Effect of output price volatility on agricultural land use

Transcription

1 Effec of oupu prce volaly on agrculural land use Esher BOERE,2, Jack PEERLINGS, Sjn REINHARD,2, Tom KHLMAN 2, Wn HEIJMAN. Inroducon Over he pas decade n he Neherlands, volale oupu prces have led o flucuang profably of agrculural land and may herefore have affeced land-use decsons. For a producer, he shadow prce of land represens he land s margnal conrbuon o prof. If a producer has no consrans on land use, prof maxmzaon occurs a he pon where shadow prces are equal among all alernave land uses. However, he equaly of shadow prces among land uses only accouns for expeced oupu prces because producers do no know oupu prces a he me hey choose her producon acves, and mus base her Absrac expecaon on pas experence. Ths causes uncerany for he producer abou he dfference beween he acual and expeced oupu prce, whch may dffer per acvy and hrough me. For a rsk-neural producer uncerany wll no nfluence hs producon decsons. For a rsk-averse producer, producon acves wh a hgh expeced oupu prce and a low prof varably are preferred. A rsk-averse producer, faced wh ncreased volaly n oupu prces, s herefore more lkely o swch o less volale producon acves. The European non s Common Agrculural Polcy (CAP) s shfng away from marke and prce suppor o lberalzed markes and decoupled paymens from producon. Ths s lkely o resul n an ncreased volaly of oupu prces and hence, farm profs, whch affecs he compeve posons of agrculural and non-agrculural land uses (Rder and Jacque, 2002; Scko - ka and Moro, 2006; Brady e al., 2009). However, because he degree of volaly s crop-specfc, he effec on farm plans has so far remaned unclear. Compeng agrculural and non-agrculural clams arse, especally n areas such as he Neherlands where land s scarce. In hs paper our focus s solely on agrculural land use, gnorng compeon wh oher secors and akng he oal (decreasng) amoun of agrculural land as gven. There s an exensve leraure on he esmaon of models ha analyze mulpleoupu supply decsons and agrculural land allocaon decsons. Broadly, wo lnes of hnkng can be dsngushed: esmang a sysem of oupu supply, npu demand, and land-use equaons (Coyle, 992; Oude Lansnk, 999; Sckoka and Moro, 2006), and esmang land-use response equaons (Moore and Negr, 992; Wu and Segerson, 995; Fezz and Baeman, 20). Esmang a sysem of oupu supply, npu demand, and land-use equaons has been appled by Coyle (990,; 992,; 999), who combned he effecs of rsk averson, prce uncerany, and yeld uncerany on crop producon decsons n mean-varance dualy models of producon. Oude Lansnk (999) elaboraed on Coyle s work by usng a lnear mean-varance uly funcon ha ncorporaed rsk o deermne he npu demand, oupu supply, and area allocaon smulaneously among varous crops. More recenly, Sckoka and Moro (2006) adaped Coyle s frame- The E s CAP reform o lberalze markes and decouple paymens from producon has led o ncreasngly volale oupu prces, and herefore, more prce and ncome rsk. In hs sudy, eg land use share equaons are specfed and esmaed usng regonal daa from 2000 hrough 203. A mulple-equaon panel daa model s used o deermne he conrbuon of ncreased prce volaly and rsk o land-use change. More specfcally, s nvesgaed how relave perceved rsk affecs land use change. We found oppose effecs beween complemenng and subsung land uses, leadng o compeon whn he dary secor and whn crop producon. Keywords: CAP, land-use change, panel daa, prce volaly, rsk percepon. Résumé La réforme de la PAC de l E, vsan à lbéralser les marchés e à découpler les paemens drecs de la producon, a enraîné une plus fore volalé des prx de producon e a provoqué, par conséquen, une augmenaon du rsque de prx e de revenu. Le bu de ce raval es de présener e évaluer hu équaons concernan les modes d ulsaon des erres, en consdéran les données régonales de 2000 à 203. n modèle à équaons smulanées sur données de panel a éé reenu pour mesurer l mpac de l accrossemen de la volalé des prx e du rsque de prx sur le changemen d affecaon des sols. En parculer, nous avons focalsé l aenon sur le changemen d affecaon des sols lé à la percepon du rsque relaf. Nous avons observé des effes opposés enre ulsaons des erres complémenares e de subsuon, qu génèren une concurrence au nveau du seceur laer e de la producon agrcole. Mos-clés: PAC, changemen d affecaon des erres, données de panel, volalé des prx, percepon du rsque. Wagenngen nversy, Agrculural and Rural Polcy Group, WR, Wagenngen, hthae Neherlands. Correspondng auhor: Esher.Boere@wur.nl 2 Agrculural Economcs Research Insue, LEI, Thae Hague, he Neherlands. Jel codes: Q5, C6, Q 0

2 work o accoun for he ncreased oupu prce volaly caused by CAP reforms n a sudy of crop producon. Esmang land-response equaons has been appled by Moore and Negr (992) o develop land and waer allocaon equaons based on a flexble funconal form of a mul-crop producon funcon. Wu and Segerson (995) elaboraed on hs model by adjusng o accoun for land heerogeney. The wo approaches were negraed by Chambers and Jus (989), who used a wo-sep modelng framework: hs approach allocaes land among dfferen producon acves afer he opmal levels of oupus and npus have been deermned. Arnade and Kelch (2007) exended hs framework by dervng shadow prce equaons for crop areas. Fezz and Baeman (20) used he Chambers and Jus framework o esablsh a jon prof funcon o derve e- quaons for land-use share (he proporon of he land area allocaed o each use) ha can be esmaed as a sysem. There also exss a grea body of leraure on yeld rsk (Jus and Pope, 979; Chavas and Hol, 990). However, n order o focus on prce rsk, we choose o gnore yeld rsk. Esmang land-use response equaons ha no only accoun for he effec of prce uncerany on s own land use (e.g. prce uncerany of whea on he land use of whea), bu also on alernave land uses (e.g. sugar bees) has no ye been underaken. The purpose of hs paper s o assess he effec of volale agrculural oupu prces on changes n agrculural land use snce 2000 n he Neherlands by esmang a sysem of land-response equaons. The land-response equaons are based on a resrced prof funcon, akng boh rsk and farm echnology no accoun. We used daa on 66 Duch a- grculural regons from 2000 hrough 203 o analyze he land-use decsons of producers. In he nex secon we esablsh land use share funcons ha accoun for he rsks ha resul from ncreased prce volaly. Moreover, we hypohesze ha he effec of agrculural oupus beng complemens and subsues affecs land use decsons. Nex, we descrbe he sudy area and daa sources. We hen develop an emprcal model n whch he producer opmzes hs prof by allocang land among dfferen uses whle accounng for rsk. In he fnal secons, we economercally esmae he land-use share equaons, dscuss he resuls, provde a general dscusson, and presen he man conclusons drawn from our sudy. 2. Theorecal Framework Buldng upon he work of, amongs ohers, Chavas and Pope (982), Coyle (990, 992) and Wu and Segerson (995), we derve a sysem of land use share equaons based on a uly maxmzng producer. We assume a prof funcon wh mulple oupus (land uses or crops), where he producer mus decde how o allocae hs/her hecares a- mong dfferen land uses n order o maxmze oal profs (Wu and Segerson, 995). The prof funcon s elaboraed by accounng for rsk n producon decsons; he producer herefore becomes a uly maxmzer (Oude Lansnk, 999). Expeced uly s deermned by he expeced prof, he varance of prof, and he coeffcens of absolue rsk averson per crop (see e.g. Coyle, 990, 992). Based on uly maxmzaon we derve land-use share funcons ha represen he proporon of he land ha producer h allocaes o land use n year : where Cv r s he 3-year movng average of he coeffcen of varaon, he sandard devaon dvded by he average, of he oupu prce of he alernave (subsue or complemen) crop and Cv s he 3-year movng average of he coeffcen of varaon of he oupu prce of he crop of neres. Hence, n he rao of he coeffcens of varaon he CV of he alernave crop s n he numeraor and ha of he crop of neres n he denomnaor. We used coeffcens of varaon nsead of varances because, n comparson o varance, he coeffcen of varaon s a unzed measure of rsk. So, dvdng he rao of wo coeffcencoeffcens of varaons (see equaon 2) does no lead o a volaon of he homogeney assumpon. Subsues and complemens In he model presened, land use change depends on he facors deermnng he land shares,.e. expeced oupu prces, varable npu prces, yelds, quanes of fxed facors and he varance of oupu prces. Implc s also farm echnology relevance, showng o wha exen he producs h = s h ( ˆp, w, q, z, Vp)= n h h=,,h; =,,I; =,,T. () N The land-use share of producer h for crop n year (s h ) depends on all expeced oupu prces (p^ ) and known varable npu prces (w ) n year, yelds (q ) of producer h n year, fxed npu quanes (z ) of producer h n year, he varance of prces (Vp), and he degree of rsk-averson. The land use shares equal he number of hecares n h of producer h allocaed o crop n year dvded by he oal number of hecares N of producer h n year. When Vp=0, he land-use share equaon for he uly-maxmzng producer equals he land-use share equaon for he prof-maxmzng producer. For he mahemacal dervaon from he prof funcon o he land use shares, we refer he reader o he Appendx. Rao of coeffcen of varaons Fgure shows ha for all oupu prces here s some degree of volaly. We assume ha, when deermnng opmal land use, he producer looks a he relave prce volaly beween crops; hence he varaon of a crop compared wh he varaon of he alernave crops. To ake hs no accoun, we ake he raos of he coeffcens of varaon as elemens of Vp: / μ r r v r = = / μ Cv Cv r,r=,,i; r, (2)

3 Table - Specfcaon of land uses and her oupus. Land se Crops Oupu prce and yeld Cereals Wner whea, Summer whea Summer whea Wner barley, Summer barley Grassland Permanen grassland Mlk Temporary grassland Sugar bees Sugar bees Sugar bees Poaoes Seed poaoes, Man crop poaoes Consumpon poaoes Fodder maze Fodder maze Fodder maze Onons Seed onons, Seed onons Seed onons Vegeables Endves, caulflowers, leeks, broccol, Brussels sprous Caulflowers Oher All oher crops Overall ndex er s able o adjus acves whn hs enerprse. One aspec of farm echnology s wheher producon acves are complemens or subsues. Complemens are defned as hose acves ha are n jon supply, eher because of crop roaon requremens or because one oupu s needed as an npu n producng anoher oupu. Subsues are defned as (ses of) acves ha are rval o each oher. For arable producon n he Neherlands, he common roaon sysem s he jon producon of cereals, poaoes and sugar bees. For dary producon, fodder maze and grassland can be vewed as complemenary o mlk producon. When facng a larger expeced uly, s lkely o be easer for a producer o swch acves whn hese wo ses of producon raher han beween hem. Based on he raos of coeffcens of varaon we can examne wheher wo land uses are subsues or complemens. For subsues and n case of rsk-averson a producer wll ncrease he share of a crop when he rao of coeffcens of varaon ncreases (he coeffcen of varaon of he crop beng n he denomnaor). For complemens he oppose s rue. 3. Daa We dvded he Neherlands no 66 agrculural regons usng an exsng classfcaon based on homogeney of sol ypes (Helmng, 2005; Helmng and Renhard, 2009). One of he advanages of usng hs classfcaon for he ypes of agrculural regons s he relave homogeney of he sol whn hese regons. All regons can be classfed based on he sol ype (clay, sand, or mxed sol ha ncludes peas and loams). Dfferen sol ypes generae dfferen crop yelds and herefore arac dfferen producon acves. We aggregaed farm srucure survey (FSS) daa for all farm households n he Neherlands from 2000 hrough 203 no he 66 agrculural regons (Sascs Neherlands, 203). Based on he avalable daa, we defned eg agrculural oupus as he dfferen ypes of land use. Specfcally, we grouped he agrculural land uses no cereals, grassland, sugar bees, poaoes, fodder maze, o- nons, vegeables, and oher (Table ). In he Neherlands, grassland s manly used for dary producon. Alhough beef and oher cale are also grazed n Duch grassland areas, hey accoun for a small proporon of he oal grassland use. Moreover, nrae regulaons requre a mnmum amoun of land per cow and hereby make dary farmng heavly dependen on he avalably of grassland. Thus, n he res of he arcle, we wll refer o grassland exclusvely n he conex of dary cale. For each year and each regon, we calculaed he amoun of land (ha) for each land use usng Duch FSS daa. We convered ha area (ha) no land-use shares by dvdng he area of each land use n a gven regon and year by he correspondng oal amoun of agrculural land. Table 2 summarzes he descrpve sascs for he agrculural land uses for he frs and las years of he panel and for he panel as a whole. Table 3 summarzes he descrpve sascs for he explanaory varables. The aggregaon from ndvdual crops o he eg land uses led us o use prce ndces nsead of absolue prces for each land use. We frs sandardzed all nomnal absolue prces usng 2000 as he base year before we normalzed oupu prces by dvdng hem by he oupu prce ndex of ferlzer (Eurosa, 204; LEI, 204). nforunaely, was no possble o rereve all daa on oupu and npu prces from he same daabase. Therefore, daa on absolue oupu prces for several land uses (cereals, grassland, poaoes, fodder maze, and onons) were rereved from LEI (204), whereas daa on absolue oupu prces for he oher land uses (sugar bee, vegeables, and oher) were rereved from Eurosa (204). Daa on he npu prce of pescdes was rereved from LEI (204), whereas daa on he npu prce of ferlzer was rereved from Eurosa (204). We only nclude ferlzer and pescdes as varable npus because all seleced crops requre hese npus. For some land uses, we chose a proxy for oupu prce (Table ). For onons, here was a lmed amoun of prce daa avalable. Ths led us o replace he oupu prces for onons from 2000 hrough 2004 wh he correspondng prces from 995 hrough 999. The resulng oupu prce ndces are shown n fgure. As a measure of he expeced oupu prces, we calculaed an annual 3-year movng average (endng wh he year prevous from o he year beng suded) of he oupu prces. Producer expecaons abou prce flucuaons are based on pas experence. We assumed ha prce varaon was equal across regons. The coeffcen of varaon of he 2

4 NEW MEDIT N. 3/205 Table 2 - Summary sascs for agrculural land uses a he sar and end for he Neherlands by year and whole panel by regon and year ( ) Whole panel Share a) share Absolue Absolue nonzero (000 Share Share Mean S.D. Mn. Max. (000 ha) ha) obs Cereals Grassland Sugar bees Poaoes Fodder maze Onons Vegeables Oher Toal a) (absolue = he acual area; share = absolue area dvded by he oal area) normalzed oupu prce ndces over he 3 years prevous o he year beng suded was used as a proxy for he expeced varaon n oupu prces. In addon o he oupu and npu prces, we ncluded he quany of fxed npus, yelds and he presence of drec paymens as explanaory varables. As a proxy for fxed npus, we used he average sze of a farm n a regon, whch was obaned from he FSS daa. Sze s measured by he sandardzed annual revenue of a specfc producon ype per hecare of land or per anmal. The average sze was calculaed as he sum of all farm szes n a regon, dvded by he number of farms n he regon and subsequenly convered no an ndex. For each land use, he producon (yeld n kg/ha; Table 3) was convered no an ndex value smlar o he way we dd for oupu prces (wh he value n 2000 = 00). The presence of drec paymens s referenced o as a dummy rend, sarng n 2006 when drec paymens were nroduced, and akng he value zero pror o The descrpve sascs n Table 2 show ha average land use shares of he dfferen agrculural land uses over Fgure - Changes n nomnal oupu prces from 2000 o 203. Values are normalzed by seng he prce n he base year (2000) o 00. all regons have changed only slgly over me. However, some land uses have changed consderably more han ohers. In parcular, he area of sugar bees, poaoes and oher decreased, whereas he area of grassland and fodder maze. Ths ndcaes a endency owards dary producon. Grassland remaned he man land use hroughou he sudy perod, wh a share of more han 50% of he oal agrculural land. The columns represenng sandard devaons, mnmum and maxmum shares of land use n Table 2 ndcae large regonal dfferences n land uses. Ths may be because of he dvson of regons based on homogeney of sol. In varyng degrees, almos all land uses are prevalen n each regon durng he whole perod (see las column Table 2). Compared o he relavely small changes n he land-use shares, fgure shows relavely large changes n oupu prces. The oupu prces seemed o follow some common rends n her flucuaons, such as decreases beween 2003 and 2005 and beween 2007 and 2008 and an ncrease over he las wo years. However, large dfferences n he volal- Table 3 - Summary sascs of explanaory varables over he whole me perod ( ). Land-use Mean Sd. Dev. Mn. Max. Expeced oupu prce ndces (normalzed by he prce of ferlzer) Cereals Grassland Sugar bees Poaoes Fodder maze Onons Vegeables Oher Expeced yeld ndces (/00 n esmaon for scalng purposes) Cereals Grassland Sugar bees Poaoes Fodder maze Onons Vegeables Inpu prce ndces (normalzed by he prce of ferlzer) Pescdes subsdes Fxed cos ndces (/00 n esmaon for scalng purposes) Farm sze Coeffcen of varaon of he normalzed expeced oupu prce ndces a) Cereals Grassland Sugar bees Poaoes Fodder maze Onons Vegeables Oher a) For scalng purposes and clary of esmaon resuls, he rao of coeffcens of varaon ares dvded by 0. 3

5 y of he oupu prces can be observed. Oupu prce volaly was especally hgh for onons and poaoes, boh n erms of he larges ncrease beween wo years (respecvely and 72.7 percen) and he larges decrease beween wo years (respecvely and -79 percen), compared o an average ncrease of 3.8 and an average decrease of 5.7 percen over all land uses beween wo years. The large dfferences n oupu prce volaly are refleced n he coeffcens of varaon of oupu prces (Table 3). Poaoes and onons experenced much larger prce varaons han oher land uses. 4. Emprcal Model As ndcaed n equaon he allocaon of land among d- fferen producon acves for a uly-maxmzng producer does no depend only upon oupu and npu prces, and fxed npu quanes, bu also depends upon he varaon n oupu prces n relaon o farm echnology and he producer s degree of rsk-averson. Gven he land-use share equaons for a uly-maxmzng producer developed n he heorecal model, we have specfed he followng reduced-form land-use share equaons: S * h = + J h j j j= + g + x + R r= r r M m= q + m m + T + u K k = z hk k h=,,h; =,,I; =,,T (3) (3) Where S * h represens he N land-use shares of crop n regon h n year ; φ h represens he regon-specfc nercep for regon h and land use ; β j represens he coeffcens for normalzed npu and oupu prces j for crop ; X j represens he normalzed npu and oupu prces j n year ; ρ m represens he coeffcens of yelds m for crop ; q m represens he yelds m n year ; γ hk represens he coeffcens of fxed facors k for regon h; z k represens he fxed npu facors k for regon h n year ; ω represens he coeffcen for crop for he presence of drec ncome paymens, g represens he drec ncome paymens dummy rend, δ r represens he coeffcens for he raos of he coeffcens of varaon of he expeced prces r for crop ; ν r represens he raos of he coeffcens of varaon of he expeced alernave prces r wh respec o expeced prces n year ; λ represens he coeffcen of crop for he rends; T represens he me rend; and u represens he unobservable effecs ha affec land-use change for crop n year. Equaon 3 specfes he share of land use for each crop n regon h n year. Because only relave prces maer, he model has been made homogeneous of degree zero by normalzng he sandardzed oupu prces and he sandardzed prce of pescdes usng he prce of ferlzer. Each Noe ha wh frs-dfferencng he panel s reduced by one year;.e. observaons sar as of he second year of observaons n he orgnal panel. Moreover, frs-dfferencng only occurs beween me perods and no beween regons or land uses. land use share equaon only ncludes expeced oupu prce of s own land use and no expeced oupu prces of alernave land uses n order o avod mulcolllneary. Due o daa lmaons, he fxed npu quanes (z hk ) are only represened by he average farm sze per regon per year and no allocaed o ndvdual land uses. A me rend has been ncluded o accoun for crop-specfc rends n landuse shares. We assume he covarances of oupu prces o be zero. In realy, he covarances are no zero, bu he large amoun of covarance values caused mul-collneary problems. For a producer, he covarance of alernave producs may be of mporance n decdng upon land allocaon. However, by esmang he effec of he raos of he coeffcens of varaon all alernave land uses are aken no accoun. We esed for censorng from below, meanng ha here s a lower bound of zero for all land use shares. In case many land use shares acually ake he value zero hs could lead o nconssen esmaes of he parameers (Fezz and Baeman, 20). The resuls, provded n Table 2, show ha censored observaons are only presen for vegeables, bu no enough ha nconssen esmaes of he parameers may be expeced. Ths, ogeher wh he few non-zero observaons for crop shares (see Table 2), means ha we do no have o ake sample selecon problems no accoun. We herefore esmaed he land-use share equaons as a sysem usng he seemngly unrelaed regresson (SR) echnque akng no accoun ha he dsurbances from dfferen share equaons are lkely o be correlaed because of common unobservable facors (Febg, 200). Ths correlaon could have several causes, such as weaher, polcy changes affecng he agrculural secor as whole, or economy-wde shocks. The yearly observaons over he same s- udy areas lead o a panel ha requred a fxed-effecs ransformaon of he SR regresson. Because we deal wh naonal values for boh prce and yeld ndces, a fxed effecs ransformaon usng devaons from he mean was no possble. We herefore chose a frs-dfference ransformaon on he model of he eg land-use shares: J M * * ( S h S h ) = j ( x j x j ) + m ( qm qm ) + ( g g ) + j= K hk ( z hk z hk ) + r ( vr vr ) + + ( u u ) k = m= R r= h=,,h; =,,I; =,,T (4) Equaon 4 mples ha he nercep (f h ), whch represens he regon-specfc effec, cancels ou. The new nercep λ represens he coeffcen of he crop-specfc rend n equaon 3. The ransformed explanaory varables are composed of he frs-dfferenced expeced oupu prces (p' ), frs-dfferenced npu prces, frs-dfferenced yelds per hecare (q m ), frs-dfferenced average farm sze (z hk ), frs-dfferenced dummy rend represenng he presence of drec ncome paymens (g ), and he frs-dfferenced raos of he coeffcens of varaon (ν r ν r ). Noe ha he dummy me rend for governmen subsdes ransforms n- 4

6 o a dummy represenng he presence of drec paymens. Tables 2 and 3 ls he dependen and explanaory varables and her descrpve sascs. Because all land-use shares ogeher mus sum o 0 n he frs-dfferenced model, esmang all he land-use equaons ogeher resuls n a sngular covarance marx of error erms. Whle here are varous ways o handle hs sngulary problem (Takada e al., 995), we decded o drop he resdual equaon oher from he sysem (Fezz and Baeman, 20). The resdual equaon can hen be recalculaed because, by defnon, he land-use shares mus sum o. 5. Resuls We esed he conemporaneous correlaon usng he Breusch-Pagan es. The null hypohess (.e., no conemporaneous correlaon) was rejeced a he % level (χ 2 (2) = and P < 0.00). Ths suggess ha here s sgnfcan correlaon because common elemens exs n he seven equaons ha relae he equaons hrough her resduals. The sronges correlaons occurred beween he resduals for whea and meadows (33%) and poaoes and onons (22%). We esed for groupwse heeroskedascy usng he Lagrange Mulpler es. The null hypohess (.e., no groupwse heeroskedascy) was rejeced a he % level of sgnfcance for each of he seven equaons. Ths means ha he varances are consan over me whn he equaons, bu dffer beween hem. We esed for groupwse auocorrelaon usng he Durbn-Wason es. For all land uses he null hypohess (.e., no-auocorrelaon) was rejeced a he AR() level. Ths resul means ha here s eher posve or negave auocorrelaon and ha he dfferen error erms are correlaed. Hence, sascal effcency ncreases by esmang he seven equaons as a sysem, and SR s herefore he approprae esmaon mehod. Whou SR, he observed heeroskedascy and auocorrelaon would lead o based and nconssen esmaes. Table 4 summarzes he esmaed regresson coeffcens for he seven land-use share equaons. The able consss of wo pars. The upper par of he able repors he regresson coeffcens of all varables excep hose relang o rsk. The lower par of he able repors he regresson coeffcens for perceved rsk due o prce volaly. Moreover, he χ 2 value for all equaons excep for vegeables was sgnfcan a he % level. For vegeables, he χ 2 value was sgnfcan a he 5% level. Ths means ha a leas one of he regresson coeffcens n he model does no equal zero. Hence, we can be confden ha he dependen varable s correlaed wh he ndvdual varables. The coeffcens of he land-use equaons were generally small, ndcang ha land-use change s a slow process. We wll dscuss he esmaon resuls for all varables excep hose relang o rsk n he nex secon. Non-rsk esmaon resuls An ncrease n he expeced oupu prce of a parcular land use s expeced o lead o an ncrease n he share of ha parcular land use. Only grassland showed a negave and sgnfcan coeffcen (Table 4), whch suppors hs hypohess. In he Neherlands, grassland s manly assocaed wh dary farmng. Dary farmng has been subjec o quoa resrcons for he whole observaon perod;, makng more dffcul o ncrease mlk producon followng an ncrease n he oupu prce of mlk. sng he expeced prces and land use shares of 203 we calculaed he elasces wh respec o oupu prce of he land use shares. Table 5 shows he resulng percenage change n land shares, akng no accoun he effec of a % ncrease n a parcular oupu prce on s own and on alernave land use shares. All percenage changes n land share are nelas- Table 4 - Esmaon resuls (regresson coeffcens) usng he sysem of land use a), b), c). Oupu prce Yeld per ha subsdes Pescde prce Farm sze Consan Cereals Sugar Bee Poaoes Grassland Fodder Maze Onons Vegeables (0.02) (0.008) (0.005) (0.056) (0.005) (0.00) (0.005) * *** *** *** * ns ns (0.03) (0.02) (0.03) (0.8) (0.067) (0.0) (0.000) ** *** ** *** ns *** ns (0.002) (0.00) (0.003) (0.003) (0.002) (0.00) (0.000) ns *** *** *** ns *** ns (0.008) (0.002) (0.02) (0.02) (0.009) (0.00) (0.00) ns ns *** *** ns *** ns (0.007) (0.002) (0.003) (0.04) (0.005) (0.002) (0.002) *** *** ns ns ns ** * (0.002) (0.00) (0.002) (0.006) (0.00) (0.00) (0.000) ns *** *** *** *** ns ns Rao of coeffcens of varaon (rows represen nomnaor, columns denomnaor) Cereals Sugar Bee Poaoes Grassland Fodder Maze Onons Vegeables Oher (0.003) (0.053) (0.07) (0.05) (0.009) (0.003) *** *** *** ns ** *** (0.096) (0.023) (0.05) (0.04) (0.06) (0.003) *** *** ns *** *** * (0.02) (0.003) (0.0) (0.004) (0.009) (0.002) *** *** *** *** *** ns (0.30) (0.008) (0.03) (0.006) (0.037) (0.06) *** *** ns ns ns ns (0.66) (0.004) (0.072) (0.025) (0.06) (0.005) *** *** *** *** *** ** (0.08) (0.00) (0.02) (0.004) (0.002) (0.00) *** *** *** *** *** ns (0.026) (0.006) (0.073) (0.027) (0.007) (0.08) *** *** *** *** ns *** (0.036) (0.04) (0.080) (0.062) (0.06) (0.02) (0.009) *** *** *** *** ns ** ns a) In he lower half of he able, he values equal he varance of he alernave crop (lsed n he rows of he able) dvded by he varance of he curren crop (lsed n he columns of he able). b) Sandard error n parenheses. c) Where (*), (**)and (***) represen sgnfcance 0, 5 and % level respecvely, and ns means no sgnfcan. 5

7 c wh respec o s oupu prce. Ths s as expeced; land use change s a slow process and s dependen on many oher facors such as farm echnology. Sugar bee and poaoes show he hghes percenage change n land share (respecvely 0.54 and percen), grassland he lowes ( percen). Yeld per ha s assumed o have a posve effec on he land use share because yeld ncrease makes producng he crop more profable. For cereals and poaoes an ncrease n he expeced yeld leads o a sgnfcan ncrease n landuse share. For sugar bee, grassland and onons, an expeced yeld ncrease has a sgnfcan negave effec. Agan, for boh sugar bee and grassland, hs may have o do wh he quoas, resrcng he ably o ncrease yelds. For o- nons, hs resul mg be couner-nuve, bu may be caused by he large flucuaons n yeld for hs crop. When subsdes are compleely decoupled from producon, hey should no aler he producon plan (Hennessy, 998). However, producon decsons may be affeced ndrecly because of he so-called wealh effec, ncreasng a farmer s wealh and hereby reducng hs level of rsk averson (Fnger and Lehmann, 202; Hennessy, 998). Prevous sudes found ha hs may have some mpac on crop allocaon (Sckoka and Moro, 2009; Koundoury e al., 2009). Ths would mean ha due o he sngle farm paymens (SFP), farmers are more wllng o culvae crops wh a large prce volaly. We fnd a posve and sgnfcan effec for cereals, sugar bee and grassland and a negave and sgnfcan effec for poaoes. Due o he decrease n he share of poaoes, a crop wh large volaly, we do no fnd ndcaon of a wealh effec. For grassland and sugar bee, he ncrease n share may have o do wh he fac ha he nroducon of SFP was accompaned by a reducon n producon resrcons. The rend for subsdes may herefore no only represen he nroducon of SFP, bu also he wder on-gong lberalzaon of he CAP. An ncrease n he prce of pescdes s expeced o lead o a decrease n he share of any land use ha uses pescdes a a hgh nensy, bu o an ncrease n he land-use share for a land use ha uses pescdes a a low nensy. For grassland, he prce of pescdes had a sgnfcan negave coeffcen (Table 4). In conras, poaoes and onons have a sgnfcan posve coeffcen for pescdes. If he prce of pescdes ncreases, hs means ha becomes more favorable o culvae ferlzer depended on wheher he crop was nuren-nensve or no. Snce fxed npus are no crop-specfc we neher expec posve nor negave coeffcens for average farm sze. The coeffcens represenng average sze showed lle effec on he land-use shares (.e., all values > and <0.06; Table 4). For cereals, sugar bee, onons and vegeables, s- mall sgnfcan effecs were found. The consan represens he overall rend n he land-use shares of he dfferen crops. There was a posve and sgnfcan rend for sugar bee, poaoes and fodder maze and a negave and sgnfcan effec for grassland (Table 4). Rsk esmaon resuls The lower par of Table 4 repors he raos of he coeffcens of varaon of he prces of wo land uses as a measure of perceved rsk due o he expeced prce volaly of he wo land uses. The advanage of usng he raos of coeffcens of varaon raher han varances and covarances resuls from he fac ha accouns for he rsk-averse producer who compares he alernave crop wh he curren crop. In he lower half of Table 4, he values equal he coeffcen of varaon of he alernave crop (lsed n he rows of he able) dvded by he coeffcen of varaon of he curren crop (lsed n he columns of he able). We esed each of he land use share equaons for model dfferences wh and whou he raos of he coeffcens of varaon usng he lkelhood rao es. For all land use shares, excep for vegeables, he null hypohess was rejeced a he % level. For vegeables he null hypohess was rejeced a he 5% level. Hence, es resuls showed ha addng he raos of he coeffcens of varaons o he model sgnfcanly mproved he model f. The resuls show many sgnfcan posve and negave coeffcens, ndcang ha he raos of he coeffcens of varaon successfully capured dfferences n he perceved rsk. Ths s conssen wh prevous work by Sckoka and Moro (2006) ha hghlged he mpac of cross-crop effecs on boh he relave prce and he varably of ncome. Suppose we have he rao of coeffcens of varaon (CV) of he oupu prces of wo crops: CV crop Y / CV crop X. A posve sgn mples ha an ncrease n he rao leads o an ncrease n he share of land allocaed o crop X. So, for a rsk-averse producer hs means ha when he prce volaly of crop Y ncreases compared o ha of crop X, he land share of crop X ncreases. Ths may mply ha crops X and Y are subsues. Wh complemens or rsklovng producers, an ncrease n he relave prce volaly of crop Y leads o a reducon n he land share of crop X. So, n case of complemens, he coeffcen has a negave sgn. Hence, he lkelhood for land use change depends on wheher he crops are complemens or subsues and on he degree of rsk averson perceved by he producer. For cereals (column of Table 4), he rao of he coeffcens of varaon wh respec o sugar bee, fodder maze and vegeables showed a negave and sgnfcan coeff- Table 5 - Elasces of land use wh respec o prce. elascy cereal 0.74 grassland sugar bee 0.54 poaoes fodder maze onons 0.9 vegeables hese crops. Because ferlzer and pescde use are posvely correlaed n nensve agrculure, hs reasonng s n lne wh ha of Fezz and Baeman (20), who repored ha he prce effec of 6

8 cen. Wh respec o sugar bee, he negave sgn mples ha cereals and sugar bees are consdered complemens. Ths means ha a smaller area of cereals would be grown f he prce varaon of bees ncreases compared o he prce varaon of cereals. Ths resul s as expeced because he mos common crop roaon scheme n he Neherlands nvolves cereals, sugar bee and poaoes. The raos of he coeffcens of varaon wh respec o poaoes, grassland, o- nons and oher show posve effecs a he % sgnfcance level. Ths means hese crops are subsues for cereals. More relave prce varaon for hese crops leads o an ncrease n he land share of cereals. For poaoes hs resul s unexpeced. A possble reason may be ha especally seed poaoes are also grown ousde he common crop roaon of cereals, sugar bees and poaoes. For sugar bees (column 2 of Table 4), he raos of he coeffcens of varaon wh respec o cereals, poaoes and vegeables were sgnfcan and negave, ndcang ha hese are complemenary producs because of crop roaon requremens. Grassland, fodder maze, onons and oher had a sgnfcan and posve effec, ndcang ha hey are subsue producs. For poaoes (column 3 of Table 4), sugar bees, fodder maze and vegeables were complemens. Sugar bee s a complemen because of crop roaon requremens, whereas onons were subsues. Cereals does no show he expeced negave sgn, whereas fodder maze does no show he expeced posve sgn. A possble explanaon may be ha roaon schemes only allow lmed culvaon of poaoes, whch leads farmers o ren land from dary producers o culvae poaoes. Grassland and fodder maze are producon acves ha are relaed o dary producon. For grassland (column 4 of Table 4), he raos of he coeffcens of varaon for fodder maze had a large negave and sgnfcan effec. Ths s expeced, because boh are grown for dary producon and can herefore be seen as complemens. Also, poaoes can be seen as a complemen as dscussed prevously. The rao of coeffcens of varaon of vegeables showed a posve and sgnfcan effec, meanng ha hey can be seen as subsues. For he oher crops, onons and cereals, he esmaed coeffcens were negave and sgnfcan. For fodder maze (column 5 of Table 4) he esmaed coeffcens were low and ofen no sgnfcan. A possble explanaon for hs could be mlk quoas, whch have been enforced hroughou Europe as par of he CAP and are sll bndng n he Neherlands. If producers produce a he quoa level, a change n prof wll no drecly lead o a change n land use. Prevous sudes showed ha quoa hamper changes n land use (Hueel and Jongeneel, 20; Pe e al., 202). Anoher explanaon may be ha land used for dary producon s more dffcul o change compared wh land used for crop producon. Ths s due o he relavely large amoun of fxed capal requred for dary producon and he fac ha a large par of he sols n he Neherlands are no suable for crop producon. Sgnfcan coeffcens are however observed for sugar bees and poaoes, acng as a subsue, and for onons, acng as a complemen. For onons (column 6 of Table 4), he volaly n prces s so hgh (fgure ) ha we argue ha he degree of rsk he crop carres s more mporan han beng par of a crop roaon sysem. Onons are he smalles land use; herefore producers may no be fully specalzed n producng onons. Ths may lead producers o se asde some of her land for rsk-lovng behavor. The raos of he coeffcens of varaon of onons wh sugar bees, poaoes, and vegeables had sgnfcan negave effecs, ndcang rsk-lovng behavor. For vegeables (column 7 of able 3), almos none of he raos of he coeffcens of varaon were sgnfcan. Ths s conssen wh our dea ha vegeables do no funcon n a common roaon scheme wh he oher crops consdered and ha changes n vegeable producon largely ake place whn s own caegory. Noneheless, we found low, bu sgnfcan and posve values for cereals, sugar bee and fodder maze. Dscusson and Conclusons The European non s CAP s shfng away from marke and prce suppor owards marke lberalzaon and decoupled paymens. The resulng ncreasngly volale oupu prces and farm ncomes pose challenges o agrculural producers ha affec he compeve posons of varous a- grculural land uses. The objecve of he presen sudy was o assess he effec of volale agrculural oupu prces on changes n agrculural land use snce 2000 n he Neherlands. Our analyss used daa on 66 Duch agrculural regons from 2000 hrough 203 o analyze land-use decsons. We defned eg land use acves: producon of cereals, grassland, sugar bees, poaoes, fodder maze, onons, vegeables, and oher crops. For each land use, we esablshed resrced prof funcons ha depended on expeced oupu prces, varable npu prces, he presence of drec paymens, crop yelds, he quany of fxed npus, and he raos of coeffcen of varaon of expeced oupu prces wh hose of alernave crops. Coeffcens of varaon were used n order o oban a unzed measure of rsk. sng raos enabled us o dsngush beween complemens and subsues n farmer s acves. Land-share equaons were esmaed usng a mulple-equaon panel-daa model o deermne he conrbuon of ncreased prce volaly o land-use change. Our esmaon of he non-rsk varables showed ha for all land-use shares excep for grassland, an ncrease n he expeced oupu prce of a parcular land use led o an ncrease n he share of ha parcular land use. Ths s conssen wh prevous research, whch showed sgnfcan posve effecs of oupu prce on land-use responses and suggess ha prce expecaons are mporan n land-use decson-makng (Sckoka and Moro, 2006; Fezz and Baeman, 20). Regresson coeffcens for expeced yeld 7

9 showed negave resuls for land uses where he level s dependen on quoa resrcons, namely sugar bee and grassland. For hese wo land uses, he nroducon of sngle farm paymens leads o an ncrease n her share of land. However, hs resul may be relaed o easng he producon resrcons for hese producs ha accompaned he nroducon of he sngle farm paymens. Therefore, he varable may be more lkely o represen he on-gong lberalzaon of he CAP. An ncrease n he prce of pescdes showed varaons n her effecs, suggesng ha an ncrease n he prce of pescdes favors land uses ha use hese chemcals less nensvely. The average farm sze n a regon had lle o no effec on he land-use shares. The raos of he coeffcens of varaon of he prces of wo alernave land uses can be used as a measure of expeced relave prce volaly. Two man conclusons can be drawn based on he presen resuls. Frs, he resuls show many sgnfcan posve and negave coeffcens, ndcang ha relave prce varaon maers and serves as a proxy for he degree of perceved rsk. Rsk-lovng behavor was observed for onons and poaoes. Producers only devoed a small proporon of her land o hese acves. These resuls dffer from hose of Sckoka and Moro (2006), who confrmed her hypohess of rsk-averse behavor for all ypes of farms. A possble explanaon may be he un of analyss; producers may be rsk-averse overall, bu may no show rsk-averse behavor for all acves. Second, changes beween land uses depend on wheher producon acves are complemens or subsues. For dary farmng, fodder maze and grassland appear o be complemens. For arable farmng, cereals, sugar bees, and poaoes appear o be complemens, whereas onons and grassland appears o be a subsue. Ths s conssen wh Phlppds and Hubbard (2003) who fnd a change from olseeds o cereals and a change from cale o mlk under he Agenda 2000 reform. Vegeables sare no culvaed n roaon sysems wh oher crops, whch s refleced by he low response n relaon o oher land uses. The complemens whn dary farmng and he complemens and subsues whn arable farmng may ndcae compeon whn boh caegores of land use, and separaon beween hem. A producer may vew alernave producon decsons only whn he conex of eher arable farmng or dary farmng dependng on her curren producon acves. Swches beween arable and dary farmng would nvolve hgher ransacon coss. Ths dfference may also resul from he perceved dffculy of converng grassland no oher land uses due o sol condons. Furher research, splng he land beween arable and dary secors s necessary o es o wha exen hs hypohess holds. There are several caveas relaed o our approach. Daa lmaons dd no allow us o dsaggregae yelds o he regonal level. Because he regons had largely homogeneous sol ypes whn a regon bu heerogeneous sol ypes beween regons, dsaggregang yelds o he regonal level could lead o more accurae esmaes. Moreover, alhough we dvded he Neherlands no regons based on homogeney of sol ype, we dd no accoun for he effec of sol ype on culvaon decsons. Snce some sols may be unsuable for some crops, a more precse verson of our model would accoun for hs. The ncrease n rsk due o oupu prce volaly may be parly offse by rsk-reducng drec paymens from he governmen (Rder and Jacque, 2002; Sckoka and Moro, 2006) and nsurance measures such as forward conracs (Sanos, 2002), whch we dd no accoun for n our analyss. By ncludng a dummy rend for he nroducon of sngle farm paymens, we red o accoun for changes n CAP polces. However, oher polces, such as producon resrcons (quoas) or envronmenal regulaons, may lead o dsorons n analyzng he effecs of rsk. References Arnade C. and Kelch D., Esmaon of area elasces from a sandard prof funcon. Amercan Journal of Agrculural Economcs, 89: Brady M., Kellermann K., Sahrbacher C. and Jelnek L., 2009 Impacs of decoupled agrculural suppor on farm srucure, bodversy and landscape mosac; Some E resuls. Journal of Agrculural Economcs, 60,: Chambers R.G. and Jus R.E., 989. Esmang muloupu echnologes. Amercan Journal of Agrculural Economcs, 7: Chavas J. and Hol M., 990. Acreage decsons under rsk: The case of corn and soybeans. Amercan Journal of Agrculural Economcs, 72: Chavas J. and Pope R., 982. Hedgng and producon decsons under a lnear mean-varance preference funcon. Wesern Journal of Agrculural Economcs, 7: Coyle B., 990. A smple dualy model of producon ncorporang rsk averson and prce uncerany. Canadan Journal of Agrculural Economcs, 38: Coyle B., 992. Rsk averson and prce rsk n dualy models of producon: A lnear mean-varance approach. Amercan Journal of Agrculural Economcs, 74: Coyle B., 999. Rsk averson and yeld uncerany n d- ualy models of producon: A mean-varance approach. Amercan Journal of Agrculural Economcs, 8: Eurosa, 204. Agrculural prces and prce ndces. Avalable a: p://epp.eurosa.ec.europa.eu/poral/page/ poral/agrculure/daa/daabase (las accessed 4 December 204). Fezz C. and Baeman I.J., 20. Srucural agrculural land use modelng for spaal agro-envronmenal polcy analyss, Amercan Journal of Agrculural Economcs, 93: Febg D.G., 200. Seemngly unrelaed regresson. In: B.H. Balag (eds), A companon o heorecal economercs. Massachuses: Blackwell publshers, Massachuses, 0-2. Fnger, R., and Lehmann, N., 202. The nfluence of d- 8

10 rec paymens on farmers hal nsurance decsons. Agrculural Economcs 43: Helmng J., A model of Duch agrculure based on posve mahemacal programmng wh regonal and envronmenal applcaons, PhD dsseraon, Wagenngen nversy. Helmng J. and Renhard. S., Modellng he economc consequences of he E waer framework drecve for Duch agrculure. Journal of Envronmenal Managemen, 9: Hennessy, D.A., 998. The Producon Effecs of Agrculural Income Suppor Polces under ncerany. Amercan Journal of Agrculural Economcs 80: Hueel S. and Jongeneel R., 200. How has he E mlk quoa affeced paerns of Herd sze change? European Revew of Agrculural Economcs, 38: Jus R. and Pope R., 979. Producon funcon esmaon and relaed rsk consderaons. Amercan Journal of Agrculural Economcs, 6: Koundour, P., Laukkanen, M., Myyrä, S. and Nauges, C., The effecs of E agrculural polcy changes on farmers rsk audes. European Revew of Agrculural E- conomcs 36(): LEI, 204. Agrculural and horculural fgures. Avalable a: p:// unbouwcjfers/ (las accessed 5 December 204). Moore, M. and Negr, D.., 992. A mulcrop producon model of rrgaed agrculure, Appled o waer allocaon polcy of he bureau of reclamaon. Journal of Agrculural Economcs, 7: Oude Lansnk A., 999. Area allocaon under prce uncerany on Duch arable farms. Journal of Agrculural E- conomcs, 50: Phlppds G. and Hubbard L.J., Agenda 2000 reform on he CAP and s mpacs on member saes: A noe. Journal of Agrculural Economcs, 54: Pe L., Laruffe L., Le Mouël C. and Desjeux Y., 202. How do agrculural polces nfluence farm sze nequaly? The example of France. European Revew of Agrculural Economcs, 39: Rder A. and Jacque F., Decouplng drec paymens and he dynamcs of decsons under prce rsk n cale farms. Journal of Agrculural E- conomcs. 53: Sanos J., Dd fuures markes sablse S gran prces? Journal of Agrculural Economcs,. Vol. 53: (2002) pp Sckoka, P. and Moro. D., Modelng he reforms of he Common Agrculural Polcy for arable crops under uncerany. Amercan Journal of Agrculural Economcs, 88: Sckoka, P. and Moro, D., Modellng he mpac of he CAP Sngle Farm paymen on farm nvesmen and oupu. European Revew of A- grculural Economcs 36: Sascs Neherlands, Farm srucure survey. Avalable a: p:// NL/menu/hemas/landbouw/mehoden/daaverzamelng/koreonderzoeksbeschrjvngen/landbouwellng ob.m (las accessed 9 December 204). Takada H., llah A. and Chen Y.-M., 995. Esmaon of he seemngly unrelaed regresson model when he error covarance marx s sngular. Journal of Appled Sascs, 22: Wu, J. and Segerson K., 995. The mpac of polces and land characerscs on poenal groundwaer polluon n Wsconsn. Amercan Journal of Agrculural Economcs, 77:

11 Appendx: Dervaon from prof funcon o land use shares Prof-maxmzng producer Assume a producer who akes he prces of npus and oupus as exogenous. We defne a prof funcon wh mulple oupus (land uses or crops) ha reas he oal land area as a fxed allocable npu: (, w, z, N ) max p ( p, w, z, n ) h=,,h; =,,I; =,,T 2 Subjec o: n = h N nh h where π (p, w, v, N ) represens he oal prof for producer h n year ; p represens he vecor of exogenous oupu prces n year ; w represens he vecor of exogenous varable npu prces n year ; z represens he vecor of quanes of fxed npus for producer h n year ; N represens he oal number of hecares o be allocaed o dfferen land uses by producer h n year ; π h (p, z, n h ) represens he prof for a producer of land use n year ; p represens he oupu prce of land use n year ; n h represens he number of hecares for producer h allocaed o land use n year. Exogenous oupu prces (p ) dffer among land uses and years, whereas exogenous npu prces (w ) are he same for all land uses. The use of varable npus dffers among land uses. However, alhough he amoun of fxed npus dffers among producers and years we make he resrcve assumpon ha land use depends on he oal amoun of fxed npus on a farm. So, fxed npus are no allocaed o ndvdual land uses. In hs arcle, we wll assume ha here s no varaon n sol ype whn regons. However, here s varaon beween regons as regons are dvded on he bass of sol ype. The oal land area avalable o all producers s N = n h, whch equals he oal amoun of agrculural land avalable n a specfc year. h Assumng ha oupu n erms of quany of a crop (land use) s he produc of a fxed exogenous yeld per hecare () and he number of hecares, equaon can be wren as: ( p, w, q, z, N ) max { p q. n C( w, n, q, z )} n = h N nh h 2 For reasons of smplcy we dscard he specfcaon for h,, and from furher equaons. h h h h () (2) (3) (4) Where q s he vecor of dfferen crop yelds for producer h n year. Because producers do no know he prce for a gven produc a he me hey make her producon decsons, we mus deal wh expeced oupu prces nsead of observed oupu prces. Inpu prces are ypcally known a he me of purchase, and herefore producers do no le her land-use decsons be deermned by her expecaons on he varably of npu prces (Chavas and Hol, 990). Thus, equaon 3 can be rewren as: E ( p ˆ, w, q, z, N ) max { pˆ q. n C( w, n, q, z )} (5) nh where Eπ (pˆ, w, q, z, N ) represens he expeced prof for producer h n year, and represens he vecor for he expeced oupu prces. ly-maxmzng producers Expeced uly s deermned by he expeced prof defned n equaon 5, he varance of prof, and he coeffcens of absolue rsk averson per crop. The uly funcon ( ) can be denoed by he followng equaon (see e.g. Coyle, 992): ( pˆ, w, q, z, N, V ) E (ˆ p, w, q, z, N ) 0.5 h V Where (pˆ, w, q, z, N, Vπ ) represens he ndrec uly for producer h n year ; Vπ represens he vecor of varance of prof for producer h and year ; and α h represens a vecor of coeffcens of absolue rsk averson for he dfferen oupus for producer h. Followng he mehod of Coyle (992), we assumed ha he varance of prof s gven by: = n Vp n where Vp represens he symmerc, posve, defne covarance marx of oupu prces. n represens he vecor of he number of hecares allocaed o he dfferen land uses for producer h n year, n T represens he ranspose of n. If we subsue he expeced value of he profs (Eq. 5) and he expeced varance of he profs (Eq. 7) no he expeced uly funcon (Eq. 6), we oban he followng ndrec uly funcon: The ndrec uly funcon represens he relaonshp beween he maxmum aanable uly (max ) and he exogenous varables pˆ, w, q, z, Vp, and N (Oude Lansnk, 999). Ths uly funcon has he followng properes: ncreasng n expeced oupu prces and yelds, decreasng n varable npu prces, decreasng n he varance of oupu prces, lnear homogenous and convex n oupu prces, npu prces and he varance of oupu prces (Coyle, 990). The varable of absolue rsk averson α h s measured per producer and per crop. For any value of α h > 0, he producer s rsk-averse (Chavas and Pope, 982). In he case of h h = (6) V (7) ( pˆ, w, q, z, Vp, N ) = max ( pˆ q. n C( w, q, n, z ) nh h 0.5 n Vp n ) h h n T (8) 20