AGRICULTURAL COOPERATIVES AND COST-REDUCING R&D IN THE AGRI-FOOD SYSTEM

Transcription

1 AGRULTURAL OOPERATVES AND OST-REDUNG R&D N THE AGR-FOOD SYSTEM Konstantinos Giannakas Associate Professor Deartment of Agricultural Economics University of Nebraska-Lincoln 16 H.. Filley Hall Lincoln, NE Phone: (4) Fax: (4) kgiannakas@unl.edu Murray Fulton Professor Deartment of Agricultural Economics University of Saskatchewan 51 amus Dr Saskatoon, SK S7N 5A8 Phone: (36) Fax: (36) Murray.Fulton@usask.ca Paer reared for resentation at the American Agricultural Economics Association Annual Meeting, Montreal, anada, July 7-3, 3 orresonding author. oyright 3 by Konstantinos Giannakas and Murray Fulton. All rights reserved. Readers may make verbatim coies of this document for non-commercial uroses by any means, rovided that this coyright notice aears on all such coies.

2 1 AGRULTURAL OOPERATVES AND OST-REDUNG R&D N THE AGR-FOOD SYSTEM Abstract - This aer develos a sequential game theoretic model of heterogeneous roducers to examine the effect of cooerative involvement on rocess innovation activity in the agricultural inut-sulying sector. Analytical results show that the involvement of an oen-membershi cooerative in rocess innovation activity can be welfare enhancing and, thus, socially desirable. The resence of the co-o can increase the arrival rate of rocess innovations and roductivity growth while reducing the rice of agricultural inuts. The effectiveness of the co-o in innovation activity is determined by its initial market share and the size of the innovation costs. nnovation activity is a critical element of business conduct affecting the cometitiveness of firms, the arrival rate of innovations in the economy, roductivity growth and social welfare. The strategic interactions among innovating firms and their effect on innovating behavior have received considerable attention. n articular, the main focus of the economic literature on innovation has been on R&D cometition in a ure oligooly (i.e., a small number of rofit-maximizing, investor-owned firms (OFs)), and the consequence of this cometition for the structure of the market and the arrival rate of innovations (see Fudenberg et al; Grossman and Shairo; Sutton; Delbono; Aoki; and Malueg and Tsutsui. For Schumeterian models of innovation cometition see Aghion and Howitt (199, 1998); and Segerstrom, Avant, and Dinooulos). Desite the revalence of mixed markets where cooeratives (co-os) comete alongside OFs, the effect of cooerative organizations on innovation activity and the imact of this activity on the equilibrium market conditions have not been considered. While revious studies have focused on the strategic interaction between co-os and OFs and the role that co-os lay in ensuring a cometitive market, they have not considered the imact that the cooerative structure has on innovation activity in these mixed markets and the resulting imact of this activity on the rivals cost structure and ricing decisions. 1 1 A number of aers have examined the imact of agricultural cooerative involvement on rices and outut in an oligoolistic market. Tennbakk considers the effect of a fixed membershi marketing co-o on the equilibrium conditions of a ournot oligooly. Fulton and Giannakas examine an oen membershi consumer co-o that is involved in rice cometition in a model where consumers differ in their commitment to the co-o and an OF. Sexton models a rocessing co-o that cometes with an OF, where the co-o and the OF are satially searated. He considers both an oen and a closed membershi co-o and analyzes the equilibrium conditions under different conjectural variations of the cometing firms. Outut cometition between a co-o and an OF is also considered by Karantininis and Zago, while otterill imlicitly considers rice cometition between the two firms. None of these aers considered the innovation activity in the mixed oligooly, however.

3 The objective of this aer is to examine the role of co-os in rocess innovation activity and to determine the consequences of cooerative involvement for the innovation investment that is undertaken, the subsequent ricing behavior of the co-o and its cometitors, and the social welfare resulting from this cometition. Secifically, the aer examines the outcome of rocess innovation and rice cometition in a mixed duooly where an oen membershi co-o and an OF comete in sulying an inut to agricultural roducers. The oen membershi co-o is chosen for analysis because of its revalence among co-os and articularly among inut suly co-os (ook). To determine the imact of cooerative involvement on innovation activity, the case of a ure oligooly is also analyzed and used as a benchmark for the analysis (note that since underinvestment in innovation is a standard result when OFs engage in rice (Bertrand) cometition, the resence of a co-o has the otential to raise innovation activity). The aer also ays attention to the caital constraints that are tyically thought to exist in cooeratives and their effect on innovation activity and social welfare. The research reorted in this aer fills an imortant ga in the literature on innovation activity in mixed duoolies, which to date has focused on either labor-managed firms (LMFs) or ublic firms. Secifically, since oen membershi inut suly co-os have different objectives than a ublic firm or an LMF, the model of a co-o is likely to yield different outcomes. For instance, while ublic firms are tyically assumed to maximize total economic welfare (see, for examle, Poyago-Theotoky, Delbono and Denicolò, and the references therein), a co-o considers only the welfare of its members. As will be seen in this aer, the result is that the imact of a co-o on total innovation exenditures and the distribution of these exenditures between the cometing firms can differ from that of a ublic firm. Part of the reason for the lack of research on cooerative involvement in innovative activity is the view that co-os are largely concentrated in the vertical stages just before and just after the farm enterrise (Rogers and Marion). While suly and roduct handling co-os may not engage in new roduct innovation, they do engage in rocess innovation. For examle, HS ooeratives Refined Fuel Distribution system uses GPS technology to allow fuel orders to be automatically generated whenever a member s fuel tank level falls below a re-determined level (enex). Also on the suly side, Federated o-oeratives Limited has made major investments in an Efficient onsumer Resonse (ER) system designed to remove costs from each ste of the suly chain. One examle of ER is a cross-docking initiative in which suliers deliver their roducts to FL s food distribution centers where the roducts are then loaded directly onto FL s delivery trucks (Fulton and Gibbings). Of course, rocess innovation is not limited to suly co-os. A major marketing co-o, Ocean Sray, for instance, has worked with Microsoft to develo a Web-based retail audit solution running on Windows E-based handheld Ps (Microsoft).

4 3 n addition, an oen membershi co-o is likely to make different decisions than would a closed membershi co-o, as Sexton shows in his aer. Models of LMFs tyically assume closed membershi (see, for examle, Neary and Ulh, Okuguchi and references therein). As well, since LMFs utilize an inut sulied by their members (i.e., labor) to roduce a roduct sold downstream, LMFs are more akin to marketing and rocessing co-os than to the inut suly co-os examined in this aer (note that marketing and rocessing co-os are more likely to have closed membershi than are suly co-os, thus further strengthening the distinction between these two tyes of cooeratives). n the model of this aer, the oen membershi co-o behaves in a different manner than does an LMF. This different behavior results in art because the co-o s otimal innovation effort is unresonsive to that of the OF. The rest of the aer is organized as follows. The next section describes the methodological framework of this study followed by the develoment of a simle model of horizontal differentiation where agricultural roducers differ in the returns they receive from the use of inuts sulied by different agri-business firms. The aer then analyzes rice and innovation cometition between two rofitmaximizing OFs, followed by an examination of the effect of cooerative involvement on innovation activity, the ricing of agricultural inuts and the welfare of the grous. The section following examines the imlications for the analysis of caital constraints faced by co-os. Finally, the results are linked to the literature on innovation activity in mixed oligoolies before the concluding section of the aer. Methodological Framework The strategic interaction between the inut suliers in the ure and mixed oligooly cases is modeled as a two-eriod sequential game. n eriod 1, the two agri-business firms make their innovation investment decisions that allow them to make rocess innovations and reduce their (marginal) cost of roduction. n eriod, the (ost-innovation) roduction costs are fixed and the two rivals engage in rice cometition. Once the equilibrium rices have been determined, the agricultural roducers make their urchasing decisions observing the rices of the two inuts.

5 4 To avoid Nash equilibria involving non-credible strategies, the different formulations of the game are solved using backward induction (Gibbons) after deriving the roducer demands for the inuts sulied by the two firms, the ricing behavior of the two inut suliers is analyzed first, and the solution to their innovation investment roblem determines the subgame erfect equilibrium amount of innovation, ricing of the agricultural inuts, and farmers urchasing decisions and welfare. Producer Decisions and Welfare n analyzing the role of co-os in innovation activity, a distinct feature of this aer is that it relaxes the conventional assumtion of roducer homogeneity. nstead, farmers are ostulated to differ in such things as the location and quality of land, education, exerience, management skills, and the technology adoted. Farmer heterogeneity in terms of roduction factors is a key comonent in our model and catures the differences in the relative returns received by farmers from the use of inuts sulied by different firms. Secifically, consider a roducer whose net return deends on the agricultural inut that is urchased from an agri-business firm. t is assumed that two suliers Sulier and Sulier suly the inut. The net returns earned by the farmer deend on the inut emloyed in the roduction rocess. The returns differ because the nature of the inut sulied by the two firms is different and because the rices charged by the two firms may be different. As well, farmers differ in the benefits that they receive from a articular inut, since farmers differ in terms of attributes mentioned above. 3 To cature these elements, let a [, 1] denote the attribute that differentiates roducers. A roducer with attribute a has the following net returns function: (1) F F ( + a) Π µ f a unit of Sulier s inut is urchased F F [ + ( a) ] Π µ 1 f a unit of Sulier s inut is urchased 3 The framework for examining farmer heterogeneity develoed in this aer is similar to that found in both Sexton and Fulton and Giannakas. Sexton examines the situation where farmers differ in their geograhical location, while Fulton and Giannakas develo a model where consumers differ in their commitment to the co-o and OF.

6 5 where Π F and Π F are the net returns associated with unit outut roduction using the inut sulied by Sulier and Sulier, resectively; and are the rice of the inut sulied by Sulier and Sulier, resectively; F is the farm rice (net of all roduction costs excet for the inut) of the outut roduced by the farmer; and µ is a non-negative agronomic factor associated with the use of the inut rovided by the two suliers. eteris aribus, Sulier s inut is more suitable to the roduction rocess of farmers with large values of the differentiating attribute a, while roducers with low values of a refer the inut rovided by Sulier. To allow for ositive market shares for the two agri-business firms, it is assumed that µ is greater than or equal to the difference in inut rices (see equations (3) and (4) below), while, to retain tractability of the model, the analysis assumes that roducers are uniformly distributed between the olar values of a. 4 Each farmer roduces one unit of the farm outut and the choice of inut sulier is determined by the relationshi between Π F and Π F. Figure 1 illustrates the decisions and welfare of roducers. The downward sloing curve grahs the net returns when Sulier s inut is urchased, while the uward sloing line shows the net returns when Sulier s inut is urchased for different values of the differentiating attribute a (i.e., for different farmers). The intersection of the two net return curves determines the level of the differentiating attribute that corresonds to the indifferent roducer. The roducer with differentiating characteristic a given by: F F F F + µ () a : Π Π ( + µ a ) [ + µ ( 1 a )] a µ is indifferent between buying from Sulier and buying from Sulier the net returns from using these two inuts are the same. Producers located to the left of a (i.e., roducers with a [, a )) urchase from Sulier while those located to the right of a (i.e., roducers with a ( a, 1]) buy from 4 Note that this is a standard assumtion in the literature of horizontal and vertical roduct differentiation (see Shy).

7 6 Sulier. Aggregate roducer welfare is given by the area underneath the effective net returns curve shown as the (bold dashed) kinked curve in Figure 1. Since roducers are uniformly distributed with resect to their differentiating attribute a, the level of a corresonding to the indifferent roducer, a, also determines the share of farm outut roduced with the inut rovided by Sulier. The share of farm outut roduced with the inut rovided by Sulier is given by 1- a. Assuming fixed roortions between the inut and farm outut, a and 1- a give the market shares of the two inut suliers. By normalizing the mass of roducers at unity, the market shares give the roducer demands faced by Sulier, x, and Sulier, x, resectively (Mussa and Rosen). n what follows, the terms market share and demand will be used interchangeably to denote x or/and x. Formally, x and x can be written as: (3) (4) x x + µ µ + µ µ Benchmark ase: nnovation and Pricing Decisions in a Pure Oligooly Price ometition ( nd Stage of the Game) onsider now the otimizing decisions of two rofit-maximizing OFs that are involved in a Bertrand rice cometition (i.e., they choose their rices simultaneously). The roblem of each sulier is to determine the rice of the inut that maximizes its rofits given the rice of the other sulier and the roducer demand for its roduct. Secifically, Sulier i s roblem (where i, ) can be written as: max Π, (5) i ( ) ( i i ) i i c x

8 7 where c i reresents Sulier i s constant marginal cost of roducing its roduct. Recall that c and c are determined by the innovation decisions of the two inut suliers at the first stage of the game and are fixed when the two OFs choose their rices. Solving the inut suliers roblems shows the standard result that rofits are maximized at the rice-quantity combination determined by the equality of the marginal revenue and the marginal cost of roduction. Secifically, for any, Sulier s best-resonse function (i.e., the rofit-maximizing rice of Sulier ) is given by + µ + c. Similarly, for any, Sulier s best-resonse function is + µ + c. Solving the best resonse functions of the two suliers simultaneously and substituting and into equations (3) and (4) gives the Nash equilibrium rices and quantities for the two cometitors as a function of marginal costs of roducing the inut, c and c, and the agronomic arameter µ, i.e., (6) (7) (8) (9) x 3 + c µ 3 + c + c c 6µ x 3 + c µ 3 + c c + c 6µ The equilibrium rofits of the two suliers from selling their inuts are then equal to: (1) (11) Π Π ( + c c ) 18µ ( c + c ) 18µ

9 8 nnovation ometition (1 st Stage of the Game) At this stage, Sulier and Sulier seek to determine the otimal amount of innovation, t and t, resectively. Exenditures on rocess innovation at the beginning (1 st stage) of the game enable the two firms to reduce their marginal cost of roduction ( c and c ), which can affect the firms cometitiveness (and rofits) when they determine their rices in the nd stage of the game. The relationshi between the amount of innovation and the marginal costs of roducing the inut is given by: (1) ci ( ti ) ci βti where c i is Sulier i s (strictly ositive) marginal cost of roducing the inut rior to (and in the absence of) innovation activity (i.e., the ex ante marginal cost of roduction) and t. The arameter β reresents the effectiveness of innovation effort (i.e., the rate at which innovation effort is translated into rocess innovations for the two rivals). 5 For simlicity of exosition, β is normalized to equal 1. To close the model, we assume that innovation effort is costly for the two suliers with the innovation costs being an increasing function of the amount of innovation (Shy), i.e., i 1 (13) ( t ) ψt i i i where ψ is a strictly ositive scalar reflecting the size of innovation costs. The roblem of Sulier i at this stage of the game is the determination of innovation effort that maximizes its total rofits, T Π i (i.e., rofits from sulying the inut, Π i, minus innovation costs, i ), i.e., (14) max Π ti T i Π i 1 ψt i 5 While the assumtion of deterministic rocess innovations is adoted in this aer, the model can be easily modified to examine the case of stochastic innovations (when innovation effort affects the robability that certain roduction cost reductions will be realized). While consideration of stochastic innovations changes the results quantitatively, the qualitative nature of our results regarding the effect of cooerative involvement in innovation activity remains unaffected.

10 9 To rule out unrealistic corner solutions involving zero ost-innovation roduction costs for the two inut suliers, we assume that the innovation costs are such that t i < c i the firms otimal innovation efforts are below the level that reduces their roduction costs to zero. 6 Solving the otimality conditions for the two suliers, we derive their best resonse functions (i.e., the otimal amount of innovation as function of the other sulier s innovation effort) as: (15) + c c t t and 9µψ 1 (16) t 3 µ c + c t 9µψ 1 Solving simultaneously the best resonse functions of the two inut suliers we derive the Nash equilibrium levels of innovation in the ure oligooly as: 3ψ ( + c c ) (17) t 3ψ 3ψ ( c + c ) (18) t (19) T t t + t 3ψ 18µψx ( 9µψ ) 3ψ ( 9µψ ) 18µψx ( ) ( ) 9µψ 3ψ 9µψ 3ψ where + c c x and 6µ c + c x are the ex ante market shares of Sulier and 6µ Sulier, resectively, i.e., the market shares of the two suliers rior to (and in the absence of) the innovation activity in eriod c t can be shown that if ψ ψ +, then Sulier exerts maximum innovation effort, i.e., 9µ c + c results in c. Similarly, if ψ ψ +, Sulier s otimal innovation effort is 9µ c + + zero. n what follows we assume that ψ exceeds both ψ and ψ. t c, which t c and c falls to

11 1 omaring equations (17) and (18) shows that the relative innovation activity of the two inut suliers in the ure oligooly deends on their ex ante market shares which are determined, in turn, by the relative ex ante roduction costs. n articular, the firm with the lower costs of roduction at the beginning of the game, enjoys higher market share and invests more in rocess innovation activity, i.e., () c ( > ) c x ( < ) x t ( < ) t Equation () catures a standard result in the literature on innovation cometition, namely that a firm with an initial advantage eventually becomes a monoolist (see for instance Fudenberg et al and Aoki). Secifically, ut in a reeated interaction framework, equation () indicates that the firm with an initial cost advantage will enjoy an ever-increasing share of the market since it will undertake relatively higher rocess innovation activity which will further enhance its cost advantage and, thus, its future innovation activity relative to its rival. nnovation and Pricing Decisions in a Mixed Oligooly n this scenario Sulier is a cooerative that cometes with a rofit-maximizing OF (Sulier ). Price ometition in the Mixed Oligooly ( nd Stage of the Game) Similar to the ure oligooly case, the roblem of Sulier in the nd stage of the game is to determine the inut rice that maximizes its rofits given the rice of the other sulier and the roducer demand for its roduct. n fact, Sulier s roblem is the same as the one secified in equation (5) and the rice that maximizes its rofits is given by the equality of marginal revenues with marginal costs of roduction. + µ + c Thus, for any, Sulier s best-resonse function is given by. Unlike Sulier in the ure oligooly case, however, the objective of the co-o is to maximize the welfare of its members. Secifically, the roblem of the co-o is to determine the rice that maximizes the welfare of roducers that atronize the co-o at this stage of the game (shown by the shadowed area MW in Figure 1) subject to a non-negative rofit constraint, i.e.,

12 11 (1) max MW s. t. Π F (, ) ( ) c x 1 µ x where all variables are as reviously defined. Note that equation (1) catures the oen-membershi nature of the co-o since the co-o takes into account the welfare of all roducers that buy its roduct when determining its otimal strategy at this stage of the game. 7 Solving the co-o s roblem secified above shows that the otimality (Kuhn-Tucker) conditions for a maximum are satisfied when the co-o rices its roduct at marginal cost, i.e., MW is maximized when c. Solving the best resonse functions of the OF and the co-o simultaneously we derive the Nash equilibrium rices for the inuts, and. Substituting and into equations (3) and (4) gives the Nash equilibrium quantities for the two cometitors as a function of c, c, and µ. Mathematically, the Nash equilibrium rices and quantities in the rice cometition subgame are: 8 () (3) x + µ c + c µ + c c 4µ (4) c (5) x c + c 4µ The rofits of the two rivals from selling their inuts and the welfare of roducers atronizing the co-o are then equal to: 7 n an oen membershi co-o, membershi is endogenous in that the decision to join the co-o is u to the roducers the co-o cannot revent a articular roducer from joining. Since the decision to urchase from the coo is based on the relative returns obtained from urchasing the co-o s roduct or the OF s roduct, a member in this eriod is effectively anyone that urchases from the co-o. 8 t should be noted that even if the co-o considered only the welfare of a fixed grou of members when ricing its roduct at stage two, the otimal strategy would still be to rice the agricultural inut at marginal cost. The reason is that the total welfare of this fixed grou of roducers is maximized when the inut sulied by the co-o is riced at marginal cost. Thus, the equilibrium conditions at the ricing subgame are identical regardless of whether membershi is endogenously or exogenously determined.

13 1 (6) Π Π (7) ( µ + c c ) 8µ F (8) MW ( c ) x µ x Note that, when comared to the ure oligooly case, the co-o involvement reduces, and x, while increasing x and roducer welfare. This result holds for given costs of roduction c and c, however. f the cooerative involvement affects the otimal amount of innovation undertaken by the two suliers, it will also affect their cost structures. The next section examines how the co-o involvement affects c and c through the rocess innovation activity of the two suliers. nnovation ometition in the Mixed Oligooly (1 st Stage of the Game) At this stage the two suliers seek to determine the amount of innovation to reduce their cost of roduction. Maintaining the same assumtions regarding the structure and size of innovation costs (equation (13) and footnote 6) and the relationshi between the amount of innovation and the marginal costs of roducing the inut, we can determine the effect of cooerative involvement on innovation activity. Similar to the ure oligooly case, the roblem of Sulier (OF) is to determine the amount of innovation that maximizes its total rofits, i.e., (9) T max Π t Π 1 ψt n contrast, the roblem of Sulier (co-o) is to determine the innovation effort that maximizes the total welfare of roducers that are members of the co-o (i.e., atronize the co-o) at the time the investment decisions are being made (i.e., at the beginning of the game). While the co-o knows that its innovation activity will reduce the roduction cost (and rice) of its roduct and will attract new members to the co-o, the welfare of roducers who might find it otimal to atronize the co-o ex ost

14 13 (i.e., after the costly investment decisions have been made) is not accounted for by the cooerative. nstead, when the co-o determines its innovation effort at the beginning of the game (in eriod 1), it seeks to maximize only the welfare of roducers that atronize its activity at that oint in time. The assumtion that the co-o considers only its eriod one membershi reflects the roblem that oen membershi co-os have in getting future members to ay for innovation activities. As a number of authors have ointed out (see, for examle, ook, and Porter and Scully), the oorly defined roerty rights (e.g., the lack of tradable shares) in the oen membershi co-o make it difficult for the benefits of future members to be reflected in the decisions made today. n this aer, the model assumes that innovation activity is financed through a membershi fee levied on the existing membershi (see footnote 9). The imlication is that the future membershi cannot be used as a source of funds and consequently their welfare is not considered when innovation decisions are made. As will be seen, this inability of the co-o to fully internalize the benefits that will accrue to future members has imortant imlications for co-o s innovation effort. Formally, the roblem of the co-o can be exressed as: 1 T F (3) max MW MW ψt ( c ) x ψt t µ x 1 where c + c x is the ex ante market share of the co-o, i.e., the share of roducers that 4µ atronize the co-o rior to (and in the absence of) the innovation activity in eriod 1. 9 The best resonse functions of the two inut suliers are: (31) µ + c c t t and 4µψ 1 (3) t c + c 4µψ 9 As noted in the text, imlicit in this formulation of the co-o s roblem is the assumtion that the co-o funds its innovation activity through some sort of fixed membershi fee that is elicited at the beginning of the game and is irrecoverable (sunk) once incurred. An alternative formulation could be the one where the co-o incororates the innovation exenses into the rice of its roduct. n such a case, the rice charged by the co-o in the nd stage of the game equals the average cost of roviding its roduct (Ramsey ricing). onsideration of this ricing strategy of the co-o reduces the tractability of the analysis considerably, however.

15 14 Solving simultaneously the best resonse functions of the two suliers we derive the Nash equilibrium levels of innovation in the mixed oligooly as: 4 ( µ + c c ) ( c + c ) (33) (34) t t ( 4µψ + 1) x 1 ( ) ψ 4µψ 1 µψ 4µψ ( 4µψ 1) 4µψ x ψ c + c 8 ψ ( c + c ) (35) t T t + t µψ 4µψ x µ ( 4µψ 1) ( ) ψ 4µψ 1 where µ + c c x is the ex ante market share of the OF. 4µ omaring equations (33) and (34) shows that, similar to the ure oligooly case, the relative innovation activity of the two inut suliers deends on their ex ante market shares the firm with the greater market share at the beginning of the game will exert the higher innovation effort. Unlike the ure oligooly case, however, there is not a one-to-one corresondence between the ex ante market shares and the costs of roduction at the beginning of the game. n articular, even if the co-o has higher ex ante roduction costs, it can still invest more than the OF since, because of its ricing strategy, it can enjoy a relatively higher market share. Secifically, the relative innovation activity of the two rivals in the mixed oligooly is determined as follows: (36) c + µ ( > ) c x ( < ) x t ( < ) t c Put in a reeated interaction framework, equation (36) shows that if the initial cost difference ( c ) is greater (less) than µ, the result will be ever-increasing (-decreasing) cost differences between the two firms and an ever-decreasing (-increasing) market share for the co-o since the co-o will be investing less and less (more and more) in innovation activity relative to the OF.

16 15 The Effect of ooerative nvolvement on nnovation Activity After having determined the subgame erfect equilibrium conditions in the ure and mixed oligoolies, we can now examine the effect of cooerative involvement on innovation activity and the welfare of the grous involved (i.e., agricultural roducers and inut suliers). The effect of co-o involvement on the equilibrium amounts of innovation undertaken by the two agricultural inut suliers is shown grahically in Figure. Figure deicts the innovation reaction functions (best resonse functions) of the two inut suliers in the ure and mixed oligooly cases (equations (15), (16), (31) and (3)) when innovation costs are relatively high (see footnote 6). 1 t is shown that, when comared to the reaction function of the rofit-maximizing Sulier in the ure oligooly ( RF ), the reaction function of the co-o ( RF ) is x shifted outwards while rotating rightwards so that it becomes vertical at ψ i. At the same time, i cooerative involvement affects the rofitability of investment in rocess innovation by the OF. n articular, the resence of the co-o shifts the reaction function of Sulier i RF inwards along the t axis while rotating it rightwards relative to the reaction function of this same sulier when it cometes with another rofit-maximizing OF (i.e., i RF in Figure ). The outcome of these changes in the reaction functions is increased innovation activity of the co-o relative to Sulier in the ure oligooly, i.e., (37) t t > This result arises because, comared to an OF in the ure oligooly, the co-o internalizes the effect of reduced costs and rices (due to rocess innovation) on the welfare of its members, thus 1 Recall that when innovation costs are relatively low both suliers will exert maximum innovation effort and reduce their roduction costs to zero. This is true in both the ure and the mixed oligooly cases suggesting that, under these conditions, cooerative involvement does not affect the total amount of innovation in the market. However, even though the level of innovation activity in the mixed oligooly is the same as in the ure oligooly, the ricing strategy of the co-o reduces the rices of the agricultural inut and the rofits of the OF, while increasing the market share of the co-o, and the welfare of all agricultural roducers members and non-members of the co-o.

17 16 roviding the co-o with a greater incentive to innovate. Note that the vertical nature of effort of the co-o, i RF means that the member welfare-maximizing innovation t, does not deend on the innovation effort exerted by Sulier. The equilibrium innovation effort of the co-o is determined instead by its ex ante market share (i.e., the market share at the beginning of the game, x increase in x will result in increased ) and the size of the innovation costs, ψ. n articular, a ceteris aribus t. Since the innovation by the co-o is a strategic substitute to the innovation by the OF (recall the downward sloing i RF in Figure ), the increase in x will reduce the innovation effort of Sulier t ( < x - see equation (33)). omaring equations (17) and (33) shows that, when x exceeds µψ 5µψ ( 18µψ + 1) ( 1µψ + 3) 6 cometes with another OF, i.e.,, Sulier invests less in innovation when it cometes with a co-o than when it (38) ( < ) ( 18µψ + 1) ( 1µψ + 3) µψ x t > 5µψ 6 ( ) t increase in The decrease in t due to an increase in x ) indicating that an increase in x outweighs the increase in t (caused by this same x reduces total innovation activity in the mixed oligooly tt ( < x - see equation (35)). 11 Thus, the greater is the initial market share of the co-o, the lower is the total innovation activity of the two rivals. omaring equations (19) and (35) shows that when x 11 Total innovation activity falls with an increase in x because the co-o maximizes ex ante member welfare (i.e., the welfare of roducers that are members when the investment decisions are made) and does not internalize the effect of its innovation decisions on the welfare of roducers that find it otimal to atronize the co-o after the investment decisions are made (and the consequent cost and rice reductions have been realized). t can be shown that if the co-o was to maximize ex ost member welfare, total innovation activity in the mixed oligooly exceeds the one in the ure oligooly, i.e., t > t x (the results are available from the authors uon request). T T

18 17 exceeds 1 + µψ, total innovation activity in the mixed oligooly falls below that in the ure oligooly 3 indicating that cooerative involvement reduces the total innovation effort in the market, i.e., µψ (39) x ( > ) t ( < ) t 3 T T t is imortant to note that, while cooerative involvement can increase the amount of innovation undertaken by the inut suliers, it is not necessary that total innovation has to increase for farmers to benefit from the resence of the cooerative even if the total innovation effort falls in the mixed oligooly, roducer welfare can still increase in the resence of the co-o. n articular, as long as x is less than 3 ( 4 1) 1 + µψ + ψ µψ x, + c T tt t c < 3 (where c and c are the equilibrium costs of roduction of the two suliers in the ure oligooly case), the rice charged by Sulier falls in the mixed oligooly (i.e., < ) and, given that is also reduced, all roducers (members and non-members of the co-o) realize an increase in their welfare. n articular, (4) ( > ) ( 4µψ 1) 1 + µψ + ψ x c + c x tt tt > 3 3 ( > ) ( ) The effect of the cooerative involvement on the ricing of the agricultural inut is shown grahically in Figure 3 that deicts the rice reaction functions of the two inut suliers and the determination of the Nash equilibrium rices in the ure and mixed oligooly cases. Secifically, when Sulier is a co-o instead of an OF, its best resonse function ( RF ) is constant at c (i.e., it is not a function of the rice charged by Sulier ). For Sulier, a reduction in innovation effort in the mixed oligooly case (see equation (38)) increases its roduction cost and causes a arallel uward shift of its 1 Alternatively, exression (39) indicates that total innovation activity falls in the mixed oligooly (i.e., when ψ < 3 x 1. µ T t T t < )

19 18 best resonse function in the nd stage of the game (comare T tt t RF and RF in Figure 3). When c + c <, the outcome is the reduced rice of both inuts. 3 The reduction in the rices of both inuts increases roducer welfare by area PW in Figure 4, while the fact that the reduction in exceeds the reduction in results in a reduced market share of Sulier (OF) in the mixed oligooly case. Note that, due to the marginal cost ricing of the co-o and the reduced rice-cost margin of the OF in the mixed oligooly, the increase in farmer welfare exceeds the reduction in suliers rofits, indicating that the resence of the co-o increases total economic welfare in this market. However, increases in the mixed oligooly when + c T tt t c > 3. n this case, roducers that are not atronizing the co-o see a reduction in their welfare and they would be better off if an OF were to relace the co-o. The Effect of aital onstraints on ooerative nnovation The analysis of the mixed oligooly in the revious section examined a critical co-o feature, namely that its ownershi structure rovides it with a different objective function (i.e., the maximization of member welfare) than an OF. n addition to altering the objective function, the co-o s ownershi structure has other imlications for its innovation decisions. Due to its collective nature and to limitations on its members ability and/or incentive to rovide caital, a co-o might face caital constraints (haddad and ook). Proerty right and free-rider roblems might make internal financing difficult to attract 13 while the inability of external investors to exercise control over the co-o s assets might make external financing costly. The imact of the caital constraint roblem on the co-o s innovation decision can be examined using the framework of analysis develoed above. 13 For instance, while the otential for free-rider roblem exists (each member would like to see the other members make the investment while not having to make the investment themselves), all of the stage one membershi would be willing to make the investment if this is required of all members (since making the investment is beneficial to each member). Solving the roblem of how all members can be made to ay the fee that finances the innovation activity may be one of the reasons for the higher cost of caital faced by the co-o.

20 19 n articular, the difficulties that a co-o might have in raising caital for innovation activity can be examined by increasing ψ relative to ψ (where ψ and ψ are the arameters of the innovation cost function for the co-o and OF, resectively). That is, the caital constraint roblem can be viewed as a situation in which the co-o s effective cost of innovation has increased relative to that of the OF. Simly ut, the more binding is the caital constraint, the higher is the oortunity cost of caital, and hence the larger is ψ. Of course, the co-o s cost of innovation may be higher (or lower) than the OF for other reasons. n the analysis that follows, the examination of higher co-o innovation costs is used to cature the imact of the caital constraint roblem as well as any other factors that raise the co-o s cost of acquiring caital for innovation activity. The imlications of introducing differences in innovation costs between the co-o and the OF in our analysis are quite straightforward the greater are the innovation costs for the co-o, the lower are the otential roductivity and social welfare gains from the resence of the co-o. n articular, an increase in ψ causes a arallel inward shift of its innovation best resonse function ( RF in Figure ). 14 The outcome is reduced innovation activity by the co-o and this reduction outweighs the increased amount of innovation undertaken by the OF because the absolute value of the sloe of i i RF is less than 1. Thus, increased innovation costs of the co-o reduce the total innovation activity in the market the greater are the innovation costs of the co-o, the lower is the total amount of innovation undertaken by the two rivals. The reduction in the co-o s innovation due to higher innovation costs increases its cost of roviding the inut, c, and thus, the rice faced by agricultural roducers,. Grahically, the increased rice of the co-o can be seen as a rightward shift of the co-o s rice reaction function in Figure 3. Since the OF s rice reaction function, RF is a strategic comlement to the rice charged by the OF), the increase in RF, is uward sloing (i.e., the rice of the co-o causes to also increase, 14 Note that when innovation costs differ between the two rivals, the best resonse functions of the OF and the coo can be derived by substituting ψ and ψ for ψ in equations (31) and (3), resectively.

21 albeit to a lesser degree. 15 This greater increase in results in a reduced market share of the co-o, while the fact that both the OF s and the co-o s rices increase means that all roducers lose when coo s innovation costs rise. Relative to the ure oligooly outcome of innovation cometition, it can be shown that when the co-o s innovation costs are above a critical level ψ x 3ψ µψ ( µψ 1) ( 3x 1) 1 x, the total innovation activity in the mixed oligooly falls below that in the ure oligooly (i.e., T t T t < ). As long as the innovation costs are below ψ xx µψ 3ψ ( µψ 1) ( 3x 1) 1 ψ ( 4µψ 1) x x, however, + c T tt t c < 3, and both the OF s and the co-o s rices will fall in the mixed oligooly (see Figure 3), i.e., cooerative involvement increases the welfare of all agricultural roducers when ψ <ψ xx. 16 However, if ψ exceeds ψ xx, then increases in the mixed oligooly and roducers that are not atronizing the co-o see a reduction in their welfare. Thus, if the co-o s innovation costs are sufficiently large, some of the roducers would be better off if a lower-cost OF were to relace the co-o. nterreting the Results: A Link to the Literature Before concluding the aer, it is useful to comare and contrast our findings with the results of the literature on innovation activity in mixed oligoolies mentioned in the introductory section of the aer. n articular, this section focuses on total innovation exenditures in the mixed duoolies, on the distribution of R&D exenditures between the cometing firms, and on the ability of firms that ursue objectives other than rofit-maximization to effectively comete with an OF. 15 The increase in is less than the increase in for two reasons. First, the sloe of RF is less than 1 and, second, the increased innovation activity of the OF reduces c and, thus, the intercet of RF in Figure Exressed in terms of the initial market share of the co-o, the results show that total innovation falls in the mixed T t T oligooly (i.e., t < ) when x > 3ψ ( 1+ µψ ) ψ [ µ ( ψ ψ ) + 1] however, inut rices fall in the resence of the co-o (since t. As long as [ ] x ( 1 + µψ ) ( ) + ψ 4µψ 1 x < 3ψ [ µ ( ψ ψ ) + 1] T tt c + c < 3 ψ ) and roducer welfare rises.,

22 1 Similar to Poyago-Theotoky, who finds that the introduction of a ublic firm leads to a reversal of the underinvestment in R&D that occurs in a ure oligooly, the analysis in this aer shows that the introduction of a co-o can also lead to increased R&D activity, roviding certain conditions are met (see equation (39)). The basic result that R&D sending can increase follows directly from the somewhat similar objective functions of the ublic firm and the co-o (each incororates the welfare of at least some of those consuming the good). n Poyago-Theotoky s model, the fact that the ublic firm fully internalizes the costs and benefits of R&D activity means that total R&D sending always increases. 17 n the model of this aer, however, an increase in total R&D sending does not always occur. The reason is that the oen membershi co-o can only artially internalize the costs and benefits of innovation, thus underscoring the imortance of modeling this secific organizational attribute. This artial internalization occurs because the membershi that funds the innovation activity ex ante is less than the grou of roducers that benefit from the innovation. As mentioned reviously (see footnote 11), innovation activity will always increase if the imact of innovation on the ex ost membershi is fully accounted for when the innovation decisions are being made. Like Poyago-Theotoky, this aer also shows that the co-o invests more than its OF counterart does in the ure oligooly (see equation (37)). Unlike the OF that reduces its innovation activity when cometing with a ublic firm however, an OF cometing with a co-o can either increase or decrease its innovation activity relative to the ure oligooly case (see equation (38)). Finally, similar to the case examined in Poyago-Theotoky, an increased investment by the co-o in the mixed market crowds out OF investment. Because the co-o more fully internalizes the benefits of innovation than does an OF oerating in the same market, the co-o will exert higher innovation effort than its OF counterart rovided that the (roduction and innovation) costs of the two firms are the same (see equation (36)). Since the rival s innovation is a strategic substitute to the rofit-maximizing innovation of the OF in both this 17 n Poyago-Theotoky s model, the underinvestment in R&D in the ure duooly case results because each firm can easily imitate innovations discovered by the other firm. When innovations are not easily imitated and firms engage in a atent race, the ure duooly results in over investment. Under these circumstances, Delbono and Denicolò show that a ublic firm can result in reduced R&D exenditures, again because the ublic firm more fully internalizes the costs and benefits. See Beath et al. for a general model of these results for the ure duooly case.

23 aer and in Poyago-Theotoky s aer, an increase in innovation activity by the co-o/ublic firm results in reduced exenditures by the OF (recall the downward sloing reaction function i RF in Figure ). The observation that rival innovation exenditures are strategic substitutes to the innovation effort of the OF rovides a link to the aer by Neary and Ulh. n their aer, Neary and Ulh show that a labor-managed firm (LMF) cannot be forced from the market by an OF, a result that derives directly from the difference in the strategic nature of innovation exenditures by the LMF and the OF while innovation by the LMF is a strategic substitute to the innovation by the OF, the OF s innovation effort is a strategic comlement to the amount of innovation undertaken by the LMF (an outcome that derives directly from the LMF s closed membershi). The result is that increased innovation by the OF leads to increased innovation exenditures by the LMF, which in turn leads to decreased innovation by the OF. This aer derives a somewhat similar result as long as the co-o does not face too much of an initial cost disadvantage (see equation (36)), it can comete effectively with an OF and can continue to oerate in the industry. However, survival of the co-o is not assured under all conditions. f the co-o s initial market share is too low, the co-o can eventually be driven from the market, since the smaller is the market share, the less is the innovation undertaken and the less cometitive is the co-o vis-à-vis the OF. This contrasting result to that in Neary and Ulh derives directly from the vertical nature of the co-o s reaction function, which in turn stems from the difficulty that oen membershi co-os have in getting future members to finance innovation activity. Thus, the co-o s organizational structure has imortant imlications for its behavior and success in the market. oncluding Remarks This aer develos a sequential game theoretic model of heterogeneous roducers to examine the effect of cooerative involvement on innovation activity in the agricultural inut-sulying sector. Secifically, the aer analyzes the consequences of the involvement of an oen membershi cooerative for the arrival rate of innovations, the ricing of agricultural inuts, and social welfare in the context of a mixed duooly where a co-o and an OF comete in sulying an inut to agricultural roducers.

24 3 Analytical results show that cooerative involvement in innovation activity can be roductivity and welfare enhancing. The resence of the member welfare-maximizing co-o which relaces a rofitmaximizing OF can increase the arrival rate of innovations and roductivity growth while reducing the rices of agricultural inuts. The effect of cooerative involvement, however, deends on the initial market share of the co-o and the size of its innovation costs. n articular, the greater is the initial market share of the co-o, the greater is its innovation activity and the lower is the OF s innovation activity. The reduction in OF s innovation effort outweighs the co-o s increased innovation, resulting in total innovation falling with an increase in the co-o s initial market share. Total innovation effort also falls when the co-o faces higher innovation costs than the OF. When the initial market share of the co-o or/and its innovation costs are too high, cooerative involvement is shown to reduce the amount of innovation below the level that would emerge under a ure oligooly and the ossibility arises that at least some roducers would be better off in the absence of the inut-sulying co-o. n addition to identifying the ramifications from cooerative involvement in innovation activity, the results of this aer underscore the imortance of costs in allowing the co-o to survive and meet its members needs. A co-o is vulnerable to being driven from the market by an OF if it is unable to kee ace with the OF in terms of lowering its marginal cost of roduction; alternatively, it can be successful if it is able to make the required investments in innovative activity. As a result, cooeratives are correct to focus attention on caital availability and member willingness to invest, since these are critical to the coo s ultimate survival. As well, since the amount of innovation undertaken by the cooerative affects the rices charged by both it and the OF, and consequently the rofits of the OF and the welfare of all agricultural roducers, the factors affecting co-o innovation activity are of interest to all layers in the agricultural industry.

25 References Aghion, P. and P. Howitt (199). A Model of Growth through reative Destruction. Econometrica 6(): Aghion, P. and P. Howitt (1998). Endogenous Growth Theory. The MT Press. Aoki, R. (1991). R&D ometition for Product nnovation: An Endless Race. American Economic Review, Paers and Proceedings, 81: Beath, J., Y Katsoulacos, and D. Ulh. (1989). Strategic R&D Policy. The Economic Journal 99(onference Paers): enex (). ororate Website. (htt:// haddad, F.R. and M.L. ook (). Testing for the Presence of Financial onstraints in U.S. Agricultural ooeratives. Deartment of Agricultural Economics Working Paer AEWP - 5, University of Missouri-olumbia. ook, M.L. (1995). The Future of U.S. Agricultural ooeratives: A Neo-nstitutional Aroach. American Journal of Agricultural Economics 77(5): otterill, R.W. Agricultural ooeratives: A Unified Theory of Pricing, Finance, and nvestment. ooerative Theory: New Aroaches. J. S. Royer, ed., Washington D..: U.S. Deartment of Agriculture, Agricultural ooerative Service, Delbono, F. (1989). Market Leadershi with a Sequence of History Deendent Patent Races. Journal of ndustrial Economics XXXV: Delbono, F. and V. Denicolò. (1993). Regulating nnovative Activity: The Role of a Public Firm. nternational Journal of ndustrial Organization 11(1): Fudenberg, D., R. Gilbert, J. Stiglitz, and J. Tirole (1983). Preemtion, Leafrogging and ometition in Patent Races. Euroean Economic Review : Fulton, M.E., J.R. Fulton, J.S. lark, and. Parliament (1995). ooerative Growth: s it onstrained? Agribusiness: An nternational Journal 11: Fulton, M.E. and K. Giannakas (1). Organizational ommitment in a Mixed Oligooly: Agricultural ooeratives and nvestor-owned Firms. American Journal of Agricultural Economics 83(5): Fulton, M.E. and J. Gibbings. Resonse and Adatation: anadian Agricultural o-oeratives in the 1st entury. Ottawa: anadian o-oerative Association and Le onseil anadien de la ooeration, October. Gibbons, R. (199). Game Theory for Alied Economists. Princeton University Press.