THE EFFET OF MARKETNG OOPERATVES ON OST-REDUNG PROESS NNOVATON ATVTY KYRAKOS DRVAS AND KONSTANTNOS GANNAKAS + Selected Pape pepaed o pesentation at the Ameican Agicultual Economics Association Annual Meeting, Potland, OR, July 9-August 1,007 + Kyiakos Divas is a Ph.D. Student, Depatment o Agicultual and Resouce Economics, Univesity o alionia, Bekeley. Konstantinos Giannakas is Poesso, Depatment o Agicultual Economics, Univesity o Nebaska-Lincoln. oesponding autho: Kyiakos Divas, Depatment o Agicultual and Resouce Economics, Univesity o alionia, Bekeley, 07 Giannini Hall, Bekeley A 9470, U.S.A. Phone: (510) 64-3345; Fa: (510) 643-8911; E-mail: kdivas@ae.bekeley.edu opyight 007 by Kyiakos Divas and Konstantinos Giannakas. All ights eseved. Reades may make vebatim copies o this document o non-commecial puposes by any means, povided that this copyight notice appeas on all such copies.
1 THE EFFET OF MARKETNG OOPERATVES ON OST-REDUNG PROESS NNOVATON ATVTY Abstact - This pape eamines the maket and elae eects o coopeative involvement in costeducing pocess innovation activity in the contet o a mied oligopsony hee an open-membeship maketing co-op competes ith an OF. The pesence o the maketing co-op is shon to esult in inceased poduce pices and elae gains o all ames, membes and non-membes o the co-op. The eect o the maketing co-op on pocess innovation activity depends on the elative quality o its inal poducts, the degee o poduce heteogeneity, and the size o innovation costs. Keyods: coopeatives, pocess innovation, mied oligopsony, etained eanings. oopeative oganizations constitute an integal pat o the inceasingly industialized agi-ood system accounting o 5% to 30% o total am supply and maketing ependitues (USDA, 003). When compaed to poit-maimizing investo-oned ims (OFs), a distinguishing eatue o coopeatives (coops) is that the ones ae also the uses o the sevices povided by the oganization (USDA, 1995; Hansmann, 1996). With membes as both ones and uses o its sevices, a co-op is typically assumed to ocus on maimizing membe elae athe than poits. The economic amiications o the dieent objective unction o the coopeative oganization have eceived consideable attention in the elevant liteatue ith the main ocus being on the eect o dieent types o co-ops on the equilibium conditions o vaious ounot and Betand mied maket settings [see Seton and Seton (1987), otteill (1987), Seton (1990), Tennbakk (1995), Albaek and Schultz (1998), Fulton and Giannakas (001), Kaantininis and Zago (001)]. A key esult o this liteatue is that the pesence o co-ops esults in moe competitive conduct and inceased elae. Being an integal pat o the industialized agi-ood system, many co-ops have esponded to the pessues o the inceasingly competitive maket place by tying to position themselves via thei R&D activities. mpotant eamples include Limagain, ebeco, and osun in Euope, hile co-ops in the U.S. such as Ocean Spay have had substantial innovation activity. Recognizing the inceased coopeative involvement in R&D, Giannakas and Fulton (005) (G&F, heeate) eamined the maket and elae eects o the involvement o input supplying co-ops in cost-
educing, pocess innovation activity. G&F sho that the pesence o the coopeative oganization in an oligopolistic agicultual input maket (i) can incease total pocess innovation activity and (ii) enhances economic elae by educing the pices o agicultual inputs. An impotant eatue o the input-supply co-ops studied in G&F is that they constitute a backad integation o thei membes i.e., they ae omed by agicultual poduces to poduce inputs (such as seeds, chemical etilizes, pesticides etc.) used in agicultual poduction. Thus, the membes/ones o an input supply co-op ae pat o the demand side o the co-op s maket as they buy the poduct supplied by the co-op. Unlike supply co-ops that constitute a backad integation o thei membes, the othe impotant type o coopeative oganizations, the maketing co-ops, constitute a oad integation o thei membes. n paticula, maketing co-ops ae omed by poduces to pocess and maket the agicultual poduce o thei membes. Thus, the membes/ones o a maketing co-op ae pat o the supply side o the co-op s maket as they supply the co-op ith an input in its poduction pocess. Given the pevalence o these undamentally dieent types o coopeative oganizations, the question that natually aises is Does the type o coopeative oganization matte hen consideing the maket and elae eects o coopeative involvement in innovation activity? This pape ill ty to anse this question by detemining the eects o the involvement o maketing co-ops in pocess innovation activity and compaing the esults ith those o G&F. n paticula, this pape eamines the maket and elae eects o the involvement o maketing co-ops in cost-educing pocess innovation activity in the agi-ood system. The pape analyzes the consequences o coopeative involvement o the amount o pocess innovation, the picing behavio o ims, and social elae in the contet o a mied duopsony hee an open-membeship maketing co-op and an OF compete in pocuing an agicultual poduct om ames. The agicultual poduct is an input in the poduction pocess o the to ims and it is combined in ied popotions ith pocessing sevices to poduce the inal poducts o the co-op and the OF. By ocusing on a mied oligopsony, the study pays paticula attention to the impact o eplacing a poit maimizing OF ith a membe elae-
3 maimizing co-op. The case o a pue oligopsony is also analyzed and is used as a benchmak o detemining the consequences o coopeative involvement in cost-educing R&D. To analyze the eects o the involvement o maketing co-ops in cost-educing pocess innovation activity, ou study ollos the appoach developed by G&F hen eamining the eects o input-supplying co-ops. n paticula, the stategic inteaction beteen the ims in the pue and the mied duopsonies is modeled as a thee-stage sequential game hee: in stage 1, the ims compete in (input) pices and a ne pocess innovation that can educe thei pocessing costs is announced; in stage, the ims detemine thei optimal level o investment in the ne cost-educing innovation; and in stage 3, pocessing costs ae ied and the ims engage in (input) pice competition. n hat ollos, stage 1 ill oten be eeed to as the pe-innovation stage, stage as the innovation stage, and stage 3 as the post-innovation stage. To captue the geogaphic natue o agicultual makets (Roges and Seton, 1994), e assume that, even though the to ims have maket poe hen pocuing the agicultual poduct, they ae pice-takes donsteam, i.e., in the makets they sell thei pocessed poducts. n addition, to account o the act that agicultual poducts ae used as inputs in the poduction o multiple ood poducts, ou analysis allos o the inal poduct pices to vay beteen the to ims, i.e., it allos o the to ims to supply dieent value (quality) makets. To avoid Nash equilibia involving non-cedible stategies, the dieent omulations o the game ae solved using backad induction the picing behavio o the ims at the post-innovation stage is consideed ist, the optimal investment in the cost-educing innovation is analyzed net, and the solution to the pe-innovation picing poblem detemines the subgame peect equilibium amount o cost-educing R&D, the picing o the agicultual poduct, and poduce decisions in the pe- and post-innovation stages o the game. n addition to being intuitively appealing, this stuctue o the stategic inteaction in the mied oligopsony enables us to eplicitly account o the dieent objective unction o the co-op (membe elae maimization vs. poit maimization pusued by OFs) as ell as o the need o the co-op to
4 ely on eanings aised at the pe-innovation stage to inance its subsequent investment in cost-educing innovation. Note that the inability o open membeship co-ops to estict the allocation o beneits om an investment activity to those membes that have incued the investment costs (i.e., thei inability to eclude om the beneits o an investment the membes that have not contibuted to the inancing o this investment), ceates incentives o oppotunistic behavio and ee iding that undemine the co-ops ability to aise investment capital (Vitaliano, 1983; ook, 1995). A common stategy employed by co-ops to cope ith this popety ights poblem is the inancing o thei investment though etained eanings (see Knoebe and Baume (1983). On the diiculties o open membeship co-ops to aise investment capital and the ole o etained eanings in addessing vaious popety ights poblems see also G&F and the eeences theein). Othe than acilitating the eplicit consideation o these impotant idiosyncasies o coopeative oganizations, this stuctue o stategic inteactions makes ou esults diectly compaable to those o G&F. Given that both studies conside the maket and elae eects o coopeative involvement in costeducing, pocess innovation, a compaison o ou esults ill enable us to detemine hethe the type o co-op (input-supply co-op consideed in G&F vesus the maketing co-op consideed hee) mattes hen consideing the eect o coopeative involvement in pocess innovation activity. As mentioned peviously, in addition to being involved in dieent activities, input supply co-ops die om maketing co-ops in a athe undamental ay hile the input supply co-ops constitute a backad integation o thei membes, maketing co-ops constitute a oad integation o thei membes. The est o this pape is oganized as ollos. The net section eamines the poduce decisions and deives the supplies aced by the duopsonists beoe and ate the pocess innovation activity. Sections 3 and 4 deive the equilibium conditions in the pue and mied oligopsonies, espectively. Section 5 detemines the eect o maketing co-ops on cost-educing pocess innovation, the pices eceived by agicultual poduces, and the elae o the goups involved. Section 6 summaizes and concludes the pape.
5. Poduce Decisions and Welae Beoe eamining the innovation and picing decisions in the pue and mied oligopsonies, e need to analyze the ay ames make thei selling decisions at the pe- and post-innovation stages. By doing so, e can deive the supplies aced by each im and obtain measuements o poduce (ame) elae beoe and ate the cost-educing pocess innovation activity. n both the pe- and post-innovation stages o the game, ames have to decide hethe to sell thei poduct to Fim o Fim. Due to dieences in thei location, commitment to the to ims (Fulton and Giannakas, 001), and/o the pices oeed by the to ims, thei net etuns depend on the im they ill delive thei poduct to. Let α [0,1] be the attibute that dieentiates agicultual poduces. The ame ith attibute α has the olloing net etuns unction at the pe- and postinnovation stages o the game: ( k) ( k) ( k) ( k) (1) Π c tα a unit o poduct is sold to Fim ( α ) Π c t 1 a unit o poduct is sold to Fim hee k denotes the stage o the game; Π ( k) and Π ( k) ae the pe unit net etuns hen the am output is deliveed to Fim and Fim, espectively; ( k) and ( k) ae the pe unit pices paid by Fim and Fim, espectively; and c is the ames cost o poducing the agicultual poduct. The paamete t is nonnegative and captues the degee o poduce heteogeneity (hen poduces die in thei physical location, t denotes the tanspotation cost they ace). eteis paibus, poduces ith lage values o α pee to sell thei poduct to Fim, hile poduces ith lo values o α pee selling to Fim. The geate is t, the geate the dieence in the net etuns associated ith selling the am poduct to the to ims. To ensue positive maket shaes o the to ims, it is assumed that t eceeds the dieence in the pices o the to ims (see equations (3) and (4)), hile, to etain tactability, the analysis assumes that poduces ae uniomly distibuted beteen the pola values o α. Each ame poduces a unit o the agicultual poduct and thei selling decision is detemined by the elationship beteen Π and Π. k k
6 Figue 1 shos the decisions and elae o poduces. The donad sloping cuve shos the net etuns hen the am poduct is supplied to Fim, hile the upad sloping cuve shos the net etuns hen the poduct is supplied to Fim o dieent values o the dieentiating attibute α (i.e., o dieent poduces). The intesection o the to net etuns cuves detemines the level o the dieentiating attibute that coesponds to the indieent poduce. The poduce ith dieentiating chaacteistic α ( k) given by: ( k) ( k) ( k) ( k) ( k) () α : Π Π > c tα c t(1 α) > t+ ( k) ( k) α ( k) t is indieent beteen selling to Fim o to Fim as the net etuns om selling to the to ims ae the same. Fames located to the let o α ( k) (i.e., ames ith α [0, α ( k )) ) sell to Fim hile ames ith α ( α ( k ),1] sell to Fim. Aggegate poduce elae is given by the aea undeneath the eective net etuns cuve shon as the (bold dashed) kinked cuve in Figue 1. When ames ae uniomly distibuted ith espect to thei dieentiating attibute α, α ( k) detemines the shae o poduces deliveing thei poduct to Fim. The shae o poduces supplying Fim is given by α. By nomalizing the mass o poduces at unity, these shaes give the input 1 k supplies aced by Fim, ( k), and Fim, ( k), at the kth stage o the game, espectively. Fomally, and can be itten as: ( k) k (3) (4) ( k) ( k) t + t t+ t ( k) ( k) ( k) ( k) Ate detemining the supplies aced by the to ims at the pe- and post-innovation stages, e ill no poceed to deiving the subgame peect equilibia in the pue and mied oligopsonies.
7 3. Benchmak ase: nnovation and Picing Decisions in a Pue Oligopsony Pice ompetition at the Post-nnovation Stage (3 d Stage o the Game) n the post-innovation stage o the pue duopsony, the to OFs seek to detemine the input pices that maimize thei poits holding Nash conjectues (i.e., assuming that thei decisions ill not aect the behavio o thei ival). 1 Speciically, the poblem o the to OFs at the 3 d stage o the game can be epessed as: i (3) (5) ma Π p c i(3) i i i(3) i(3) hee i {, }, p i is the pice o Fim i s inal poduct, and c i is the post-innovation maginal pocessing cost o Fim i. All othe vaiables ae as peviously deined. Solving the poblem o the to OFs gives thei best esponse unctions as: 1 + p t c i(3) j(3) i i hee j {, } and i j. Solving these best esponse unctions simultaneously and substituting (3) and (3) into equations (3) and (4) gives the Nash equilibium pices and quantities as: 1 (6) i(3) pi + pj ci cj 3t 3 3t c i + cj + pi pj (7) i (3) 6t The equilibium poits o each OF ae then given by: (8) i(3) Π ( 3t c ) i + cj + pi pj 18t and ae a unction o the degee o poduce heteogeneity, the pices o the poducts poduced by the to OFs, and thei post-innovation pocessing costs. eteis paibus, the loe the post-innovation pocessing cost o a im, the geate its poits at the 3 d stage o the game. 1 The assumption o Nash conjectues is maintained thoughout the analysis.
8 nnovation ompetition ( nd Stage o the Game) n stage, the to OFs seek to detemine thei optimal cost-educing, pocess innovation eot. The elationship beteen the amount o innovation,, and the post-innovation maginal costs o pocessing the am input is given by: β (9) ci(3) ci(1) ii hee c i(1) is Fim i s (stictly positive) maginal cost o pocessing the am input at the pe-innovation stage o the game, and i 0. The paamete β i epesents the eectiveness o innovation eot, i.e., the degee to hich innovation eot is tanslated into cost eductions o the to ivals. We assume that the to ims have the same pe-innovation pocessing costs (i.e., c(1) c(1) c) and β i 1. n addition to simpliying ou eposition, imposing symmety on the to ims pe-innovation costs and eectiveness o innovation eot allos us to ocus on the eect o the dieent objective unction o the co-op in the mied duopsony on the equilibium innovation and picing decisions. While, as indicated by equation (8), innovation eot has the potential to incease the postinnovation poits o a im, cost-educing innovation equies esouces. Without loss o geneality, innovation costs ae assumed to be an inceasing unction o the innovation eot (Shy), i.e., (10) 1 i ψ i hee ψ is stictly positive scala electing the size o innovation costs. Thus, at the innovation stage o the game each OF seeks to detemine the innovation eot that maimizes its post-innovation poits minus the cost o innovation eot, i.e., ( t+ ) i j + pi pj 3 1 (11) ma Π Π i 18t i(,3) i(3) i ψ i Fom the ist ode conditions o each OF s poblem e obtain thei best esponse unction as: (1) 3t j + pi pj i 9tψ 1
9 Solving the best esponse unctions simultaneously, e get the Nash equilibium levels o innovation o each im as: (13) i ( i j) 9tψ + 3ψ p p 3ψ 9 ( tψ ) Substituting the equilibium levels o innovation in the epessions o innovation costs and postinnovation poits, e get the net poits o each im in stages and 3 as: (14) ( 9tψ 1) 9tψ + 3ψ ( pj pi) 18ψ 9 i(,3) Π ( tψ) Pice ompetition at the Pe-nnovation Stage (1 st Stage o the Game) n this stage, the to ims seek to detemine the input pices that maimize thei poits. Since the ims payos in stages and 3 ae not dependent on pe-innovation pices o quantities, the objective o the to OFs in stage 1 is to maimize thei pe-innovation poits only, i.e., i (1) (15) ma Π p c i(1) i i(1) i(1) The Nash equilibium pices, quantities and poits at the pe-innovation stage ae then: 1 (16) i(1) ( pi + pj) c t 3 (17) (18) i(1) i(1) Π 3t+ pi p 6t ( 3t+ p ) i pj 18t j Table 1 summaizes the subgame peect equilibium in the pue oligopsony. t can be seen that the equilibium is asymmetic ith the dieences in input pices, quantities, poits and innovation eot being detemined by the elative quality o the inal poducts poduced by the to OFs (elected in the elative pices o these poducts). n paticula, the im ith the highe quality poduct ill oe a highe pice to ames, ill enjoy highe maket shaes and poits in the 1 st and 3 d stages o the game, and ill eet highe innovation eot than its lo quality ival.
10 4. nnovation and Picing Decisions in a Mied Oligopsony n this case, Fim is a co-op instead o an OF. The maket stuctue is, thus, a mied duopsony consisting o an OF (Fim ) and a co-op (Fim ). Pice ompetition at the Post-nnovation Stage in the Mied Oligopsony Simila to the pue oligopsony case, at the 3 d stage the OF seeks to detemine the input pice that maimizes its poits. Thus, both its objective unction and its best esponse unction ae identical to those in the post-innovation stage o the pue duopsony. Unlike Fim in the pue oligopsony, the co-op seeks to identiy the input pice that maimizes the elae o its membes (i.e., ames that patonize its activities) subject to not incuing economic losses. Membe elae is given by the shadoed aea MW ( k ) in Figue 1 hee k3 and the coopeative s poblem can be epessed as: 1 (19) ma MW c t (3) (3) (3) (3) (3) s.t. Π 0 > p c 0 (3) (3) Solving the optimality conditions o the co-op s poblem, shos that the co-op ill ind it optimal to not eecise its oligopsonistic poe hen pocuing the am poduct at the post-innovation stage (i.e., (3) p c ). The Nash equilibium pices and quantities at the post-innovation stage o the mied oligopsony ae: 1 (0) (3) ( p + p c c t) (1) () (3) (3) t c + c p + p 4t (3) p c (3) 3t c + c + p p 4t t should be noted that this ill be the optimal picing stategy o the co-op at the post-innovation stage no matte i it seeks to maimize the elae o all ames that delive thei poduct to the co-op at this stage o the elae o only a subset o its post-innovation membeship. The obvious eason is that the elae o any poduce goup is positively elated to the am poduct pices.
11 The poits o the to ims and the elae o the goup that patonizes the co-op ae then: (4) (3) (3) (5) Π 0 (6) Π ( t c + c p + p ) 8t 1 MW p c c t (3) (3) (3) nnovation ompetition in the Mied Oligopsony n this stage, the to ims seek to detemine thei optimal innovation eot. Simila to the pue oligopsony case, the poblem o the OF is to detemine the amount o innovation that maimizes its postinnovation poits minus its innovation costs, i.e., ( t+ p + p ) 1 (7) ma Π Π 8t Ι(,3) (3) ψ On the othe hand, the poblem o the co-op is to maimize the elae o ames that ae membes at the time the decision to invest in innovation is being made (this goup ill be eeed to as the pe-innovation membeship ). As ill be shon belo (in stage 1), the pe-innovation membeship is the goup that, by selling to the co-op at educed pices in the pe-innovation stage, povides the co-op ith eanings that inance its subsequent cost-educing innovation eot. Thus, even though the co-op knos that its cost-educing pocess innovation activity ill esult in inceased input picing that can attact ne ames/membes to the co-op at the post-innovation stage, hen making its innovation decisions the co-op consides only the elae o ames that inance its innovation activity (by patonizing the co-op in stage 1). Algebaically, the poblem o the coop can be epessed as: 1 1 (8) ma MW MW p c c t (,3) (3/1) + (1) (1) ψ hee (1) is the shae o the co-op in stage 1, MW (,3) is the elae o the pe-innovation membeship in stages and 3, and MW (3/1) is the elae o the pe-innovation membeship in stage 3. Solving the poblems o the co-op and OF, e get thei best esponse unctions as:
1 (9) (30) () 1 ψ t + p p 4tψ 1 Solving these best esponse unctions simultaneously, e get the equilibium levels o innovation: (31) (3) ψ (1) tψ + ψ p p ψ(4tψ 1) (1) The total innovation in the mied duopsony is then: (33) tψ + (1) 4tψ + ψ p p T + ψ(4tψ 1) Plugging e get: and in the epessions o innovation costs, post-innovation poits, and membe elae, (34) (35) tψ + ψ p p Π (,3) ψ(4tψ 1) (1) (1) 1 (1) (,3) + (1) (1) MW p c c t ψ ψ Pice ompetition at the Pe-nnovation Stage in the Mied Oligopsony Unlike the pue oligopsony case, in the mied duopsony the outcome o pice competition in the peinnovation stage aects ims optimal decisions and payos in subsequent stages (see equations (31), (3), (34) and (35)). Thus, in stage 1 the OF seeks to detemine the input pice that maimizes its total poits (i.e., its poits at the pe-innovation stage plus its poits at the post-innovation stage minus its innovation costs), i.e., tψ + ψ p p T (36) ma Π ( p c (1) ) (1) + (1) ψ(4tψ 1) The best esponse unction o the OF is given by: (1)
13 ctψ + 4tψ + 8ct ψ t ctψ p + 8t ψ p + 8t ψ tψ 1 (1) (1) 16t ψ 4tψ 1 Regading the co-op, its poblem at this stage is to detemine the pice that maimizes the elae o its pe-innovation membeship in both the pe- and post-innovation stages o the game, subject to aising eanings that can be etained to inance its cost-educing innovation in stage. The capital equied o the subsequent investment in innovation is at the pe-innovation stage can be epessed as: (1) 1 ψ t and the poblem o the co-op ψ 1 1 (37) ma MW MW MW ( c ) t ( p c c ) t (1) ψ T (1) (1) + (3/1) (1) (1) (1) + + (1) (1) (1) s.t. Π(1) 0 > ( p (1) c) (1) 0 ψ hee MW (1) is the elae o the pe-innovation membeship in stage 1. The optimality conditions o the co-op s optimization poblem suggest that the co-op ill ind it optimal to choose its pice such that the investment constaint binds, i.e., the co-op ill pice its input so that it aises eactly the amount o capital needed o its innovation activity in stage. The best esponse unction o the co-op is then: (1) ae given by: ( ψ ) 4tψ p + (1) t 4c + 1 4tψ + 1 The Nash equilibium pices and quantities at the pe-innovation stage o the mied oligopsony (38) (39) (40) (41) (1) (1) (1) (1) t 4t ψ + 4tψ 3 p + 4tψ p c 8tψ 3 ( ) ( 4tψ + 1)( 8tψ 3) 8t ψ + 4tψ 3+ 8tψ p p 4t 1t ψ + 3t ψ 8tψ 3 p + 4tψ p c ( 4tψ + 1)( 8tψ 3) + ( ) ( 4tψ + 1)( 8tψ 3) 8tψ 3tψ 1 ψ p p
14 Substituting the equilibium pe-innovation membeship o the co-op (equation (41)) in equations (31)-(33) gives the subgame peect equilibium innovation levels in the mied duopsony. Substituting the ne epessions o and into equations (0)-(6) gives the subgame peect equilibium conditions in the post-innovation stage o the game. Table summaizes the subgame peect equilibium in the mied oligopsony. t can be seen that, simila to the pue oligopsony case, the equilibium is asymmetic ith the dieences in equilibium conditions being detemined by the elative quality o the ims inal poducts, the degee o poduce heteogeneity, and the size o innovation costs. When the co-op is the high quality im (i.e., hen p > p ), it ill oe highe pices to the ames, ill enjoy highe maket shaes in the pe- and postinnovation stages, and ill undetake highe innovation eot than the lo quality OF. nteestingly, because o its objective to maimize membe elae, even hen the co-op is the lo quality im (i.e., hen p < p ) it can still pice the am poduct above the high quality OF, enjoy highe maket shaes, and innovate moe than its ival. Fo the high quality OF to oe highe pices to poduces and innovate moe than the lo quality co-op, it should enjoy a signiicant quality advantage elative to the co-op. When the dieence in the pices o the poducts poduced by the to ims is 3tψ 1 p p, ψ the lo quality co-op is diven out o the maket and the high quality OF becomes a monopsonist at the post-innovation stage o the game (i.e., 0 and 1). Since the co-op eits the maket in stage 3, 3 3 it ill not invest in cost-educing innovation in stage and ill seek to maimize the elae o its peinnovation membeship in stage 1. Table 3 pesents the subgame peect equilibium o the case hee the maket stuctue is alteed at the post-innovation stage due to the eit o the lo quality maketing co-op. Finally, hen t(8tψ 5) p p it is the co-op that becomes the sole buye o the am 8tψ + 3 poduct at the post-innovation stage o the game. Since the OF eits the maket in stage 3, it ill not invest in cost-educing innovation in stage, and ill seek to maimize its pe-innovation poits in stage
15 1. Table 4 pesents the subgame peect equilibium o the case hee the maket stuctue is alteed at the post-innovation stage due to the eit o the OF. t is inteesting to note that it is not necessay o the co-op to poduce the highe quality poduct o it to end up being a monopsonist at the post-innovation stage. ndeed, the elationship t(8tψ 5) p p indicates that, o cetain (lo) values o the degee o poduce heteogeneity and 8tψ + 3 the size o innovation costs, the pesence o the maketing co-op can induce eit o the OF at the postinnovation stage even hen the co-op poduces the loe quality poduct, i.e., hen p < p. 5. The Maket and Welae Eects o oopeative nvolvement in Pocess nnovation Having detemined the subgame peect equilibium conditions o the pue and mied oligopsonies, e can no eamine the amiications o coopeative involvement o cost-educing pocess innovation activity, pe- and post-innovation agicultual poduce pices, and the elae o the goups involved. We begin by consideing the geneal case o the mied duopsony at the post-innovation stage o the game. Figue gaphs the innovation eaction unctions o the ims in the pue and mied oligopsonies. When compaed to the eaction unction o Fim in the pue oligopsony ( RF () ), the eaction unction o the co-op ( RF () ) is shited outads and otated ightads. The co-op has inceased incentives to innovate because, by seeking to maimize the elae o its membes, it is bette able to intenalize the cost and beneits associated ith its pocess innovation activity. At the same time, the coopeative involvement educes the maginal poitability o the OF s investment in innovation by inceasing the equilibium agicultual poduct pices. Gaphically, the involvement o the co-op esults in the eaction unction o Fim (the OF in both the mied and pue oligopsonies) shiting inads in ightad otation. These changes in the eaction unctions esult in inceased innovation by the co-op elative to Fim in the pue duopsony and educed innovation by Fim in the mied duopsony case, i.e.,
16 (4) > and < Regading the total cost-educing pocess innovation activity, the eect o coopeative involvement depends on the elative quality o the poducts poduced by the maketing co-op and the OF, the size o innovation costs, and the degee o ame heteogeneity. n paticula, the dieence beteen the total innovation activity in the mied and pue duopsonies is given by: (43) ( ) ( t + )( t ) 3t ψ 31tψ + 6 + 9ψ p p T T 3ψ 4ψ 1 8ψ 3 t is impotant to note that the dieence T T is negatively elated to p indicating that the loe is the quality o the maketing co-op s poduct, the moe likely it is that coopeative involvement ill esult in inceased total pocess innovation in this maket. When the elative quality o the co-op s poduct is the loest (i.e., hen p p appoaches its maimum value o 3tψ 1 ψ unde the co-eistence o the to ims in stage 3), Τ Τ > tψ. When p p, Τ Τ > i tψ > 0.701444, hile, hen the elative quality o the co-op s inal poduct is the highest (i.e., hen p p appoaches t(8tψ 5) ), then 8tψ + 3 Τ Τ > i tψ > 0.914764. An inteesting implication o these esults is that the eect o maketing co-ops on innovation activity is moe likely to be negative hen the co-op is the high quality im. The easoning is as ollos. When the co-op is the high quality im, it eceives a high pice o its poduct and is able to aise moe capital o innovation activity in stage 1. nceased pocess innovation by the high quality co-op leads to educed costs and inceased am pices at the post-innovation stage o the game. Since innovation eots ae stategic substitutes and the pices oeed to ames ae stategic complements, the inceased innovation eot and pices o the co-op educe the OF s incentive to innovate. The geate the elative quality o the co-op s poduct, the moe likely it is that the incease in co-op s innovation ill be outeighed by the eduction in OF s innovation and the total innovation activity ill be educed.
17 Regading the eects o the degee o poduce heteogeneity, t, and the size o innovation costs, ψ, on total innovation activity, the analysis shos that the geate is tψ, the moe likely it is that the mied oligopsony ill esult in highe total innovation than the pue oligopsony. The inceased likelihood that total innovation is geate in the mied oligopsony unde highe innovation costs is the diect outcome o the co-op intenalizing the eects o its innovation activity to (at least some) ames. n tems o the eect o the degee o ame heteogeneity on the total innovation undetaken unde the pue and mied oligopsonies, the agument is slightly dieent. To begin, note that hile t does not aect the amount o total innovation in the pue oligopsony, it aects the innovation eot o both the co-op and the OF in the mied oligopsony case. n paticula, a high value o t allos the co-op to incease its eanings in stage 1 (used to inance its innovation activity in stage ) ithout dastically educing the size o its pe-innovation membeship. At the same time, a high value o t povides the OF ith incentives to incease its innovation eot since, unde inceased ame heteogeneity, this im can educe its pice (and incease its poits) at the post-innovation stage o the game. Thus, as ame heteogeneity inceases, so does total innovation in the mied oligopsony. onside net the eect o coopeative involvement on am poduct pices. Figue 3 gaphs the pice eaction unctions in the pue and mied oligopsonies and illustates the changes in equilibium pices caused by the pesence o the membe elae maimizing co-op at the pe-innovation stage o the game. When compaed to Fim in the pue oligopsony, the co-op s eaction unction ( RF (1) ) is shited outads in letad otation. At the same pice, the pesence o the co-op causes the eaction unction o Fim (OF in both the pue and mied oligopsonies) to shit upads in ightad otation. The esult is that both ims in the mied duopsony pay highe pices to ames than the OFs in the pue duopsony. Since both pices ae inceased in the mied oligopsony, all ames, membes and non-membes o the co-op, beneit om the pesence o the co-op in the pe-innovation stage o the game. Figue 4 gaphs the post-innovation pice eaction unctions in the pue and mied oligopsonies and illustates the changes in equilibium pices caused by the pesence o the membe elae
18 maimizing maketing co-op. When compaed to Fim in the pue oligopsony, the co-op s eaction (1) unction ( RF ) is shited outads and becomes vetical at p c (ecall that the optimal postinnovation stategy o the co-op does not depend on the picing o its ival OF). At the same time, the pesence o the co-op causes the eaction unction o Fim to shit outads in a paallel mode. The esult is that both ims in the mied duopsony pay highe pices than the OFs in the pue duopsony. Since both pices ae inceased in the mied oligopsony, all ames, membes and non-membes o the co-op, beneit om the pesence o the co-op in the post-innovation stage o the game. The eect o coopeative involvement on the elae o poduces in the pe- and post-innovation stages o the game is shon in Figue 5. The geate the elative quality o the co-op s poduct (i.e., p p ), the geate the poduce elae gains om the pesence o the maketing co-op. ntiguingly, even though total innovation alls ith an incease in the elative quality o the maketing co-op, its picing stategy esults in agicultual poduces beneiting the most hen the maketing co-op is a high quality im. Finally, it should be noted that the picing stategy o the co-op and the educed pice-cost magins unde a mied duopsony indicate that the involvement o the maketing co-op in pocess innovation activity enhances competition and, thus, it enhances total economic elae in this maket. Ate analyzing the case hee both the co-op and the OF ae in the maket in stage 3, conside no the case hee 3tψ 1 p p and the lo quality maketing co-op eits the maket at the post- ψ innovation stage o the game (i.e., 0 and 1; see Table 3). n tems o innovation eot, not 3 3 only does the high quality OF that ends up being a monopsonist in the 3 d stage o the game innovate moe than each individual OF in the pue duopsony, it undetakes moe than the total innovation in the pue duopsony. n tems o am pices, simila to the case hen both ims ae in the maket at the postinnovation stage o the mied oligopsony, pe- and post-innovation pices incease in the mied maket indicating that the pesence o the co-op beneits all poduces, membes and non-membes o the co-op.
19 onside inally the eects o coopeative involvement hen t(8tψ 5) p p and the co-op 8tψ + 3 becomes a monopsonist at the post-innovation stage o the game (Table 4). Even though the eect o coopeative involvement on total pocess innovation activity tuns out to be, once again, ambiguous T ( T [ < ) hen p p 1 tψ ( < ) ], both ims pay highe pices in the mied oligopsony than thei 3ψ countepats in the pue oligopsony indicating that the pesence o the co-op beneits all ames at the peinnovation stage o the game. This is also tue o the post-innovation stage since (3) (3) > and (3) (3) > + t. Thus, even though the pesence o the co-op does not alays esult in inceased innovation, the pice eect is such that the net etuns associated ith selling the poduct to the co-op is geate than the net etuns associated ith selling the poduct to the to OFs in the pue oligopsony. Figue 6 depicts both the dominance o the co-op in the post-innovation stage and the ame beneits om its pesence. 6. onclusions This pape analyzed the maket and elae eects o coopeative involvement in cost-educing, pocess innovation activity. The open-membeship maketing co-op consideed in the analysis seeks to maimize membe elae and addesses its popety ights poblems by inancing its investment activity though etained eanings. Analytical esults sho that the involvement o the maketing co-op in cost-educing pocess innovation is elae enhancing the pesence o the membe elae maimizing co-op is shon to esult in inceased poduce pices and elae gains o all ames, membes and non-membes o the co-op. n tems o innovation activity, the eect o the maketing co-op on pocess innovation as shon to depend on the elative quality o the poducts supplied by the co-op and the OF, the degee o poduce heteogeneity, and the size o the innovation costs. ntiguingly, even though total innovation activity can all ith an incease in the elative quality o the maketing co-op, the picing stategy o the membe elae maimizing co-op esults in agicultual poduces beneiting the most hen the co-op is a high quality im.
0 Beoe concluding this pape it is impotant to note that ou key indings on the eects o the involvement o maketing co-ops in pocess innovation activity ae consistent ith the esults o G&F on the eects o input-supplying co-ops. While the natue o innovation activity consideed in ou study is the same as the innovation activity in G&F (both studies ocus on pocess innovation activity), the types o coopeative oganizations consideed in the to studies ae dieent in that maketing co-ops constitute a oad integation o thei membes (i.e., they ae omed by goups that ae pat o the supply side o these co-ops), hile input-supplying co-ops constitute a backad integation o thei membes (i.e., they ae omed by goups ho ae pat o the demand side o these co-ops). An impotant implication o this is that, hen consideing the eect o coopeative involvement in pocess innovation activity, the type o the co-op does not seem to matte. Regadless o hethe they ae a backad o a oad integation o thei membes, the involvement o coopeatives in cost-educing innovation activity can incease the innovation activity in the maket, is elae enhancing and, thus, socially desiable. Reeences Aghion, P., and P. Hoitt. A Model o Goth though eative Destuction. Econometica 60(199): 33-351. Aghion, P., and P. Hoitt. Endogenous Goth Theoy. ambidge MA: The MT Pess, 1998. Albaek, S., and. Schultz. On the Relative Advantage o oopeatives. Economics Lettes 59(1998): 397-401. Aoki, R. R&D ompetition o Poduct nnovation: An Endless Race. Ameican Economic Revie (Papes and Poceedings) 81(1991): 5-56. ook, M.L. The Futue o U.S. Agicultual oopeatives: A Neo-nstitutional Appoach. Ameican Jounal o Agicultual Economics 77(1995): 1153-1159. otteill, R.W. Agicultual oopeatives: A Uniied Theoy o Picing, Finance and nvestment. n J.S. Roye, ed. oopeative Theoy: Ne Appoaches. Washington D: U.S. Depatment o Agicultue, Agicultual oopeative Sevice, 1987, pp.171-58. Delbono, F. Maket Leadeship ith a Sequence o Histoy Dependent Patent Races. Jounal o ndustial Economics 38(1989): 95-101.
1 Fudenbeg, D., R. Gilbet, J. Stiglitz, and J. Tiole. Peemption, Leapogging and ompetition in Patent Races. Euopean Economic Revie (1983): 3-31. Fulton, M.E., and K. Giannakas. Oganizational ommitment in a Mied Oligopoly: Agicultual oopeatives and nvesto-oned Fims. Ameican Jounal o Agicultual Economics 83(001): 158-165. Giannakas, K., and, M.E. Fulton. Pocess nnovation Activity in a Mied Oligopoly: The Role oopeatives. Ameican Jounal o Agicultual Economics 87(005): 406-4. Gibbons, R. Game Theoy o Applied Economists. Pinceton NJ: Pinceton Univesity Pess, 199. Gossman, G., and. Shapio. Dynamic R&D ommpetition. The Economic Jounal 97(1987): 37-387. Hansmann, H. The Oneship o Entepise. ambidge MA: Havad Univesity Pess, 1996. Kaantininis, K., and A. Zago. oopeatives and Membeship ommitment: Endogenous Membeships in Mied Duopsonies. Ameican Jounal o Agicultual Economics 83(001): 166-17. Knoebe,.R., and D.L. Baume. Undestanding Retained Patonage Reunds in Agicultual oopeatives. Ameican Jounal o Agicultual Economics 65(1983): 30-37 Malueg, D., and S. Tsutsui. Dynamic R&D ompetition ith Leaning. Rand Jounal o Economics 8(1997): 751-77. Roges, R.T., and R.J. Seton. Assessing the mpotance o Oligopsony poe in Agicultual Makets. Ameican Jounal o Agicultual Economics 76(1994): 1143-1150. Segestom, P., T. Avant, and E. Dinopoulos. A Schumpeteian Model o the Poduct Lie ycle. Ameican Economic Revie 80(1990): 1077-1091. Seton, R. mpeect ompetition in Agicultual Makets and the Role o oopeatives: A Spatial Analysis. Ameican Jounal o Agicultual Economics 7(1990): 709-70. Seton, R., and T.A. Seton. oopeatives as Entants. RAND Jounal o Economics 18(1987): 581-595. Shy, O. ndustial Oganization: Theoy and Applications. ambidge MA: The MT Pess, 1995. Sutton, J. Technology and Maket Stuctue. ambidge MA: The MT Pess, 1998. Tennbakk, B. Maketing oopeatives in Mied Duopolies. Jounal o Agicultual Economics 46(1995): 33-45. United States Depatment o Agicultue (USDA). What is a oopeative? Rual Business and oopeative Development Sevice, oopeative nomation Repot 50, Washington D, Mach 1995. United States Depatment o Agicultue (USDA). Fame oopeative Statistics 001. Rual Business oopeative Sevice, Repot 61, Washington D, Mach 003. Vitaliano, P. oopeative Entepise: Altenative onceptual Basis o Analyzing a omple nstitution. Ameican Jounal o Agicultual Economics 65(1983): 1078-1083.
Net Retuns to Poduction Π ( k ) Π ( k) c ( k ) ( k) t MW( k ) c c t ( k) ( k ) t α ( k ) ( k ) 0 1 c t ( k) Dieentiating Poduce Attibute (α) Figue 1. Poduce Decisions and Welae at the Pe- and Post-nnovation Stages
RF () RF () RF () RF () Figue. Eect o oopeative nvolvement on nnovation Activity
(1) RF (1) RF (1) (1) RF (1) RF (1) (1) (1) (1) (1) Figue 3. Eect o oopeative nvolvement on Pe-nnovation Pices
(3) RF (3) RF (3) (3) RF (3) RF (3) (3) (3) (3) (3) Figue 4. Eect o oopeative nvolvement on Post-nnovation Pices
Net Retuns to Poduction ( k) ( k) c c ( k) ( k) c c ( k) ( k ) ( k ) 0 α 1 ( k) α ( k) ( k ) Figue 5. Maket and Welae Eects o oopeative nvolvement in nnovation at the Pe- and Post- nnovation Stages
Net Retuns to Poduction (3) c (3) (3) c t c ΔPS (3) (3) c (3) (3) α (3) (3) 0 1 Figue 6. Maket and Welae Eects o oopeative nvolvement hen the Maketing o-op ends up being a Monopsonist at the Post-nnovation Stage
Table 1. Subgame Peect Equilibium in the Pue Oligopsony Pe-innovation Stage (1 st Stage) 1 p + p c t 3 3t+ pi pj 6t 3t+ pi pj 18t 9tψ + 3ψ pi pj 3ψ 9tψ i(1) ( i j) i(1) nnovation Stage ( nd Stage) i Π i(1) Τ Post-innovation Stage (3 d i(3) Stage) i(3) 3ψ 3ψ ( 6tψ 1) pi + ( 3tψ 1) pj ( 9tψ )( 3tψ + 3cψ 1) Π i(,3) ( tψ ) 3ψ 9 3ψ pi pj + 9tψ 18tψ 4 9tψ 1 9tψ + 3ψ pj p i 18ψ 9tψ
Table. Subgame Peect Equilibium in the Mied Oligopsony Pe-innovation (1) Stage (Stage 1) nnovation Stage (Stage ) Post-innovation Stage (Stage 3) (1) (1) (1) T (3) (3) 4t 1t ψ + 3t ψ 8tψ 3 p + 4tψ p ( 4tψ + 1)( 8tψ 3) c t 4t ψ + 4tψ 3 p + 4tψ p c 8tψ 3 8tψ 3tψ 1+ ψ ( p p ) ( 4tψ + 1)( 8tψ 3) 8t ψ + 4tψ 3+ 8tψ ( p p) ( 4tψ + 1)( 8tψ 3) 8t 3tψ 1+ ψ ( p p ) ( 4tψ + 1)( 8tψ 3) t( 8tψ 5) + ( 8tψ + 3)( p p) ( 4tψ + 1)( 8tψ 3) t( 3tψ 13) + 3( p p) ( 4tψ + 1)( 8tψ 3) 8t 3tψ 1+ ψ ( p p ) p c+ ( 4tψ + 1)( 8tψ 3) 3 3 5 t+ 18 t ψ 16 t ψ + 16 t ψ tψ 3 p + tψ 8 tψ 1 p ( 4tψ + 1)( 8tψ 3) ( 8tψ + 3) 3tψ 1+ ψ ( p p ) ( 4tψ + 1)( 8tψ 3) ψ t( 8tψ 5) + ( 8tψ + 3)( p p) 4tψ + 1 8tψ 3 (3) (3) c
Table 3. Subgame Peect Equilibium in the Mied Oligopsony hen the OF is a Monopsonist in Stage 3 Pe-innovation Stage (Stage 1) (1) p c 1 nnovation Stage (Stage ) ( p + p c t) (1) 3t+ p p 4t t+ p p 4t 0 1 ψ 1 T ψ (1) (1) Post-innovation Stage (Stage 3) (3) (3) p + t c (3) 0 (3) 1
Table 4. Subgame Peect Equilibium in the Mied Oligopsony hen the o-op is a Monopsonist in Stage 3 Pe-innovation Stage (Stage 1) nnovation Stage (Stage ) Post-innovation Stage (Stage 3) 8tψ p + p 3t (1) c 8tψ + 1 4tψ p + ( 4tψ + 1) p t( tψ + 1) (1) 8tψ + 1 ψ ( 3t+ p p ) (1) 8tψ + 1 tψ + 1+ ψ ( p p) (1) 8tψ + 1 3 ( t+ p p ) 8tψ + 1 0 3 ( t+ p p ) T 8tψ + 1 6t+ ( 8tψ + 3) p p (3) c 8tψ + 1 (3) (3) 1 (3) 0 c