Crop-Based Biofuel Production under Acreage Constraints and Uncertainty

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1 Crop-Based Bofuel Producon under Acreage Consrans and Uncerany Mndy L. Baker, Dermo J. Hayes, and Bruce A. Babcock Workng Paper 08-WP 460 February 2008 Cener for Agrculural and Rural Developmen Iowa Sae Unversy Ames, Iowa Mndy Baker s a graduae asssan n he Cener for Agrculural and Rural Developmen (CARD); Dermo Hayes s Poneer H-Bred Inernaonal Char n Agrbusness and a professor of economcs and of fnance; he heads he rade and agrculural polcy dvson n CARD; and Bruce Babcock s a professor of economcs and drecor of CARD; all a Iowa Sae Unversy. Ths paper s avalable onlne on he CARD Web se: Permsson s graned o excerp or quoe hs nformaon wh approprae arbuon o he auhors. Quesons or commens abou he conens of hs paper should be dreced o Mndy Baker, 75 Heady Hall, Iowa Sae Unversy, Ames, IA ; Ph: (515) ; Fax: (515) ; E-mal: bakermn@asae.edu. Iowa Sae Unversy does no dscrmnae on he bass of race, color, age, relgon, naonal orgn, sexual orenaon, gender deny, sex, maral saus, dsably, or saus as a U.S. veeran. Inqures can be dreced o he Drecor of Equal Opporuny and Dversy, 3680 Beardshear Hall, (515)

2 Absrac A myrad of polcy ssues and quesons revolve around undersandng he boeconomy. To gan nsgh, we develop a sochasc and dynamc general equlbrum model and capure he unceran naure of key varables such as crude ol prces and commody yelds. We also ncorporae acreage lmaons on key feedsocks such as corn, soybeans, and swchgrass. We make sandard assumpons ha nvesors are raonal and engage n bofuel producon only f reurns exceed wha hey can expec o earn from alernave nvesmens. The Energy Independence and Secury Ac of 2007 mandaes he use of 36 bllon gallons of bofuels by 2022, wh sgnfcan requremens for cellulosc bofuel and bodesel producon. We calculae he level of ax creds requred o smulae hs level of producon. Subsdes of nearly $2.50 per gallon o bodesel and $1.86 per gallon o cellulosc bofuel were requred, and long-run equlbrum commody prces were hgh, wh corn a $4.76 per bushel and soybeans a $13.01 per bushel. Hgh commody prces are due o nense compeon for planed acres among he commodes. Keywords: bodesel, bofuels, cellulosc, dynamc, ehanol, general equlbrum Mone Carlo, marke.

3 CROP-BASED BIOFUEL PRODUCTION UNDER ACREAGE CONSTRAINTS AND UNCERTAINTY The Energy Independence and Secury Ac of 2007 (EISA) was sgned no law n December Ths ac mandaes he use of 36 bllon gallons of bofuels by 2022, of whch 15 bllon gallons mus come from corn-based ehanol and 21 bllon from advanced bofuels, ncludng 1 bllon gallons of bomass-based desel and 16 bllon gallons of cellulosc bofuels. Ths new mandae means a sgnfcan ncrease n curren bofuel producon levels. Corn-based ehanol producon was 1.63 bllon gallons n 2000, and by he end of 2007 producon reached 7.23 bllon gallons (see hp:// Ths ncrease n corn ehanol producon has led o record hgh nomnal corn prces n Compeon for acreage has ransferred some of he demand pressure experenced n corn markes o soybean and hay markes; he prces of hese commodes have ncreased subsanally as well. EISA does no specfy how he mandaes are o be me bu saes ha he Admnsraor shall promulgae rules esablshng he applcable volumes no laer han foureen monhs before he frs year for whch he applcable volumes wll apply. These mandaes, and he mehods used o ensure ha hey are me, wll have a profound mpac on agrculural markes and agrculural land use paerns n he Uned Saes. In heory, he admnsraor could smply requre ha fuel companes blend hese quanes even f hey are sellng he end produc a a loss. Or, he admnsraor could mandae he producon of he bofuels even f produced a a loss, alhough he legal mechansm by whch producon would be forced s unknown. I seems far more lkely, however, ha he mandaes wll be me usng axes and/or subsdes. The purpose of hs 1

4 sudy s o examne he ncenves needed o ensure hese mandaes are me, and o projec he mpac of hese ncenves on U.S. agrculure. The model we presen s based on he assumpon ha decsons nfluencng bofuel producon can be predced f one undersands he opmal decsons of raonal agens n he economy. Farmers wll make raonal planng decsons based on expeced marke prces and roaonal consrans. Furher, hey wll recognze ha land used o produce he raw maeral for bofuels has an opporuny cos. Invesors who buld bofuel plans wll do so only f hey can expec a rsk-adjused reurn a a par wh or superor o nvesmens made elsewhere n he economy. In hs sudy we ake each of he key decsons jus descrbed and use parameers and daa from he leraure o model he decson and he marke forces gudng he decson. The resulng sub-models are hen combned whn a raonal, dynamc, sochasc general equlbrum model of U.S. crop and bofuel markes ha s calbraed o reflec acual marke condons as of December We wsh o evaluae he lkely response of marke parcpans o changes n ncenves such as exogenous shocks o crude ol prces and bofuel creds and subsdes. Prevous Leraure Rozaks and Soure (2005) develop a paral equlbrum lnear programmng model of he French bofuels secor. Ther goal s o make polcy suggesons regardng he effcen allocaon of land o boenergy crops and effcen ax exempons. Zhang, Vedenov, and Wezsen (2007) develop a srucural vecor auoregressve model o examne f producers of mehyl erary buyl eher (MTBE) engaged n lm prcng o prohb growh of ehanol as a gasolne addve. They fnd suppor for hs hypohess, 2

5 concludng ha he U.S. ehanol ndusry s vulnerable o he mpor of less expensve sugarcane-based ehanol. Elobed e al. (2007) provde he frs comprehensve model of he boeconomy, and laer Tokgoz e al. (2007) fll some gaps assocaed wh he frs arcle, ncludng work on he equlbrum prces of co-producs of he bofuel ndusres, mos mporanly dsllers grans. The laer wo sudes use a world agrculural model from he Food and Agrculural Polcy Research Insue (FAPRI) o deermne he poenal sze of he corn-based ehanol secor and descrbe how wll affec crop and lvesock markes. The auhors assume ha nvesmen n each bofuel secor wll occur unl expeced prof s zero. They do so by calculang he break-even corn prces ha drve margns on new corn-based ehanol plans o zero and hen smply assume ha hs corn prce wll be he marke-clearng prce. They hen calculae he sze of he bofuel secor ha drves he marke o hs prce and evaluae he mpac of hs break-even corn prce on U.S. and world agrculure. The use of hs marke-clearng corn prce allows hem o decouple decsons made a he farm from hose n he res of he economy. They gnore bofuels from cellulose and bodesel because he model resuls sugges ha hese are no economcally vable. They also gnore rsks assocaed wh nvesmens n bofuel plans. Our model enhances he leraure by ncorporang awareness of rsk no he nvesor s decson problem. Reurns o bofuel producon are unceran because of varably n crop yelds and also n he crude ol prce, whch deermnes he prce of gasolne, ehanol, and oher ransporaon fuels. By ncorporang he sochasc naure of hese varables no he model, we can compare he endogenous rsk-adjused reurn o dfferen ypes of bofuel producon and deermne whch wll be aracve o nvesors. 3

6 Accounng for rsk-adjused reurns s more realsc, and a sochasc model delvers probably dsrbuons over fuure commody prces and reurns of he bofuel ndusry. In addon, we model he boeconomy n a general equlbrum framework, allowng us o consder an array of ssues such as he lnk beween he marke prces for bofuel feedsocks and rsk-adjused nvesmen decsons ha are no approprae n a paral equlbrum seng such as ha used n he Elobed e al. and Tokgoz e al. sudes. To he bes of our knowledge, hs s he frs aemp o model he neracon beween he U.S. energy and agrculural secors n a heorecally conssen way. The Economy The economy we model consss of farmers; agrculural commody demanders, who wll use he commody as an npu eher n producng food or energy; and nvesors, who can choose among four dfferen nvesmen alernaves. An nvesor can choose o nves n a corn ehanol plan, a bodesel plan, a cellulosc ehanol plan, or smply choose o nves n he marke porfolo. The collecve acons of hese nvesors wll affec fuure commody demand bu no curren demand, as he plans ake me o buld and come onlne. We recognze ha as echnology advances, cellulosc bomass may be convered no anoher form of bofuel, such as buanol. However, for he purpose of hs sudy, we consder cellulosc maeral beng convered no ehanol snce hs s he bes nformaon we have a hs me. Fundamenal uncerany n he economy comes hrough uncerany n agrculural commody yelds and crude ol prces. We assume hese wo random varables are ndependen wh jon probably dsrbuon ( ζ, ε ) ( ζ ) ( ε ) f = g h, where ζ s a vecor of yeld realzaons, and ε s he realzaon of crude ol prces. Assumng ndependence of commody yelds and crude 4

7 ol prces s equvalen o assumng ha domesc bofuel producon wll no nfluence world crude ol prces. These varables produce uncerany n agrculural commody prces, reurns o bofuel producon, and n oher energy prces such as ha of gasolne, desel, ehanol, and bodesel. The melne of decsons n he economy, as shown n fgure 1, unfolds as follows. A me zero, governmenal polcy on axes and subsdes are se, he bofuel capacy currenly exsng s known, and agens whn he economy have belefs abou he dsrbuons of crude ol prces and crop yelds no he fuure. A me perod one, nvesors plan bofuel expanson or conracon. Many years elapse beween me perods one and wo, wh farmers makng crop allocaon decsons each year. These allocaon decsons are drven by maxmzaon of expeced profs, roaonal consrans, and land scarcy. The decsons show some neresng cyclcal paerns, as farmers end o favor soybeans n years followng years n whch a large number of corn acres are grown. We need hese annual decsons because we calbrae he model o acual marke daa for lae However, he resuls are no oherwse useful because he economcally relevan neracons occur afer plans are bul, and hs can ake several years. Therefore, we do no presen resuls for hese nermedae years, and we allow me perod wo o represen he long-run equlbrum n our model. Commody Supply Producon of agrculural commodes ncurs crop-specfc coss and affecs sol ferly he followng year. The crops avalable are heerogeneous n her neremporal effecs on sol producvy; some enhance sol ferly whle some degrade. Producers wegh he benef of connuously planng hgh-value crops, such as corn, agans he cos of 5

8 decreased sol ferly n he nex planng season. In addon, expeced harves-me prce plays a crucal role n agrculural supply. Under he raonal expecaons hypohess, producers form expecaons abou he curren season s aggregae producon level, and harves-me prce for each crop. The acons of producers, herefore, cause he producon and harves-me prces o be nosy realzaons of her ex-ane expeced values (Muh 1961). Ecksen (1984) develops a dynamc model n whch producers make land allocaon decsons n each perod and he equlbrum s defned by raonal expecaons of he agens. Ecksen s model ncorporaes pas land allocaon decsons no he producon funcons, and uses dynamc programmng o deermne he pah of equlbrum land allocaons and prce vecors. Several emprcal models have borrowed from he basc srucure of Ecksen s work (Aradhyula and Hol 1989; Orazem and Mranowsk 1994; Tegene e al. 1988). Many oher arcles consder problems ha focus on allocang acreage heerogeneous n producvy (Wu and Adams 2001). We model commody supply n he spr of boh Ecksen and Muh, because scarcy of land s a facor we canno overlook as we are hnkng abou he poenal of he bofuel ndusres. In he model, here exss a sngle represenave compeve producer who has an endowmen of one un of land. Ths un of land s represenave of he producvy of U.S. cropland n erms of s yeld poenal and s roaonal consrans. The producer akes boh oupu prces and a cos funcon as gven. Oupu prces and yelds are unceran, bu all agens n he economy know he jon dsrbuon among prces and yelds. Faced wh hese, he producer allocaes hs land n he begnnng of he perod o hree dfferen crops, corn, soybeans, and swchgrass, n each perod. We could gve he 6

9 farmer he ably o plan mscanhus and qualavely he resuls would reman he same; only he magnude of he mpac of land-nensve cellulosc crop producon would change. We chose swchgrass, n par, because we have scenaros n whch cellulosc bofuel producon s no vable, and s easy o magne a marke for swchgrass n he absence of bofuel producon. I smply would be markeed as hay for cale consumpon. Mscanhus currenly has no such alernave use. We ndex he crops as follows: corn, = 1; soybeans, = 2; and swchgrass, = 3. In perod, he producer s prof s gven by = ( π j,, ζ ) ( πj) = 1 j= 1 w pq s c where p s crop s oupu prce n me. The quany produced of crop s Q ( ). The sae varable, 1 s, mposes a yeld penaly assocaed wh connuous croppng pracces. The nomnal cos funcon for crop s ( ; ) c π Θ, where Θ s a vecor of parameers defnng each crop s nomnal cos funcon. Thus, does no accoun for he opporuny cos of he land. The proporon of land allocaed o crop a me ha was n crop j las year s π j. Crop yelds are a funcon of he crop planed las year, he proporon of land endowmen n crop, and me, n addon o a random error erm. c Producon echnology s characerzed by > 0. The producer s rsk neural n prof, π and hus wshes o maxmze he presen value of curren and fuure expeced prof subjec o land consrans. To hs end, she chooses a sequence of land allocaon vecors, { π } = 1, o solve her problem: j 7

10 [ ] n max β E w.. 1 1, 2,... s πj = = { π } = 0 = 1 j= 1 n ( ) 1 π1 + π2 + π3 = π, 1 2 3, ( ) π + π + π = π ( ) πj 0, j, 0 π j gven and where π11 π21 π31 π = π12 π22 π32. π13 π23 π 33 The oal proporon of crop planed n me s π. We can bes hnk of he consrans as a mechansm accounng for he law of moon of he land allocaons. The necessary condons for opmaly follow. Euler Equaons: Q c Q c Q c Q c = π j : E p 1 p β E p1 1 1 p π 1 1 1j π1j πj π j π + 1j π + + 1j π π + j j 1 Q c + 1 Q c Q 1 c Q 1 c 1 E p β p 1 1 E p1 β p πj π + j π + j π + = j π1j π + 1j π + 1j π + 1j These necessary condons requre he producer o equae he margnal ne benef of growng soybeans (swchgrass) o he margnal benef of growng corn. The margnal benef s realzed hrough he crop s margnal conrbuon o uly hs perod and he nex me perod. The conrbuon o nex perod s uly s hrough he benefs of crop 8

11 roaon on nex perod s yeld. There are nne Euler equaons n nne unknowns. Gven our assumpons abou producon echnology and preferences, we are guaraneed a soluon o he farmer s acreage allocaon problem, and we can solve for a farmer s expeced uly maxmzng acreage allocaon decsons. Afer subsung hese acreage allocaon decsons no he producon funcons, we recover he perod commody supples for each crop gven he random yeld shock, ζ. Noce from he Euler equaons ha boh prce and he nomnal cos of producng oher crops are mporan n deermnng a crops supply funcon: 3 ( p Θ ζ ) = ζ π () Q ;,, s s. s, 1 1 * j j j= 1 Ths funcon s upward slopng n boh he proporon of land allocaed o a specfc crop and o oupu n aggregae. Ths separaon allows for easer parameerzaon of he model. Commody Demand Demand for agrculural commodes comes from wo prmary sources, food and energy. The commodes are used as food hrough ulzaon as anmal feed and for drec human consumpon n he form of vegeable ols or cereal grans. Addonally, hey are used o creae bofuels (ehanol or bodesel). We do no specfy he opmzaon problem n hese secors; we only consder a reduced-form aggregae demand funcon for each commody, whch capures demand derved from boh food uses and energy uses. We assume, hough, ha aggregae demands for he commodes are he resul of many compeve frms n hese secors maxmzng profs usng he commodes as npus n, d, her producon processes. Demand for commody n perod s gven by Q ( p, n ) 9

12 and s a funcon of he sochasc vecor of curren commody prces, number of bofuel plans p, and he n n operaon a me. We assume he aggregae demand for each commody,, has he expeced properes, Q ( p, n ) d, p < 0 and Q ( p, n ) d, n > 0. We do no make a pror assumpons abou he sgn of he cross-prce dervaves n he concepual model. I s concevable for he commodes o be eher subsues or complemens, especally wh respec o lvesock feed, and we leave hs o be esablshed n an emprcal specfcaon laer. Snce bofuel plans ake me o buld and come onlne, he number of plans n exsence for a gven crop year s fxed. Hence, he curren year s demand curve for hese commodes s fxed and known o all agens n he economy for gven yeld shock realzaons and pas crude ol prce realzaons. Laer, when we mplemen he model, we wll specfy funconal forms for he demand equaons. The Invesors The fnal agens of noe n our economy are he poenal nvesors n bofuel plans. There s an obvous connecon beween nvesors and agens demandng agrculural commodes, bu wll be useful o model her behavor ndependenly. In each perod, nvesors can choose among four dfferen nvesmens: a corn ehanol plan, a bodesel plan, a swchgrass ehanol plan, or n a marke porfolo. 1 The marke porfolo alernave s a porfolo of S&P 500 socks, whch gves he nvesor an opon f none of he bofuel nvesmens seems aracve. A he begnnng of each perod, nvesors selec one of he nvesmens. If an nvesor chooses o buld a bofuel plan, wll no come onlne unl he end of he perod. 10

13 We wsh o examne he behavor of a raonal nvesor and deermne he marke condons under whch each bofuel secor wll expand. We assume nvesors seek he larges rsk-adjused reurn on nvesmen possble, and here exss a rskless asse n he economy reurnng RFR, he rsk-free rae. The nvesors use he Capal Asse Prcng Model (CAPM) o evaluae nvesmen alernaves (Sharpe 1964). The nvesors calculae he secury marke lne o gve a measure of he expeced (requred) rae of reurn for an asse, a: where M s he marke porfolo, he varance of marke porfolo reurns, β Cov R (, R ) a a M ( ) Requred Reurn = RFR + β R RFR 2 R M s he expeced reurn of he marke porfolo, σ M s R a s he reurn of asse a, and a M a =. Armed wh esmaes of hese parameers, an nvesor can calculae 2 σ M he dfference n expeced reurn and requred reurn of asse a as calculaed wh he CAPM. The raonal nvesor chooses he projec wh he hghes excess reurns over he requred reurn. However, f he dfference s negave for each of he bofuel plans, an nvesor wll choose o nves n he marke porfolo. Reurns o Bofuel Producon Inpu coss n each secor are deermned by feedsock coss and oher producon and capal coss. We do no consder echnologcal advancemen n he producon of bofuels. We ake echnology as gven and consder how he boeconomy wll develop over me. Therefore, non-feedsock producon coss and capal coss are exogenous n he model. Feedsock coss are he mos mporan npu cos o bofuel producon, and hese are deermned by marke equlbrum. The per gallon annual rae of reurn o 11

14 producng bofuel of ype a s R a qa ( ε ) =, where a ( ) ka ( ζ ) q ε s he effecve prce receved by he plan for s produc, whch s he marke prce plus any subsdy, such as he blenders ax cred. The marke prce s a funcon of he crude ol prce realzaon, The per gallon cos of producng bofuel of ype a s a ( ) k ζ, whch ncludes boh feedsock and non-feedsock producon coss. Hence, he rae of reurn depends on he yeld realzaon n ha year as well as he acreage allocaon decsons of farmers. Compeve Equlbrum In our economy, a long-run compeve equlbrum a me s defned by { } = 0 () a sequence of prcng funcons p (,, ζ ε n ) for = 1, 2, 3 ; { } d, () a sequence of agrculural commody demand funcons Q ( p, n ) = 1, 2, 3 ; = 0 ε. for { } for () a sequence of agrculural commody supply funcons s, (, Q 1 p s, ) = 1, 2, 3 ; { } (v) a sequence of nvesmen funcons n ( p ) for = 1, 2, 3 ; = 0 = 0 (v) he law of moon of land allocaon ( ) π 1 π π π π π π π = 1, 2, 3, = 1, 2, 3 Gven he sequence of prcng funcons, he sequence of bofuel plans n operaon, crop yeld realzaons, and crude ol prce realzaons, commody markes clear n each perod. Tha s, s, * 1 d, * * ( p ) ( p ) Q, s, = Q, n = 1, 2, 3and. 12

15 We no only requre ha markes clear bu also mpose he condon ha, a he margn, he reurns of each projec equal he requred rsk-adjused reurns as deermned by he CAPM: * * ( p, ) * * ( p, ) * * ( p, ) R n = RR corn ehanol corn ehanol corn ehanol R n = RR bodesel bodesel bodesel R n = RR swch ehanol swch ehanol swch ehanol where RR s he requred reurn o he bofuel plan as deermned by he CAPM. The zero excess reurn condons ensure we have nvesmen n each of he bofuel plans unl he prces of feedsock (corn, soybeans, and swchgrass) are bd up o he pon a whch an nvesor s ndfferen beween nvesng n any of he bofuel plans and nvesng n he marke porfolo. When nvesmen n one or more plans canno mee hs condon, hen nvesmen equals zero. Implemenng he Model Our queson s emprcal n naure. The ncenves presen for he bofuel ndusry o expand or conrac depend upon many facors, ncludng he prce of crude ol, demand for corn and soybeans for food uses, and weaher varably. Explorng more han he mos basc resuls of hs model requres us o specfy funconal forms and evaluae he resuls numercally va he Mone Carlo mehod. 2 The model sars wh he monh of December 2007 when producers of corn, soybeans, and swchgrass (hay) were plannng how hey would allocae acres n he 2008 croppng season. Our sraegy for smulang he economy s o specfy funconal forms for boh agrculural commody supply and demand and o calbrae he dsrbuon of crude ol prces and commody yelds a specfed daes n he fuure. A jon draw from hese dsrbuons mples an equlbrum prce for corn, soybeans, and swchgrass and hus 13

16 mples reurn levels n each bofuel ndusry. Commody Supply We parameerze he producon funcon for he agrculural commodes as ( ζ ) * j ζπj j= 1 Q p,, s, = s, j = 1,2,3 where 1 s s he yeld penaly assocaed wh connuous croppng pracces. We mpose a yeld penaly only for connuous corn roaons. 3 We draw from he jon bea dsrbuon of yelds, μ ζ β μ μ corn 1 soybean,, q max, q mn swchgrass Σ μ = , μ = , μ = corn soybean swchgrass μcorn + 3σ corn , 3 σsoybean, μswchgrass + 3σswchgrass 1 Σ = qmax = μsoybean + q mn μcorn 2σ corn = μsoybean 2 σsoybean, μswchgrass 2σswchgrass usng he algorhm developed by Magnussen (2004). The mean of hs jon dsrbuon follows a lnear rend hrough me, whch was esmaed from hsorcal yeld daa for years 1980 hrough 2006 mananed by he Naonal Agrculural Sascs Servce. 4 The marx 1 Σ s he varance-covarance marx for he yelds of he hree crops. We assume he nomnal oal cos funcons of he agrculural commodes are quadrac, gven by 14

17 c ( π ) a π κ ( π ) 2 = + = 1, 2, 3. We use esmaes of U.S. annual supply j elasces for each crop from FAPRI s agrculural oulook model. Usng hese elascy esmaes, we can solve for he κ parameers. We calbrae he nerceps, a, so ha he model maches curren marke condons. Movaon for upward-slopng margnal cos curves s ha as land becomes more concenraed n a ceran crop, coss wll rse because of he need o nves n addonal pes conrol and nuren npus. Commody Demand We specfy a smple, consan elascy, reduced-form demand funcon for each commody. We use he nermedae-erm own- and cross-prce demand elasces for beef from he Economc Research Servce/Penn Sae World Trade Organzaon model as our esmaes of he α, α, α. The prce dsrbuon of crude ol nfluences commody demands ndrecly hrough he number of bofuel plans of each ype n he economy; n our smulaon, crude ol prces are lognormal and calbraed o mach curren condons n he fuures marke: 5, 6 ( p ε ) α ( 0 1) ( 2) ( 3) ( ) d ,, = α α α α = 1, 2, 3. Q n p p p n One of he equlbrum condons requres he number of bofuel plans n each ndusry o be such ha here are no excess reurns over he requred reurn. The parameer α4 s smply an elascy measurng he percenage change n quany demanded over he percenage change n he number of plans when an addonal plan s bul. To calculae α 4, we assume ha all plans of a gven ype are homogeneous n capacy 7 and ha whle onlne hey run a full capacy. Usng hese parameerzaons of commody supply and demand, as shown n able 1, and makng draws from he jon 15

18 yeld and crude prce dsrbuon, we can solve for equlbrum commody prces and deermne he dsrbuon of reurns o each knd of bofuel plan. Accounng for Cellulosc Ehanol from Corn Sover and Wood Chps If swchgrass ehanol s commercally vable, hen presumably cellulosc ehanol produced from corn sover and wood chps wll be commercally vable. Ths s because hese bomass sources do no compee drecly for acres from hgh-value crops such as corn and soybeans and hus would no have as large an mplc land cos. Because producon of hese feedsocks occurs ousde he framework of our model, we need o make some assumpons abou how much ehanol wll be produced from hese sources. In he case of vable swchgrass ehanol, we assume ha ehanol from boh corn sover and woody bomass s produced also. Whle s unceran how much corn sover realscally wll be colleced, and how much wood chps wll be avalable for bofuel producon, we have o make some assumpon n order o smulae he model. For example, f sover s ulzed a a 25% removal rae, and corn sover mass s produced n a rao of 1:1 wh corn gran mass, hen 5.45 bllon gallons of ehanol wll be produced from corn sover (Blanco- Canqu and Lal 2007; Graham e al. 2007). Furher, sx bllon gallons of bofuel produced from wood chps or oher woody resdue sources may be a reasonable expecaon gven he bllon on sudy by Perlack e al. (2005). Noe ha n hs example 4.54 bllon gallons per year mus come from swchgrass ehanol or oher land-nensve bomass sources o mee he cellulosc mandae n he EISA Renewable Fuel Sandard (RFS). Snce remans unclear exacly how cellulosc bofuel wll come no exsence, we also presen afer he secon conanng he man resuls a sensvy analyss varyng he amoun of cellulosc ehanol ha mus come from swchgrass ehanol. 16

19 Calculang Reurns o Bofuel Producon The forces mos affecng reurns o bofuel producon are feedsock coss and governmenal polcy. Feedsock coss are deermned endogenously whn he model; corn and swchgrass are fed drecly no he ehanol and cellulosc ehanol plans. For bodesel, soy ol (no soybeans drecly) s he feedsock. Our model produces equlbrum soybean prces bu no soy ol prces. We esmae a smple lnear relaonshp beween he prce of soybeans and he prce of soy ol usng recen daa: 8 Soy Ol Prce = * Soybean Prce R = Each ype of bofuel produces a co-produc ha generaes value ha can offse some of he feedsock cos. Corn ehanol produces dred dsllers grans, dred dsllers grans wh solubles (DDGS), or we dsllers grans, whch are used n beef, pork, and poulry raons n lmed quanes. These co-producs subsue for corn and soybean meal n lvesock raons. Therefore, he prce of DDGS moves wh he prces of corn and soybean meal. Dsllers grans have approxmaely he same dgesble energy conen as corn, so here we gve a cred o corn ehanol plans for DDGS conssen wh s ably o subsue for corn n lvesock raons (Shurson e al. 2003). The bodesel producon process yelds glycern, fay acds, and fler cakes. We cred 8 per gallon o he bodesel producer based on he curren marke value for hese co-producs (Paulson and Gnder 2007). Producon of ehanol from swchgrass produces lgnn, whch s combusble and wll be used o generae elecrcy whn he facly or wll be sold back o he elecrcal grd (Aden e al. 2002). We cred swchgrass ehanol wh 10 per gallon as suggesed n Aden e al. (2002). The per gallon non-feedsock coss of producng corn-based 17

20 ehanol and cellulosc ehanol are 76 per gallon and 97 per gallon, respecvely, whle he non-feedsock cos of producng bodesel s 55 per gallon (Paulson and Gnder 2007; Tokgoz e al. 2007). Revenue realzed by bofuel plans relaes drecly o crude ol prces. For smplcy, we assume ha he prce of ehanol and desel are deermnsc lnear funcons of he prce of crude ol. We used monhly spo prces from January 1994 hrough Augus 2007 of he Cushng Oklahoma crude ol, New York Harbor convenonal gasolne, and U.S. No. 2 wholesale/resale markes o esmae he lnear relaonshp: 9 Wholesale Gasolne Prce = *Crude Ol Prce Wholesale Desel Prce = * CrudeOl Prce 2 R = 2 R = E10 s he erm gven o a 10% ehanol, 90% gasolne blend. E85 refers o an 85% ehanol, 15% gasolne blend. E10 blend ehanol s ulzed for s ably o oxygenae gasolne, whch enhances combuson and reduces emssons (NSTC, 1997). E85 blend ehanol s currenly used only n flex-fuel vehcles ha have been specally desgned o whsand he corrosve properes of alcohol-based fuel. Ehanol has abou wo-hrds he energy value of gasolne (Shapour e al. 1995). Followng Tokgoz e al. (2007), we assume based on he demand-sde model ha when annual producon s greaer han 14 bllon gallons per year, he E10 marke becomes sauraed, causng ehanol o be prced a he margn accordng o s energy value compared o gasolne. When producon s below hs hreshold, we assume ha ehanol s prced a a premum o gasolne, valued for s properes as an addve (Hur e al. 2006). To accoun for hs ranson n ehanol prcng, we nerpolae beween he 18

21 addve and energy value prcng rules, as follows: 1.05* Pgasolne f ehanol producon < 14 bl gal Pehanol = ( 1.05 λ +.667( 1 λ) )* Pgasolne f 14 bl gal < ehanol producon < 16 bl gal.667* Pgasolne f ehanol producon > 16 bl gal ehanol producon 14 where λ = We are gnorng shor-erm dsrbuon-relaed bolenecks because marke forces wll reward hose who solve hese localzed problems. There s a much more serous boleneck ha occurs once all gasolne conans a 10% blend. To go pas hs pon, ehanol needs o sell below s energy value o ncenvze he sale of 85% blends. Ths new prce s subsanally below ha whch can be charged when ehanol s beng used as an oxygenae, and he need for hs prce change canno be elmnaed by he consrucon of new nfrasrucure. Reurns o bofuel producon are calculaed and compared o he requred reurn as defned by he CAPM. There wll be enry (ex) no a bofuel secor unl he excess reurns over he requred reurn are elmnaed. Snce we are neresed n long-run equlbrum, we solve for he number of bofuel plans n he crop year conssen wh hs condon. Lmaons of he Model Before we presen he resuls, we should dscuss some lmaons of he model.the assumpons ha allow he model o be run boh n erms of relaonshps n he daa and he behavor of parcpans represen a smplfcaon of rue marke condons ha currenly exs and ha are lkely o exs n he fuure. The resuls we presen should be nerpreed wh hs lmaon n mnd. Inernaonal rade s no presen n our model. Currenly here s a $0.54-per- 19

22 gallon specfc arff and a 2.5% ad valorem arff on mpored ehanol, whch effecvely lms he mporaon of Brazlan sugarcane-based ehanol. These arffs could be removed, or adopon of cos-reducng advances n sugarcane-based ehanol mgh make Brazlan ehanol aracve even wh he mpor arffs n place. If eher of hese suaons were o happen, an nernaonal secor would need o be added o he model n order o undersand fully he domesc boeconomy. The model adjuss o long-run equlbrum whereby he number of bofuel plans n each secor s such ha none earns excess reurns over he requred reurn. Ths s clearly no he way he ndusry would evolve n realy; he ransons would be gradual and carred ou over a number of years, and he ndusry mgh possbly overshoo he equlbrum oucome. Whle consderaon of hese facors would add some realsm o he model, would also add a level of complexy no requred o address our quesons of neres. Resuls There are wo forces ha can sgnfcanly affec he evoluon of he bofuel ndusry: governmenal polcy and energy prces. We smulae wha long-run equlbrum n he boeconomy would look lke under dfferen scenaros regardng bofuel ax creds, bofuel producon mandaes, and crude ol prces. To esablsh a baselne agans whch we can compare dfferen scenaros, we smulae he model usng pre-eisa governmenal polces. Tha s, we nclude he Volumerc Ehanol Excse Tax Cred from he Amercan Jobs Creaon Ac of 2004, whch ncludes a $0.51-per-gallon cred for ehanol, and a $1.00-per-gallon cred o bodesel. We also use curren expecaons of fuure crude ol prces. As a proxy for hs, we use he mean of he daly NYMEX December 2008 conrac prce for crude ol durng Ocober 2007, whch s $ The 20

23 baselne case ncludes an exsng corn ehanol ndusry wh a capacy of 6.8 bllon gallons per year, a bodesel ndusry wh a capacy of 1.2 bllon gallons per year, and no cellulosc ehanol ndusry n , 11 The baselne resuls (able 2) show susaned hgh commody prces and perssence n corn-nensve croppng paerns. The corn ehanol secor expands unl oal producon exceeds 18 bllon gallons per year. Bodesel and cellulosc ehanol from swchgrass are no vable n hs scenaro. Cellulosc ehanol never expands, and he bodesel secor conracs so ha here are no bodesel plans operang n he long run. These resuls sugges ha under pre-eisa polcy, once he opporuny cos of land s aken no accoun, raonal farmers wll no grow swchgrass or soybeans for bofuel producon, and raonal nvesors wll no buld hese plans. In our resuls, he bodesel ndusry dsappears a pre-eisa subsdy levels. So, why does he curren bodesel ndusry exs? Bodesel producon connues o expand every year (Wesco 2007) despe he fac ha he bodesel ndusry s no producng a capacy (Radch 2004), and poenal for prof looks grm as he ndusry connues o face hgh soybean prces. Perhaps bodesel producers were counng on a successful lobbyng effor ha would secure hgher subsdes for bodesel relave o corn ehanol; hs sraegy proved que raonal afer he passage of he EISA. Renewable Fuel Sandard Scenaros In he remanng scenaros, we mpose he bofuel producon levels ndcaed by he new RFS n he EISA of 2007 and consder he boeconomy s equlbrum oucomes for hree dfferen long-run crude ol prce scenaros. We assume ha he greenhouse gas reducon requremens n he legslaon are me for all bofuels. Afer mposng he bofuel 21

24 producon levels, our model allows us o solve for he level of subsdy (ax cred) requred o manan he zero-excess-reurn condon n addon o delverng equlbrum agrculural commody prces and acreage allocaons. Corn has a mean long-run equlbrum prce of $4.76 per bushel, soybeans, $13.01 per bushel, and swchgrass, $ per on. Long-run equlbrum acreage allocaons are 61% of acres n corn, 19% n soybeans, and 20% n swchgrass or hay. The varable we are neresed n comparng across dfferen crude ol prce scenaros s he level of ax cred requred o manan he no-excess-reurn condons (see able 3). We canno say, a pror, wheher hgh crude ol prces wll mply hgher or lower zero-excess-reurn ax cred levels. Crude ol prces ac on bofuel reurns n wo ways. Mos obvously, hgh crude ol prces mply hgh bofuel prces, posvely affecng reurns o bofuel producon. In addon, hgh crude ol prces affec reurns o bofuel producon n he followng way. Consder he reurns o bodesel producon. Bodesel benefs from hgh crude ol prces by he resulng srong oupu prces enjoys, bu so does corn ehanol, and swchgrass ehanol. Ths creaes more nense compeon for acreage among he energy crops, and resuls n hgher commody prces. Ths prce ncrease reduces he reurn o each knd of bofuel producon. Whou smulang he model, we canno deermne whch effec wll be sronger. Land allocaons, under he EISA RFS, shf oward he crops whose derved fuels are mandaed a a hgh level. Incenves provded o he greener fuels dffuse hrough he economy and cause a shf n land allocaon paerns. The mandae resuls n much hgher commody prces han n he baselne. If he cellulosc mandaes n he ac are desgned o avod he feed-versus-fuel rade-off, our resuls sugges wll acually 22

25 exacerbae he suaon by nducng even hgher feedsuff coss han under he regme wh only corn ehanol n producon. Wh a fxed amoun of land, s mpossble o ncrease he amoun of each crop devoed o energy and manan he same level of consumpon of each commody for food uses such as feedng lvesock. Sensvy of Resuls o Requred Levels of Swchgrass Producon The amoun of cellulosc bofuel producon ha s feasble from corn sover and woody bomass s unceran. Ths amoun could be a sgnfcan facor n deermnng long-run commody prces and acreage allocaon paerns because he amoun of cellulosc bofuel no covered by corn sover and woody bomass wll need o be made up wh land-nensve bomass crops such as swchgrass. The more land-nensve bomass crops are needed o mee he cellulosc ehanol requremens, he greaer he nensy of compeon for acreage. Table 4 presens he resuls of several scenaros ncreasng he amoun of swchgrass ehanol needed o mee he new RFS. In he frs scenaro, we consder he case n whch he new RFS for cellulosc ehanol can be me exclusvely wh corn sover and woody resdue, and no land-nensve bomass s needed. Noe ha we calculae ha he subsdy gven o cellulosc ehanol (ncludng corn sover and wood chp ehanol) mus reach $0.90 per gallon before he swchgrass ehanol secor would begn o expand. The fnal scenaro requrng bllon gallons of swchgrass ehanol per year s arhmecally equvalen o assumng 25% of corn sover wll be colleced for ehanol and here s no producon of ehanol from wood chps. Wh ncreasng requremens on land-nensve bofuel, we see hgher commody prces and hgher subsdy levels needed o manan he requred bofuel ndusry szes. The sensvy analyss s also useful n 23

26 ha hns a how he resuls mgh have been dfferen had we smulaed he model wh mscanhus nsead of swchgrass as he domnan cellulosc bomass crop. Conclusons Our resuls lead o some general conclusons abou he fuure of bofuels n he Uned Saes. Compeon for land ensures ha provdng an ncenve o jus one crop wll ncrease equlbrum prces of all. Also, a pre-eisa subsdy levels, neher bodesel nor swchgrass ehanol s commercally vable n he long run. In order for swchgrass ehanol o be commercally vable, mus receve a dfferenal subsdy over ha awarded o corn-based ehanol. Homogeneous subsdy levels for all ypes of ehanol canno ence expanson of swchgrass ehanol. Snce swchgrass compees for he same acres as corn, and corn-based ehanol s less expensve o produce, corn-based ehanol wll always have a comparave advanage over swchgrass ehanol n he absence of a dfferenal subsdy. Corn and soybeans compee for he same acreage, so when energy prces are such ha corn-based ehanol s smulaed, hen he prce of soybeans mus also ncrease f he farmer s o connue o allocae some land o soybeans. Ths ncrease n soybean prces reduces he profably of bodesel even n scenaros n whch energy prces are hgh. Ths means ha under pre-eisa subsdy levels, he soy ol bodesel secor s no vable under any energy prce consdered. If he EISA mandaes are o be me n a volunary fashon, hen he bodesel secor wll requre a hgher relave subsdy han has oday. We calculae he subsdes requred o smulae bofuel producon o he levels requred by he EISA RFS. We fnd ha subsdy levels are needed n he range of $0.22 o $0.78 per gallon for corn ehanol, $1.97 o $2.90 per gallon for bodesel, and $1.55 o 24

27 $2.11 for cellulosc ehanol. Crude ol prce realzaons n he fuure wll deermne he subsdy levels requred o manan ndusry szes requred by he new RFS. The new RFS resuls n much hgher commody prces han n he baselne. Ths suggess ha he cellulosc mandaes n he EISA ha appear desgned o avod he feed-versus-fuel radeoff may acually exacerbae he suaon relave o a suaon n whch corn-based ehanol s allowed o expand. Cellulosc ehanol s more expensve o produce, and swchgrass-based ehanol s more land nensve han corn-based ehanol. Therefore, he severy of upward pressure on commody prces caused by he new RFS wll be deermned largely by he ably o produce cellulosc ehanol from bomass ha s no land nensve o produce. Polces ha expand cellulosc ehanol beyond levels ha can be suppled by corn sover and woody bomass are herefore more expensve n erms of he subsdy ha s requred and he resulng ncrease n food and feed prces ha resul. 25

28 Endnoes 1 We consder only corn, soybeans, and swchgrass because we focus on he decson of a farmer who mus allocae crop ground. Oher cellulosc feedsocks such as woodchps are no well sued o crop ground (Lewandowsk e al. 2003). 2 All smulaons were conduced n Malab. 3 We assume a 10% yeld drag on connuous corn roaons. 4 Ths s gven n per harvesed acre. We use alfalfa as a proxy for swchgrass yelds, snce he onnage per acre s approxmaely equvalen o he swchgrass yelds projeced n he leraure. See hp:// 5 The prces of oher fuels (e.g., gasolne and bodesel) are based on her relaonshp o crude ol prces. 6 Impled volaly n crude ol prces s esmaed from 2007 opon daa. In he frs scenaro we ake as he mean of he crude ol prce dsrbuons n each perod o be he NYMEX prce of he December fuures conrac n he relevan year on Ocober 2, In a subsequen scenaro, we ncrease he crude ol fuures prce o reflec he dramac ncrease n ol prces ha occurred beween Ocober 2007 and December We assume corn ehanol plan capacy s mgy, bodesel plan capacy s 20 mgy, and cellulosc ehanol plan capacy s 51.1 mgy. Corn ehanol and bodesel capacy s based on capacy of curren plans as publshed by he Renewable Fuels Assocaon and he Naonal Bodesel Board. Cellulosc ehanol capacy s based on Aden e al See hp:// and hp:// 8 The relaonshp s esmaed from he daly neares cash prces on he CBOT from Ocober 17, 2005 o Sepember 14, Hsorcal daa are mananed a hp://ono.ea.doe.gov/dnav/pe/pe_pr_sp_s1_d.hm. 10 For exsng ehanol ndusry capacy and locaons, see hp:// (Sepember 2007). 11 For exsng bodesel ndusry capacy and locaons, see hp:// (Sepember 2007). 26

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30 Random Varables wh Known Margnal Dsrbuons and a Specfed Correlaon. Compuaonal Sascs & Daa Analyss 46(2): Muh, J.F Raonal Expecaons and he Theory of Prce Movemens. Economerca 29(3): Naonal Scence and Technology Councl, Commee on Envronmen and Naural Resources (NSTC) Ineragency Assessmen of Oxygenaed Fuels. Repor o he Offce of he Presden of he Uned Saes, Washngon, DC. Orazem, P.F., and J.A. Mranowsk A Dynamc Model of Acreage Allocaon wh General and Crop-Specfc Sol Capal. Amercan Journal of Agrculural Economcs 76(3): Paulson, N.D., and R.G. Gnder The Growh and Drecon of he Bodesel Indusry n he Uned Saes. CARD Workng Paper 07-WP 448, Cener for Agrculural and Rural Developmen, Iowa Sae Unversy. Perlack, R.D., L.L. Wrgh, A.F. Turhollow, R.L. Graham, B.J. Sokes, and D.C. Erbach Bomass as a Feedsock for Boenergy and Boproducs Indusry: The Techncal Feasbly of a Bllon-Ton Annual Supply. Jon sudy sponsored by he U.S. Deparmen of Energy and U.S. Deparmen of Agrculure. Oak Rdge, TN: Oak Rdge Naonal Laboraory. Radch, A Bodesel Performance, Coss, and Use. Analyss repor. Energy Informaon Admnsraon, U.S. Deparmen of Energy. Rozaks, S., and J.C. Soure Mcro-economc Modellng of Bofuel Sysem n France o Deermne Tax Exempon Polcy under Uncerany. Energy Polcy 33(2):

31 Shapour, H., J.A. Duffeld, and M.S. Grabosk Esmang he Ne Energy Balance of Corn Ehanol. Agrculural Economc Repor No U.S. Deparmen of Agrculure, Economc Research Servce, Offce of Energy and New Uses. Sharpe, W.F Capal Asse Prces: A Theory of Marke Equlbrum under Condons of Rsk. Journal of Fnance 19(3): Shurson, J., M. Spehs, J. Wlson, and M. Whney Value and Use of New Generaon Dsller s Dred Grans wh Solubles n Swne Des. Allech s 19h Inernaonal Feed Indusry Proceedngs, May 12-14, 2003, Lexngon, KY. Tegene, A., W.E. Huffman, and J.A. Mranowsk Dynamc Corn Supply Funcons: A Model wh Explc Opmzaon. Amercan Journal of Agrculural Economcs 70(1): Tokgoz, S., A. Elobed, J.F. Fabosa, D.J. Hayes, B.A. Babcock, T-H. Yu, F. Dong, C.E. Har, and J.C. Beghn Emergng Bofuels: Oulook of Effecs on U.S. Gran, Olseed, and Lvesock Markes. CARD Saff Repor 07-SR 101, Cener for Agrculural and Rural Developmen, Iowa Sae Unversy. Wesco, P.C Ehanol Expanson n he Uned Saes: How Wll he Agrculural Secor Adjus? Repor FDS-07D-01, Economc Research Servce, U.S. Deparmen of Agrculure, May. Wu, J., and R.M. Adams Producon Rsk, Acreage Decsons and Implcaons for Revenue Insurance Programs. Canadan Journal of Agrculural Economcs 49(1): Zhang, Z., D. Vedenov, and M. Wezsen Can he U.S. Ehanol Indusry Compee n he Alernave Fuels Marke? Agrculural Economcs 37(1):

32 Table 1. Parameers Used n Mone Carlo Smulaon κ a α 0 α1 α2 α3 α 4 Corn Soybeans Swchgrass Table 2. Assumpons n he Baselne Scenaro Corn Bodesel Swchgrass 2007 Bofuel ndusry szes (bllon gallons) Acreage proporons a Tax creds ($/gal) $0.51 $1.00 $ Curren expecaon of fuure crude prces ($/barrel) $78.63 $78.63 $78.63 $78.63 $78.63 a From NASS (hp:// 30

33 Table 3. Long-Run Resuls under Dfferen Tax Creds, RFS Mandae, and Crude Ol Prce Scenaros Baselne New RFS Md Crude New RFS Hgh Crude New RFS Low Crude E[ p ] ($/barrel) $78.63 $78.63 $95 $65 crude E[ p ] ($/bu) $4.29 $4.76 $4.76 $4.76 corn E[ p ] ($/bu) $11.37 $13.01 $13.01 $13.01 sb E[ p sg ] ($/on) $ $ $ Land allocaons ( π π π ) ( ) ( ) ( ) ( ) Corn ehanol producon (bllon gallons) Bodesel producon a 0bgy (bllon gallons) Swchgrass ehanol producon (bllon gallons) Tax cred Corn ehanol $0.51 $0.53 $0.22 $0.78 ($/gal) Tax cred bodesel $1.00 $2.49 $1.97 $2.90 ($/gal) Tax cred cellulosc ehanol ($/gal) $0.51 $1.86 $1.55 $2.11 Noe: Shaded porons are exogenous n he scenaro. a Producon from soy ol feedsock. 31

34 Table 4. Sensvy of Crop Prces and Requred Subsdy Levels o Increasng Swchgrass Ehanol Levels New RFS Md Crude New RFS Md Crude New RFS Md Crude New RFS Md Crude E[ p ]($/barrel) $78.63 $78.63 $78.63 $78.63 crude E[ p ] ($/bu) $3.98 $4.66 $4.83 $4.96 corn E[ p ] ($/bu) $10.29 $12.65 $13.25 $13.67 sb E[ p sg ] ($/on) $ $ $ $ Land allocaons ( π π π ) ( ) ( ) ( ) ( ) Corn ehanol producon (bllon gallons) Bodesel producon a (bllon gallons) Swchgrass ehanol producon (bllon gallons) Tax cred corn ehanol ($/gal) Tax cred bodesel ($/gal) Tax cred cellulosc ehanol ($/gal) Noe: Shaded porons are exogenous n he scenaro. a Producon from soy ol feedsock. 32

35 Polcy decsons made Exsng bofuel capacy known Belefs formed abou fuure crude prce and crop yeld dsrbuons Farmers make land allocaon decsons each year Bofuel nvesmen decsons ake place Long-run crude ol prces and crop yelds are realzed Fgure 1. Decson melne for commody producon 33