Coalition Development in the Agricultural Marketing System*

Transcription

1 oalton Development n the Agrcultural aretng System* Hubertus Puaha Graduate Research Assstant Department of Agrcultural Economcs Olahoma State Unversty 415 AgHall Stllwater OK Telp Fa e-al: hubertu@ostate.edu Danel S. Tlley Professor Department of Agrcultural Economcs Olahoma State Unversty 4 AgHall Stllwater OK Telp Fa e-al: dtlley@ostate.edu ABSTRAT: The theory of agrcultural coalton formaton s enhanced by ncorporatng nonmonetary benefts rs and farness. Producers epected utlty and nvestment decsons n the agrcultural cooperatve are affected by ther percepton about non-monetary benefts rs and farness assocate wth the cooperatve nvestment. KEY WORDS: coaltons game theory cooperatves nvestment theory. * Selected paper for presentaton n the Amercan Agrcultural Economcs Assocaton 00 Annual eetng July Long Beach A. Research reported n ths paper was supported by USDA Rural Busness ooperatve Servce Grant RBS opyrght 00 by Hubertus Puaha and Danel S. Tlley. All rghts reserved. Readers may mae verbatm copes of ths document for non-commercal purposes by any means provded that ths copyrght notce appears on all such copes. 0

2 oalton Development n the Agrcultural aretng System People are stll very gnorant about nsttutons a unfed theory that accepts pluralsm s epected. Olver E. Wllamson 000 Introducton Wthn agrcultural marets n the Unted States new generaton cooperatves are one of the most mportant new nsttutonal nnovatons. In many states agrcultural producers are nvestng n relatvely rsy new generaton cooperatve ventures. Developng a theoretcal eplanaton of ths phenomenon s the goal of ths paper. The nvestment n many closed cooperatves nvolves a hgh degree of rs. Investors should carefully consder the rss assocated wth alternatve nvestments before mang an nvestment decson. Some of the rss that cooperatves face relate to the ablty of the cooperatve to attract and retan a relable customer base and qualfed personnel to epand the maretng channels and to refne the qualty and quantty of the product to meet customer needs. Insttutons 1 le new generaton cooperatves potentally have sgnfcant mpacts on economc growth and development. The capacty of nsttutons to change n response to changes n culture and socety resource endowments and technology s an mportant determnant of economc progress Ruttan and Hayam The theme of ths study s that the effcency of the maret for nsttutonal nnovaton s a crtcal determnant of economc progress. New generaton cooperatves are among the most mportant nsttutonal nnovatons reshapng agrcultural marets n rural areas. 1 Insttutons are seen both as rules of a socety or of organatons that facltate coordnaton among people by helpng them form epectatons whch each person can reasonably hold n dealng wth others Ruttan and Hayam p.04 and unplanned and unntended regulartes of socal behavor that emerge from the repettve play of games Schotter p Tradtonal cooperatves have struggled to acqure equty because cooperatve ownershp per se conveys no beneft. Benefts generally come only on the bass of patronage. New generaton cooperatves attempt to solve the equty problems of tradtonal cooperatves by changng the property rghts structure oo and Ilopoulos

3 Greater understandng of forces nfluencng new generaton cooperatve development could help estng cooperatves mae changes to survve and facltate the creaton of new cooperatves. For agrcultural economsts to be n a poston to provde approprate and effectve polcy advce to groups consderng new generaton cooperatve formaton they must frst understand the nature of the overall cooperatve formaton process ncludng ts drvng forces and essental features. Evaluaton of new generaton cooperatves requres an understandng of factors that nfluence the commtment of agrcultural cooperatve partcpants to nvest and be loyal members. learly the mportance of nsttutonal change suggests a need for theoretcal models to analye nsttutonal change as well as emprcal analyses. Wllamson 000 suggests that people are stll very gnorant about nsttutons and he epects a unfed theory that accepts pluralsm. oase 1998 Wllamson 000 and Demset 1997 proposed the New Insttutonal Economcs that promses more new deas for the study of nsttutons ncludng cooperatves. A very rch theoretcal foundaton for the analyss of nsttutonal change can be developed n game theory. Schotter 1986 argued that because of the eplct treatment of rules game theory s a partcularly useful way of analyng and understandng the probablty of nsttuton or rule evoluton. ooperatve game theory remans partcularly under-eploted by agrcultural economsts. The strength and capacty of cooperatve game theory for applcaton has been recogned by only a few agrcultural economsts Horowt Just and Netanyahu New generaton cooperatves have a more clearly defned membershp polcy closed or well defned a secondary maret for members resdual clams patronage and resdual clamant status restrctons and an enforceable member pre-commtment mechansm. Frequently new generaton cooperatves vertcally ntegrate forward n the dstrbuton chan. Farmers as members/owners attempt to mantan control over ther operatons reduce rs stable ncome and secure new and estng marets. New generaton cooperatves can contrbute as an etenson of the farm operaton that allows farmers to mae decsons and have some control over the processng and maretng of products.

4 As dscussed by Togerson Reynolds and Gray 1997 the theory of agrcultural cooperatves has a rch hstory. The development of theory of agrcultural cooperatves has led to a greater understandng of many practcal problems. For eample the Helmberger and Hoos model provded better understandng of the ncentves to lmt membershp and revealed conflcts of nterest Torgerson Reynolds and Gray. Ths paper etends the prevous theory of agrcultural cooperatves by ntegratng nvestment theory non-monetary benefts and farness nto a theory of cooperatve development. ost responses to the forces nducng change nvolve the formaton of coaltons 3 that frequently requre fnancal nvestments and have the potental to create monetary and non-monetary benefts for members. New generaton agrcultural cooperatves are coaltons of agrcultural producers. The theory of coaltons has been developed largely ndependently n the economcs lterature. Both Staat 1983 and Seton 1986 have used cooperatve game theory to study agrcultural cooperatves. Some evdence ndcates that behavoral and economc decsons are drven by farness consderatons Fehr and Schmdt 1999; Rabn 1993; Aerlof 1979; Oun 1981; Kahneman et al Ths lterature suggests that producers perceptons of farness n dstrbuton of patronage refunds affects ther nvestment decsons n new generaton cooperatves. Farness behavor n cooperatve nvestment nvolves strateges and decsons ether from the cooperatve or nvestors to acheve ther mamum epected utlty. The essental dfference between ths paper and prevous studes s that t treats the decson to on a closed cooperatve as an nvestment decson and suggests that non-monetary payoffs may nfluence nvestment decsons. losed cooperatve nvestments are consdered 3 oaltons n agrcultural maretng systems are horontal and/or vertcal groups of ndvduals or frms wthn the agrcultural maretng system for whom a new set of bndng rules or contracts are formed. 3

5 wthn the contet of a portfolo of nvestment choces a producer can mae. A member of a closed cooperatve receves specfc rghts frequently delvery rghts n return for hs/her nvestment. These rghts are often transferable and may change n value. Payoffs are based on the amount of nvestment and whether the delvery oblgaton has been met. The value of the delvery rght s epected to be drectly related to both the se of the monetary dstrbutons to the members as well as the perceved non-monetary benefts created for members. Ths s consstent wth Staat s fndng that the non-monetary benefts that some members may derve from belongng to a cooperatve broaden the set of potentally stable solutons Staat 1989 p.0. The se and value of benefts of a cooperatve are affected by the busness envronment and nternal decsons of estng cooperatves. The benefts of a coalton are evaluated n utlty functons that have monetary and non-monetary benefts farness and rs as arguments. Wthout a clear unfyng theory of coaltons n agrculture that ncorporates the underlyng non-monetary motvatons and characterstcs of the partcpants t wll be dffcult for agrcultural economsts to develop approprate hypotheses and complete approprate emprcal wor about cooperatve development. ost mportantly producers polcy maers and other maretng channel partcpants who need solutons to maretng problems wll not have access to the nformaton they need to evaluate new cooperatve development. onsstent wth Seton 1990 producers may be motvated to partcpate n cooperatves because they understand that cooperatves alter decson-mang n non-cooperatve frms. In addton consstent wth Ladd 1974 cooperatves may also produce non-monetary benefts whch are restrcted to members and may motvate membershp. 4

6 In the net secton we present the theoretcal model of coalton formaton based on the barganng concept. In secton II we develop a game-theoretc model that ncorporates nonmonetary benefts and nvestment theory nto the analyss of closed cooperatve nvestment. An ntal nvestment decson analyss and the mean-varance model of agrcultural maretng cooperatve are dscussed n secton III. A dscusson of the mplcatons of our model n an agrcultural cooperatve settngs and concluson are presented n secton IV. I. A odel of oalton Formaton A game n coaltonal form specfes for every coalton of players a set of monetary payoff vectors that are feasble for players wthn the coalton f they agree to cooperate. We also specfy for each coalton the amount of non-monetary benefts avalable to members. A player can be an agrcultural frm or an ndvdual farmer. A coalton s formed and a feasble monetary payoff vector s chosen only when the coalton the payoff vector and the nonmonetary benefts are accepted by all players nvolved. embershp n the coaltons and the monetary and non-monetary payoffs to each member are the soluton to the cooperatve game. The dea of a barganng set Aumann and aschler 1964; as-olell 1989; Zhou 1994 s used to provde a soluton concept that specfes the coalton formaton and payoff dstrbuton. By assumng that all players n the game can bargan together wth perfect communcaton the stablty of outcomes of a game depend on obectons and counter obectons to each coalton that ests. A coalton s stable f all obectons can be met by counterobectons. The set of all stable outcomes s called the barganng set. onsder an n-person cooperatve game Φ wth a gven set of n players N = { 1 L n}. Let { } be the non-empty subsets of N called the permssble coaltons. For each {} a number v s gven and t s called the value of the coalton. In the standard model of 5

7 coaltons v s measured by materal payoffs whch are a prerequste to coalton formaton and stablty. Assume that all 1-person coaltons n { } have a ero value.e. { } v = 0 and the value of the coalton s postve v 0 { }. A payoff confguraton wll now defned as an epresson of the form 1 ; 1 L n; 1 L m where 1 m are mutually dsont sets of { } whose unon s N.e. = Ø ; m =1 and = N and the ' s are the amounts receved by each player real numbers whch satsfy = v ; = 1 L m Thus a payoff confguraton s a representaton of a possble outcomes of the game n whch the players dvde themselves nto groups so-called coaltons 1 m and each coalton dstrbutes ts value among ts members and each player receves the amount = 1 L n. When people are faced wth a game logcally t s reasonable that one does not epect that a payoff confguraton wll occur f < 0 snce player alone can secure more by playng as a 1-person coalton wth a ero value. By assumng that v for each { } = 1 L m the payoff confguraton wll be a coaltonally ratonal payoff confguraton. Thus the coalton ratonalty assumpton s very strong as t forces the game to be essentally superaddtve. 4 Superaddtvty requres that a coalton whose value s less than the 4 A game s superaddtve f the value of the unon of two dsont coaltons eceeds the sum of the values of each coalton. 6

8 sum of the values of dsont subcoaltons cannot occur n any coaltonally ratonal payoff confguraton. Usually the barganng process starts when each player tres to get at least as much as possble. At the same tme there s a desre for far play. People wll be happy wth ther coalton f they agree that the worther partners wll get more. Thus durng the negotatons pror to coalton formaton each player tres to convnce hs/her partners that n some sense she/he s worthy of hgh payoffs. Ths process can happen n varous ways among whch an mportant factor s a players ablty to show that she/he has other perhaps better alternatves. Partners besdes pontng out ther own alternatves may argue n return that even wthout hs/her help they can perhaps eep ther proposed shares. A negotaton s a sequence of obectons and counter-obectons. Stablty s reached f all obectons can be answered by counter-obectons. 5 The essence of the study of cooperatve formaton s that producers wll not on a cooperatve unless they receve a beneft from dong so. Seton 1986 bulds the model of cooperatve formaton based on the assumptons that cooperatve membershp s voluntary then ndvduals decde whether to on or not to on based on proft consderatons. learly Seton s model s based on monetary payoffs that specfcally emphase the ndvdual decson maers and ther ncentves to undertae ont acton based upon monetary payoffs. II. Theoretcal odel of ooperatve Investment An ntegrated model of cooperatve nvestment based on game theory s proposed. Ths model eplans coalton development factors nfluencng coalton stablty and the producers 5 The formal mathematcal defnton of obectons and counter-obectons s found n Aumann and aschler 1964 p

9 perceptons of the actual payoffs from coalton partcpaton. oalton structures and ther evoluton are eamned. Dynamc Games wth Perfect Informaton We consder the process of decson mang n a closed cooperatve nvestment as a dynamc game between the cooperatve and the nvestors. In order to determne the set of strateges for ether the cooperatve assocaton or the nvestors the moves the players have the order n whch they choose these moves and the nformaton they have when they mae ther decsons must be specfed. One way to organe ths nformaton s through the development of a game tree. 6 Decson nodes n game tree are represented by boes whch contan the dentty of the players who move at that node. A branch represents a possble move by a player. Every branch connects two nodes and has a drecton whch s depcted by an arrowhead. Fgure 1 dsplays the game tree for a dynamc closed cooperatve formaton and operaton game. The game begns at the top of the game tree where cooperatve assocaton ntally wrtes a prospectus for the closed cooperatve. For smplcty t s assumed the cooperatve ether offers an optmstc or conservatve prospectus as shown by each branch. Each branch ponts to a decson node for the producers snce producers mae ther nvestment decsons after they learn and evaluate the type of strateges the cooperatve has adopted. From each of the two decson nodes etend two branches representng the two possble moves producers can mae. Agan the decson s smplfed as a decson to nvest or not to nvest. If an nsuffcent number of producers decde to nvest a cooperatve frm does not form. 6 A game tree s a pcture composed of nodes and branches where each node n the game tree represents a decson pont for one of the players and s sad to belong to the player that moves at that pont. 8

10 ooperatve Assocaton Optmstc Prospectus onservatve Prospectus Stage 1 Producer Producer Not Invest Invest Invest Not Invest No ooperatve ooperatve Formed ooperatve Formed No ooperatve Low Return Hgh Return Stage Producer Producer Producer Producer Decrease Investment Increase Investment Decrease Investment Increase Investment oop. Operates oop. Operates Low Return oop. Operates Hgh Low Return Return oop. Operates. Hgh Return. The game s nfnte as long as the cooperatve ests Fgure 1. The Game Tree for Dynamc Games n the ase of losed ooperatves 9

11 Unts of nvestment gve the producer delvery rghts to the cooperatve and the value of the nvestment wll change f condtons affectng the cooperatve s busness change. If enough nvestor captal and delvery commtments are secured then producers delver ther nputs and the company operates for the year. As the cooperatve operates ts busness t develops a hstory of earnngs and cash patronage dstrbutons to ts members. At the cooperatve s decson nodes cooperatves elect to dstrbute hgh or low cash patronage refunds. Agan to smplfy the game tree a contnuous decson s treated as two dscrete choces. Usng the outcome for the frst year and epectatons for the future each producer can decde to buy more or sell transfer stoc/delvery rghts. They also decde how much to delver so they can partcpate n net year s patronage dstrbuton. The sequental decson mang process contnues as long as the frm ests. III. A odel of Agrcultural aretng ooperatve An ntegrated model of coalton development s a model that consders maor determnants nfluencng the stablty of coaltons. Investment decsons and non-monetary benefts from the cooperatve nvestment are ncorporated nto the analyss of the model of cooperatve membershp. The crucal feature of the model s how producers nvestment decsons and non-monetary benefts from the nvestment affect the stablty of coalton structures. Another mportant aspect of ths model s the effect of farness on welfare allocatons. Two mportant elements of farness are the actual outcome of an acton and the epected outcome reference pont from membershp. Farness s formaled n the framewor developed by Rabn Rabn s model ncorporates farness nto economc research. He modfes conventonal game theory by allowng payoffs to depend on farness. We assume nvestors are more lely to nvest n a cooperatve as 10

12 part of ther portfolo f that nvestment s perceved to be far to have relatvely low rs and to provde non-monetary benefts. Producers are presented wth a prospectus for an agrcultural maretng cooperatve that wll add value to the raw commodty they produce. To on ths coalton an nvestor must be an agrcultural producer and produce the raw materal further processed by the cooperatve. embers are provded the rghts to subscrbe for and purchase shares of common stoc n the cooperatve and also agree to delver for the raw materal to the cooperatve each year. The cooperatve assocaton dstrbutes one delvery rght for each share of common stoc held on the record date. Each delvery rght enttles an elgble member to delver one unt of commodty. For eample a member may eercse the rghts to purchase mnmum 1000 shares for $5000. Each year the producer has the oblgaton to delver 1000 bushels of wheat. If the cooperatve s proftable the ownershp shares and the delvery rghts wll apprecate n value and surpluses generated by the cooperatve wll be dstrbuted to the members as stoc and/or cash n proporton to how much of the raw product wheat they delver annually. The potental apprecaton n share value and the cash patronage refund represent the monetary benefts from membershp. Unle prevous wor by Seton we assume that nvestors mame epected utlty of the nvestment and ther utlty functon ncludes the epected monetary benefts from nvestment rs farness and non-monetary benefts and s mamed subect to ther wealth constrant. embershp n a new generaton cooperatve s assumed to be voluntary and potental members choose whether to nvest or not to nvest a cooperatve based on monetary nonmonetary benefts farness and rs. Non-monetary benefts are ncluded because the frm s 11

13 located n an area n whch the producer may want to create employment opportuntes and support economc development. Investment theory and the prevous wor about revealed preference condtons for valdty of the utlty mamaton model are used and etended Varan The meanvarance model of cooperatve nvestment captures the nvestor s ratonalty n undertang nvestment decson based on the epected return on nvestment rs farness and non-monetary return assocated wth the nvestment. The substantal dfference between ths model and Varan s wor are the non-monetary benefts and farness terms n the nvestor s utlty functon. The ean-varance ooperatve Portfolo odel Let p = p K p denotes for the vector of prces for the assets. 1 A = 1 K A represents the assets or portfolo choces. The varable R = R 1 K R A denotes epected return on the portfolo choces 1 A and G = G 1 K G A represents the non-monetary benefts from portfolo. The nvestor s epected return for portfolo s denoted by W = R ; f s a vector of the nvestors percepton of farness for each asset f = f 1 K f A and W represents ntal 0 level of wealth. U s the von Neuman-orgenstern utlty functon whch s enhanced wth non-monetary benefts rs and a farness component. The rss assocated wth cooperatve nvestment as a part of producers portfolo are represented by varance of return on nvestment from the portfolo. The varance of return from portfolo s represented by φ V where φ < 0 s the rs-averson parameter and V s the varance/covarance matr of the nvestment. The nvestor s utlty from portfolo has a mean µ and varance σ. Utlty s a functon of epected return on nvestment the varance of return from the portfolo percepton of farness and non-monetary benefts assocated wth that portfolo choce. Producers are hypothesed to mame utlty subect to a wealth constrant: 1

14 3 mau R φ V G f subect to p = W o and 0 Defnton 1. We have observed a portfolo choce for = 1 K n a mean-varance utlty functon ratonales the observed nvestor behavor f and only f 4 U R φ ' V G f U R φ V G f for all portfolos that cost the same or less than. That s: p p or p 0. Ths epresson tells us that gven the epected return R varance/covarance matr V non-monetary return vector G and farness vector f nvestors decde to nvest n the cooperatve membershp f the epected utlty from a portfolo contanng a cooperatve nvestment eceeds any other affordable portfolo. There are two ways of provng that Equaton 4 s true. Necessary and suffcent condtons for Equaton 4 can be derved usng ether Slutsy condtons or revealed preference condtons Varan Revealed preference condtons are used because ths approach s more applcable for emprcal analyss. The necessary and suffcent condtons for the meanvarance utlty mamaton of Equaton 4 are descrbed n Theorem 1. Theorem 1. If we assume that the mean-varance utlty functon s a monotonc concave and dfferentable then we now from the standard propertes of concave functons that for and 5 U U + U ' = 1 K n. Furthermore the hypothess of utlty mamaton mples that frst-order condtons must be satsfed by the data. That s 13

15 6 U K ' = λ p = 1 n and λ > 0 For the utlty functon represented n Equaton 4 Equaton 5 and 6 are rewrtten as Equaton 7 and 8. 7 U U + R R + E G G + S φ ' V φ ' V + H f f = 1 K n 8 R + E G + S φ ' V + H f = λ p wth = 1 n and λ > 0 K where U = U R φ ' V G f ; E S U R φ ' V G f = R U R φ ' V G f = G ; ; U R φ ' V G f = ; φ ' V H U R φ ' V G f = f λ = margnal utlty of ncome. Equaton 7 s the standard requrement for utlty mamaton whch s property of concavty from Equaton 5 and Equaton 8 s the frst-order condtons of the utlty functon that satsfed the Equaton 6. Gven the nformaton about p we can show U > 0 E > 0 S < 0 H > 0 and λ > 0 then Equaton 7 holds and our mean-varance utlty functon s concave dfferentable and monotonc. Proof. Equaton 7 descrbes the standard propertes of concave functons and Equaton 8 s the usual frst-order condtons of the mean-varance utlty functon. We assume U est 14

16 > 0 E > 0 S < 0 H > 0 and λ > 0. That s the margnal utlty of monetary returns s postve the margnal utlty of non-monetary benefts s also postve the margnal utlty of rs s negatve the margnal utlty of farness s postve and the margnal utlty of ncome s postve as well. We must show that gven any wth p p U U. In dervng the suffcent condtons for the mean-varance utlty mamaton model we need to defne: U R G φ ' V f = mn{ U + R R + E G G + S φ ' V φ ' V + 9 H f f } Snce the varance-covarance matr V s postve sem-defnte for all and we can wrte the varance of portfolo as ' V 0. By arrangng ths nequalty we get the algebrac dentty ' V ' V ' V. Now suppose that some such that p p. For notatonal convenence let us defne U = U. Then we have 10 U R G φ ' V f = mn{ U + R R + E G G + S φ ' V φ ' V + H f f } 11 U R G φ ' V f U + R R + E G G + S φ ' V φ ' V + H f f whch can be wrtten as: 1 U R G φ ' V f U + R + E G + S φ ' V 13 U R G φ 'V f U + R + E G + S φ ' V + H f + H f because R + E G + S φ 'V + H f = λ p then we can say 15

17 14 U R G φ ' V f U + λ p Snce p 0 then 15 U R G φ ' V f U and 16 U R G φ ' V f U R G φ ' V f Ratonalng the observed behavor of nvestors usng a dfferentable concave monotonc utlty functon wll guarantee the estence of U > 0 E > 0 S < 0 H > 0 and λ > 0 that satsfy the nequaltes: U U + λ p for = 1 K n. If there est some values U > 0 E > 0 S < 0 H > 0and λ > 0 for = 1 Kn that satsfy the nequaltes above for some observed behavor of nvestors p = 1 K n then there must est a contnuous concave monotonc utlty functon that ratonales the observed behavor. Stage I: Intal Investment Decson The nvestor s nterest s choosng to mame utlty. hanges n are changes n demand for nvestment. Suppose that s chosen to mame the nvestor s utlty. Let µ be the monetary returns D be the non-monetary benefts σ be the varance of returns and F represents farness 7. For eample the amount of delvery rghts purchased monetary and non-monetary benefts rss and percepton of farness. Let us denote the mamum utlty as for dfferent choces of. µ D F mau σ subect to g W0 = 0 and 0 7 In ntal nvestment decson analyss the notatons µ D σ and F are used for dervaton purposes nstead of R G φ ' V and f to mae the utlty functon more general. 16

18 so that the Lagrangan s 0 W g F D U L λ σ µ λ = and the frst-order condtons wth respect to and λ are = D D F D U F D U L σ µ µ µ σ µ + F F F D U F D U σ µ σ σ σ µ 0 0 = W g λ = = W g L λ for 1 = Kn These condtons determne the optmal choce of whch n turn determne the mamum utlty functon. Snce ; ; ; and then the nvestment demand functon F D U σ µ f F = 0 0 W p W g = R = µ D = G 'V σ = φ 19 0 W p f V G R φ = The envelope theorem 8 gves a formula for the dervatve of mamum utlty functon wth respect to choce varable : L d d = 0 = W g F D U d d 0 λ σ µ 8 The proof of the envelope theorem can be found n Varan 199 p

19 Ths equaton shows how the mamum utlty changes gven changes n. Stage II: losed ooperatve s Decson odel The closed cooperatve s obectve functon s to mame net surplus and the cooperatve surplus functon s determned by revenue total producton costs and cash patronage refunds. Suppose there s a coalton S of potental nvestors n a closed cooperatve = 1 K m. We assume that closed cooperatve coalton S produces consumer product usng purchased nput from non-members plus nput from members where the margnal cost of producng s c and the total cost s. From our dervaton of the nvestor s demand for cooperatve nvestment we have = R G φ V f p W0. Assume ths s a contnuous and dfferentable for all varables n the model. The aggregate demand for cooperatve nvestment from the cooperatve members n coalton S 1 = R G φ V f p W for S S S 0 where * S s equvalent to owners equty whch s determned by Equaton 1 n Stage I. Total nvestment captal K can be obtaned from owners equty and/or loans. Let L s the amount of nvestment captal to produce consumer product from loans that s proportonal to amount of captal nvested/owners equty n the cooperatve L * = γ where γ s the loan leverage S parameter. The cooperatve nvestment captal s K = + γ = 1+ γ. S Let θ K be the revenue that an nvestor obtans from an nvestment n a closed cooperatve. Then we can say that the revenue for cooperatve as a coalton S s * * S * S 18

20 θ K = θ K S S snce S. If the cooperatve s producton functon s y S = h K then cooperatve s revenue can be wrtten as θ K = p h K where S S p S s the prce of consumer product. The cooperatve s surplus s: Π' K = ma θ K for S > 0 9 where = w s the total producton costs assocated wth producng and s the prce w for one unt of raw materal/nput. If s the optmum quantty of nput that mames Π' K then we wll get * = 0 f θ K for all > 0. S The cooperatve s retaned earnngs RE are: 3 RE K = Π K = Π K R for S Π K > RS where R = w S r s the cash patronage refunds whch can be earned by nvestors n coalton S wth w r as the boo value of each share of common stoc at the present tme. We can epress the cooperatve s retaned earnngs RE: 4 RE K = ma[ Π K 0] The cooperatve s retaned earnngs RE K = 0 f cooperatves are not proftable to delver R S to nvestors or f not enough captal and delvery commtments. In ether case the cooperatve fals to operate. To formally derve the cooperatve mamng behavor Equaton 4 may be rewrtten as an optmaton problem: Π ' = ma Π 5 K S p h K w K 9 The nvestment captal s a constant term whch determned and fed from Stage I of closed cooperatve nvestment game tree. We assume that the cost of owner equty and loans are fed. 19

21 subect to and E w r > 0 where E s the mamum amount of shares allowable to be offered by the cooperatve and s the ntal boo value of each share of common stoc one share s equvalent to one unt of nput delvered. w r The Lagrangan functon s 6 ] [ E w w K h p K L r S = λ λ By assumng that s dfferentable then the frst-order and the second-order condtons wth respect to and K h λ are 0 ' = = r S w w K h p L λ 0 = = E w L λ 0 = S K h p L and 0 = λ L then we get compettve factor demand 7 * * E w w p r S = so the soluton for the supply functon mamng the cooperatve net surplus s 8 { } r S S K E w w p h y * The Role of Farness Suppose there s a two-player cooperatve game wth perfect nformaton. The two players are the cooperatve and an nvestor. The med strategy sets are T and T for the nvestors and the cooperatve respectvely. Let be the nvestor s epected return of R 0

22 portfolo choce. We assume that mamaton of each player s epected utlty s determned by ther chosen strategy and ther belefs about the other player s strategy choces. Let a and a be the strateges chosen by the nvestor and the cooperatve respectvely. The nvestor s belefs about the strategy the cooperatve s choosng s represented by T b T T and the cooperatve s belefs about what strategy the nvestor s choosng s represented by b T. The farness term f measures how far an nvestor perceves the treatment of other players cooperatve n the coalton. To formale the nvestor s perceptons t s necessary to develop a model that eplctly ncorporates belefs. The term f a b eplans how far the cooperatve s beng by choosng strategy a. If the cooperatve beleves that the nvestor s choosng strategy b. The term f a b measures how much more than or less than nvestor s equtable payoff the cooperatve beleves the assocaton s gvng to the nvestor. The cooperatve has the opportunty to choose the payoff par [ R a b R b a ] from among the set of all feasble payoffs f the nvestor s choosng strategy b. The nvestor s equtable payoff s epressed by the followng relatonshp e R b = [ h R l b + R b ]/. e R b provdes a reference pont aganst whch to measure how far the cooperatve s perceved as h l beng to the nvestor where b s the nvestor s hghest payoff n X b and R b s R the nvestor s lowest payoff among ponts that are Pareto-effcent 10 n X b. The feasble set of Pareto-effcent ponts are the ponts n the set { } X b R a b R b a a T where X b s the set of alternatve payoff combnatons and R ; and T s the set of pure R 10 Pareto-effcent s a pont n whch t s not possble to mae one person better off wthout mang at least one other person worse off. The pareto-effcent stuaton always reflects optmal pont n the set of feasble ponts. 1

23 strateges of the cooperatve. The term X b loos at the set of payoff combnatons from the cooperatve s perspectve and the cooperatve taes nto account ts belef about whch strategy the nvestor wll choose b. Accordngly X b reflects the cooperatve s belef about all players payoff combnatons n the opportunty set. From these payoffs the farness term s defned. Ths term captures how much more than or less than nvestor s equtable payoff the cooperatve beleves the assocaton s gvng to nvestor. Defnton. The percepton about the cooperatve s farness to the nvestor s gven by 9 f a b e R b a R b h l R b R b If R h l b R b = 0 then all of the cooperatve s responses to strategy b provde nvestor the same payoff. Therefore there s no farness ssue and f a b = 0. learly f a b = 0 f and only f the cooperatve gves the nvestor the equtable payoff. If f f a b < 0 a b > 0 the cooperatve s gvng the nvestor less than the equtable payoff. Fnally f the cooperatve s gvng the nvestor more than the equtable payoff. The nvestor s farness to the cooperatve s gven by f a b. If the nvestor beleves that the cooperatve s choosng strategy then the term b measures how far the nvestors b f a are beng to the coopertatve. Fgure shows the outcome term f a b as a functon of the level of payoff R s. Ths fgure captures the producer s percepton of farness: the hgher the nvestor s payoff offered by the cooperatve s compared to the equtable payoff the hgher the percepton of farness.

24 f a b Postve outcome term 0 R s payoff offered Negatve outcome term l R e R h R Fgure : The Outcome Term as a Functon of the Level of Payoff Offered for a Gven otvaton Factor 3

25 The central feature of ths farness term s that f nvestors beleve that the cooperatve s treatng them unfarly then f a b < 0 and the nvestor wshes to respond to the cooperatve negatvely by choosng strategy such that f a b < 0. However f cooperatve s a delverng far acton to nvestors f a b > 0 and then nvestors wll provde the cooperatve far feedbac. Hypotheses Ths theory of cooperatve nvestment shows that the cooperatve enterprses that generate mamum epected utlty to producers are preferred more than those that do not. Jonng a closed cooperatve may ncrease the nvestor s rs especally f t s a start-up enterprse. There must be a meanngful reason that encourages nvestors to nvest n a closed cooperatve. Equaton 19 n the prevous secton clearly generates three hypotheses related to the closed cooperatve nvestment decsons. The frst queston to be addressed n ths analyss then s whether non-monetary benefts from cooperatve nvestment motvate producers to nvest n a closed cooperatve. Therefore the frst hypothess s: H 1: Producers who want to create employment opportuntes and support economc development n ther local communty are more wllng to nvest n a cooperatve as part of ther portfolo f that nvestment provdes those non-monetary benefts. The mpact of rss assocated wth cooperatve nvestment on producer s epected utlty and nvestment decsons s an mportant ssue n ths study. The second hypothess s: H : Rs-averse producers are more wllng to nvest n a closed cooperatve f they perceve that nvestment to have relatvely low rs. The thrd hypothess s related to the psychologcal lterature that eventually was used to study the mplcatons of farness n economc transactons. Evdence ndcates that people s 4

26 notons of farness are heavly nfluenced by the status quo and other reference ponts Rabn 1993; Kahneman et al. 1986a b. Followng ths reasonng the thrd hypothess s: H 3 : Producers who are concerned about farness are more wllng to nvest n a closed cooperatve f that enterprse provdes treatment that s perceved as far. IV. Summary and oncluson The forces nducng change n agrcultural cooperatve nsttutons have lead to the demand for a clear unfyng theory of agrcultural maretng cooperatve development. A model of new generaton cooperatve nvestment based on nvestment theory s proposed by ncorporatng monetary non-monetary farness and rs components n the model. Our model ncorporates non-monetary percepton of the nvestors as an essental determnant nfluencng the formaton of a cooperatve. Investors udgng whether or not to nvest n a new generaton cooperatve not only consder monetary benefts from ther nvestment but non-monetary benefts farness and rs as well. Our theory suggests that the ratonal nvestor wll choose a new generaton cooperatve as part of hs portfolo f the utlty of a new generaton cooperatve nvestment eceeds any other affordable portfolo. The role of farness n the new generaton cooperatve nvestment model captures several mportant ssues of nvestor behavor. Investors percepton of farness s heavly nfluenced by ther reference ponts. For nstance the nvestors vew of the farness of closed cooperatve management to the members can be nfluenced by how that frm has treated them n the past relatve to ther epectaton. The model of closed cooperatve nvestment can be vewed from a game theoretcal approach as a sequental game wth perfect nformaton. In the cooperatve formaton stage the 5

27 potental nvestors observe the cooperatve s management behavor and ths provdes nformaton on whch nvestors mae ther nvestment decsons. In ths game the cooperatve s management behavor can concevably change the motvaton of the nvestor to nvest. A sequental game nvolves sequental strateges and a decsons process and t wll contnue as long as the frm ests. In the earler stage the success of a coalton formaton s greatly determned by the prospectus of that cooperatve. If the cooperatve s prospectus provdes overly optmstc nvestment return epectatons ntal postve perceptons may be created. In the second stage of the game the nvestors have two alternatve strateges: ncrease or decrease the nvestment for the net perod of the operaton. The decson s determned by utlty as a member of the closed cooperatve. If the cooperatve delvers hgh utlty to ts members agan the nvestors wll respond postvely to the cooperatve s management and ncrease ther nvestment. Investors mame utlty subect to a wealth constrant and they wll decde to nvest n the cooperatve f the epected utlty from a portfolo contanng a cooperatve nvestment eceeds any other affordable portfolo. Sequentally the cooperatve mames net surplus subect to mamum allowable shares to be offered to nvestors. The ntal nvestment decson analyss provdes the optmal value of demand for a closed cooperatve nvestment n achevng mamum utlty as a functon of monetary return socal/non-monetary benefts varance of the return and farness. The stage II analyss obtans and derves the supply functon of the closed cooperatve nvestment. Further research s obvously requred snce comprehensve analyss wth respect to the closed cooperatve pont of vew needs to be developed. 6

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