Should we internalize intertemporal production externalities in the case of pest resistance? Elsa Martin* AgroSup Dijon, CESAER (UMR 1041 of INRA)

Transcription

1 Should we nernalze neremporal producon exernales n he case of pes ressance? Elsa Marn AgroSup Djon CESAER (UMR 04 of IRA) Conrbued Paper prepared for presenaon a he 88h Annual Conference of he Agrculural Economcs Socey AgroParsech Pars France 9 - Aprl 04 Copyrgh 04 bye. Marn. All rghs reserved. Readers may make verbam copes of hs documen for non-commercal purposes by any means provded ha hs copyrgh noce appears on all such copes. [Correspondng auhor] AGROSUP Djon CESAER (UMR 04) 6 Boulevard Dr Pejean BP Djon France. el. +33(0) Fax. +33(0) E-mal: elsa.marn@djon.nra.fr [Acknowledgemens] I would lke o hank he French envronmenal mnsry for fnancal suppor whn he framework of he research program GESSOL. Absrac Pescdes effcency decreases wh her global applcaon by farmers. Whn a sraegc dynamc framework hs resuls n a classc neremporal producon exernaly. We analyze ax and subsdy schemes ha can be used n order o nernalze hs exernaly. We show ha hey are able o resore socally opmal pahs bu ha fnal me of pescde use dffers. Wh hese schemes farmers have a endency o swch o alernave pes-conrol echnology as negraed pes managemen earler han s opmal. A lump-sum ransfer s shown o be necessary o oban a swchng me equal o he socally opmal one for he subsdy case only. Furhermore he socally opmal swchng me can be laer han he one obaned under a suaon whou conrol. Keywords sock exernaly pes ressance echnology change. JEL code Q0 Q3 H3 C73.

2 Inroducon Pess are well-known for beng dffcul o manage because hey ofen develop ressance o pescdes. Ressance has been documened for a long me n several ways. For nsance Georghou (986) enumeraed pes speces found o be ressan a one or more locaons for a leas one crop season for varous pescdes. Carlson (977) aggregaed ressan pess for major crop areas a varous pons over me and measured farmer pescde use choces over me for varous pescde classes. he desgn of ressance managemen programs has consequenly been a queson of huge neres. For nsance Roush (989) crcally revewed a ls of ressance managemen accs o brng o he fore he mos promsng accs for general use n ressance managemen. In a dynamc framework effecveness of a pescde can be consdered as a sock ha s declnng over me because of pes ressance (lke a non-renewable resource). Regev e al. (983) n an exenson of Regev e al. (976) developed a heorecal model n order o deermne opmal pescde use n hs framework. hey compared he opmal soluon wh he compeve soluon n order o brng o he fore neremporal producon exernales a work and o derve some polcy recommendaons. hese recommendaons were que basc snce hey conssed n ax per un of pescde use or n resrcons on pescde use. he major purpose of our work s o refne he polcy recommendaons ha can be formulaed wh respec o he nernalzaon of such neremporal producon exernales especally by explcly akng no accoun he possbly of farmers o swch o oher echnologes han pescde use. he que recen developmen of ransgenc agrculure has nduced a wde leraure ha focus on refuge polces. Whn he framework of refuge polces farmers can culvae rangenc crops ressan o pes upon he condon ha some refuge areas are culvaed wh convenonal crops. he man dea s o avod he developmen of pess ha are ressan o ransgenc crops and o bologcal conrol (specally for B crops). Some auhors followed a que smlar dynamcal heorecal framework as Regev e al. (983) n order o sudy he opmal managemen of pes ressance wh refuge polces. For nsance Laxmnarayan and Smspon (00) derved he opmaly condons for he refuge sze n a sylzed dynamc model adaped from epdemology; Ambec and Desqulbe (0) added a spaal seng no he basc dynamc seng and compared he performance of refuge areas and axes on pescde varees. Oher auhors proposed o assess economcally he effes of refuge polces. For nsance Hurley e al. (00) assessed her mpac on agrculural producvy on convenonal pescde use and on pes ressance; Frsvold and Reeves (008) focused on her welfare mpacs by akng no accoun producer surplus consumer surplus seed suppler profs and commody program coss; Qao e al. (009) proposed an assessmen appled o a developng counry framework. All hese papers manly focus on a sngle echnology ha allows farmers o sruggle agans pess: ransgenc crops. he purpose of our work s o consder he possbly of farmers o swch o echnologes ha consue an alernave o a sngle pescde use whou specfyng hs echnology. Anoher par of he recen leraure concerned wh pes ressance focus on R&D argeed owards echnologes ha can sruggle agans pess. Some auhors focused on nnovaon process of he boechnology secor. For nsance O Shea and Ulph (008) suded he role of pes ressance n boechnology R&D nvesmen sraegy; Yerokhn and Moschn (008) suded he

3 mpac of nellecual propery rghs on he nvesmens n bologcal nnovaons whch value can be reduced o zero because of pes ressance. Here he new echnology s manly undersood as an alernave molecule of pescde or as ransgenc crops. Oher auhors focused on new echnologes ha rely on farmers sraeges. For nsance Mullen e al. (005) descrbed he role of publc nvesmens n pes-managemen R&D and emphaszed he developmen of negraed pes managemen (IPM) sraeges. he IPM concep was frs developped by Sern e al. (959). I s a muldscplnary concep whch man prncple s o combne chemcal mecancal and bologcal conrol sraeges agans pess. Mullen e al. (005) summed up ha he anhess of IPM s applyng broad-specrum pescdes on a fxed schedule relaed o he physologcal developmen of he crop rrespecve of pes populaons. Kngh and oron (989) explaned ha one of he movaons for he developmen of IPM sraeges had been he problem of pes ressance. IPM s hus an alernave echnology ha s a farmers dsposal n order o sruggle agans pess. For nsance Llewellyn e al. (007) suded he case of negraed weed managemen sraeges. hey nvesgaed he deermnans of he adopon of hese sraeges by Wesern Ausralan gran growers. We seek o desgn a framework ha s able o consder alernave pes-conrol echnologes as IPM n order o sudy no more deals he polcy ha can be mplemened n order o nernalze neremporal producon exernales lnked wh pes ressance. We propose o develop a sngle pes and sngle crop managemen model. We assume lke n he non-renewable resources leraure 3 ha here s a backsop echnology wh respec o he pescde.e. a echnology ha does no ncrease he pescde ressance of he pes populaon. hs echnology can be new molecule of pescde ransgenc crop ressan o pess or IPM sraeges. In order o do so we manly rely on Regev e al. (983) work. her compeve soluon reled on he assumpon ha farmers were non-sraegc: hey were sac mzers ha dd no ake no accoun effecs of her acons on he dynamcs of he sysem. hs assumpon was a plausble one n he 980s. owadays progress of knowledge allowed farmers o be perfecly aware of he phenomena of pes ressance (see for nsance Benley and hele 999 for a leraure revew appled o developng counres). Furhermore pes ressance s a spaal phenomena (see for nsance Georghou and Mellon 983 or Peck e al. 999 or Peck and Ellner 997) ha can be a work a a local level. As a consequence he number of farmers concerned wh he phenomena of pes ressance can be small. Whn such a framework he farmers perfecly know he effecs of her acons on he dynamc of he sysem. One queson of neres s hus o hnk of farmers ha consder he mpac of her choces on he sock of he pescde effecveness. In hs work we propose o exend he queson of Regev e al. (983) o sraegc farmers. For hs purpose we have o resor o dfferenal games heory. Whn he framework of dfferenal games s necessary o make src assumpons on he specfcaons of he funcons n order o oban closed form soluons boh for he seady saes and for he pahs. Closed form soluons are essenal o brng o he fore neremporal producon exernales n a que general case. Indeed o do so soluons obaned n he MPE case have o be compared o he soluons obaned n he socally opmal case. In mos works concerned wh dfferenal games funcons are assumed lnear quadrac. Here we explore he resuls of Long and Shmomura (998) by choosng homogeneous funcons ha are more general han lnear quadrac funcons. In a companon paper of Long and Shmomura (998) Cornes e al. (00) developed non-cooperave dfferenal games based on conceps of 3 See for nsance Am (986). 3

4 open-loop ash equlbrum and Markov perfec ash equlbrum n order o nvesgae he queson of pes ressance n a dfferenal game seng. hese conceps of equlbrum dffer by he fac ha players comm hemselves a he begnnng of he game for he enre horzon of me n he open-loop case. In he Markov perfec case hey revse her decson a each perod of me accordng o he sae of he sock. Appled o he pescde case an open-loop srucure means ha farmers are able o comm hemselves wh respec o her pescde applcaon for an enre me horzon. Snce farmers can observe he sae of he pescde effecveness a each perod of me we focus on he Markov perfec equlbrum concep n whch farmers are able o revse her decson a each perod of me accordng o he sae of he pescde effecveness. Cornes e al. (00) developed a dscree me model wh hree perods and a connuous me one wh an nfne number of perods. For clary of presenaon of resuls we concenrae on a connuous me model. Cornes e al. (00) assumed ha he ermnal me was fxed (o hree n he dscree me model and o nfne n he connuous me one). As Example of Long and Shmomura (998) we assume a free fne ermnal me ha s endogenous: he planners (farmers and cenral planner) choose he fnal me of he pescde use. Furhermore and conrary o Cornes e al. (00) and Example of Long and Shmomura (998) we assume ha here s a backsop echnology wh respec o he pescde.e. a echnology ha does no ncrease pescde ressance of he pes populaon. In order o consder hs possbly of an alernave pes-conrol echnology whou a pror knowledge on he exac form of hs echnology we nroduce a scrap value funcon ha reflecs he value aached by he decson-maker o he pescde effecveness ha s lef over a he ermnal me. hs assumpon s lnked wh echnologes evocaed prevously: new molecule of pescde ransgenc crops and IPM. A new molecule of pescde s generally used n combnaon wh old one ha mus sll be effecve. In order o avod ha pess develop ressance o ransgenc crops s generally mposed by governmen o keep radonal crops on whch pescde could sll be effecve. IPM sraeges conss n combnaon of mechancal chemcal and bologcal conrol ha can be effecve only f chemcal conrol works. In secon we wll presen he model and assumpons. Secon 3 wll be devoed o he dervaon of he Markovan perfec ash equlbrum. hs wll help us o brng o he fore n secon 4 he neffcences ha can occur n such a framework. Secon 5 wll be devoed o he schemes ha can be used n order o oban a socally opmal swch o an alernave pes-conrol echnology. Fnally we wll conclude. All echncal proof wll be relegaed o an appendx. he model We consder n symmercal farmers ha use pescdes n order o produce a homogenous good. Each farmer apples a quany a of pescde a me. he effecveness of hs applcaon s gven by a. e where e denoes he effecveness of he pescde under consderaon. We know ha pess develop ressance o pescde over me. We assume ha ressance s a negave lnear funcon of he pescde applcaon. herefore he moon of he pescde effecveness over me s gven by: n e ba () where b measures he sensvy of he pescde effcency o he amoun of pescde appled; 4

5 s a consan ha s exogenously gven. We consder ha he pescde effecveness s lke a nonrenewable sock ha declnes over me. he pescde effecveness before pess develop ressance s exogenously gven: e0 e. We dsregard oher npus han pescde for smplcy and assume ha each farmer s prof ncreases wh he effecve amoun of he pescde ha he apples a a decreasng rae: / a e 0< < () where / s he elascy of he prof o he effecve amoun of he pescde appled. hs assumpon does no seem excessve n vew of he hgh use of pescde by farmers despe he effecs on her healh for nsance (see Mullen e al. 005 for nsance). o sum up he curren pes-conrol echnology s used by farmer unl some fuure me when he wll use an alernave pes-conrol echnology. A me snce we do no make any assumpon on he form of he alernave pes-conrol echnology we assume ha he alernave pes-conrol echnology brngs n a ne reurn of: e exp( ( )) E e d where he effecveness of he pescde a me e s a proxy of he ne benef from he sock of he pescde effecveness lef over a he ermnal me and s a fxed dscoun rae. s also named a scrap curren value funcon. I represens he mum curren value of an negral of fuure uly flow sarng from me wh an nal sock of he pescde effecveness e. E he economc problem s defned as he choce of he amoun of pescde o apply a and he swchng me o he new echnology whch mze: de 0 exp( ) exp( ) (3) subjec o () and e 0 e and a 0. For he sake of clary he las consran wll be omed n he connuaon. Fnally our model s manly a developmen of Example of Long and Shmomura (998) n whch we add a scrap value funcon n he same way as Regev e al. (983). 3 he Markovan Perfec ash Equlbrum (MPE) We look frs a he suaon n whch he n farmers play a dfferenal game. Farmer looks for a sraegy of pescde applcaon gnorng he sraegy chosen by he oher farmers. Each farmer sraegy s a funcon of he pescde effecveness e ha s easly observable: ( e ). herefore e sums up he nfluence of he pas a me. Each farmer s perfecly aware of he fac ha he ohers selec her sraegy on he bass of he curren pescde effecveness. hs s why we assume ha he farmers sraegy are Markovan. 4 4 See Chaper 4 of Dockner e al. (00) for more deals on Markovan equlbrums. 5

6 For he purpose of he resoluon s convenen o ransform varables. We defne a new / conrol varable c a e ha nduces modfcaon of equaons () and () as respecvely n c e b and c e. More precsely he MPE of he game modfed s he soluon of problem: 0 c de c j( e) j exp( ) exp( ) s..: e b e e e0 e We use he Ponryagn s mum prncple n order o solve hs problem. We focus on a symmercal soluon. We defne he Hamlonan of hs problem n curren value: c j( e ) Hc ( e ) c b e j e If ( e) s a soluon o hs problem and he opmal swchng me (from farmer s pon of vew) hen here exss a connuous funcon ha sasfes he condons: b ( e) ( e) (4) e H e ( ( e ) e ) (5) bn ( e) e (6) e bn ( e) ( e) e e 0 (7) e Based on Long and Shmomura s (998) resul we assume ha farmer s sraegy s of he form ( e ). e f all oher farmers use sraeges ha are homogeneous of degree one: j ( e) j. e j. Equaon (4) s he usual margnal condon of long-run prof mzaon. I saes ha for each perod of me he margnal prof of pescde applcaon s equal o s margnal cos. he cos s a measuremen of fuure losses mpled by ncreasng ressance. I s gven by farmer s prvae shadow prce. Equaon (5) defnes he dynamcs of he co-sae varable. When equaon (6) s also vald we can conclude as n Example of Long and Shmomura (998) ha: Remark If n >0 and farmers sraeges are of he form ( e ). e hen here 6

7 exss a unque MPE for whch he equlbrum sraegy of farmer s. he resulng me pah of he pescde effecveness s b n e e exp( nb ). a e where We see ha when n approaches he amoun of pescde appled ends o nfny because farmers know ha hey wll no be able o apply pescde he me afer: her effecveness wll be oo low. Furher compuaons sae ha: n e n a exp 0 b( n) n ne n e exp 0 n n hs means ha he effecveness and he applcaon of pescde declne over me bu unl when? o answer hs queson we need o acheve he resoluon of he problem by deermnng he opmal swchng me (from farmer s pon of vew). o do so we can drecly apply heorem 7.6. of Leonard and Long (99). he condon s vald for an Hamlonan funcon n presen value. We work wh an Hamlonan n curren value. Sandard compuaons lead o equaon (7) ha s he necessary ransversaly condon. Equaon (7) conrols he swch o a new pes-conrol echnology and saes ha he opmal swchng me (from farmer s pon of vew) s such ha he value of he opmal Hamlonan evaluaed a equals he margnal scrap value. We oban: Proposon he opmal swchng me (from farmer s pon of vew) from he pescde use o an alernave pes-conrol echnology s nb ln ln. nb e n 5 I ncreases wh e. Snce s dfferen from nfny some effecveness s lef over before swchng o an alernave pes-conrol echnology. hs effecveness reflecs he need of pescde effecveness of he alernave pes-conrol echnologes. he opmal swchng me (from farmer s pon of vew) from he pescde use o an alernave pes-conrol echnology s a funcon of all parameers. We check ha he opmal swchng me (from farmer s pon of vew) ncreases wh he nal effecveness of he pescde e.. 5 We assume ha he se of parameers s such ha: 0 7

8 4 he neremporal producon exernaly o value he effcency of he prevous MPE we need o specfy he socally opmal soluon. Indeed he MPE should be neffcen snce farmers do no ake no accoun boh he mpac of her own pescde applcaon on he pescde effecveness and he mpac of he oher farmers pescde applcaon on he effecveness. he mplcaon s ha hey may overuse pescde n order o benef from her effecveness before he oher farmers apply hem. In order o check hs we frs characerze he socally opmal soluon and hen compare o he MPE. 4. he socally opmal soluon We assume here ha an agrculural auhory seeks o mze he aggregaed prof of he n farmers. hs auhory hus chooses he amoun of pescde appled by each farmer a me ( a ) n and he swchng me o an alernave pes-conrol echnology ha mzes he presen value of he fuure aggregaed profs. o make comparsons easly we follow a smlar resoluon mehod as for he MPE we make he same varable ransformaon as prevously and we agan assume symmercal soluons. he agrculural auhory solves he followng problem: nc exp( d ) ne exp( ) 0 nbc s..: e e e0 e he Hamlonan of hs problem n curren value s: nbc Hc ( e ) nc e where reflec he socal shadow prce of he sock of pescde effecveness. We know from he concavy of hs Hamlonan and from he Mangasaran condons ha he opmal soluon of he problem sasfes: nbc nc (8) e nbc (9) e bnc e (0) e 8

9 bnc n nc e ne e 0 () In order o be able o easly compare hs soluon wh he MPE we choose o assume agan a rule such ha c e and we show ha s possble o fnd a > 0 such ha condons (8) (9) and (0) are checked. We fnally show ha: Proposon here exss a unque such ha he decson rule e s a socally opmal rule of pescde applcaon ha mzes he prof of farmers. () he socally opmal pescde applcaon s a e exp( nb ) where. he resulng me pah of he pescde effecveness s e e exp( nb ). bn( ) () he socally opmal swchng me from he pescde use o an alernave pesconrol echnology s nb ln ln. nb e 6 I ncreases wh e. We see from sandar compuaons ha he socally opmal pahs of pescde applcaon and of pescde effecveness declne over me as for he MPE pahs. he socally opmal swchng me from he pescde use o an alernave pes-conrol echnology s a funcon of all parameers. We check ha he varaons of he socally opmal swchng me s he same as n he MPE case wh respec o he nal effecveness of he pescde e. 4. he neffcences of he MPE soluon he expressons of and are oo complex o be compared on analycal grounds. We can only conclude ha hey are dfferen. We have run a se of smulaons n order o derve more conclusons. 7 he resuls are summarzed n able 3 4 and 5 of Appendx A.4. he man concluson s ha he swchng me from pescde use o an alernave pes-conrol echnology s laer n he socally opmal case han n he MPE: In order o explan hs resul s mporan o compare he pescde applcaon and effecveness n boh cases. We now urn o hs comparson. For clary sake we frs reason on he same me for he MPE case and for 0. 6 We assume ha he se of parameers s such ha: 7 he dea of he smulaons s o pu values on our parameers. he parameerzaon s no made on emprcal bass because we do no wan o resrc ourselves o a specfc case. As a consequence we run a se of smulaons for dfferen feasble values of he parameers. 9

10 he socally opmal case. Equaons (4) and (8) are usual margnal condons of long-run prof mzaon. hey sae ha for each perod of me he margnal prof of pescde applcaon s equal o s margnal cos. he cos ha s a measuremen of fuure losses mpled by b ( e) ncreasng ressance s no he same n he MPE case and n he socally opmal e case nbc. Indeed s a prvae cos n he MPE case and s a collecve cos n he e socally opmal case. Furhermore he shadow prce ( ) dffers n boh cases. he dfference beween boh can easly be undersood by comparng he dynamc of he co-sae varable n he MPE case: b ( n) wh he one n he socally opmal case: bn In he MPE case farmers value he mpac of her own pescde use on he pescde effecveness b. Whereas he socal planner values he mpac of each farmer pescde use on he pescde effecveness: bn. In addon n he MPE case ( n ) reflecs he assumpon accordng o whch farmers use Markovan sraegy: each one knows perfecly ha he ohers use a rule ha s a funcon of he pescde effecveness a each perod of me. hs erm mples ha n he MPE case each farmer s gong o use more pescde han would have been socally opmal o use. he dea s ha n order o benef from effecve pescde s opmal for each ndvdual farmer o use pescde before he oher farmers. hese nuons are analycally confrmed by Proposon 3. Proposon 3 he comparson beween he MPE and he socally opmal pah whou consderng he swchng me from he pescde use o an alernave pes-conrol echnology allows us o conclude ha: () he amoun of pescde appled n he MPE case s hgher han he amoun appled n a n n( ) he socally opmal case unl he me ln >0 afer whch ( n) ( n) he amoun appled n he MPE case can be lower han he amoun appled n he socally a opmal case: a > a <. () he effecveness of he pescde s always lower n he MPE case han n he socally opmal case: e < e. Concluson () confrms he prevous nuons: n he MPE case farmers overexplo he common ha here s he effecveness of he pescde. he mplcaon s ha he effecveness of he pescde s lower n he MPE case han n he socally opmal case. A frs glance one can be que surprsed by he second par of resul () ha saes ha he amoun of pescde appled n he MPE case can be lower ha he amoun appled n he socally opmal case. hs resul s vald afer a frs regme durng whch he amoun of pescde appled n he MPE case s hgher han he amoun appled n he socally opmal case whch fs more closely o he nuons. hs can help us explan he surprsng par of he resuls. Indeed n a frs phase farmers apply more pescde n he MPE case han n he socally opmal case. By 0

11 dong so hey conrbue o he decrease of he sock of pescde effecveness unl a me a whch hey begn o apply less pescde han n he socally opmal case because of pescde reducng drascally n effcency: hs s he second phase. Anoher nerpreaon of a can be o consder ha hs s he me of overexploaon of he sock of pescde effecveness n he MPE case. he me a s a funcon of he number of farmers n of a proxy of he elascy of he prof o he effecve amoun of pescde appled and of he dscoun rae. Basc comparave sac allows us o conclude ha: Remark he me a decreases wh he number of farmers n and wh he dscoun rae. hese resuls are drec when one keeps n mnd he nerpreaon of a as he me of overexploaon of he sock of pescde effecveness. Indeed when he dscoun rae ncreases he value of he fuure decreases and he sock of pescde effecveness s exhaused early. In he same way when he number of farmers ncreases he sock of pescde effecveness s exhaused early. o acheve our comparsons we now need o compare he pahs of boh he pescde applcaon and effecness afer. Beween and boh he pescde effecveness and applcaon end o zero n he MPE case because of he swch o alernave pes-conrol echnology. he consequence s ha beween and boh he pescde effecveness and applcaon mus be hgher n he socally opmal case han n he MPE case. Fnally we can conclude from smulaons presened n able 3 4 and 5 of Appendx A.4 ha () he fnal (a ) pescde applcaon s lower n he socally opmal case han n he MPE case a a and () ha he fnal pescde effecveness s lower n he MPE case han n he socally opmal case e e. o sum up we have shown ha he swchng me from he pescde use o an alernave pes-conrol echnology s earler n he MPE case han n he socally opmal case. hs can be explaned by he fac ha he over-applcaon of pescde by farmers n he MPE case consderably reduces he pescde effecveness and her profs. hs means ha n he MPE case s more neresng for farmers o swch o alernave pes-conrol echnologes sooner han n he socally opmal case snce he common consued by he pescde effecveness s already exhaused. 5 oward he resoraon of he socally opmal soluon Once he neffcences ha are a work have been brough o he fore he queson of her nernalzaon remans. In hs secon we propose o ry some sraeges n order o resore effcency. We have wo neffcences here: he neremporal producon exernales ha are brough o he fore by he dfference beween he MPE and socally opmal pahs of pescde applcaon

12 and effecveness he swchng me from he pescde use o an alernave pes-conrol echnology ha s laer n he socally opmal case han n he MPE case. Snce here s wo neffcences one can hnk of wo nsrumens n order o correc hem. We wll frs check f ax or subsdy desgned n order o nernalze exernales are able o reach he opmal swchng me from he pescde use o an alernave pes-conrol echnology. We wll show ha s no he case and we wll look for a polcy ha s able o resore boh he socally opmal pahs and swchng me. 5. Obanng he socally opmal pahs of pescde applcaon and effecveness: equvalence beween ax and subsdy he exernaly leads o subopmal pahs boh for he amoun of pescde appled and for he pescde effecveness. wo ways exs n order o nernalze hs exernaly and o oban he socally opmal pahs of pescde applcaon and effecveness: s possble eher o ax he profs from pescde applcaon or o subsdze he amben pescde effecveness. In hs subsecon we propose o gnore he horzon of me ha wll be he subjec of he nex subsecon. In he ax case he dea s ha a ax on he profs generaed by pescde applcaon wll gve farmers ncenves o reduce pescde applcaon. he Hamlonan n curren value becomes: c j( e) Hc ( e )( ) c b e j e Only equaon (4) and (7) are modfed wh respec o he MPE case. he frs order condon now saes ha for each perod of me he margnal ne prof of pescde applcaon s equal o s margnal cos ha now ncludes he ax: ( e) ( e) b ( e) () e n Proposon 4 he opmal ax on profs >0 s such ha here n( ) exss a MPE for whch he equlbrum sraegy of farmer s equal o he socally opmal one. he resulng me pah of he pescde effecveness s also equal o he socally opmal one. We see ha he opmal ax s a funcon of he number of farmers n and of a proxy of he elascy of he farmers prof o he effecve amoun of pescde appled. Some basc compuaons allow us o conclude ha: Remark 3 he opmal ax on profs decreases wh and ncreases wh n. As a consequence when he elascy of he farmers prof o he effecve amoun of pescde appled ncreases he opmal ax decreases snce farmers are more reacve o he prce

13 sgnal. Furhermore when he number of farmers ncreases he compeon beween hem s sronger n he MPE case and here s a need for a sronger fscal ncenve n order o resore effcency. In he subsdy case he nuon s ha snce farmers know perfecly how her pescde applcaon has an mpac on he pescde effecveness subsdzng he amben level of pescde effecveness by wll gve hem ncenves o reduce her pescde applcaon. Such a subsdy scheme assumes ha a each me he agrculural auhory perfecly knows he pescde effecveness. he Hamlonan n curren value becomes: c j( e ) Hc ( e ) c e b ( n) e e Only equaons (5) and (7) are modfed wh respec o he MPE case. he dynamc of he cosae varable s now reduced by he value of he subsdy whch means ha farmers are gong o gve more value o he pescde effecveness snce he co-sae varable eners n a negave way no he Hamlonan funcon: H e ( ( e ) e ) (3) I s precsely he man am of hs subsdy. Proposon 5 he opmal amben subsdy ( n ) e >0 s such ha here exss a MPE for whch he equlbrum sraegy of farmer s equal o he socally opmal one. he resulng me pah of he pescde effecveness s also equal o he socally opmal one. As for he opmal ax he opmal subsdy s a funcon of he number of farmers n and of a proxy of he elascy of he farmers prof o he effecve amoun of pescdes appled. In addon because he subsdy s proporonal o he pescde effcency s a funcon of he dscoun rae of he me of he sensvy of he pescde effcency o he amoun of pescde appled b and of he nal effecveness of he pescde e. Remark 4 he opmal amben subsdy on he pescde effecveness ncreases wh n and and decreases wh b and e. he sensvy of he subsdy o he number of farmers can be nerpreed as he one of he ax. Furhermore he subsdy ncreases wh me because s proporonal o he pescde effecveness ha decreases wh me. hs decrease has o be compensaed by he subsdy n order o slow down he pescde applcaon. I s for he same reason ha he subsdy decreases wh he nal effecveness of he pescde and wh he sensvy of he pescde effcency o he amoun of pescde appled. he subsdy also ncreases wh he dscoun rae. Equaon (3) helps o undersand hs. We see ha he subsdy nervenes n he defnon of he shadow prce of he sock of pescde effecveness. Snce hs shadow prce ncreases over me wh he dscoun rae he subsdy mus decrease wh he dscoun rae o compensae he effec of he dscoun rae ncrease on he shadow prce. he fac ha he opmal subsdy s a funcon of me can be a problem for 3

14 mplemenaon purposes. Indeed hs means ha has o be adjused a each perod of me by he regulaor. We can hus conclude ha ax and subsdy are only heorecally equvalen. Boh are able o make farmers behavor resul n he socally opmal pahs of pescde applcaon and effecveness bu he queson remans as o wheher boh schemes allow for a socally opmal swch from pescde applcaon o an alernave pes-conrol echnology. 5. Obanng he socally opmal swchng me: ax versus subsdy? Once he equvalence beween ax and subsdy has been shown for he pah of pescde applcaon and effecveness wha remans o check s f he socally opmal swchng me can be obaned wh such schemes. Inuvely we canno expec o reach hs resul. hs can be seen wh he modfed ransversaly condons: bnc c e e 0 (4) e for he ax case and: bnc c e ee 0 (5) e for he subsdy case. he fscal schemes seem o have an mpac on he swchng me from pescde applcaon o an alernave pes-conrol echnology. Proposon 6 confrms hs nuon. Proposon 6 () In he ax case he swchng me from he pescde use o an alernave pes-conrol echnology s nb n ln ln ln. nb e n n 8 As before ncreases wh e. () In he subsdy case he swchng me from he pescde use o an alernave pesconrol echnology s nb ln ln. nb e ( n ) 9 As before ncreases wh e. ()he swchng me n he subsdy case s always lower han he swchng me n he socally opmal case:. If we recall 8 We assume ha he se of parameers s such ha: >0. 9 We assume ha he se of parameers s such ha: >0. 4

15 ln ln he swchng me n he nb socally opmal case and nb ln ln he swchng me n nb e n he MPE case we see ha hey are dfferen from he swchng mes obaned n he subsdy and ax cases. he equaons of he swchng mes are oo complex o conclude n a general way on he rankng of swchng mes. We can only conclude ha a subsdy decreases he swchng me wh respec o he socally opmal case. nb e I s well known ha axes and subsdes have dsrbuonal effecs. In order o delee hese dsrbuonal effecs we hen propose o add o he fscal schemes a lump-sum ransfer. Such a modfcaon wll have an effec only on he ransversaly condon. We oban he resuls saed n Proposon 7. Proposon 7 () When we add a lump-sum ransfer o he subsdy we reach he socally opmal pahs of pescde applcaon and effecveness and he socally opmal swchng me. () When we add a lump-sum ransfer o he ax we agan reach he socally opmal pahs of pescde applcaon and effecveness bu no he socally opmal swchng me. echncally for he ax case wh a lump-sum ransfer he ax also nervenes n he frs order condon ha s used o derve he swchng me (see equaon ). Equaon s dfferen from he frs order condon of he socally opmal case (see equaon 8). Indeed he shadow prce of he pescde effecveness s also a funcon of he ax o be aken no accoun. I explans why he swchng me s formally dfferen from he socally opmal one. More nuvely he neffcency of he lump-sum ransfer n he ax case s due o he non-lnear effec of he ax on he shadow prce of he pescde effecveness. he comparson beween he swchng mes n he dfferen cases s unclear. he general conclusons ha we can derve are relaed o he sensvy of he dfferences o he parameer values. he conclusons are summarzed n he followng remark. Remark 6 he dfferences beween all swchng mes are ncreasng wh or ndependan of parameers e and b. In order o oban more neresng resuls we have run a se of smulaons. For he followng se of parameers b e and n 50 we oban he followng rankng: LS < < (6) In order o es he robusness of hs rankng we have run a se of smulaons n whch 5

16 parameers n and vary. he resuls are summarzed n able and 0 of Appendx A.4. Havng n mnd Remark 6 we have also run a se of smulaons n whch parameers e and b are lower han he prevous se. he smulaons show ha he dfferences beween all swchng mes decrease wh he dscoun rae and are ndependan of he sensvy of he pescde effcency o he amoun of pescde appled b. hs las resul mus come from he low values aken n he smulaons bu we know from Remark 6 ha hese value are he only one for whch he rankng n (6) can be reversed. Furhermore he dfference beween he swchng me n he socally opmal case and he swchng me n he subsdy case s he lowes one. hs means ha he amben subsdy leads o a soluon very close o he socally opmal case even when no lump-sum ransfer s assocaed o he subsdy. We can also observe from he smulaons ha he dfference on he one hand beween he swchng me n he ax case wh a lump-sum ransfer and he socally opmal case ls and on he oher hand beween he swchng me n he ax case wh a lump-sum ls ransfer and he subsdy case are reversed for hgh number of agens n for hgh elascy of he farmers prof o he effecve amoun of pescde appled and for low nal effecveness of he pescde e. hs means ha he rankng n (6) s no robus o hese ls parameer values snce can become lower han or lower han. Anoher resul shows he nsably of he ax case: when e s small he swchng me from he pescde use o an alernave pes-conrol echnology n he ax case become lower han n he MPE case. Fnally he man mplcaon of all hese smulaons s ha a robus rankng s as follows: < < hs means ha a subsdy on he amben pescde effecveness fals o acheve he socally opmal swchng me from pescde use o an alernave pes-conrol echnology. Proposon 7 shows ha f a lump-sum ransfer s added o he subsdy he socally opmal soluon s acheved. hs resul seems o be manly due o he fac ha a lump-sum ransfer delees dsrbuonal effecs nduced by he subsdy. However a ax on farmers profs generaed from pescde applcaon even when a lump-sum ransfer s added o fals o acheve he socally opmal soluon. hs resul s manly due o he form of he schemes and ha can be seen n Proposons 4 and 5. he ax s more basc han he subsdy snce he ax does no depend on he effecveness of pescde over me (he ax s only a funcon of parameers and n ); he subsdy can be adjused over me and wh respec o he oher parameers. As a consequence a scheme ha s desgned wh respec o he amben effecveness of pescde has beer chance o acheve he socally opmal soluon (pescde applcaon and effecveness pah plus swchng me o an alernave pes-conrol echnology) han a scheme ha s no desgned lke hs. 6 Concluson and dscusson hs paper s concerned wh he queson of he nernalzaon of neremporal producon exernales. We concenrae on pes ressance: s well known ha he amoun of pescde appled by farmers decreases her effecveness over me. Developmens n dynamc 6

17 game heory leraure show how s possble o assume ha on he one hand each farmer s perfecly aware of he mpac of hs decsons on he pescde effecveness. On he oher hand we assume ha each farmer does no know how he oher farmers ac. We hus model he neremporal producon exernales n he pescde case as a dfferenal game. Furhermore we add o he pcure a scrap value of he swch from he pescde use o an alernave pesconrol echnology. he frs sep s o brng o he fore he neremporal producon exernales ha are a play. In order o do hs we solve and compare wo problems for he complee me horzon (and no only a he seady sae as s commonly he case): he MPE one and he socally opmal one. We show ha he effecveness of he pescde s always (over me) lower n he MPE case han n he socally opmal case. We hus propose o assmlae he sock of pescde effecveness o a common ha s overexploed by farmers because of exernales. he second sep concerns he swchng me from he pescde use o an alernave pes-conrol echnology. We show ha s laer n he socally opmal case ha n he MPE case. We hen look for he fscal schemes ha can be mplemened n order o nernalze hese neremporal producon exernales. We show ha boh a ax and a subsdy are able o nernalze hem. We hen explore he full poenal of a dynamc model by sudyng he mes of swch from pescde applcaon o an alernave pes-conrol echnology. We show ha ax and subsdy do no lead o he same swchng me. When one adds a lump-sum ransfer o he subsdy he swchng me from he pescde use o an alernave pes-conrol echnology becomes he same one as n he socally opmal case. hs resul underlnes he mporance of desgnng an addonal redsrbuve polcy n order o couerbalance he unwaned effecs ha a fscal scheme can have.we show ha hs resul s no valdaed n he ax case: when one adds a lump-sum ransfer o he ax he socally opmal swchng me from he pescde use o an alernave pes-conrol echnology s no reached. hs s manly due o he non-lnear effec of he ax on he shadow prce of he pescde effecveness. he lack of effecveness of axes n he pescde case was recenly confrmed emprcally by Skevas e al. (0): hey shew ha boh pescde axes and a prce penaly on pescde mpac on waer organsms are unable o consderably reduce pescde use. hey obaned he same resul n he subsdy cases as n he ax cases. Conrary o hs las resul we show ha a subsdy can be effcen. However he subsdes ha hey suded are no he same as he one suded n our work. hey consdered a subsdy on he use of low-oxcy pescdes subsdes on research and developmen of low-oxcy alernaves and subsdes on R&D of more envronmenal frendly pescdes. We raher consder an amben subsdy: a subsdy ha s a funcon of he amben effecveness of pescde. We show ha n a dynamcal framework and when a lump-sum ransfer s added o hs amben subsdy boh he socally opmal pahs of pescde effecveness and applcaon and he swchng me from he pescde use o an alernave echnolgy can be reached. he sudy of he swchng me o an alernave pes-conrol echnology can have neresng mplcaons from a publc polcy perspecve. Indeed f he am of he polcy-maker (an agrculural auhory n our work) s smply o nernalze neremporal producon exernales s necessary o mplemen basc nernalzng schemes. However f he polcymaker s also concerned by he socally opmal swch from he pescde use o an alernave pes-conrol echnology an amben subsdy s beer han a ax. Furhermore f he polcy-maker has envronmenal goals n mnd mplcaons are 7

18 dfferen. If we assume ha alernave pes-conrol echnologes o pescde applcaon are more envronmenally frendly he nernalzng polcy could be consdered as no beng necessary. Indeed we show ha a subsdy pospones he swchng me o alernave pes-conrol echnologes. hs s rue f a huge quck applcaon of pescdes does no harm envronmen more han a low long applcaon. One neresng exenson of our work would be o add an envronmenal damage lnked wh he applcaon of pescde n order o conrol hese effecs. Such an exenson s beyond he scope of our work ha concenrae on producon exernales. I s why s lef for a fuure work on envronmenal exernales of pescde use. Appendx A. Proof of remark In order o solve he modfed game we frs observe from he frs order condon (4) ha: Ae ( ) Ae e where A s a new consan. We hen have: ( ) Ae bn. We also know from equaon (5) and from he assumpon on symmery of soluons ha: bn ( ). We replace by Ae n hs equaon and we oban:. Ae b( n) We now look for A ha solves: ( ) Ae bn Ae b( n ) Ae Ae b ( n ) b ( n ) (7) Before gong furher we express order condon (4) n whch we pu Ae : c Ae bc 0 c Ae b c e( ba) wh respec o We assume ha c e. he mplcaon s ha expresson n equaon (7) and we oban: b n b n ( ba ) ba A. o do so we depar from he frs ( ba ). We now pu hs 8

19 b n A : A b I drecly resuls from hs ha: b n We can now look for he equlbrum pahs of he modfed game. We begn wh equaon ne (6) ha can now be wren as: e wh e0 e n he soluon of hs dfferenal equaon s: n e e exp e exp nb n ha gves: n c eexp eexp nb b n n and n a eexp eexp nb b( n) n A. Proof of proposon We depar from frs order condon (4): pu no ransversaly condon (7): c n c e e 0 c e e n c c e c b ha we e b 0 exp e nb e nb exp nb n e nb exp nb n 9

20 e nb exp nb n e nb nb ln n ln ln : nb Our assumpon on symmercal farmers nsures ha here s no possble devaon from hs swchng me. Some basc compuaons hen lead o: n e >0 e n nb e n A.3 Proof of proposon We use a smlar mehod as he one used for he proof of Remark and Proposon. () We frs observe from he frs order condon (8) ha: Ae ( ) Ae e where A s a new consan. We hen have: ( ) Ae bn We also know from equaon (9) ha:. We replace by Ae n hs equaon and we oban: Ae bn. We now look for A ha solves: ( ) Ae bn Ae bn Ae Ae b n( ) nb ( ) (8) Before gong furher we express wh respec o A. o do so we depar from frs order condon (8) n whch we pu Ae : n c Ae bc 0 c Ae b c e ( ba) We assume ha c e. he mplcaon s ha expresson n equaon (8) and we oban: ( ba). We now pu hs 0

21 bn bn ( ba) ba bn A : A b I drecly resuls from hs ha: bn We can now look for he equlbrum pahs of he modfed game. We begn wh equaon e (0) ha can now be wren as: e wh e0 e he soluon of hs dfferenal equaon s: e e exp e exp nb ha gves: exp c e e exp nb bn n and a e exp e expnb nb( ) c c e () We depar from frs order condon (8): c b 0 ha we e b pu no ransversaly condon (): c n n nc e ne 0 c e e e nb e exp nb exp nb e nb exp nb

22 e exp nb nb e nb nb ln ln ln : nb nb e Some basc compuaons hen lead o: e >0 e A.4 Resuls of he smulaons comparng he soluons n he socally opmal case and n he MPE case We have run some smulaons n order o see how he dfferences beween he socally opmal soluons and he MPE soluons vary accordng o parameer values. We oban he resuls n able 3 4 and 5. n 5 n 50 n 500 n a a e e a a able : Dfferences for he se of parameers: b e and a a e e a a able : Dfferences for he se of parameers: b e and n 50.

23 a a e e a a able 3: Dfferences for he se of parameers: b e 000 n 50 and e 0000 e 000 e 00 e a a e e a a able 4: Dfferences for he se of parameers: b 0.00 n 50 and b 000 b 00 b b a a e e a a able 5: Dfferences for he se of parameers: 0.00 e 000 n 50 and A.5 Proof of proposon 3 Frsly we know from he assumpons ha: n > b( n ) < b( ) > b( n ) b( ) > () We look for a crossng pon: a a exp n e e exp b( n ) n nb( ) 3

24 n( ) n exp ( n ) n n ( ) ( ) exp n n ( n) n n( ) ( n) exp ( n) n n n( ) a ln : ( n) ( n) We hen look for he sgn of hs crossng pon. Frsly we know from he assumpons n >0. Furhermore we know ha: ( n ) n < nn< n n( )<( n ) n( ) > ( n ) ha: n( ) ln > 0 ( n ) a We can hen conclude ha: >0. We now have o compare a a before and afer hs crossng pon. 0 occurs a before. Frsly we know ha a 0 b( n ) know ha : n( )<( n ) > n( ) ( n ) e < e nb( ) b( n) a 0 < a 0 a We can hus conclude ha: a > a <. nb( ) e and a e 0. We also I s more complcaed o conclude analycally for > a. ha s why we use smulaons presened n ables 3 4 and 5 of Appendx A.4. We observe from hese smulaons ha a a > a. We can hus conclude ha: a a. () We know from () ha: > b( n ) b( ) 4

25 > b( n ) b( ) > nb < nb e exp( nb ) < e exp( nb ) e < e A.6 Proof of remark n a a n ( ) nn( )ln ( ) n <0 n( n) n n( )ln ( ) n <0 ( n) A.7 Proof of proposon 4 he begnnng of hs proof s smlar o he one of Remark excep ha he frs order condon s now gven by equaon (). hs mples modfcaons of he proof when hs equaon s used o express wh respec o A : ( ) c Ae bc 0 wh Ae c Ae b ba c e ( ) We assumed ha c e. he mplcaon s ha expresson n equaon (7) and we oban: ba bn ba b n ( ) b n A b ba. We now pu hs 5

26 n( ) > ( n ) Remark 7 Le us observe ha and ha <0 ( n ) A A n( ) ( n ). We can hen conclude ha >0. n( ). We know ha When A bn b and bn. We can now look for he equlbrum pahs of he modfed game. We begn wh equaon e (0) ha can now be wren as: e wh e0 e he soluon of hs dfferenal equaon s: e e exp e ha gves: exp c e c bn and a e exp a nb( ) A.8 Proof of remark 3 n ( ) n <0 ( n ) n n n( ) ( n ) ln ( n) n n n >0 ( n ) A.9 Proof of proposon 5 he begnnng of he proof s he same as n he proof of Remark. We hen know from equaon (3) and from he assumpon on he symmery of soluons ha: 6

27 bn ( ). We replace Ae b( n). by Ae n hs equaon and we oban: he nex sep s o look for A ha solves: ( ) Ae bn Ae b( n) (9) Remark 8 Le us observe ha: (3) (9) ( n )Ae b Le us se and go furher: (9) ( ) Ae bn Ae ( bn) Ae ( ) Ae bn b n( ) (0) We know from he proof of Remark ha ( ba). We now pu hs expresson n equaon (0) and we oban: bn bn ( ba ) ba bn A : A b I drecly resuls from hs ha: bn We can now look for he equlbrum pahs of he modfed game. We begn wh equaon e (0) ha can now be wren as: e wh e0 e he soluon of hs dfferenal equaon s: e e exp e Remark 9 Snce ( n ) e we hen drecly have 7

28 e ( n) exp >0 bn and We fnally have: c e exp c bn a e exp a nb( ) A.0 Proof of remark 4 ( )( n) e exp bn >0 ( n) e exp exp ( ) bn >0 e ( ) snce <0 e exp exp ( n n) bn n >0 e n ( n) e exp exp bn b <0 be e ( )( n) e exp exp bn <0 e A. Proof of proposon 6 () We depar from frs order condon (): 8

29 c ( ) c e ( ) c b 0 ha we pu no he ransversaly condon e b (4): ( ) c n ( ) c e e 0 n nc e e n n n c e e n n nb n n e exp nb e exp nb n nb nb e nb exp n n e nb n exp n n e nb n exp nb n n e nb n nb ln n n n ln ln ln : nb e n n Some basc compuaons hen lead o: e >0 e nb c c e () We depar from frs order condon (4): c b 0 ha e b bnc we pu ransversaly no condon (5): c e ee e 0 9

30 c n c e e e 0 n c ( n ) e e e n e exp nb ( n) e expnb nb e exp nb nb e nb e nb n exp exp e exp nb nb ( n ) e nb ln nb ( n ) ln ln : nb ( ) nb e n Some basc compuaons hen lead o: e >0 e nb nb () ln ln nb ( n ) nb ( n ) ln ln nb nb nb ( n ) We know ha n > n > ( n ) 30

31 ( n ) ln > 0 >0 snce <0 A. Proof of proposon 7 () We drecly see ha when we add LS e n he ransversaly condon used n he () of he proof of proposon 6 we oban he same expresson as n he socally opmal case (see he () of he proof of proposon ). () As n he proof of () of proposon 6 we depar from frs order condon () ha s unchanged. We pu he expresson of no he new ransversaly condon: bnc c e e LS 0 where LS e c and we oban: ( ) c n c e e 0 n n c e e n n nb n e exp nb e exp nb n e nb exp nb n n n e nb exp nb n n n 3

32 e nb nb ln n n n nb n ln ln ln n : nb e n Whch s dfferen from. 0 A.3 Proof of remark 6 Some basc compuaons lead o: ls n e >0 e e e ne ls ( n ) b b b b 0 bn ( ) LS LS e LS LS b ls 0 e e e e 0 b b b b 0 e e ls ( ) b 0 b ( ) A.4 Resuls of he smulaons comparng he swchng mes n he dfferen cases We have run some smulaons n order o see how he dfferences beween he swchng mes vary accordng o parameer values. We oban he resuls n able and 0. LS 0 LS We assume ha he se of parameers s such ha 0. 3

33 n 5 n 50 n 500 n ls ls ls ls able 6: Dfferences for he se of parameers: b and ls ls ls ls able 7: Dfferences for he se of parameers: b and n ls ls ls ls able 8: Dfferences for he se of parameers: b 33

34 and e 500 e 00 e 75 e ls ls ls ls able 9: Dfferences for he se of parameers: b 0.00 n 50 and b 0.9 b 0.5 b 0. b ls ls ls ls able 0: Dfferences for he se of parameers: 0.00 n 50 and

35 References Ambec S. M. Desqulbe (0) "Regulaon of a Spaal Exernaly: Refuges versus ax for Managng Pes Ressance" Envronmenal and Resource Economcs 5() Am R. (986) "Peroleum reservor exploaon: swchng from prmary o secondary recovery" Operaons Research 34(4) Carlson G.A. (977) "Long-run producvy of nseccdes" Amercan Journal of Agrculural Economcs Cornes R.. Long K. Shmomura (00) "Drugs and pess: neremporal producon exernales" Japan and he World Economy 3 (3) Dockner E.J. S. Jorgensen. Long G. Sorger (00) Dfferenal Games n Economcs and Managemen Scence Cambrdge Unversy Press Cambrdge Frsvold G.B. and Reeves J.M. (008) "he coss and benefs of refuge requremens: he case of B coon" Ecologcal Economcs 65() Georghou G.P.(986) "he magnude of he ressance problem" n Pescde Ressance: Sraeges and accs for Managemen. aonal Academy Press Washngon DC Georghou G.P. R.B. Mellon (983) "Pescde Ressance n me and Space" n Georghou G.P.. Sao (Eds) Pes ressance o pescdes Plenum Press London -46 Hurley M Babcock B Hellmch RL (00) "B crops and nsec ressance: an economc assessmen of refuges" Journal of Agrculural and Resource Econonomcs Kngh A.L. G.W. oron (989) "Economcs of agrculural pescde ressance n arhropods" Annual Revew of Enomology Laxmnarayan R. R. Smpson (00) "Refuge Sraeges for Managng Pes Ressance n ransgenc Agrculure" Envronmenal and Resource Economcs (4) Leonard D. and. Long (99) Opmal Conrol heory and Sac Opmzaon n Economcs Cambrdge Unversy Press Cambrdge Llewellyn R.S. R.K. Lndner D.J. Pannell S.B. Powles (007) "Herbcde ressance and he adopon of negraed weed managemen by Wesern Ausralan gran growers" Agrculural Economcs Long. K. Shmomura (998) "Some resuls on he Markov equlbra of a class of homogenous dfferenal games" Journal of Economc Behavor and Organzaon Mullen J.D. J.M. Alson D.A. Summer M.. Kreh.V. Kumnoff (005) "he payoff o publc nvesmens n pes-managemen R&D: general ssues and a case sudy emphaszng nergraed pes managemen n Calforna" Revew of Agrculural Economcs 7(4) O'Shea L. and Ulph A. (008) "he role of pes ressance n boechnology R&D nvesmen sraegy" Journal of Envronmenal Economcs and Managemen 55 () 3-8 Peck S.L. S.P. Ellner (997) "he Effec of Economc hresholds and Lfe-Hsory Parameers on he Evoluon of Pescde Ressance n a Regonal Seng" he Amercan aurals 49 () Peck S.L. F. Gould S.P. Ellner (999) "Spread of Ressance n Spaally Exended Regons of ransgenc Coon: Implcaons for Managemen of Helohs vrescens (Lepdopera: ocudae)" Journal of Economc Enomology 9() -6 Qao F. J. Wlen J. Huang S. Rozelle (009) "Dynamcally opmal sraeges for managng he jon ressance of pess o B oxn and convenonal pescdes n a developng 35