Bargaining on Ecological Main Structures for Natural Pest Control: Modelling Land Use Regulations as Common Property Management

Transcription

1 Barganng on Ecologcal Man Structures for Natural Pest Control: Modellng Land Use Regulatons as Common Property Management Ernst-August Nuppenau Justus-Lebg-Unversty, Gessen, Germany Contrbuted paper prepared for presentaton at the Internatonal Assocaton of Agrcultural Economsts Conference, Gold Coast, Australa, August 12-18, 2006 Copyrght by Ernst-August Nuppenau. Readers may make verbatm copes of ths document for non-commercal purpose by any means, provded that ths copyrght notce appears on all such copes.

2 1 Abstract In ths paper we argue that the loss of bo-dversty should be of concern for farmers, though t seems to be of lttle or no concern to them at the moment. As dversty s a component of nature that controls the growth of pests, a loss of bo-dversty means ncreased exposure to pests, danger of crop falures and, n the long run, lower average yelds and profts. So far farmers buy costly pestcdes for compensatng the reducton of bo-dversty. We argue that nsttutonal problems are the reason why farmers are not concerned wth bo-dversty, and show that under pure prvate property rghts farmers have nterest n pestcdes and not n bodversty as a measure of crop protect because they have perhaps to devote land to the natural eco-system. In contrast, publc polcy whch s assumed to make bo-dversty mprovements, and ths polcy may pay off. Note, the prerequste for mproved n bodversty through the establshment of an ecologcal man structure (EMS), may reveres ths trend. We show that ont efforts n a communty of farmers can result n buldng up an adequate sze of nature elements n landscapes (an EMS) for mantanng the bo-dversty. These nature elements shall allow, n parts, a more sustanable performance of pest control than chemcal control. The publc control nstrument s the EMS sze. For ths, n the paper, we extend the nsttuton economcs model of Rausser and Zusman (1992) on productve governments to bo-dversty. Keywords: Common property management, nsttuton, crop rsk and bo-dversty; JEL: Q28

3 2 1 Introducton The overall loss of speces n farmng areas through modernzaton, ntensfcaton and mechanzaton of agrculture, ncreased applcaton of chemcal substances, and, n partcular through a mnmsng of nature elements such as hedgerows, small forest and wetlands, has attracted the attenton of ecologsts. Especally n the past nature elements n an ecologcal man structure, EMS, have strongly supported bo-dversty n the countrysde as well as mantaned an equlbrum between pest pressure and agrcultural productvty. Nowadays, n many regons of the world we see a retreat of nature or nature elements n cultural landscapes; though general delberatons tell us that we need nature (as nature servces). In farm lands, nature servces (FAO-MA, 2004) such as pest control, water purfcaton, and sol fertlty, are usually provded by nature elements n these landscapes. These elements can coexst wth farm land only by dmnshng productve land and seemngly lowerng profts. Ecologsts tell us that the observable great loss of nature elements n rural landscapes, and hence the loss of bodversty, should not only be a concern of the publc, but also of the farmers as ther nterest also maybe harmed. Ecologsts as a lobby group want multfunctonal agrculture (Cahll, 2001) and urge governments to take measures to preserve bo-dversty, n general, and especally nature elements n cultural landscapes. Opposng multfunctonalty, farmers react to publc conservaton concerns by argung requests for ncreased bo-dversty and nature elements n ther felds wll reduce ther compettveness and ncome. Farmers thnk that they can lve wth reduced bo-dversty qute well, because the prevous functon of bo-dversty n farmng systems, essentally as a medum of pest control, has been taken over by chemcal nputs. And, as long as farmers produce enough as well as hgh qualty food, the publc should not be concerned. In contrast, ecologsts warn of long-term negatve mpacts of pestcdes and prefer natural pest control ; they assume that a further declne of cultural landscapes threatens mult-functonalty and they challenge the sustanablty of modern

4 3 farmng systems. Ths seems to be a conflct that can only be poltcally solved. Others see the conflct as an nsttutonal problem of property rghts (Hodge, 1988) and favour prvate property; but a deeper nsght nto nsttutonal problems may be nvolved n the debate on natural pest control. The queston s: What happens f farmers work together? In ths context a local government, as a publc manager who prevents pest by a dverse nature, may play a role (see Rausser, 1992, on predatory versus productve government). Accordngly, we argue that nsttutonal problems have been overlooked and both, farmers and ecologsts, may beneft from natural elements and multfunctonalty. It s the prmary obectve of the paper to develop a model whch helps to understand why farmers are reluctant to support bo-dversty proects that are based on EMSs. To show the potental for common property management fosterng bo-dversty and controllng pest bologcally, we explan how to depct optmal publc regulatons wthn a framework of publc barganng. In ths case publc barganng s about feld margn provson of farmers. The secondary obectve s to show that a based manager rather than a benevolent dctator can be perceved and that a based though effectve regulaton results. The paper s structured as follows: Secton 2 gves an outlne of the dea. It provdes arguments for developng a model that caters for publc choces on measures aganst producton rsk usng a landscape approach (EMS). Secton 3 presents a framework for modellng an EMS n conuncton wth farm behavour. Secton 4 dscusses the tragedy of the commons and a benevolent dctator, and secton 5 offers the result for group management by choosng a poltcally corrupt but powerful manager. Herby nature s a common property reducng costs and we assgn nature servce a value. 2 Outlne of the approach The presented model uses the poltcal economy approach on barganng for publc goods of Rausser and Zusmann (1992) to derve an obectve functon of a farmer communty n nature

5 4 conservaton. The obectve functon wll contan an EMS as a ontly producble, communally owned and managed resource. Bodversty s retaned through preservng nature elements n an EMS embedded n farmng (McNeely and Scherr, 2002). Though losng profts by cultvatng less land, farmers concede land to a communty because they gan ndrectly from a better envronment. The am s attanng less pest pressure n farm lands through a more dverse bota by allocatng land for nature. Farm land s prvate, but a nature manager has the rght to mpose statutory regulatons on some land. Regulatons mposed by a manager for the publc good nature are obeyed by farmers. Here, the bass for the common property management s an EMS to whch farmers voluntarly contrbute. Land s used for hedges, stone walls, dtches, wet lands, etc.. The producton and cost functons as well as the decsons of farmers are orented towards bo-dversty gvng hgher prvate profts. The ratonal s to use the EMS as a bass to conduct a communty-wse and prvate evaluaton of nature. Snce bo-dversty n the form of multple speces occurrence shall reduce rsk of crop falures, the publc manager cares about nature and farmers. Carng requres a communal obectve functon contanng nature. In modellng, for techncal reasons, nature s represented by a bo-dversty ndex, whch counts n management and enters the obectve functon. Then communally produced bo-dversty becomes an element n the producton functon of farmers, as t reduces the rsk of crop falure. As wll be shown by dualty theory, bo-dversty appears n a cost functon of mnmzng rsk. We assume substtuton between both, purchased chemcal nputs and nature. Bo-dversty s then an effectve rsk reducng natural devce through publc management. A reducton of fnancal costs n plant protecton shall be acheved through a poltcal economy approach of managng the commons. Note that costs enter the obectve functons of farmers and the communty. The model shows how aggregaton of prvate obectves can be perceved. On behalf of a communty, a manager of the natural envronment maxmses hs

6 5 net benefts from addtonal nature elements and mnmses costs from economc rsks of crop falures. As opposed to an unorgansed communty, whch degrades the envronment, the managed communty shall be better off. But the beneft s not the beneft of a benevolent dctator; t s skewed through a poltcal process of rent seekng. However, for farmers costs and benefts count dfferently. Ther ndrect benefts are reduced fnancal costs of rsk, expressed as reduced purchases of equvalent chemcal substances to combat pests. These pests occur f natural predators are not avalable due to lack of habtats. Drect costs are created by wavers of full utlsaton of land, such as buffer strps or feld margns used for the EMS. Furthermore, farmers must use resources for rent seekng (Rausser and Zusman, 1992), hence, nteractons must be researched. Snce nature "producton" relatonshps are essentally confronted wth potental mprovements, farmers are normally sceptcal whether a rsk reducton can really be acheved. In contrast, pestcdes mostly offer mmedate cures of pests and guarantee hgh yelds. Apparently, there s a trade off between a wll to save pestcdes and the uncertanty of gettng the delvery. The model reconsders the problem of uncertanty by puttng certan probabltes on natural processes and modellng decson makng as a stochastc problem of crop falure and rsk. It uses standard approaches of cost functons, technques to cater for rsk, and strateges of farmers to assure aganst rsk. 3 Modellng of farm behavour, rsk and Ecologcal Man Structures (EMS) 3.1 A framework for farmers partcpaton n bo-dversty/ems and nterest functons Our basc analytcal framework for the descrpton of farmers partcpaton s an EMS (Oskam and Slangen, 1998). For dversty provson t focuses on spatal allocaton of land by farms (Wossnk, et al, 1998). Ths spatal frame wll enable us to (re)formulate Rausser and Zusman s (1992) ntally tme orented model as a spatal model. A stylzed framework s necessary to get dmensons of space and farms n one dmenson of decson makng, gven

7 6 lmted space. It also provdes a tool for emprcal applcaton, snce feld margns and the sze of the EMS are dsplayed. Fgure 1, below, depcts the dea of a plot orented agrculture longtudnal farm extenson ( dentfcaton bl ) of farms: ncludng feld margns. X maxmum extenson of farm area x b x b feld:, The lattudnal axs wth equal dstances (a 1, a 2,..., a,... to a n ) shows the horzontal stretch of farm sze spread of x 2 of x 1 b 2 x 2 b 1 x 1 feld: 1,1 feld: 2,2 b 1 a b 2 a dstance of feld margn a 1 a 2 a dstance of felds: a lattudnal farm extenson fxed dstance A dentfcaton of feld: a farmng communty at equal dstances of felds (conceved n a polder or settler framework of land dstrbuton). Fgure1: Spatal Allocaton and Ecologcal Man Structure Farm szes dffer on the longtudnal-axs allowng farms to have dfferent szes accordng to dstances (x 1, x 2,...x,... x m ). Ths framng of farms enables us to depct land allocaton and the mplementaton of the EMS n the mode of feld margns. From defnton l = a x (1) we derve the sze l of a feld. Next, the area contrbuted to the ecologcal man structure f, whch can be dentfed on feld of a farm, can be depcted as percentage of the sze of the feld. Usng a Taylor seres expanson for a rectangular feld a x multpled by a percentage b, we receve an approxmated f as sze of feld margn, appled, dependng on b f = a,0 b x + x,0 a b - a b x b 2 x a b (2) where: 0 b 0.2 and a b x b 0 Accordngly, the remanng area that s not subect to feld margns s defned as: l = (1-b ) l = (1-b )2 x A/n (3) In ths formula, the part of the lattudnal-axs,.e. the dstance of the feld a, s already measured by the length of a farm A dvded by the number n of felds (equal length of feld

8 7 "a" and half dstance of x). The advantage s an equvalent expresson of a constrant mposed by an EMS B by the length of a farm (Rausser and Zusman, 1992: tme frame becomes a spatal frame and B expressed n feld margns). For nstance, f 300 hectares have to be obtaned from 1000 farms of average sze of 10 ha, each farm has to provde a sze of 0.3 ha: B a x b ; and snce A = a by assumpton: B A x b A Ths spatal presentaton helps to specfy the ndvdual use of agrcultural farm land, ncludng the provson of feld margns b, n terms of the overall constrant mposed on farmers. l = (1- b ) l = (1-b ) x A/n = (1-b ) x n B x b Havng specfed the ndvdual farm land as part of a rsk reducng EMS and knowng ecologcal mpacts of the EMS on crop rsk, we can proceed to model ndvdual farm behavour. B x b (5) (4) 3.2 Farmers' behavour n feld margn provson for an Ecologcal Man Structure Ths secton presents a mathematcal expresson of four aspects of farm behavour. They are: 1. A representaton of rsk and decson-makng, whch shall enable us, most drectly, to nclude nature and the EMS nto cost functons; 2. A possble voluntary provson of feld margns by farmers for an EMS, whch enables us to reduce rsk, has to be dscussed formally. Ths wll be done on the bass of a farm behavour that corresponds to the relevant mcro-economc theory of farmers; 3. A depcton of an ordnary proft maxmsng, whch shows farmers lmted ncentves to provde feld margns (tragedy of the commons: Rausser and Zusman, 1992). (Anyhow, the allocaton of feld margns towards an EMS has to be seen n conuncton wth obtanable bo-dversty and the use of agrcultural land for profts (Wossnk et al. 1998).); and 4. A postve effects from ecology whch reduces costs due to hgher bologcal actvty,.e. effects from the EMS. Hereby, the EMS s managed as publc goods.

9 Rsk and Costs We propose to use two steps to reduce complexty and mnmse on notaton n stochastc affars. In a frst step we assume that a farmer faces two dstnct stuatons to whch he attrbutes probabltes: y g stands for good and y b for bad yelds. In a second step, we ntroduce ρ, whch stands for the probablty of good yelds and (1-ρ) for dsaster, respectvely. Ths means, decson, rsk and actual profts are splt n two sequental perods. Frst, farmers wth a probablty of ρ wll obtan a gross margn p c and have cost C c. Gross margns and costs are favourable n case of prevalence of hgh bo-dversty assocated wth the EMS, and there s no need for addtonal measures of pest control. However ths depends on the probablty ρ. Average costs are lower than wthout EMS because pestcde use s low. However, wth a counter probablty (1-ρ) farmers detect pest on ther feld (for nstance nsects or fung) and ether wll have lower yelds or use addtonal chemcal nputs ncreasng costs. In the second perod, anyhow, we can assume that a dsaster occurs wth a probablty of (1-ρ) (as sad, the good stuaton where pest control, bologcal or chemcal, helps s ρ). Note a dsaster (crop falure wth a certan probablty) can occur even f an EMS exsts or pestcdes are used, respectvely. Dsaster apples also to preventve pestcde use, the alternatve to the EMS, perhaps on a lower probablty but at hgher costs. Strategcally expressed, farmers who wll on a communty have, as a reference, a stuaton where profts from non-onng a communty are gven as addtonal pestcde costs and good yelds. Proft consderatons of farmers and correspondng decson makng are focused on ncremental profts from onng a communty. These complex ssues are modelled assumng a probablstc decson where the two probabltes are nterlaced. Alternatve uses of pestcdes preval;.e. to go for a strategy of natural control or to apply a strategy of chemcal control. We start wth an expected dfference ~ ~ c ~ p E Π ] = E[ Π ] E[ Π ] (6) [, A, A

10 9 of profts as prme crtera for mprovement and use a probablstc approach of yelds, where ~ E [ Π = ρ + Θ Π + Θ Π (6 ) c s, c, A ] l (1 ), A (1 ρ l )( 1 ) as well as consder the second term as a calculated reference at gven probabltes ~ p n, p s, p E[ Π ] = (1 ρ ) Π + ρ Π (6 ) p p n, c, A where: E[Π,A ] Π s,c,a Π n,c,a Π n.p,a Π s,p,a ρ l Θ ρ p = expected proft gan on farm (the reference of the fx proft has been dropped) composed of = successful profts wth EMS and communty, hgher probablty of good yelds due to good nature = profts are dmnshed due to pest nfecton though an EMS exsts and no use of pestcdes = low profts though a chemcal pest control has been conducted and expendtures for pestcdes = profts wth no EMS put pestcde applcaton and hgher yelds due to chemcal pest control = probablty of farmers wth no pestcde use modfed under the prevalence of the EMS = change n the probablty of farmers to face pest, beng altered by the sze of the EMS as ndex = probablty ndcatng the rsk of farmers after applcaton of pestcdes or prevalence of the EMS For smplcty, further we sort for and focus on elements that contan the mpact of the change n probablty. Dstnct profts and strateges have to be specfed, whereas we focus on profts "wth" and profts "wthout" a communty orented EMS. Moreover, we assume a lnear shft n the supply functon and a quadratc cost functon (Chambers, 1988); at least we do t later to get decsons. The maor thng to be notced concerns the cost modellng of EMS. In ths respect, we assume that farmers see communty orented rsk reducton by an EMS as a yeld changng functon. Yelds are assocated wth a changed probablty ρ(1+θ) due to an ndex Θ (explaned later). As well, f the preferable stuaton of havng good yelds (low exposure to pests) s not occurrng, farmers wll buy pestcdes. Wth the probablty (1-ρ)(1-Θ) a threshold s exceeded where farmers have to apply pestcdes whch reduce ther gross margns. Fnally, f a dsaster occurs, n a bad stuaton, after decson, costs are forgone and revenues are low. c c ~ p ΛΠ, = p y, ρ (1 +Θ) l C ( l ρ (1 +Θ), r )] + p y, (1 ρ )( 1 Θ) l C ( l (1 ρ )( 1 Θ), r )] E[ Π ](6a) A [ [ g d (+) (-) (+) (-) where addtonally : p y, = adusted gross margns per hectare, ncludng yelds, (proft ) ncludng y yelds l = remanng area of the feld on farm, area cropped, (proft )

11 10 C c (.) r r ' = cost functon on quantty of q at feld l wth the yeld y=q /l, (cost =>proft ) f the EMS exsts = costs of nputs, farm specfc, especally pestcdes, etc. (cost =>proft ) = costs of addtonal nput after detecton of pest problems, farm specfc, especally pestcdes (proft ) Ths specfcaton of rsk ncludes varyng cost functons. These functons must be gven exante. Fnancal costs are apparently lower when no pestcdes are appled. Alternatves are expected costs: From our gven specfcaton of rsk, as a dscrete representaton of yeld fluctuatons, alternatves of choce and opportunty costs emerge assocated wth dfferent regmes and probabltes. Note, we can subtract equal terms, but must assume rsk neutral behavour. c c ' ' ' ΛΠ = [ p ρ l C ( l ρθ, r ) C ( l (1 ρ )( 1 Θ), r ) (1 Θ) ρr l + (1 ρ)( 1 Θ) p l c ] (6b), A Presentaton (6b) and proft notaton can be further smplfed takng addtonal costs and revenues as opportunty costs nto account and ntegratng them n perceved new cost functon c c ' ' ΛΠ = [ p ρ l C ( l ρθ, r )]: C ( l ρθ, r )] = C ( l ρθ, r )] + C ( l (1 ρ )( 1 Θ ), r ) (1 Θ) ρrl + (1 ρ)( 1 Θ pl (6c), A ) Feld margns and balancng prvate cost benefts In a second step we add the postve ndrect effect of a crop nsurance (average better profts by less expendture for pestcdes), whch has been dscussed above as dfference n expected profts, and the drect negatve mpact of land allocaton on profts (less profts due to feld margns as land reallocaton) whch wll be dscussed. In equaton (6d), we ntroduce as polcy measure a land share (%) to be devoted to an EMS, b, and farmers balance effects. l ~ r Π, A = Π, A(..., b ) + E[ Π, A] (6d) From now on we must dstngush between a farm margn, b, and the overall sze of the EMS, B. For a farm we state a small b, though a postve mpact of land devoted to feld margn θ b n costs exst; the collectve mpact Θ s explaned later. For notce, farmer behavour n feld margn provson s wrtten as constraned optmsaton (Chambers, 1988) and broadly forms: c Π,A = [ p l (1 b ) C ( l (1 b ), ρθ b, ρθ, r )] (6d ) (+) (-) (-) (+) (+) (+) (-)

12 11 where: ncrease: and decrease : b = feld margn as percent of feld sze (proft ) C c ( ) = corrected cost functon (see above) ncludng choces accordng to rsk varaton through the EMS Then we splt horzontal and vertcal components of the sze of a plot as explaned prevously. In that case of a regulator s nfluence on feld margns, as a %: b, profts are adusted to Π,A = [ p x a (1 b ) C( x a (1 b ), θ b, Θ, r )] wth constant lattude a: x =a x (6e) Now, assumng lnear homogenety n land wth respect to the cost functon and equal dstances of felds on the horzontal axs, Σa=A, a sum of profts from felds can be rewrtten as: Π,A = A[ p x (1 b ) C( x (1 b ), θ b, Θ, r )] (6f) In the gven context, ths s a most smple representaton of profts as land allocaton, as gross margns per hectare, as nput costs of pestcdes, and as strategc varables of rsk. It also enables a treatment of publc management. But, frst, no publc management serves as reference. 4 Tragedy of the commons n publc rsk management for EMS The maor argument for a postve relatonshp between publc management of rsk reducton by an EMS and feld margns s depcted n relatonshp (7a). A change n rsk of crop falure shall be lnear regressble on szes of the EMS. Note that the szes of effects are ndvdualsed n order to care for specal mpact and nterest of farmers. We state a constant and lnear part: Θ = Θ B 0 Θ1 (7a) As a further explanaton: Functon (7a) can be consdered a reduced form of a sequental functonal relatonshp between a rsk of crop falure and bo-dversty on the one hand and bodversty and constructon of EMS on the other hand. A dversty ndex D serves as measure. Θ = Θ Dand D = Θ B Θ = Θ Θ [ Θ Θ B] = Θ Θ Θ + Θ B] (7b) 0 Θ1 0 Θ Θ1 Admttedly, ths s only a crude representaton and a more elaborated scheme s percevable. But, t suffces to explan the core arguments. Any complex representaton of bo-dversty

13 12 would requre a more detaled argument on the management sde. Introducng the ecologcal constrant B, derved from the correspondng A of farm length (see equaton 4 and 5), gves profts on an ndvdual level expressed as dependent on ndvdual allocaton b of feld margns and communal achevement (requrement) rsk depend on "B" for farm : Π,A B[p = x (1 b ) C(x (1 b x b ), θ b, Θ 0 Θ 1 B,r)] For nterpretaton: A communty of small farmers may decde on B, but only, because the pressure on all of them prompts the allocaton of feld margns. The queston remans: Wll ndvdual optmsaton behavour go for the b s recognsng the postve effects on Θ? Nothng has been sad on voluntary provson of feld margns for the EMS, so far, and the benefts to ndvdual farmers. As a publc good the ecologcal man structure B,.e. the emprcally measurable equvalent of nature provson by the communty of all farmers, s only of potental nterest; t may not appear due to common property problems. To sketch the argument, we look at the optmsaton towards b n (7) by settng frst dervatves equal 0: (6') Π b,a = B[p x + C(x (1 b ), θ b, Θ x b 0 Θ1 B,r)] B[p x(1 b) C(x (1 b ), θb, Θ + 2 [ x b ] 0 Θ1 B,r)]x = 0(8a) Π,A Π x,a = [p x C (x (1 b ), θ b, Θ0 Θ1B,r)] = 0 (8b) b B Equaton (8b) conssts of two parts. The frst part [..] shows how the determnaton of feld margn sze s dependent on prvate margnal costs C (.). The second part can be nterpreted as the share of farm s proft n the provson of the publc EMS. There s a prvate beneft n terms of reduced publc purchase of pestcdes, though t s small. Two cases can be dstngushed. 1. For the frst part, we assume that on an ndvdual farm the mpact on cost reducton of an own feld margn b s small (whle mpacts of B may be hgh) and, for the second part, we assume, that the proft share s also small. If ndvdual shares can be neglected, narrowly ratonal farmers wll not provde the envsaged EMS. The arguments are not new (arguments

14 13 follow Rausser and Zusman, 1992): Snce the mpact of the EMS as a publc good can be neglected,.e. a lmted sze of B (lm B 0) s perceved, t s a domnant strategy not to co-operate; the tragedy of the commons result. 2. Farmers wll focus on the frst part [...] (maybe feld margns already make a strong contrbuton), but no poltcal pressure exsts; then they wll contrbute, albet lmtedly. However, the sze and ntensty of farmng matters (Fgure 2). Farmers wll contrbute dfferently, but at a very low level. Note, the wllngness to contrbute, n the case of a "tragedy of the commons" (equaton 8), s ndependent of the level of B. A dvergence between socal and prvate (tragedy) margnal wllngness to contrbute to a crop rsk reducng EMS prevals (a Nash equlbrum), though potentally there s a beneft. A: Large Farmer margnal wllngness to contrbute to man structure B: Small Farmer margnal wllngness to contrbute to man structure tragedy p x p x socal tragedy socal b t share of land n man structure Fgure 2: Farmers ndvdual wllngness to contrbute b s b b t b s share of land n man structure b There s scope for nsttutonal change. The queston s: How can we establsh a socal obectve functon by a poltcal barganng process that avods the tragedy, f appled by a common property manager. Only then expendtures for pestcdes to combat crop rsk wll dmnsh. 5 Bargan Equlbrum for publc rsk management 5.1 Barganng Equlbrum Our model of barganng centres around Harsany s (1963) multple agent model. In that model a barganng process can be ultmately modelled as a specfc functonal form, such as:

15 L = [ (I I )](I I ) (15a) m m An nteror soluton of the barganng process tself, as derved smlar to the one prescrbed by Rausser and Zusman (1992), prevals. Note the soluton s also smlar to a weghted obectve functon (15b). In that functon ndvdual weghts correspond to the power of a farmer n a bargan wth the manager. But as Zusman (1976) has shown, barganng solutons are not the same as polcy preference functons. Instead, the author states that the weghts reflect the analytc propertes of two aspects, the producton functon aspect and the resources devoton aspect, n barganng (brbng). Followng these arguments and referrng to the proves the author (Zusman, 1976), a treatable verson of equaton (15a) s gven n (15b). Furthermore, (15b) reveals an over-proportonalty n costs of managers as the EMS sze ncreases B[p x (1 b ) C(x (1 b ), θ b, Θ0 Θ1B,r)] W = [1 + w ][ ]- τ x b 2 B + 0.5τ B 0 1 (15b) In equaton (15b), weghts w 1,..., w k, correspond to the rato of achevements (optmal nterest functon n the barganng process beng a frst dervatve of the strength that s acqured from the threat strategy not to co-operate, (Zusman 1976) mnus the reference nterest; formally:...; w (I = (I opt. opt. m 0 I )] s(c, δ ) = 0 I )] c m (16) Fnally, calculatng dervatves b of the publc welfare functon W provdes a soluton: W [p x + C b(x (1 b ), θb, Θ = B(1 + w )[ b x b 0 Θ1 B,r)] x [p x (1 b ) C(x (1 b ), θb, Θ + 2 [ x b ] ' W [ C B (x (1 b ),, θ b, Θ0 Θ1B,r)] = (1 + w ) + [ τ τ B] = 0 1 B [ x b ] 0 Θ1 B,r)] ] = 0 (17a) 0 (17b) To solve (17), assumptons on functons are needed. We use a reduced form of cost functon that depcts land management of farms and EMS; mplctly t contans a substtuton. Normally, lnear supply and factor demand functons match wth quadratc costs. A reduced form s:

16 15 C( x (1 ΘBθb (17c) 2 2 b ), θb, ΘB, r) = γ 0 θb + 0.5γ 1 θb + γ 2 θb r + γ 3 ΘB + γ 4 ΘB + γ 5 For smplfcaton γ coeffcents cater for scalng, for translaton of the EMS nto rsk reducton, etc. Snce they are composed of ecologcal and economc rsk components they reflect farm behavour. Insertng equaton (17b) n (17a) and usng the quadratc approxmaton of ndvdual optmalty condtons for farm we receve for farmer : (1 + w )[p x γ + γ b γ r ] [ τ τ [ x b ]] = 0 0 (18a) For convenence we have dropped the coeffcents of the eco-mpact functon (7a and b). Optmsaton of the publc manager s obectve functon (17) s a correlate between prvate farm optmsaton and publc manager s optmsaton reflectng the bargan. However, snce barganng prevals untl the number of farmer k, a lnear system of k equatons exsts. For all b we get a system that can be solved for b b =[b b 1,..., b b,..., b b k] (1 + w1 ) γ11 + τ Ax 1 τ Ax (1 + w (1 + w k k ) γ ) τ Ax 1k 1 k + τ Ax 1 k b 1 (1 + w... = b k )[p1 x1 γ01 γ21r1 ] + Ax1 τ0... (18b) (1 + wk )[p kxk γ0k γ2krk ] + Axkτ0 as a matrx and vector representaton. Fnally to solve the system, the left hand sde can be expressed wth a matrx Γ multpled by b b and the rght hand sde s a vector gven farms "": Γ 1 b b =(1+ w)[p-γ 0 -γ 2 r]+ Ax τ 0 b b =Γ 1-1 (1+w )[p-γ 0 -γ 2 r]+ Ax τ 0 (19) The resultng barganng vector b b depcts a possble soluton. Ths bargan soluton reflects the poltcal power structure w, and b b also depends on the ecologcal knowledge of the publc manager. If power s equally dstrbuted, a vector b s can be calculated showng a socal welfare soluton (droppng weghts). In contrast, Fgure 3 assumes that the socal stuaton s not acheved. A socal obectve functon s merely theoretcally achevable f weghts for dfferent pressure groups are equal (a specal case). The model can be used to analyse devatons. 5.2 Rsk reducton, payments, nsurance alternatves and nsttutons

17 16 So far, the analyss has been conducted on the presumpton that property rghts (Hodge, 1988) were ntally ll-defned (no owner of the EMS exsts that can buy land from farms and provde nature servce n exchange for money) and that a partal manager s n charge of regulatory polcy on feld margn provson to sustan bo-dversty. However, we could magne that the communty may consder nsttutonal amendments and wants to change the nfluence of groups on the manager; n partcular, after experencng statutory regulatons and poltcal lobbyng. Nevertheless, as part of an nsurance scheme, payments could be nstalled and strong contrbutors to the EMS may become enttled to compensaton. In prncple, f some farmers concede to pay an amount of money, for nstance π B (π as a porton), proft shares go to other farmers and nterest functons change. Money has to be deducted from surplus assocated wth nature servces and economcally measured. For nstance area provded below the margnal wllngness to pay curve (Fgure 3) can be redstrbuted. Admnstratvely, one can thnk of a unform premum to be collected n the communty of benefcares by the manager. But stll the sze of B has to be decded n poltcal negotatons. Let us assume the communty agrees on payng farmers over land shares n the EMS; ths would provde them wth proportonal compensaton. Indvdual payments to or from farm become noteworthy dependent on farmers decson to provde a share of land and the total sze at gven rsk: π Θ = π Θ 0 Θ 1 π B An ntroducton of proportonal payments enables a re-wrtng of ndvdual nterest functons: I B[p x (1 b ) C(x (1 b ), θ b, Θ Θ0 + Θ = x b where addtonally: π p = postve premum on buffer zones (proft ) π n C(...,θ - θ,...) 1 B,r )] p + π b π [ Θ = negatve premum as nsurance to be pad for the pool of fnance (proft ) = cost reducton on (cost =>proft ) n Θ ] (21),

18 17 The beneft of ths explct reformulaton can be seen n ts capablty to provde a new barganng soluton. A new b p ncludes payments and t mplctly solves for "rsk premums" and "quanttes". As specal cases, we can compare statutory regulatons and mxed prcng. A : Large Farm er m argnal w llngness to contrbute to m an structure B: Small Farmer m argnal w llngness to contrbute to m an structure p x p x bargan tragedy socal tragedy socal bargan b b b t b s share of land n man structure Fgure 3: Barganng soluton and modfed wllngness to contrbute after barganng b b t b s b b share of land n man structure b 6 Summary The paper has shown that statutory regulatons for the provson of feld margns n Ecologcal Man Structures, EMS, can be derved from the applcaton of a poltcal economy framework to a stylzed landscape. The EMS supports an eco-system connected to mxed farmland of prvate felds and common property feld margns; then the eco-system s conducve to reduce rsk of crop falures. The basc agronomc hypothess s that an EMS reduces pest pressure: but due to an nsttutonal defct, n a pure set of prvate rghts, an EMS would not appear. For ths we ntroduce a publc management, whch s subect to barganng, and we establsh obectve functons, whch contan feld margns. Wthout common property management, because of the publc good character of the EMS, farmers wll buy pestcdes. In partcular, the result of a bargan depends on the poltcal power of the regulator relatve to power of farmers. The model allows us to set up hypotheses on an EMS as a natural protector from pests n an ecologcal and socal context. Whle provdng an analyss of expected barganng processes n feld margn provson for an EMS and natural pest control, t assumed that an a-

19 18 pror stuaton of unclear property rghts, a so called ll-defned rght stuaton, exsts. Though the process of barganng reveals no actual property rght settng tself, amendments to pure publc managements, such as payment schemes and changed rghts, are mentoned. The mpact of power and nterest can be dstngushed and transacton costs be nvestgated. The argument s more on common property problems, but ecologcal effects can be further elaborated. 7 References: Cahll, C., The multfunctonalty of agrculture: What does t mean? EuroChoces, Sprng 2001, pp Chambers, R., 1988, Producton Economcs. New York. FAO-MA, 2004, Harsany, J. C., 1993, A smplfed barganng model for the n-person cooperatve game. Internatonal Economc Revew. Vol. 4, No. 2, p Hodge, I. D., 1988, Property nsttutons and envronmental mprovements. Journal of Agrcultural Economcs, Vol. 39, No. 3, p McNeely, J.A. Scherr, S.J., 2002, Ecoagrculture: Strateges to Feed the World and Save Bodversty. Washngton. Oskam, A., Slangen. L., 1998, The Fnancal and Economc Consequences of a Wldlfe Development and Conservaton Plan. A Case Study for EMS n the Netherlands. In: Dabbert, S., et al., The economcs of landscape and wldlfe conservaton. Wallngford, p Rausser, G., 1992, Predatory versus Productve Governments. The Case of US Agrcultural Polcy. Journal of Economc Perspectves. Vol. 6, No. 3, p Rausser, G. C., Zusman, P., 1992, Publc Polcy and Consttutonal Prescrpton. Amercan Journal of Agrcultural Economcs. Vol. 74, No. 2, p Wossnk, A., Jurgens, C., Wenun, J. van, 1998, Optmal Allocaton of wldlfe conservaton areas wthn agrcultural land. In: Dabbert, S., et al. (ed.), The economcs of landscape and wldlfe conservaton. Wallngford, p Zusman, P., 1976, The ncorporaton and measurement of socal power n economc models. Internatonal Economc Revew, Vol. 17, No. 2, p