ROW roducer surlus does not increase monotonically with sillovers. Indeed, 24

27 ROW roducer surlus is minimized at the same legal IPP and sillover levels at which home roducer surlus is maximized. The roducer surlus results under harmonization are counterintuitive. Figures 9.A and 0.A suggest that home roducers would sometimes favor research that is of some relevance to ROW roducers over research that has no sillovers at all. Analogously, figures.a and 2.A indicate that ROW roducers would sometimes refer R&D that does not sillover to them rather than R&D that can be of some use to them. The answer to this uzzle is that if neither the legal IPP level nor sillover is too high, the successful R&D firm is able to extract all otential rents from ROW roducers, but it cannot do the same with the farmers in the home country. At these levels of aroriability and sillover, the new inut has a ositive imact on ROW outut technology, but this imact is smaller than the new inut s effect on the home country outut technology. The R&D firm is able to charge ROW farmers a rice that leaves them indifferent between the old and the new inut, but it cannot do the same with the home country farmers (because the legal IPP is not strong enough to allow it). ince exected rents to R&D from ROW increase with sillovers and because these rents rovide incentives to invest in R&D, the resulting R&D can be exected to end u benefiting farmers in the home country at the exense of ROW roducers when sillovers are in an aroriate range, as home roducers gain market share at the exense of ROW farmers. Comarison of roducer surluses in the home country and ROW shows that, regardless of the level of legal IPP, farmers in both countries exerience the same level of welfare when there is full sillover (s ROW = ). This is to be exected, as the research is of eual relevance to roducers in both countries, and roducers in both countries ay an identical amount for it. Obsolescence of the Innovative Inut In real-world situations, the effective length of rotection enjoyed by the develoer of x in country is likely to be eroded or eliminated altogether by the introduction of an even more roductive new inut x 2 with α 2 > α. 8 This suggests that the sensitivity of cross-country welfare 25

28 calculations to the effective duration of rotection needs to be assessed. To this end, the basic model can be generalized to allow inut x to become obsolete T,obsol years after its introduction. This can be achieved by setting the effective length of rotection in country as T min(t,obsol, T right ), where T right denotes the life of the atent. This imlies that the develoer of inut x is able to extract monooly rents for the entire life of the atent if the latter exires before x becomes obsolete (T right T,obsol ). Otherwise (T,obsol < T right ), the innovator only enjoys monooly rents over the eriod [t, t + T,obsol ], and receives no rents thereafter. The discussion above imlies that, if time until obsolescence is taken as exogenous, olicy-makers can enhance innovators incentives by increasing the length of the atent only u to the oint where T right = T,obsol. Beyond that oint, increasing T right has no effect and the only means to affect the incentives to innovate is through the IPP aroriability level μ IPP. To exlore the uantitative and redistributional effects of time until obsolescence, the original scenarios were re-estimated using the same length of atent life as before (T right = 20 years), but letting the innovation become obsolete considerably before the exiration of the atent (T,obsol = 6 years). Early obsolescence has two main effects that are illustrated by means of figures 3.A and 4.A. Figure 3.A (4.A) deicts the the resent value of the home country consumer (roducer) surlus under no legal IPP (harmonized IPP) in ROW and is analogous to figure.a (9.A). The first effect consists of a ceteris aribus significant reduction in the magnitude of the changes in welfare, clearly illustrated by the smaller scale of the vertical axis in figures 3.A and 4.A relative to figures.a and 9.A, resectively. The second effect is to render the changes in welfare more monotonic in the IPP level. For examle, in figure.a without sillovers increasing the level of IPP beyond a certain level translates into reduced consumer welfare, but no such reduction is observed in figure 3.A. The exlanation for both effects is that, for any given level of IPP, early obsolescence revents the successful innovator from extracting as much rents as it would otherwise. Imortantly, figure 4.A shows that the non-monotonicity of the home-country roducer surlus with resect to sillovers is robust to obsolescence. 26

29 Gradual Adotion of the Imroved Variety Another asect that may be deemed unrealistic about the advocated model is that it assumes that the innovation is adoted immediately, whereas in the real world it tyically takes some time for innovations to diffuse. lower rates of adotion by otential users reduce the innovator s rents, roviding smaller incentives to erform R&D. Therefore, other things eual, the longer it takes for an innovation to diffuse, the greater the otential relevance of the IPP level. Denoting by ϑ τ [0, ] the roortion of farmers in country willing to adot the innovation τ eriods after the latter is introduced, the imact of gradual adotion was assessed by conducting simulations with ϑ Home,τ = ϑ ROW,τ = 0 for τ [0, 0.5), ϑ Home,τ = ϑ ROW,τ = /6 for τ [0.5,.5), ϑ Home,τ = ϑ ROW,τ = /2 for τ [.5, 2.5), ϑ Home,τ = ϑ ROW,τ = 5/6 for τ [2.5, 3.5), and ϑ Home,τ = ϑ ROW,τ = for τ To save sace, grahs for the simulations with gradual adotion are omitted, as they are almost undistinguishable from the lots corresonding to immediate adotion excet for the scale of the welfare changes. Comared to immediate adotion, gradual adotion reduced the absolute magnitudes of the welfare changes by around 30 ercent to 40 ercent. Imortance of illovers for Policy The results resented above suggest that if the level of sillover is a choice made by the R&D comanies, then low IPP in develoing counties will result in fewer high-sillover innovations. However, if the degree of sillover is random and large, as aears to have been the case for hybrid cros, Iowa dent corn and transgenic cros, then roducers in ROW benefit from weak IPP in their country and strong IPP in the home country, as do consumers in ROW (figure.a). This result may exlain why some countries are reticent to imose strong IPP. World welfare is enhanced by strong ROW IPP in both the deterministic sillover and random sillover cases, which motivates the international focus on harmonization. Further, in the case of random sillovers it may even justify comensation to ROW countries to encourage them to adot stronger IPP. 27

30 Results with a Public ector Figures.B through 4.B show that the shae of the welfare surfaces with a ublic sector sending as much on R&D as the rivate sector is similar to those for the rivate sector alone. Two major results from these simulations. First, the ublic sector essentially dilutes the market ower of the rivate sector and this eliminates the area of the charts where increased IPP causes reduced consumer and societal welfare. econd, the welfare level is influenced by the existence of the ublic sector. ecifically, the amount of consumer surlus is tyically 2 ercent greater with a ublic sector (without taking into account the tax burden created by the ublic sector exenditures in R&D). The resence of ublic sector research reduces the amount of rivate sector research, so that aggregate R&D is aroximately the same on both scenarios. However, because (if successful) the ublic sector sells the innovation at marginal cost and without marku, consumers gain as more roducers adot and as these roducers ass along lower inut costs to consumers. Exected rofits of the R&D sector fall by aroximately 50 ercent, as one might exect given that half of the aggregate R&D activities are erformed by the ublic sector. Producer surlus is almost identical under both the rivate and the ublic/rivate scenarios. With the same amount of aggregate research being erformed, the exected imact on the roducer comes via the lower cost of seed from the ublic sector. But in euilibrium, roducers ass most of this lower cost on to consumers. World surlus is very similar under the rivate sector when comared to the ublic/rivate sector scenario, as gains by consumers are offset by reduced rofits to the rivate R&D sector and the taxes levied to suort ublic R&D (see Figures 5 through 8). ummary and Conclusions The rovision of intellectual roerty rights in agriculture has gained increased attention as governments have attemted to stimulate rivate sector research and because the recent (as yet to be commercialized) develoment of GURTs makes it ossible for the rivate R&D sector to rotect farmers from growing future generations of the imroved variety. The welfare 28

31 imlications of increased rotection of intellectual roerty in agriculture are different from those in the rest of the economy because the customer for the imroved roduct is a farmer who uses the technology to roduce a final roduct that is then sold into cometitive markets. A key contribution of the model resented here has been the acknowledgement that in many instances the technology used in agriculture is subject to sillovers. For examle, imrovements to the genetic comosition of lants and animals develoed in one country are often catured to some extent by roducers in other countries. This fact has some imortant imlications for welfare analysis and for olicy rescritions on where the burden of aying for the research should lie. We have aid articular attention to the realistic case where some countries rovide legal rotection for intellectual roerty, while other countries do not offer such rotection. The model is designed to relicate the incentive structures and institutions that exist in the seed sector and we focus only on results that are robust across changes in key arameters. We have also worked with several different formulations of the model resented here and again we focus only on those results that were robust across model formulations. However, we acknowledge that, as with any formalized model, one should carefully evaluate the degree to which the model accurately reflects the real word before using the results to evaluate olicies. In general, world welfare rises as the amount of research sillover increases, and it increases u to an otimal oint in the level of intellectual roerty rotection (IPP) offered in countries that develo the new technologies. This otimal level of rotection also increases as sillovers increase because sillovers magnify the benefits of research. In all of the cases we examined, the relationshi between world welfare and the level of aroriability flattens at high levels of aroriability. Producers and consumers in countries with no legal IPP generally benefit from legal IPP in other countries so long as some reasonable level of sillover exists. Producers in countries with strong IPP almost always lose when sillovers exist, whereas consumers in the country rotecting intellectual roerty always gain from the existence of sillovers. Whether the latter gains are large enough to offset the former losses as sillovers increase deends on the relative 29

32 magnitudes of the sectors roducing and consuming the cro in the country with high legal IPP. When the cro roduction sector is of similar or greater size than the cro consumtion sector (i.e., when the country is an exorter of the cro), roducer losses tend to exceed consumer gains as sillovers increase. Producers and R&D comanies in countries with strong IPP lose from research that is of relevance to roducers in other countries. If roducers and R&D firms resond to this incentive and avoid research that might sill over, then world welfare falls. One solution is to harmonize legal IPP across countries via agreements or via GURTs. This rovides R&D firms with a strong incentive to conduct high sillover research and it gives roducers in research-oriented countries an incentive to suort IPP even if this sometimes sills over into other countries. When we add a ublic sector that conducts similar research to the rivate sector, consumers benefit (ignoring taxes aid to suort the ublic sector) and seed comanies lose. The net imact on total surlus is very small. However, the study focuses on the case where the ublic sector cometes with the rivate sector. Therefore, such conclusions need not aly to scenarios where ublic research is comlementary to rivate R&D, as when the ublic sector erforms basic research or does research on orhan cros. The latter are two examles of the many otentially fruitful extensions of the model resented here. 30

33 Notes. Note that the definition of μ,ipp, μ,right, and μ cost here is different from the definition of the arameters designed with similar notation in Lence et al. (2005). As it will become clear later, the former arameters are obtained by rescaling the latter arameters by the marginal cost of roducing x (c ). That is, Lence et al. s μ IPP, μ right, and μ cost are measured in dollars er unit of x, whereas μ,ipp, μ,right, and μ cost here are measured in units of marginal cost c. 2. Allowing for market ower unrelated to IPP in the x industry may significantly affect the results of the model. To illustrate this oint, consider the extreme case where the x industry consists of a monooly. Unlike the case of erfect cometition, the monooly scenario will result in R&D investment even if there is no legal IPP or cost advantage, rovided the new inut x allows the monooly to obtain greater rofits than sulying the old inut x 0. Indeed, conferring legal IPP in such a situation will not exert any imact whatsoever on the (monooly) incentives to innovate. In the real world, the R&D industry may have market ower for reasons other than IPP. However, to focus on the virtues and vices of granting monooly ower targeted at romoting innovation, we restrict attention here to the case of erfect cometition. The reason for this is that non-ipp market ower can be concetually distinguished from the IPP market ower and it can be legally challenged (e.g., by antitrust laws). 3. To make the roblem interesting, it is also assumed that c and c 0 are such that the imroved farm inut x reresents a Pareto imrovement over the standard farm inut x 0 (i.e., that Ω(x ) > Ω(x 0 ), where Ω(x ) denotes the welfare to society resulting from the use of x only, and Ω(x 0 ) is defined in an analogous manner). This reuires that the marginal cost of roducing x not be too large relative to the marginal cost of roducing x 0. The condition that c [ + max(α )] c 0 ensures that x is a Pareto imrovement over x 0, but it is more restrictive than necessary. 4. Note that μ cost is the same across countries. This assumtion is adoted to focus on the imact of differential levels of roerty rights (μ,right ) across countries and can be justified if, for examle, the costs of trading x in the absence of legal restrictions were negligible. 3

34 5. For analytical and numerical tractability, the hazard rate is assumed to be indeendent of state variables. Otherwise, the hazard rate and the recurrent R&D costs would vary with time. uch an assumtion is unrealistic in that the robability of a real-world firm develoing a new variety at any oint in time is likely to deend on its own (and ossibly the industry s) revious research activity. However, it does not invalidate our main conclusions because the study focuses on a static ex ante analysis, rather than on the evolution of the hazard rate and the recurrent R&D costs. For the resent uroses, the main imact of the hazard rate is through the exected time until discovery, whereas the hazard rate s evolution effect is only of second order of significance. In other words, the results from our model would be very similar to the results from a model with time-varying hazard rates calibrated to have the same exected time until discovery. 6. As ointed out in footnote 4 of Lence et al. (2005), changing ( + B) N exerts a scale effect and a cometition effect. Following their reasoning, attention is restricted to the cometition effect by setting A = [( B) N] K L + κ + κ, which may be interreted as normalizing the aggregate amount of fixed inut at unity. To see this, let the hazard rate have constant returns to scale by having A = φ κ K κ L, where φ is a fixed inut. Hence, the aggregate hazard rate is H = ( + B) N h(k, l) = Φ K κ κ K κ L K L L κ, where Φ ( + B) N φ, K ( + B) N k, and L ( + B) N l are the aggregate amounts of fixed inut, lum-sum investment, and recurrent costs, resectively. The advocated normalization consists of setting Φ =, so that φ = /[( + B) N] and A = [( B) N] K L + κ + κ. The rofits of the rivate R&D sector are therefore the returns to their corresonding share of the fixed factor N φ = /( + B). 7. Different outut (consumtion) market shares can be simulated by varying F Home and F ROW (D Home and D ROW ). caling factors are normalized so that F Home + F ROW = = D Home + D ROW. Hence, for examle, a 30 ercent outut (consumtion) market share for ROW is obtained by setting F ROW = An anonymous reviewer informed us that PVP data from EU countries suggests that only ercent of PVP certificates survive for more than five years, less than 30 ercent survive for more than 0 years, and less than 3 ercent survive for the full term of legal IPP rotection. 32

35 9. The ostulated ϑ τ values imly that, for examle, one year after the innovation, 6.7 ercent of roducers in both the home country and ROW adot x if it is more rofitable for them do so than using x 0, whereas the remaining 83.3 ercent of roducers are unwilling to adot the innovation and kee using x 0. 33

36 References Alston, J. M., and R. J. Venner The Effects of the U.. Plant Protection Act on Wheat Genetic Imrovement. Research Policy 3: American oybean Association AA eeks to End eed Piracy in Brazil. oybean Digest, Mid-March,. 2. Baumol, W. J., J. C. Panzar, and R. D. Willig Contestable Markets and the Theory of Industry tructure. New York: Harcourt Brace Jovanovich. Binenbaum, E., C. Nottenberg, P. G. Pardey, B. D. Wright, and P. Zambrano outh- North Trade, Intellectual Proerty Jurisdictions, and Freedom to Oerate in Agricultural Research on tale Cros. Economic Develoment and Cultural Change 5: Dixit, A. K A General Model of R&D Policy. Rand Journal of Economics 9: Evenson, R. E., and D. Gollin Assessing the Imact of the Green Revolution, 960 to cience 300: Goeschl, T., and T. wanson The Imact of Genetic Use Restriction Technologies on Develoing Countries: A Forecast. In R. E. Evenson, V. antaniello, and D. Zilberman, eds. Economic and ocial Issues in Agricultural Biotechnology. Wallingford, U.K.: CABI Publishing, Graff, G. D., B. D. Wright, A. B. Bennett, and D. Zilberman Access to Intellectual Proerty is a Major Obstacle to Develoing Transgenic Horticultural Cros. California Agriculture 58(2): Harhoff, D., P. Régibeau, and K. Rockett ome imle Economics of GM Food. Economic Policy 6: Lee, T., and L. L. Wilde Market tructure and Innovation: A Reformulation. Quarterly Journal of Economics 94: Lence,. H., D. J. Hayes, A. McCunn,. mith, and B. Niebur Welfare Imacts of Intellectual Proerty Protection in the eed Industry. American Journal of Agricultural Economics 87:

37 Loury, G. C Market tructure and Innovation. Quarterly Journal of Economics 93: Moschini, G., and H. Laan Intellectual Proerty Rights and the Welfare Effects of Agricultural R&D. American Journal of Agricultural Economics 79: chnef, R Genetically Engineered oybeans: Accetance and Intellectual Proerty Rights Issues I n outh America. Washington DC: Congressional Research ervice, CR Reort for Congress R2558. rinivasan, C.., and C. Thirtle Imact of Terminator Technologies in Develoing Countries: A Framework for Economic Analysis. In R. E. Evenson, V. antaniello, and D. Zilberman, eds. Economic and ocial Issues in Agricultural Biotechnology. Wallingford, U.K.: CABI Publishing, wanson, T., and T. Goeschl Genetic Use Restriction Technologies (GURTs): Imacts on Develoing Countries. International Journal of Biotechnology 2: Tongeren F. V., and D. Eaton The Case for Differentiated tandards in Plant Variety Protection. In R. E. Evenson and V. antaniello, eds. The Regulation of Agricultural Biotechnology. Wallingford, U.K.: CABI Publishing, Working Grou on Plant Genetic Resources for Food and Agriculture, Commission on Genetic Resources for Food and Agriculture, Food and Agriculture Organization of the United Nations (WG-FAO) Potential Imacts of Genetic Use Restriction Technologies (GURT) on Agricultural Biodiversity and Agricultural Production ystems. FAO, CGRFA/WG-PGR-/0/7, Rome, Italy. World Trade Organization (WTO) Agreement on Trade-Related Asects of Intellectual Proerty Rights. Available at htt:// (accessed February 4, 2007). Wright, B. D., and P. G. Pardey Changing Intellectual Proerty Regimes: Imlications for Develoing Country Agriculture. International Journal of Technology and Globalization 2:

38 Žigić, K Intellectual Proerty Rights Violations and illovers in North-outh Trade. Euroean Economic Review 42: trategic Trade Policy, Intellectual Proerty Rights Protection, and North-outh Trade. Journal of Develoment Economics 6: Zilberman, D., H. Ameden, G. Graff, and M. Qaim Agricultural Biotechnology: Productivity, Biodiversity, and Intellectual Proerty Rights. Journal of Agricultural and Food Industrial Organization 2(2), article 3. Available at: htt:// vol2/iss2/art3 (accessed February 4, 2007) 36

39 Present value of exected home country consumer surlus (ΔC Home ) illover A. Without ublic R&D (B = 0) Present value of exected home country consumer surlus (ΔC Home ) illover B. With ublic R&D (B = ) Figure. Present value of exected home country consumer surlus (ΔC Home ) for inelastic demand (ε = 0.5), in the absence of legal IPP in ROW 37

40 Present value of exected rofits for the R&D industry (RD) illover A. Without ublic R&D (B = 0) Present value of exected rofits for the R&D industry (RD) illover B. With ublic R&D (B = ) Figure 2. Present value of exected rofits for the R&D industry (RD) for inelastic demand (ε = 0.5), in the absence of legal IPP in ROW 38

41 Present value of exected home country roducer surlus (ΔP Home ) illover A. Without ublic R&D (B = 0) Present value of exected home country roducer surlus (ΔP Home ) illover B. With ublic R&D (B = ) Figure 3. Present value of exected home country roducer surlus (ΔP Home ) for inelastic demand (ε = 0.5), in the absence of legal IPP in ROW 39

42 Present value of exected ROW roducer surlus (ΔP ROW ) illover A. Without ublic R&D (B = 0) Present value of exected ROW roducer surlus (ΔP ROW ) illover B. With ublic R&D (B = ) Figure 4. Present value of exected ROW roducer surlus (ΔP ROW ) for inelastic demand (ε = 0.5), in the absence of legal IPP in ROW 40

43 Present value of exected home country roducer surlus (ΔP Home ) illover A. Without ublic R&D (B = 0) Present value of exected home country roducer surlus (ΔP Home ) illover B. With ublic R&D (B = ) Figure 5. Present value of exected home country roducer surlus (ΔP Home ) for elastic demand (ε =.5), in the absence of legal IPP in ROW 4

44 Present value of exected ROW roducer surlus (ΔP ROW ) illover A. Without ublic R&D (B = 0) Present value of exected ROW roducer surlus (ΔP ROW ) illover B. With ublic R&D (B = ) Figure 6. Present value of exected ROW roducer surlus (ΔP ROW ) for elastic demand (ε =.5), in the absence of legal IPP in ROW 42

45 Present value of exected home country surlus (ΔC Home + ΔP Home + RD + PU) illover A. Without ublic R&D (B = 0) Present value of exected home country surlus (ΔC Home + ΔP Home + RD + PU) illover B. With ublic R&D (B = ) Figure 7. Present value of exected home country surlus (ΔC Home + ΔP Home + RD + PU) for inelastic demand (ε = 0.5), in the absence of legal IPP in ROW 43

46 Present value of exected world surlus (ΔC Home + ΔC ROW + ΔP Home + ΔP ROW + RD + PU) illover A. Without ublic R&D (B = 0) Present value of exected world surlus (ΔC Home + ΔC ROW + ΔP Home + ΔP ROW + RD + PU) illover B. With ublic R&D (B = ) Figure 8. Present value of exected world surlus (ΔC Home + ΔC ROW + ΔP Home + ΔP ROW + RD + PU) for inelastic demand (ε = 0.5), in the absence of legal IPP in ROW 44

47 Present value of exected home country roducer surlus (ΔP Home ) illover A. Without ublic R&D (B = 0) Present value of exected home country roducer surlus (ΔP Home ) illover B. With ublic R&D (B = ) Figure 9. Present value of exected home country roducer surlus (ΔP Home ) for inelastic demand (ε = 0.5), under harmonized legal IPP 45

48 Present value of exected home country roducer surlus (ΔP Home ) illover A. Without ublic R&D (B = 0) Present value of exected home country roducer surlus (ΔP Home ) illover B. With ublic R&D (B = ) Figure 0. Present value of exected home country roducer surlus (ΔP Home ) for elastic demand (ε =.5), under harmonized legal IPP 46

49 Present value of exected ROW roducer surlus (ΔP ROW ) illover A. Without ublic R&D (B = 0) Present value of exected ROW roducer surlus (ΔP ROW ) illover B. With ublic R&D (B = ) Figure. Present value of exected ROW roducer surlus (ΔP ROW ) for inelastic demand (ε = 0.5), under harmonized legal IPP 47

50 Present value of exected ROW roducer surlus (ΔP ROW ) illover A. Without ublic R&D (B = 0) Present value of exected ROW roducer surlus (ΔP ROW ) illover B. With ublic R&D (B = ) Figure 2. Present value of exected ROW roducer surlus (ΔP ROW ) for elastic demand (ε =.5), under harmonized legal IPP 48

51 Present value of exected home country consumer surlus (ΔC Home ) illover A. Without ublic R&D (B = 0) Present value of exected home country consumer surlus (ΔC Home ) illover B. With ublic R&D (B = ) Figure 3. Present value of exected home country consumer surlus (ΔC Home ) for inelastic demand (ε = 0.5) and T,obsol = 6 years, in the absence of legal IPP in ROW 49

52 Present value of exected home country roducer surlus (ΔP Home ) illover A. Without ublic R&D (B = 0) Present value of exected home country roducer surlus (ΔP Home ) illover B. With ublic R&D (B = ) Figure 4. Present value of exected home country roducer surlus (ΔP Home ) for inelastic demand (ε = 0.5) and T,obsol = 6 years, under harmonized legal IPP 50

53 Present value of exected ublic sector surlus (PU) illover Figure 5. Present value of exected ublic sector surlus (PU) for B =, inelastic demand (ε = 0.5), in the absence of legal IPP in ROW 5

54 Present value of exected ublic sector surlus (PU) illover Figure 6. Present value of exected ublic sector surlus (PU) for B =, elastic demand (ε =.5), in the absence of legal IPP in ROW 52

55 Present value of exected ublic sector surlus (PU) illover Figure 7. Present value of exected ublic sector surlus (PU) for B =, inelastic demand (ε = 0.5), under harmonized legal IPP 53

56 Present value of exected ublic sector surlus (PU) illover Figure 8. Present value of exected ublic sector surlus (PU) for B =, elastic demand (ε =.5), under harmonized legal IPP 54