Bio-fuel multi-stage activity modelling to determine efficient public policy in uncertain agricultural markets

Transcription

1 Bo-fuel mult-stage actvty modellng to determne effcent publc polcy n uncertan agrcultural markets Stelos Rozaks (rozaks@grgnon.nra.fr) Unté Econome Publque, Insttut Natonal de Recherche Agronomque, France Agrcultural Development and Polcy Dept., Agr. Unv. of Athens Akn Kazakc LAMSADE, Unversté de Pars IX, Dauphne Abstract Support polcy to bomass-orgn lqud fuels ncorporated n gasolne and desel has been mplemented durng the last decade n France through tax exemptons to bo-fuels. Tax exempton levels as well as producton agreements determnng benefcal quanttes are allocated by the government dependng on an earmarked budget revsed every year by the parlament. A partal equlbrum model wth a detaled agrcultural sector component that s formed by a large number of representatve farms producng energy crops (wheat, sugar-beet and rapeseed) jontly wth food crops, s used to estmate costs and surpluses generated by the bo-fuel producton actvty at the natonal level. The aggregate supply of energy crops s estmated usng a starcase model of elementary farm sub-models specalsng n arable croppng. The government acts as a leader snce bo-fuel chans depend on subsdes. The model provdes the ndustry reacton to polcy schemes, takng nto account the energy crop producers supply response curve. A mult-crtera optmsaton module can assst the polcy maker to select polces that serve budgetary, envronmental and socal concerns by approachng decson-maker s objectves at the closest feasble compromse levels. In order to enhance the predctve ablty of such a model, nterval lnear programmng (ILP) s used to consder uncertanty related to yelds and prces and ts mpact to the farmer behavour. Besdes the expected gross margn maxmsaton ratonale, the dstance from optmalty once uncertanty resolves (maxmum regret) s a useful crteron that farmers apply n many cases. A hybrd mathematcal programmng model s then set up artculatng custom utlty functons for each ndvdual farmer accordng to observed behavour and the specfc propertes of each farm. Energy crop supply curves generated by the hybrd model proved to be slghtly deplaced to the rght (less costly energy crops) but stll upward sloped. Keywords : Partal equlbrum model, Lqud bo-fuels, Tax exempton polcy, Interval Lnear Programmng, Mnmax Regret, Multcrtera Analyss JEL codes: C61, D81, H23, Q12, Q42 presented n the semnar of the graduate program Economc Theory and Polcy, Dept. of Econ., Unv. of Crete, May 2004 F:\Documents and Settngs\Admnstrator\Επιφάνεια εργασίας\bof_semnar.doc 1

2 1. Introducton The lqud bo-fuel producton (ethanol and methyl esters) take-off that has occured n the last decade has placed Europe, currently representng 6% of the world volume, thrd behnd Brasl and the U.S.A (O.E.C.D.). Bofuel producton has reached a sgnfcant level n France, where more than half of the total European producton of ethanol and methyl esters s produced. The bass of green fuels, such as the early sugarbeet-ethanol fueled engnes ntroducton n 1892 n France and the brand new motor launched n the same year by Rudolph Desel, was the burnng of anmal or vegetable fat substances. A desel engne fueled by groundnut ol was exhbted n the Pars World Far n 1900 and, untl the aftermath of the Second World War, bofuels were extensvely used n Europe (mostly ethanol) and n other regons (for example, palm and cotton ol n Afrca). Bofuels had almost completely dsappeared by the sxtes because of the abundant supply of cheap fossl fuels. However, after the consecutve ol shocks of 1973 and 1979, nterest n them saw a revval. The French bo-fuel program was launched n 1993 wth the ntroducton of a tax exempton for bo-fuels 1 followng fuel supply uncertanty and envronmental concerns. Set asde land oblgatons ntroduced n the revsed Common Agrcultural Polcy (CAP) of 1992, whch amed at controllng the over-producton of cereals, created a favourable envronment for growng non-food crops 2 and was the decsve factor that ncted farmers to produce energy crops n suffcent quanttes to supply the bo-fuel ndustry. Indeed, energy crops cultvated on set asde land reached 30% of the total set asde land n Bo-fuels produced n France comprse Rape-seed Methyl Esters (RME) for use n desel engnes and ETBE (ethyl terto-butyl ether) extracted from wheat and sugar-beet for use n gasolne engnes. The total amount of bo-fuels producton n France currently represents approxmately 536 thousand tons, or 1.5% of the natonal lqud fuel consumpton. The converson of bomass to bo-fuels s concentrated n a few plants, whereas the agrcultural raw materal s produced by thousands of farms located n dfferent parts of the country at varyng costs. Table 1. Bo-fuel producton n France 3 Producton ETBE n t Producton RME n t Plant stes Plant stes Feyzn Rouen (Haute Normande) Dunkerque Compegne (Ose) Gonfrevlle Boussens (Haute Garonne) Fos-sur-mer 9 Verdun (Meuse) La Mède + Donges 155 Leer (Germany) Totals Art. 92, Fnance law voted by the French parlament n 1992 establshed tax exemptons from the I.T.P.P. (Interor Tax to Petroleum Products) for bo-fuels set at hl -1 for methyl esters and FF hl -1 for ethanol used n ETBE and provded for producton agreements of 3 or 9 years for fxed quanttes of bo-fuels. 2 Art. 32, 1997, Fnance law rectfed the 1992 law suppressng the oblgaton of the bo-fuel ndustry to use energy crops cultvated n land set-asde. However, n practce the supply of energy crops was related to the percentage of arable land oblgatorly set-asde. 3 All nformaton on bofuel producton n France has been collected usng data publshed n specalsed press (AgraValor, EuropeAgro) F:\Documents and Settngs\Admnstrator\Επιφάνεια εργασίας\bof_semnar.doc 2

3 In the cultvaton perod, a surface area of hectares was cultvated, manly on land set asde, to supply lqud bo-fuel chans. Total producton was expected to ncrease as new agreements would be allocated to the ndustry by the government by The producton of RME and ETBE was expected to reach 416 and 374 thousand tons, respectvely (Table 1). Seven years after the take-off of the tax exempton program, bo-fuels are stll more costly than fossl fuels and the agro-energy ndustral actvty largely depends on government subsdes for ts vablty. Earmarked funds for the fnancng of the tax exemptons reached 210 thousand n On the other hand, envronmental problems have become more acute and nternatonal commtments mean that the abatement of Greenhouse Gas (GHG) emssons requres ntensfed efforts. Gven the fact that bofuel substtuton for fossl fuels reduces GHG emssons, the queston arses as to whether subsdes for bo-fuels can be justfed on the grounds that they contrbute to a reducton n the greenhouse effect? Even f the recent rse n crude ol prces allevates the budgetary burden that bo-fuels represent, the queston rased by economsts concernng the effcent allocaton of ths amount among bo-fuel chans through tax exemptons to the bo-fuel processors s of prmary mportance [28] 4. In the present study, a mcro-economc model of supply chans that ncludes an agrcultural sector model has been developed for ths purpose. The ncreased mportance of the bo-fuel development program n France has stmulated our nterest n mprovng prevously used modellng tools to evaluate publc polcy [27] and n focusng on the decentralsed scale n contrast to the content of other recent works on bo-fuel analyss [5]. Thus, the model s specfed as a starcase lnear program (LP), correspondng to a representatve sample of farms, that can capture the dversty of the sector and predct qute accurately polcy mpacts regonal level, provded that they adequately artculate the goals and the constrants of ndvdual farms. Usually, such aggregate models suppose that every farmer ntends to maxmze expected gross margn. Ths hypothess however seems hardly justfable, especally, when we consder the actual gross margn varablty due to the agrcultural polcy changes. The uncertanty about crop prces and yelds may have the farmers to experence regret reflectng on how much better hs poston would have been, had he chosen dfferently. Then farm models whom observed behavor s explaned better when uncertanty s taken nto account, n other words for those farmers that mnmax regret objectve functon reproduces results closer to the base year 2002 crop mx, are hereafter usng the ILP specfcaton. When gross margn maxmsaton rule reproduces satsfactorly realty t s retaned as a decson rule and those ndvdual farm models reman LP specfed. Thus, a hybrd starcase arable croppng model s formed wth an mproved predctve ablty that the ntal LP. The man drawback s the exponental ncrease of computng tme lapse when nterval coeffcents n the objectve functon ncrease. Ths ssue s dscussed n secton 4 where relevant techncal nformaton s gven. The agrcultural sector module s supplemented by an ndustry model of French bofuel chans (ETBE from wheat and sugar-beet, rape-seed bo-desel), and by the demand scheme for products and by-products model n a way that a partal equlbrum model has been formulated. The ntegrated model s used to analyse several 4 Tax exempton levels are currently under revson by an expert commsson (Levy-Couvenhes) upon request of the French government. F:\Documents and Settngs\Admnstrator\Επιφάνεια εργασίας\bof_semnar.doc 3

4 scenaros and polcy mplcatons. A mcro-economc analyss of bofuel actvty s carred out n order to estmate agents surpluses. The deadweght loss of the actvty s calculated aganst the benefts of reductons n the emssons of greenhouse. Indrect or nduced benefts are not consdered. Fnally a methodology that ntegrates socal, economc and envronmental facets of ratonalty s appled to evaluate publc polcy and estmate effcency of subsdes on envronmental grounds. For ths purpose the mult-crtera analyss (MC), namely the reference pont method, s used to assst polcy makers to explore the feasble set n search of effcent solutons approachng the best ther (conflctng) objectves. Ths approach mples that envronmental effects need not be expressed n monetary costs or benefts. Instead, t s proposed to proceed usng physcal unts. An MC algorthm coupled wth the mcro-economc b-level model asssts n ths endeavour. The model s llustrated for the French bo-fuel ndustry of wheat-to-ethanol and rape-seed-to-ester chans. Ths paper s organsed as follows: frst, the basc LP model s brefly ntroduced and man results are presented and possbltes to reduce bo-fuel costs n the short and medum term s dscussed. Subsequently, the lmts of LP optmsaton and the effectveness of ths methodology n estmatng actvty levels and related costs as well as the welfare mpact of publc polcy s questoned. Uncertanty over profts requres recourse n bounded ratonalty and regret theory alternatve s examned n secton 3. Formal aspects of the "Interval Lnear Programmng (ILP)" approach are summarzed and the use of the mn-max regret crteron wthn the ILP framework s then presented. The mplementaton procedure and results thereof are the focus ponts of secton 4. In the last secton, the decson support methodology s proposed that ntegrates multple crtera, and the decson makng process s smulated through llustratve examples, followed by some conclusons. 2. A partal equlbrum model for the economc analyss of bo-fuel chans A partal equlbrum economc model based on mathematcal programmng prncples(oscar 5 ) was bult n order to assst n the mcro and macro-economc analyses of the mult-chan system of the bo-fuel ndustry. Ths approach, whch models the exstng bo-fuel chans n France sugar-beet and wheat to ETBE, rapeseed to RME- mples the followng: that a comprehensve and systemc method s requred (due to the bo-fuel chans nterdependency), not only at the resource producton level but also at the output level, that detaled modellng of the agrcultural supply s requred to take nto account the dversty of the arable farmng system, agronomc constrants and producton technques, that t s possble to proceed to the economc optmzaton of the whole system and to use mult-crtera methods to assst n polcy makng. 5 OSCAR : «Optmsaton du Surplus économque des Carburants Agrcoles Renouvelables» F:\Documents and Settngs\Admnstrator\Επιφάνεια εργασίας\bof_semnar.doc 4

5 Each chan conssts of fve producton stages : bomass producton, collecton, frst and second transformaton, demand for bo-fuels and by-products. The structure of ths model allows for consderaton of addtonal chans, such as straw to ETBE. The model determnes : the optmal bomass supply and farmers surplus, gven the polcy context and agronomc envronment the opportunty cost of bo-fuels, dependng on crop supply, ndustral costs and the demand for bo-fuel and by-products, the optmal tax exempton allocaton to bo-fuel chans and agents surpluses n dfferent market contexts (monopoly, cartel etc.), Bofuel contrbuton to the reducton n the greenhouse gase emssons, along wth the economc cost ncurred by socety for the dfferent scenar of budgetary expenses and tax exempton levels. The levels of actvty for each chan, the fundng requred, as well as the aggregate welfare beneft can be determned by maxmsng bofuel contrbuton to cope wth the greenhouse effect. 2.1 Model specfcaton The mcro-economc model represents the agro-energy chan structure by smulatng farmers behavour wth that of ndustry. It ntegrates the agrcultural sector 6 and a bo-fuel ndustry model (n ths case, the French mult-chan bo-fuel system) based on mathematcal programmng prncples 7 n order to smultaneously optmse economc surplus. The model proposes a decentralsed decson soluton based on the agents behavour n the respectve markets. When ndustral capacty s a contnuous varable, OSCAR s an LP, otherwse t becomes an MILP b-level model [37] 8 ; ts generc mathematcal form s specfed below: Indces and varables e farm ndces w relatve weght of each farm n the model al vector of food crop surface n ha ja vector of set asde land surface n ha nal vector of food crop surfaces n ha tr vector of varable quanttes of energy crops transformed to bo-fuels n t vt vector of bo-fuel quanttes n t vc vector of co-product quanttes n t Coeffcent matrces (Techncal parameters used are presented n Table 7, Appendx) A sub-matrx of techncal agrcultural producton coeffcents R sub-matrx of non-food crop yels n t T sub-matrx of converson coeffcents [I] untary matrx sub vector of untary subsdes to bo-fuels Agrcultural sector A1 e (al e, ja e, nal e ) w e t e agronomc constrants (1) A2 e (al e, ja e, nal e ) w e f e flexblty constrants (2) 6 Optmzaton model wth a matrx of techncal coeffcents of 7500x6800. The agrcultural sector component aggregates about 680 elementary arable farm models located n sugarbeet and cereal producton regons. 7 Models are wrtten n GAMS code [3]. 8 An equvalent model of the bo-fuel energy system assgnng transformaton unts of fxed capactes usng dscrete varables s presented by Mavrotas&Rozaks [19]. F:\Documents and Settngs\Admnstrator\Επιφάνεια εργασίας\bof_semnar.doc 5

6 A3 e (al e ) w e q e market outlets - quotas (3) A4 e (ja e, nal e ) w e s e set-asde land constrants (4) Bomass avalablty, converson process and bo-fuel demand constrants Renal e + [] I tr 0 bomass raw materal supply (5) e - T1 tr + [I]vt 0 bo-fuel supply (6) - T2 tr + [I]vc 0 co-product supply (7) sub. vt maxsub maxmal subsdy to bofuels (8) Objectve functon: to maxmse global surplus S = ( ma al + mja ja cnal nal ) ctr tr + ( pvt + sub) vt + pvc vc (9) ma mja cnal ctr pvt sub pvc e e e e e e vector of gross margns of food crops FF/ha vector of gross margns of set asde land FF/ha vector of varable costs of non-food crops vector of total costs of bomass collecton and converson to bo-fuels bo-fuel prce vector subsdes to bo-fuels vector co-product prce vector e Surplus allocaton to farmers and other stakeholders (ndustry) Dual prces that correspond to bomass avalablty constrants (relatonshp 5) are equal to the opportunty cost of the agrcultural resource. If eff denotes the margnal value of the total subsdy, t s equal to the dual value of constrant (8). The farmers' surplus or farm ncome ncrease due to energy crop producton s: S - eff * maxsub. The ndustry surplus s then equal to eff * maxsub. If the budgetary constrant s not bound, the global surplus s equal to farmers' surplus. The graph n Fgure 1 llustrates the above reasonng n smple form n the case of a sngle bofuel chan model. When no budgetary constrant exsts, the producton equlbrum s defned by the ntersecton of the demand and supply curve ; n ths case, pont B. At ths pont, the produced quantty equals OO. The producer s surplus, whch n ths case concdes wth the agrcultural surplus, total budget expenses and the deadweght loss of the actvty, can be determned graphcally as shown below : Box 1. Case A :Tax exempton to bofuels (no budgetary constrants) BB B : bofuel supply curve=bomasse opportunty cost+converson cost-coproduct value OA: bofuel market prce (perfectly elastc demand curve) OC: bofuel value=bofuel market prce + tax exempton (AC) OO : quantty produced at the equlbrum level (bofuel value equal to ts margnal cost) CBB : producer (agrcultural sector) surplus CB A A: budget cost to the government of the bofuel support program ABB A = CB A A - CBB :deadweght loss F:\Documents and Settngs\Admnstrator\Επιφάνεια εργασίας\bof_semnar.doc 6

7 FF/t C C' B'' D B' B A A' A'' O O' O'' bofuel quantty Fgure 1. Economc surpluses generated by the bo-fuel producton and tax exempton processes Box 2. Case B: Tax exempton of bofuels under budgetary constrant CC A A: total budget earmarked to bofuel OO : bofuel quantty produced (agreements approved by the government that depend on earmarked budget) CA: tax exempton for bofuel (depends on budget) DBB : producer (agrcultural sector) surplus DCC B : ndustral surplus ABB A = CC A A - DBB - DCC B : deadweght loss Takng nto account exogenously fxed tax exemptons and bofuel demand levels, techncal parameters, the ndustry s technology level and cost structure 9, as well as the materal nput cost (based on energy crop supply curves 10 ), the agents surplus can be estmated as shown graphcally n Fg. 2. The agent s surplus s maxmsed by determnng actvtes for both chans, gven a maxmum fxed amount of government expendture. 2.2 Bo-fuel costs for the horzon 2002 In practce, however, snce 1993 when the bofuel actvty kcked-off, the government has been engaged n preservng an equlbrum among dfferent chans (for hstorcal and lobbyng reasons). Thus, polcy-makers would prefer to ntroduce fxed quanttes nto the model to produce for all three chans and to examne how much the bll would cost and the surplus level generated for agents nvolved. The 2002 horzon selected snce further modfcatons n the CAP are expected to have been made by then. Frstly, the expected 2002 bofuel producton levels are ntroduced nto the model as targets to be attaned by the 9 Transformaton costs economes due to techncal developments have been taken nto account. Industral cost estmaton s based on the opportunty cost of captal hgher than the market dscount rate. Industral unts are assumed to be homogeneous havng the same costs. Capactes are consdered contnuous varables, thus economes of scale are not taken nto account n ths exercse. 10 As prce dscrmnaton s not possble, the opportunty cost of the least effcent producer determnes the prce of the resource ; n other words, the cost of the resource for ndustry. Effcent producers enjoy a surplus. The aggregate surplus s called agrcultural surplus. F:\Documents and Settngs\Admnstrator\Επιφάνεια εργασίας\bof_semnar.doc 7

8 system n order to calculate the bomass and bo-fuel costs 11. Agrcultural producton s localsed to cereal and sugarbeet producng farms n such a way as to mnmse total bomass resource costs. The model selects the most effcent farms.e., the farms that generally attan the hghest yelds. Opportunty cost of agrcultural resource, yelds and cultvated area. In order to mnmze bo-fuel cost, OSCAR localzes producton to the most effcent farms. A mnmal farm ncome ncrease of 76 ha -1 s assumed to consttute an ncentve for farmers to cultvate energy crops 12. Opportunty costs calculated by the model appear n Table 2. Table 2. Opportunty costs of resources and average yelds Yeld (t) t -1 Q (kt) Surface (ha) Rapeseed Wheat Sugarbeet Opportunty costs 13 of rapeseed and wheat are much lower than food crop prces ( t -1 et t -1, respectvely). Ths can be attrbuted to the fact that rapeseed and wheat for energy are cultvated n land set asde wth very low land rent. Actve set asde land rate reaches 5% 14. Sugarbeet costs should be compared wth the costs of sugarbeet category C that competes n the world market (around t -1 n 1999). The total surface area to be cultvated n order to satsfy the exogenous demand for bo-fuels s set at 287,300 ha (Table 2). Ths s clearly lower than the actual surface area cultvated by energy crops, whch s due to the hgh levels of average yelds resultng from the optmal localsaton of producton. In fact, the surface area harvested n 2000 reached 320,000 ha, despte the fact that actual approved amount was only 536,500 t 15. The model selects 58,800 arable farms,.e. 72% of the 81,000 farms wth the potental to partcpate n the bo-fuel program. Each farm cultvates 4 ha of energy crops on average. If the producers prce are equal to the opportunty cost (Table 2), there s an approxmate 900 ncrease n ncome per farm. The costs of bofuels are qute dfferent, ester costs beng hgher than those of ETBE (Table 3). The drect costs of ETBE are tmes hgher than unleaded gasolne costs, whereas RME costs are 2.9 tmes more expensve than those for desel fuel. These ratos decreased sgnfcantly n 2000, when current rates are taken nto account, to 1.1 and 1.6, respectvely 16. Costs nclude farmers surplus and the economc ncentve of 76 ha -1. Ethanol from wheat s produced n a plant wth a 300 m 3 per day capacty. It s a fact that operatng unts n France actually run at one thrd of ths capacty. The ndustral cost of ethanol from sugar-beet takes nto account synerges among sugar, alcohol and 11 Bo-fuel costs, partcularly the bomass agrcultural ressource cost, ncrease wth the ncrease n the quanttes produced. 12 Wth no ncentve, last suppler s (or the less cost-effcent) revenue ncrease wll be too low to compensate for addtonal labor devoted to the cultvaton of non-food crops nstead of land set asde. 13 Opportunty costs are equal to the dual values of the bomass avalablty constrants of the model. 14 The formal set asde rate s fxed at 10% of the land hstorcally cultvated land wth cereals and ol&proten seeds. A 5% rate has been used to take nto account fluctuatons n the rates revsed by Brussels each year, dependng on cereal stocks and the nternatonal market, as well as on the fxed set asde concernng low fertlty margnal land that can be re-cultvated but at too hgh a cost. 15 Source :ONIOL (Professonal Assocaton of Olseed producers) 16 Note that adjustments have also to be made to measure the effect of hgh ol prces on the bo-fuel producton cost. F:\Documents and Settngs\Admnstrator\Επιφάνεια εργασίας\bof_semnar.doc 8

9 ethanol ndustry. On the other hand, ester s produced n an ntegrated unt smlar to the one actually operatng n Rouen ( t RME/year). Table 3. Cost of bo-fuels (Source : model OSCAR results for set asde rate of 5%) 17. resource Insdustry Co-product Bofuel Bo-fuel value 2000** cost* cost 18 sales 19 costs average* ETBE wheat l ETBE sugarbeet l RME l *average FOB Rotterdam brent 18,6 per barl,$1= 0.87 ; source DIMAH **2000 brent $28,11 per barl The cost of the agrcultural resource s mportant for RME, whch makes the chan senstve to nput cost varatons. Ths cost s partly compensated for by co-product sales. Wheat-to-ETBE chan co-produces DDGS (Dstlled Dry Gran Solubles), whch are rch n protens. The co-products of ETBE from sugarbeet (pulp, nferor wne) have a low market value, but ther ndustral costs are lower than those for ETBE from wheat coproducts. The mnmal subsdy requred for bofuel ndustres to break even s presented n Table 4. Takng nto account the aforementoned hypotheses (only effcent farmers produce), a mnmum farm ncome of 76 ha -1 as an ncentve to the less effcent farmers, Table 5 ndustral costs, average ol prces and the dollar s average value for the perod ), dfferences between the actual and theoretcal mnmum subsdes vary between l -1 (see Table 4). Table 4. Mnmal subsdzaton of bo-fuels (ol and dollar prce averages for ) Bofuel value Bofuel cost Mnmum subsdy Tax exempton t -1 l -1 t -1 l -1 t -1 * l -1 * l -1 ** l -1 ** ETBE wheat ETBE sugarbeet RME *regardng ETBE, chan results fgure per t or l of ETBE. ** regardng ETBE, chan results fgure per l of ethanol Induced economc beneft of the agrcultural producton of bomass for bo-fuels Farmers surplus 20 measures the total rent enjoyed by farmers producng at a cost lower than the opportunty cost of the least effcent farmer, as shown n Table 4. The economc ncentve, presented n Table 5, corresponds to the amount of 76 ha -1 gven to all farmers. Due to bofuel per hectare yelds, ths amount s more mportant for RME than for ETBE Mass volume ratos 0,75kg dm -3 for ETBE ; 0,88kg dm -3 for RME 18 The wheat-to-ethanol study takes nto consderaton economes of scale for plant capacty of 300 m 3 per day nstead of 100 m 3 per day. Sugarbeet-to-ethanol costs (msson Levy-Couvenhes Ma 2000, personal communcaton) are dffcult to estmate due to overlappngs among the ethanol, alcohol and sugar producton processng ndustres. ETBE costs, Rapeseed Methyl Ester (RME), msson Levy- Couvenhes Ma 2000, personal communcaton. 19 Cattle cake prces ncreased from 91.5 to 130 t -1, draff prces from 102 to 122 t -1, whereas glycerne costs fell from 457 to 381 t As prevously explaned, ths surplus s generated durng the transacton of the agrcultural resource between farmers and the bo-fuel ndustry, due to the fact that ndustry s not able to dfferentate among the prces of energy corps for such a large number of farmers. In order to have a zero surplus, ndustry should offer each farmer ts specfc prce. Ths s practcally mpossble due to the large number of farmers nvolved n the process. F:\Documents and Settngs\Admnstrator\Επιφάνεια εργασίας\bof_semnar.doc 9

10 Economes over set asde subsdes exclusvely concern sugarbeet to ethanol, snce ts producton for energy reduces the amount of drect ads to the farm 22. Globally, nduced economc effects are very mportant n relatve terms, especally for the RME chan. The ETBE chan reaps beneft from the set asde subsdes. The wheat-to-etbe chan generates the least nduced economc effects at the agrcultural producton level. Table 5. Beneft nduced by the producton of bo-fuel crops n m -3 Farmers surplus Economc ncentve CAP savngs Total benefts ETBE wheat ETBE sugarbeet RME Dscusson on optmal tax exempton levels. When budget expenses for bofuels are constraned (case B n Box 2), a reduced quantty (OO nstead of OO ) wll be produced and ndustry wll also see a surplus. OSCAR can mnmse the aggregate economc cost for the three chan French bofuel systems - for a gven demand, agent s surplus s maxmsed - and determne the optmal producton levels, gven the fxed amounts of government expendture and the fxed tax exempton values per unt of bofuel volume. Maxmum fundng could be approxmately equal to the expenses earmarked for the bofuel program for the year 2004 (see ntroducton), that s, about 210 k. Parameters regardng untary tax exemptons are fxed at and /hl for bo-desel and ethanol, respectvely. The results are gven n Table 2. The soluton adopted by the model sets actvty levels for ETBE-wheat and RME, not allowng the ETBE-sugarbeet chan to produce. Dsaggregate agrcultural surplus s shown n Fgure 2, wth RME chan results gvng much hgher surpluses for agrculture (scenaro I n Table 7). Table 6. OSCAR model soluton (scenaro I) Optmal soluton (global surplus maxmsed) ETBE Ester Untary tax exempton /hl Optmal quantty n t of bo-fuel 000 t Value of bo-fuel + tax exempton /t Value of bo-fuel + co-products /t Bo-fuel cost /t Bomass nput cost /t On the bass of the average yelds shown n Table 4, RME producton per ha reaches 1.75 m 3, that of wheat-to-etbe 7.14 m 3, and that of sugarbeet-to-etbe m 3 (0.59 m 3 of ethanol per t ETBE). 22 Unlke wheat and rapeseed energy crops, sugarbeet for ethanol producton does not enjoy any CAP subsdy, whch saves the E.U. budget 425 per ha of sugarbeet cultvated surface. F:\Documents and Settngs\Admnstrator\Επιφάνεια εργασίας\bof_semnar.doc 10

11 RME value (tax exempton of 1.8 F/l RME) D ETBE value (tax exempton of 2.5F/l ethanol ) 4000 F/t ETBE 3000 A B ETBE opportunty cost 4000 F/t ester 3000 C RME opportunty cost RME prce ETBE prce rapeseed opportunty cost Opportunty cost wheat ' t ETBE ' t ester Fgure 2. Optmal OSCAR allocaton of economc welfare to agents (by bofuel chan). If agents behaved accordng to the model s hypotheses, assumng the techncal and economc assumptons presented n the prevous paragraphs, mnmal tax exemptons could be determned and producton levels for all bofuel chans proposed, thus optmsng for global surplus under budgetary constrant. In other words, the model becomes non-lnear as tax exemptons tmes bofuel volumes (tax credt aggregates) are ncluded n the objectve functon. If we re-terate the soluton process usng dfferent tax exemptons, the model proposes dfferent solutons ; for nstance, that scenaro II (30.5 and 38.1 /hl for bo-desel and ethanol, respectvely) results n ncreased economc welfare(last column n Table 7). Table 7. Economc effcency and agents surplus unts Scenaro I Scenaro II Bo-desel tax exempton per unt /l Ethanol tax exempton per unt /l Welfare deadweght loss M Producers rape-seed surplus (C) M Bo-desel ndustry surplus (D) M Wheat producers surplus (A) M ETBE ndustry surplus (B) M F:\Documents and Settngs\Admnstrator\Επιφάνεια εργασίας\bof_semnar.doc 11

12 3. Uncertanty at the farm level, LP lmts and Interval Lnear Programmng Marthematcal programmng representatons of arable agrculture supply featurng the ntegraton of farm-level decsons wth regonal aggregates, convey to the polcy makers communty the dynamcs of the agrcultural sector [29]. A farm-based model s explctly a normatve or prescrptve tool at an elementary level; the farmer specfes hs decson rule and the model smulates the consequences of that decson rule gven the constrant structure, n other words, the feasble actvty plans. On the other hand n a decentralsed economy there s no sngle decson maker at the sector level. There are multple levels of decson, namely, farmers, ndustry and the polcy makers, whose nterest do not generally concde. A model that can explan producers reactons (farmers and ndustry) to exogenous sgnals (prces, government polcy) can be normatve regardng the polcy part, but generally speakng t s a descrptve or postve model. Ths model can nform polcy makers on producers decsons under dfferent polcy scenar. There are two dstnct stages n the explotaton of such a model. The frst stage s a valdaton phase where the parameters of the model are adjusted to the set of producers under consderaton untl the model becomes able to reproduce "the observed surface allocatons" (referred to also as observed soluton or observed behavor n the text) for current prces and yelds. The second stage s a smulaton phase where the future stuaton s explored for dfferent scenaros of polcy measures and future prces. The model mplemented here contans n total 680 farms from two representatve arable croppng regons of France (cereal and sugar-beet specalzed regon, FADN OTEX 13). The results of the frst stage showed that n most of the cases the model could not satsfactorly reproduce the observed behavor of the farmers. Ths s possbly due to the combned effects of the uncertanty about crop prces and yelds, two major components of the unt profts whch are supposed to gude the choces of farmers. The am of the present work s to nvestgate f the representatve power of LP concernng farmers' behavor can be mproved by takng nto account prce and yeld varatons. To model ths uncertanty, ntervals on gross margns per surface unt were ntroduced nto the objectve functon of the model 23. The Data and LP model valdaton Arable crop farms consdered belong to cereal orented farms producng also rape-seed. Farm Accountng Data Network (FADN) data (orentatons OTEX 13) on number of farms per type, surfaces cultvated, and land 23 Ths s a problem of decson makng under rsk. There s a rch lterature on ths subject that consttutes a subject matter of decson makng on ts own. A revew of these methods can be found n [9] and n [8]. One could menton the E-V model non-lnear or quadratc as well as ts lnearsed versons such as MOTAD and target-motad but also models based on game theory reasonng such as maxmn, mnmax, safety-frst etc. models. For all these models, avalablty of covarance matrces that requre gross margns of ndvdual crops related to dfferent states of nature or years- are fundamental for effcent dversfcaton among farm actvtes as a means of hedgng aganst rsk [15]. Consequently t s extremely dffcult to apply these methods to regonal models contanng hundreds of farms precsely because of the requrement of detaled data at the farm level ndcatng those covarance relatonshps. Non-nteractve methodologes that attempted to assess mult-crtera utlty functons [1] are ncludng at least one rsk crteron thus always requrng detaled nformaton at the farm level. As expermental applcatons of ths method state [7] the rsk crteron ranks second after the gross margn maxmsaton one n the mult-objectve functon havng weghts around 30%. Ths s probably the reason that all of the above method modellng mplementaton contan at best a few dozen of farms. As our ntenton s rather to represent dversty usng bg samples we opted for the nterval LP whom only requrement s a good dea of the range of varaton of gross margns. These ranges may be assessed at the regonal level by crop usng FADN or Agrcultural Chambers census of bg samples and they apply to all farms. F:\Documents and Settngs\Admnstrator\Επιφάνεια εργασίας\bof_semnar.doc 12

13 set asde concernng the above farm types have been used n ths exercse along wth detaled data on nputs of arable crops used by each farm [29]. The year 1996 has been chosen as the bass because the percentage of land set asde then fxed by the C.A.P. at 10% of the surface of cereals and ol and proten seeds, equals the one fxed by the Berln agreement for the perod The horzon 2002 s taken as reference for the reason that CAP reform of 1999, wll then be totally appled, after two years of transton Arable farms have been selected out of a sample of 216 located n the cereal producton orented regon of the North-East Ile-de- France). Profles of the group are shown n Table 8. These farms represent adequately the dversty of arable croppng farms n the Central and Northern France. Table8. Crop mx by regon (results of the agrcultural sector model) n ha cereal farm regon Average hectareage profle Arable land % Wheat Wheat mono-culture Barley Wnter barley Corn Rape-seed Sunflower Wheat ethanol - - Rapeseed-ester. - - Set asde land In total, 216 elementary models were consdered. Each ndvdual farm model had up to 8 varables. The three varables representng set asde, set asde for rape-seed and set asde for wheat were common to all the models. These crops are cultvated through contracts sgned wth the ethanol and ester ndustry, ther part n the total arable land s a result of tax exemptons on bofuels gratfed by the government. Regardng flexblty constrants rght hand sde lmts can be reconsdered f necessary and after some teratons they can be adjusted always respectng statstcal trends so that the model result approach the most possble realty (Table 9). Table 9. Statstcs for agronomc lmts used as RHS n the flexblty constrants. Agronomc lmt for cereals n % of arable land 100% Agronomc lmt for olseed crops n % of arable land 50% Agronomc lmt for rape-seed n % of arable land 30% Agronomc lmt for sunflower n % of arable land 20% Agronomc lmt for corn n % of hstorcal surface 110% Agronomc lmt for peas n % of hstorcal surface 110% Agronomc lmt for barley n % of hstorcal surface 110% F:\Documents and Settngs\Admnstrator\Επιφάνεια εργασίας\bof_semnar.doc 13

14 Fgure 3 presents the aggregated observed soluton for the consdered regon and the LP results (.e., the sum of optmal allocatons by farm for each crop) at the end of the calbraton procedure. The surfaces are expressed n hectares. As one can see, there exsts some gaps between the observed and the optmzed allocatons for varous crops: rape-seed for food and energy as well as sunflower are underestmated. The dfference n absolute value between the observed producton levels and the optmzed allocatons (n other words, the dstance between the two solutons usng a L 1 metrc) s approxmately 2.8 mllon ha. The total arable land consdered beng 7.8 mllon ha, the relatve dstance (the dfference between the two solutons n absolute value dvded by the total arable land) s 39%. However, at the mcroscopc or farm level (.e. regardng the results of ndvdual elementary models), the dstances become more mportant: the relatve average dstance can be more than 66%. At the mcroscopc level, these results could be expected gven the penny-swtchng nature of the LP, whereas at the sectoral level compensatory effects counteract n the aggregates makng the model results to approach the observed crop mx. crop mx n cereal farms set asde est_rapeseed eth_w heat eth_sugarbeet beans sugarbeet potatoes peas sunflow er rapeseed fresh peas maze rye barley w heat '000 ha Fgure 3. Comparson of the observed crop mx and the LP solutons at the regonal level. Hence, the need for mprovement n the representatvty of the model s clear. In all evdence, such dstances can occur for two reasons: an naccurate specfcaton of the feasble regons of the models (whch would be closely related to the calbraton procedure) or an naccurate specfcaton of the objectve functons. Consderng the recent changes n the economc envronment and the natural uncertanty of yelds, we opted for nvestgatng the problems that may arse because of a possbly naccurate specfcaton of the objectve F:\Documents and Settngs\Admnstrator\Επιφάνεια εργασίας\bof_semnar.doc 14

15 functons 24. More precsely, we modfed the orgnal LP model to take nto account uncertanty about prces and yelds by usng nterval valued coeffcents for the objectve functon. In the followng paragraph, a bref revew of the lterature devoted to the subject and a formal defnton of the Interval Lnear Programmng (ILP) problem wll be gven. Fnally, two knds of approaches concernng possble soluton procedures wll be outlned.the presentaton of the formal nterval lnear programmng problem s gven n the next secton. 3.1 ILP Models and related work In mathematcal programmng models, the coeffcent values are often consdered known and fxed n a determnstc way. However, n practcal stuatons, these values are frequently unknown or dffcult to determne precsely. Interval Programmng (IP) has been proposed as a means of avodng the resultng modelng dffcultes, by proceedng only wth smple nformaton on the varaton range of the coeffcents. Snce decsons based on models that gnore varablty n objectve functon coeffcents can have devastatng consequences, models that can delver plans that wll perform well regardless of future outcomes are appealng. More precsely, an ILP model conssts of usng parameters whose values can vary wthn some nterval, nstead of parameters wth fxed values, as s the case n conventonal mathematcal programmng. Many technques have been proposed to solve the resultng problem. Shaocheng [10] studed the case where all the model parameters are represented by ntervals and the decson varables are non negatve. Recently, Chnneck and Ramadan [4] generalzed ther approach to the case where varables are wthout sgn restrcton. The case whch s of greater nterest for our purpose s the one where only the objectve functon coeffcents are represented by ntervals. Ths partcular problem s the most frequently consdered n ILP lterature (see, e.g., [2], [10], [11], [16], [17], [18], [22], [32]). We now ntroduce some defntons and notatons and brefly present the formal problem. Interval Lnear Programmng (ILP) Problem Let us consder a Lnear Programmng (LP) model wth n (real and postve) varables and m constrants. The objectve functon s to be maxmzed. Formally: max {cx : c Γ, x S} (ILP) where Γ = S = n { c R : c [ l, u ], = 1.. n} n m n m { x R : Ax b, x 0, A R, b R } The uppercase letters wth bold characters denote matrces (e.g., A). The lowercase letters wth bold characters n denote vectors (e.g., c R n, x R ). The null vector s denoted by 0. [l, u ] represents a closed nterval of real numbers where l stands for the lower bound and u stands for the upper bound. The letters wth ndces ndcate 24 Therefore, an mplct hypothess s that the feasble regon of each elementary model represents adequately the allocaton possbltes of the farmers. Let us note that the observed solutons for each farm have been verfed to be feasble n the correspondng model. F:\Documents and Settngs\Admnstrator\Επιφάνεια εργασίας\bof_semnar.doc 15

16 A = m n the elements of a matrx (e.g., ( ) nterval (e.g., l [ l, u ] ). a j m, n R ) or a vector (e.g., c = c c n ) n ( c 1,...,,..., R ) or an Let Π = { x S x = arg max{ cy : y S, c Γ } : be the set of potentally optmal solutons. Let Υ be the set of all the extreme objectve functons: Y { c Γ : c [ l, u ], = 1 n} =.To gve nsght nto what the problem.. becomes when ntervals are ntroduced, we recall the followng theorem [10], [32] : Theorem 1 Let us consder the followng multobjectve lnear programmng problem: υ max{cx : x S; c Υ} (MOLP) where the υ-max notaton stands for the vector maxmzaton. Then, a soluton s a potentally optmal soluton to (ILP) problem f, and only f, t s weakly effcent to the (MOLP) problem. Hence, (ILP) s a partcular mult-objectve lnear programmng problem where the 2 n objectves are elements of Υ and the set of potentally optmal solutons Π s the set of weakly effcent solutons to (MOLP). Theoretcally, ths knowledge enables us to moblze all the tools and concepts of mult-objectve lnear programmng lterature, especally to choose/propose sutable soluton concepts for (ILP) problem. In the lterature, two dstnct atttudes can be observed. The frst atttude conssts of fndng all potentally optmal solutons that the model can return n order to examne the possble evolutons of the system that the model s representng. The methods proposed by Steuer [32] and Btran [2] follow ths knd of logc. The second atttude conssts of adoptng a specfc crteron (such as the Hurwcz's crteron, the maxmn gan of Falk, the mnmax regret of Savage, etc.) to select a soluton among the potentally optmal solutons. Rommelfanger et al. [22], Ishbuch and Tanaka [11], Inuguch and Sakawa [10] and Mausser and Laguna [16], [17], [18] proposed dfferent methods wth ths second perspectve. Followng ths perspectve, the next secton ntroduces the approach that we have selected, namely the mnmzaton of the maxmum regret approach, and the procedure we adopted for ts mplementaton. Mnmzng the Maxmum Regret Mnmzng the maxmum regret conssts of fndng a soluton whch wll gve the decson maker a satsfacton level as close as possble to the optmal stuaton (whch can only be known as a posteror), whatever stuaton occurs n the future. The farmers are faced wth a hghly unstable economc stuaton and know that ther decsons wll be based on uncertan gans. It seems reasonable to suppose that they wll decde on ther surface allocatons prudently n order to go through ths tme of economc nstablty wth mnmum loss, whle tryng to obtan a satsfyng proft level. Ths s precsely the logc underlyng the mnmax regret crteron;.e. selecton of a robust soluton that wll gve a hgh satsfacton level whatever happens n the future and that wll not cause regret. Therefore, we make the hypothess that the farmers of the consdered regon adopt the mn-max regret crteron to make ther surface allocaton decsons. The mathematcal translaton of ths hypothess for the MAORIE was to mplement the mnmax regret soluton procedure proposed n the lterature (see e.g., [10], [16], F:\Documents and Settngs\Admnstrator\Επιφάνεια εργασίας\bof_semnar.doc 16

17 [17], [18]). The presentaton of the formal problem and the algorthm of mnmax regret are presented n the next paragraphs. 3.2 The MnMax Regret (MMR) Problem Suppose that a soluton x S s selected for a gven c Γ. The regret s then: R ( c, x) max { cy} cx = y S The maxmum regret s: max Γ { R( c x) } c, The mnmax regret soluton xˆ s then such that R ( x) R ( x) solved s: x S { max { max { cy} cx } c Γ y S max ˆ for all x S. The correspondng problem to be mn (MMR) max The MnMax Regret Algorthm The man dffculty n solvng (MMR) les n to the nfnty of objectve functons to be consdered. Shmzu and Ayosh [25] proposed a relaxaton procedure to handle ths problem. Instead of consderng all possble objectve functons, they consder only a lmted number among them and solve a relaxed problem (hereafter called (MMR )) to obtan a canddate regret soluton. A second problem (called hereafter (CMR)) s then solved to test the global optmalty of the generated soluton. If the soluton s globally optmal, the algorthm termnates. Otherwse, (CMR) generates a constrant whch s then ntegrated nto the constrant system of (MMR ) to solve t agan for a new canddate soluton. Ths process contnues n ths manner untl a globally optmal soluton s obtaned. The relaxed (MMR ) problem s: x S { max { max { cy} cx } mn (MMR ) c Γ y S 1 2 p where C = { c, c,..., c } Γ. Ths problem s equvalent to: mn r (MMR ) s.t. r k k + c x c x k, k = 1,, p c r 0, x S, c k C where x s the optmal soluton of ( c k y) k c k k max. A constrant of type r + c x c x k s called a regret y S, c k C cut. Let us denote x the optmal soluton of (MMR ) and r the correspondng regret. Snce all possble objectve functons are not consdered n (MMR ) we cannot be sure that there s no c belongng to Γ \ C whch can cause a greater regret by ts realzaton n the future. Hence, we use the followng (CMR) problem to test the global optmalty of x : F:\Documents and Settngs\Admnstrator\Επιφάνεια εργασίας\bof_semnar.doc 17 c

18 c Γ { max { cy} cx} max (CMR) y S Observe that the objectve functon value of (CMR) represents the maxmum regret for x over Γ, denoted by ( x) p+ 1 R max. If the optmal soluton S, c Γ x p of (CMR) gves R ( x) > r + 1 c max, t means that p+1 c can cause a greater regret than r by ts realzaton n the future and that t has to be consdered also n C whle solvng p+ 1 p+ 1 (MMR ). So, the regret cut r c x c x + 1 s added to the prevous constrant set of the (MMR ) to solve t + p c agan and obtan a new canddate. The process s terated untl the generated canddate regret soluton s found to be optmal by (CMR). Ths soluton procedure dea s summarzed wth the followng algorthm: MnMax Regret Algorthm Step 0: r 0, k 0, choose an ntal canddate x Step 1: k k +1, Solve (CMR) to fnd k c and ( x) R max : If ( x) = r R max then END. x mnmze the maxmum regret. k k Step 2: Add the regret cut r + c x c x k to the constrant set of (MMR') c Step 3: Solve (MMR') to obtan a new canddate x and r. r r. Go to Step 1. The dffculty n ths resoluton process les n the quadratc nature of the (CMR) problem. Inuguch and Sakawa [10] nvestgated the propertes of the mnmax regret soluton to fnd a more sutable way to solve (CRM). Mausser and Laguna [16] used ther results to formulate a mxed nteger lnear program equvalent to (CMR) whch s less costly to solve. In our experments we used ths equvalent problem formulaton (Appendx A). 4. Implementaton of the MMR Approach In a relatvely stable envronment, t s reasonable to suppose that farmers wll base ther decsons on average prces. MAORIE s orgnally desgned under ths very assumpton: objectve functon coeffcents (the gross margns per crop) are calculated based on the prce and yeld averages. As a matter of fact, n the present context, the natural uncertanty about yelds s combned wth an ncreasng uncertanty about prces. Therefore, the farmers would tend to consder ranges of gross margn nstead of average prces and yelds to make ther decsons. For ths reason, the objectve functon coeffcents, whch correspond to unt gross margns per crop, wll be represented by ntervals n the modelng. The fgure 4 shows varablty of rapeseed sales (rght sde graph) observed n 650 farms of the Centre-Northern France due to yeld and prce varatons. Total uncertanty can be represented by the range determned by µ±2σ, where µ s the mean value and σ the standard devaton of the sales dstrbuton. Table 10 summarzes ntervals of gross margns for dfferent crops. F:\Documents and Settngs\Admnstrator\Επιφάνεια εργασίας\bof_semnar.doc 18

19 Table 10. Average and standard devaton of sales value for selected crops average sales stdev sales (av+2std)/av ±%margn* wnter wheat ±33 Rapeseed-sunflower ±63 wnter barley ±39 barley sprng ±32 maze gran ±52 peas na** sugarbeet na *varaton n sales value results n hgher percentage varaton n gross margn ** not applcable n the cereal regon yeld (n 100kg) varaton sales varaton n /ha prce (n /100kg) varaton Fgure 4. Cumulatve dstrbutons of yeld, prce to the farmer and total sales value of rapeseed Gross margn ntervals have been used n the model for 6 crops, namely wheat, rapeseed and sunflower, wnter and sprng barley, and gran corn, calculated accordng to the table 4 data. Energy crops present lower but stable prces compared to ther food counterparts. Moreover, they are cultvated under 8-year contracts so we dd not use nterval coeffcents for them and kept the orgnal parameters (gross margns). Hence, for our (ILP) models, the number s of nterval-valued coeffcents s fxed at 6. F:\Documents and Settngs\Admnstrator\Επιφάνεια εργασίας\bof_semnar.doc 19