Welfare Changes from the U.S. Ethanol Tax Credit: The Role of Uncertainty and Interlinked Commodity Markets

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1 Welfare Changes from the U.S. Ethanol Tax Credt: The Role of Uncertanty and Interlnked Commodty Markets Mndy Baker Workng Paper 08-WP 483 December 2008 Center for Agrcultural and Rural Development Iowa State Unversty Ames, Iowa Mndy Baker s a research assstant n the Department of Economcs and Center for Agrcultural and Rural Development at Iowa State Unversty. Ths paper s avalable onlne on the CARD Web ste: Permsson s granted to excerpt or quote ths nformaton wth approprate attrbuton to the authors. Questons or comments about the contents of ths paper should be drected to Mndy Baker, 75 Heady Hall, Iowa State Unversty, Ames, IA ; Ph: (515) ; Fax (515) ; E-mal: bakermn@astate.edu. Iowa State Unversty does not dscrmnate on the bass of race, color, age, relgon, natonal orgn, sexual orentaton, gender dentty, sex, martal status, dsablty, or status as a U.S. veteran. Inqures can be drected to the Drector of Equal Opportunty and Dversty, 3680 Beardshear Hall, (515)

2 Abstract A model of the corn, soybean, and wheat markets calculates welfare effects of the U.S. ethanol tax credt. Crop yelds are uncertan, and demand conssts of feed, food, energy, and exports. Modelng uncertanty n crop yelds allows the valuaton of defcency payments as optons. Dsaggregatng demand records who benefts from the tax credt and by how much; ncorporatng lnked crop markets captures ndrect effects mportant for determnng the transfer from consumers to producers. There s $600 mllon n net welfare loss, ncreased taxpayer lablty, and a large transfer from consumers to farmers. A bref comparson of recent lterature s ncluded. Keywords: bofuel, commodty, ethanol, tax credt, uncertanty, welfare.

3 Welfare Changes from the U.S. Ethanol Tax Credt: The Role of Uncertanty and Interlnked Commodty Markets Who gans from tax credts granted to the ethanol ndustry, and by how much? The ncrease n gran prces assocated wth ethanol producton shfted government spendng from prce defcency programs to ethanol subsdes. Defcency payments are only made n years when market prces are low, whereas ethanol payments occur every year. The sze of payments n the prce defcency programs depend explctly on uncertanty n crop prces. Therefore, n order to compare the old program to the new we need to ntroduce prce uncertanty nto our models of welfare analyss. We nclude uncertanty n crop yelds, whch drves uncertanty n equlbrum crop prces and allows us to estmate change n the opton value of government defcency payments. We also nclude two markets closely lnked to corn soybeans and wheat. Ths s an mportant element for whch to account because farmers do not plant one crop; they typcally plant a rotaton of crops. Therefore, t s mportant to quantfy the welfare changes n those closely related markets as well. For each commodty, we dsaggregate demand, allowng us to dsentangle welfare effects felt by major segments of commodty consumers, ncludng the lvestock feedng sector, the food sector, and exports. Knowng whch sectors are most mpacted by bofuel polcy changes s mportant nformaton for polcymakers to consder. We conclude the artcle by comparng our results wth those found recently n the lterature. The comparson demonstrates the mportance of ncludng these three features 1

4 of the boeconomy uncertanty n crop yelds, ndrect effects on lnked commodty markets, and dsaggregated consumer demand n our welfare models. The Model Economy The economy has three goods: corn, soybeans, and wheat. Consumers buy agrcultural commodtes and use them as nput n producng food, feed, or energy, or for export, and we ntroduce uncertanty through agrcultural commodty yelds. In the frst perod, agents form expectatons about prces and future crop yelds, and farmers allocate acreage among corn, soybeans, and wheat. In the second perod, crop supply s determned by acreage allocatons and crop yeld realzatons. Demand from the bofuel sectors s determned by bofuel capacty, and demand for the commodtes also comes from food and export consumers. Commodty Supply There exsts a sngle representatve and compettve farmer wth an endowment of one unt of land, who takes both output prces and hs cost functon as gven. Whle output prces and yelds are uncertan, all agents n the economy know the jont dstrbuton. The farmer allocates hs land n perod one to three dfferent crops: corn, soybeans, and wheat. The endowed land s representatve of total U.S. cropland devoted to these commodtes. Snce cellulosc ethanol from crop land does not pass the Energy Independence and Securty Act (EISA) net carbon standard, ethanol from bomass wth a low opportunty cost of land (lke corn stover) s most lkely to be the frst source of commercal cellulosc ethanol (Searchnger et al. 2008). For ths reason, we exclude a cellulosc bomass crop that competes for land wth corn, soybeans, and wheat n our 2

5 model. We ndex the crops as follows: corn, = 1; soybeans, = 2; and wheat, = 3. The producer s second-perod proft s gven by 3 (1) w= pζπ c( π ; Θ ) = 1 where p s crop s output prce, and the quantty produced of crop s ( ) Q. The nomnal cost functon for crop s ( ; ) c π Θ, where s a vector of parameters defnng each crop s nomnal cost functon nomnal meanng t does not account for the opportunty cost of the land. The proporton of land allocated to crop s π, and producton technology s characterzed c by > 0. π The producer s rsk neutral n proft, wshng to maxmze the present value of expected proft subject to land constrants. To ths end, he chooses an allocaton vector π to solve the problem: Θ (2) [ ] max E w st.. π = 1 π n = 1 and π 0 for = 1, 2, 3 The frst-order condtons are Q c Q c t t t t t 2 2 t 1 1 (3) p2 + = p1 + π 2 π2 π1 π1 Q c Q c t t t t t 3 3 t 1 1 (4) p3 + = p1 + π 3 π3 π1 π1 These condtons requre that the producer equate the margnal net beneft of growng soybeans (wheat) to the margnal net beneft of growng corn, and that the 3

6 soluton to the farmer s acreage allocaton problem s defned as π ( p;, ζ) Θ. Multplyng the acreage decsons wth the producton functons, we get the commodty supply for each crop gven the random yeld realzatons, ζ. Notce both prce and nomnal cost of producng other crops enter a gven crop s supply functon, Q * ( p;, ζ) ζ π ( p;, ζ) Θ = Θ. Functonal Forms for Commodty Supply We assume the nomnal cost functons of the crops are quadratc, gven by ( π ) π κ ( π ) 2 1, 2, 3 c = a + =. The proporton of land allocated to each crop, π, s the farmer s choce varable; the parameters of the cost functon ( a and κ ) depend on the prce of crude ol. Ths specfcaton works well because we can separate out ncreasng and constant margnal producton costs, and use the commodty cost and return budgets of the Economc Research Servce (ERS) as estmates for these. 1 We parameterze the producton functon for the agrcultural commodtes as * (5) Q ( p ζ) ζ π ( p ζ ) ; Θ, = ; Θ, for = 1, 2, 3 The yeld realzatons, ζ, are drawn from the jont beta dstrbuton of yelds usng the algorthm developed by Magnussen (2004). μ β μ μ corn 1 ζ ~ soybean,, qmax, qmn wheat Σ 4

7 μcorn + 3σ corn , μ 3σsoybean μwheat + 3σwheat 1 t Σ = qmax = soybean + q t mn μcorn 2σcorn = μsoybean 2σ μwheat 2σ soybean wheat Trend yelds are mportant (especally for corn), so we set the mean at the 2007 trend level. 2 1 The matrx Σ s the varance-covarance matrx for the yelds of the three crops, 1 and the σ are the standard devatons of each crop found n Σ. 3 Commodty Demand Wth an aggregated demand functon, we are only able to consder changes n aggregate welfare, whle dsaggregatng commodty demands allows us to explore welfare changes to dfferent groups resultng from bofuel expanson. We model demand for each commodty from four dfferent subsectors: lvestock feed (l), drect human food use (f), exports (x), and energy (e). For the demand equatons, own- and cross-prce elastctes are those used n the ERS/Penn State/World Trade Organzaton trade model for lvestock feed, food/consumer demand, and export demand. We use own- and cross-prce elastctes of beef and veal feed demand n the Unted States. We use food/consumer demand elastctes for the corn, soybean, and wheat food demand parameters n our model. We calbrate the constant terms to 2007 consumpton levels for each group. Tables 1 and 2 contan parameter estmates of the supply and demand equatons used n the Monte Carlo smulaton. Corn Demand Equatons 5

8 c α ( ) ( ) c d 1 2 c, t c t t α l = α0 c sb Q p p ( ) 1 c c Q = β p β dc, t c t f 0 c d, t c t Q = γ p γ c (6) ( ) 1 x 0 c Q = δ n dc, t t e c c Q = Q + Q + Q + Q dc, t dc, t dc, t dc, t dc, t e x f l Where p t s the prce of crop at tme t. The corn-based ethanol ndustry sze at tme t s represented by n c t. 4 We nclude the prce of soybeans n the corn feed demand equaton but assume only own-prce effects n the food and export sectors. The Soybean Complex Demand for soybeans s composed of crush demand and exports. Crush demand s obvously drven by demand for soybean meal and ol, and we assume ths affects aggregate demand for soybeans n proporton to the amount of ol verses meal found n the soybean seed. Fgure 1 shows the relatonshp of aggregate soybean demand to all of ts components. Aggregate soybean demand comes from the domestc crush market and exports; crush demand comes from demand for soybean meal and soy ol. Demand for soybean meal s drven exclusvely by the lvestock-feedng sector, and we nclude a corn cross-prce elastcty. Demand for soy ol, however, comes from both food demand and bodesel producton. Crush demand depends upon the prce of soy ol and soybean meal, not the prce of soybeans drectly. However, the prces of these lnk tghtly to the prce of soybeans, 6

9 and for smplcty we estmate a smple determnstc lnear relatonshp of each wth the prce of soybeans usng recent data. 5 Wheat Demand Equatons For the wheat demand equatons we nclude only demand from the food and exports. Only a small amount s used for lvestock feedng and bofuel producton. ( ) 1 c Q = β p β dw, t w t f 0 w d, t w t Q = γ p γ w (7) ( ) 1 x 0 w Q = Q + Q + Q dw, t dw, t dw, t dw, t x f l w Compettve Equlbrum In our economy, a compettve equlbrum s defned by prcng functons p (, ε, ) d (8) crop demand functons Q (, n ) ζ n for = 1, 2, 3 s crop supply functons Q ( ; Θ, ) p for = 1, 2, 3 p ζ for =1, 2, 3 Gven the prcng functons, bofuel capacty, and crop yeld realzatons, commodty s d markets clear. That s, ( p ζ) ( p ) Q ; Θ, = Q, n for = 1, 2, 3. Calculatng Welfare Changes Ths modelng framework allows us to calculate the welfare of fve dfferent groups: farmers, lvestock producers, processors of cereal grans and olseeds for food use, gasolne consumers or blenders, and taxpayers. Suppose p s the equlbrum prce vector n the status quo scenaro, and ˆp s the equlbrum prce vector after some polcy 7

10 change. Calculatng the change n welfare of the farmer s a straghtforward calculaton of producer surplus: (9) Π Π Π Δ PS = dp + dp + dp farmer farmer farmer farmer Y c sb w pc psb pw where Y s an arbtrary curve n the prce space wth endponts p and ˆp, change n producer surplus of the farmer, and Δ PS farmer s the Π farmer s the proft functon of the farmer. Path ndependence of a lne ntegral of a contnuous, conservatve functon over an open, connected regon, along wth Hotellng s lemma, mply Δ PS farmer s equvalent to (Larson, Hosteltler, and Edwards 2002; Mas-Colell, Whnston, and Green 1995): (10) 1 ( p;, ζ, ) pˆ c s farmer p c c c Δ PS = Q Θ s dp pˆsb psb pˆ 1 w s 1 ( p;, ζ, ) ( p;, ζ, ) + Q Θ s dp + Q Θ s dp s sb sb pw w sw Agrcultural commodtes lke corn, soybeans, and wheat are not retal goods; very lttle f any of these are sold drectly to end consumers. These commodtes are used as nputs n the producton processes of food, meat, and fuel. Snce these are nput demands for producton processes, ths allows us to calculate the welfare change here as the standard consumer surplus measure. Proft-maxmzng frms do not exhbt a dfference n wllngness to pay verses wllngness to accept snce ther nput demands are derved from ther cost functon and not from a quas-concave utlty functon lke an ndvdual consumer. Notce that by ncludng cross-effects of corn prces on soybean meal demand and soybean meal prces on corn demand, the drecton of change n welfare due to a polcy 8

11 change s a pror unknown. Because of the substtutablty of the corn and soybeans, for example, f the equlbrum prce of corn ncreases, we have a shft along the demand curve for corn, but we have a shft out n the crush demand equaton due to the ncrease n the corn prce. And lkewse s the effect of an ncrease n the prce of soybean meal on the corn market. See fgure 2 for an llustraton of these drect and ndrect welfare changes. For ths reason, when a polcy causes all commodty prces to rse, n equlbrum there s a welfare loss due to the ncrease n the commodty s own prce. At the same tme there s a welfare gan due to the demand curve shftng out because the prce of the substtute has ncreased as well. By Shepherd s lemma and Larson, Hosteltler, and Edwards, agan the change n the producer s surplus s gven by (11) C C Δ PS = dp + dp l l l Y c sb pc psb pˆc pc pˆ d sb ( ) ( ) c d sb d c d sb = Q + Q dp + Q + Q dp l l sbmeal c p l l sbmeal sb sb where C () s the cost functon for lvestock producers. l Corn, soybeans, and wheat all are used n the producton of food for human consumpton. Corn s used to make sweeteners and corn meal, soybeans make ther way nto human dets drectly through soybean ol and soy-based dary or proten replacements, and wheat s consumed as flour or pasta. In ths way, we dstngush the welfare change of the wheat food-producng sector from the corn food-producng sector from the soybean foodproducng sector n a smlar manner as for the lvestock producers: 9

12 (12) Δ PS = f corn f corn Y c pc = pc ˆ pc C Q dp dc f c dp Δ PS = f sb f sb Y sb psb = psb ˆ psb C Q dsb f dp dp sb C Δ PS = + f wheat f wheat Y w pw = pw ˆ pw Q dw f dp w dp and smlarly for exports of each of the commodtes: (13) Δ PS = ex corn = Y pc ˆ pc C p Q ex corn dc ex c dp c dp c Δ PS = ex sb = Y pˆ sb psb C p Q ex sb sb dsb ex dp dp sb sb C Δ PS = + ex wheat ex wheat Y w pw = pˆ w pw Q dw ex dp w dp Taxpayer Costs Taxpayers have two potental sources of expendtures: the blender s credt and defcency payments to farmers. Loan defcency payments (LDPs) are lke cash settled put optons wrtten by the taxpayers and owned by farmers. When the market prce of the commodty s below the target rate, the taxpayer makes a payment of the dfference to the farmers based on the amount of the commodty they own. Countercyclcal payments (CCPs) are 10

13 made when the effectve prce of a commodty s less than the target prce for the commodty, and the payment s based on hstorcal yelds and recent acreage allocatons. See fgure 3 for a depcton of the payoffs of the LDP and CCP programs. Snce these defcency payment programs have opton-lke characterstcs, we can only value them approprately n a model that accounts for uncertanty n commodty markets. When buyng an opton on an exchange, the owner pays a premum upfront for the prvlege to enjoy market upsde potental, wthout exposure to downsde rsks. The loan rate 6 (LR) of the loan defcency program s the strke prce of ths opton; taxpayers subsdze farmers through LDPs wthout recevng the opton premum from the farmers. Calculatng the opton value of the loan defcency program s more accurate than assumng the market prce wll be above or below the loan rate based on hstorcal prces. Most welfare analyss s conducted based on calculatng a determnstc equlbrum corn prce based upon fxed demand and supply assumptons. Our model allows for uncertanty n the prce of corn, soybeans, and wheat through uncertan yelds, and allows us to calculate the cost to taxpayers (n terms of opton premum lost) n a more realstc way than f we were usng a determnstc model. The value of the LDP payment s the value of a put opton wth harvest-tme maturty and strke prce equal to the loan rate, LR. In realty, the value of ths opton would vary through the crop-growng season and would not reman constant. Because of decreasng tme to maturty, and also because weather shocks are realzed through the season and uncertanty about supply s resolved, the opton ether becomes more n-themoney or out-of-money, whch changes ts value. However, for the purpose of ths study 11

14 we consder the value of the opton at plantng tme for that crop sprng and early summer for corn and wheat, respectvely, and fall for wheat. We assume only wnter wheat n our analyss snce the U.S. produces sgnfcantly more wnter than sprng wheat 7 and dealng wth only one type smplfes the analyss. The put opton wrtten by the government has a value of t T (14) put ( pc, LR, T ) = exp( rt ) E max ( LR pc, 0) t T (15) put ( psb, LR, T ) = exp( rt ) E max ( LR psb, 0) t T (16) put ( pw, LR, T ) = exp( rt ) E max ( LR pw, 0) for corn, where r s the rsk-free nterest rate (assumed constant), T s the tme from plantng to harvest, and E () s the expectaton operator under the equvalent martngale measure. We choose plantng tme as the reference pont from whch we value the put opton because f t were not for the government loan defcency program, farmers could purchase the same protecton aganst low market prces on the approprate commodty exchange and presumably would do so smultaneously wth ther plantng decsons. Therefore, the loan defcency program s a transfer n the amount of the opton value from taxpayers to farmers. CCPs are smlar to LDPs, but they are determned not by the current season s producton but by past producton. Payments are made when the target prce 8 s lower than the effectve prce for the commodty. The effectve prce s (17) Effectve Prce = Drect Payment Rate +max ( p, LR) market 12

15 The drect payment rate porton of the effectve prce s constant and not determned by producton, so ths porton of the payment wll not contrbute to welfare changes n our analyss. CCPs are made accordng to the followng calculaton: (18) ( ) CCP = max Target Prce EffectvePrce,. BaseAcres HstorcalYeld The CCP s thus an opton held by the farmer as well; f the market prce falls between the target prce and the loan rate, the farmer exercses the opton and receves a payment based on hstorcal producton. At plantng tme, the value of the CCP opton s (19) t rt ( ) ( ) CCP p, Target, Effectve, T = e E max Target - Effectve, BA HY and the net payment of the defcency payment programs as a functon of harvest tme prce s that of a put opton wth strke prce equal to the target, but the farmer receves a payment (nstead of payng a premum) for holdng the opton. Results In table 3 we present the welfare results from our smulaton. We smulate crop prces wth the ethanol tax credt of $4.11 for corn, $11.69 for soybeans, and $10.11 for wheat. Wthout the tax credt we smulate crop prces of $3.17, $8.43, and $6.74 for corn soybeans, and wheat, respectvely. 9 The frst result of note s that under the blender s credt, government expendtures (the farm program and ethanol tax credt combned) are not reduced. Taxpayers were net losers by nearly $144 mllon under the current bofuel program n The welfare loss to taxpayers s because the reduced opton 13

16 value of the defcency payment programs ($542 ml CCP and $2,629 ml LDP) 10 s not enough to offset the addtonal cost of the ethanol tax credt. The reduced defcency payment opton value comes at the expense of farmers. They are the owners of ths opton, and under the bofuel program they lose $3.2 bllon on ths opton. Farmers are not net losers, however. The defcency payments lose value because the ncrease n demand for corn causes the equlbrum prces of all commodtes to be hgher and drves the defcency payment optons out of the money, reducng ther value. Hgh market prces more than compensate the farmer for the reducton n ths opton value, though. Farmers are better off by $7.4 bllon n the corn market, by $7.1 bllon n the soybean market, and by $8.7 bllon n the wheat market; n total, farmer s net welfare gan from the 2007 ethanol tax credt s $23.2 bllon. Gasolne consumers or blenders receve welfare gans from the ethanol tax credt n an amount equal to taxpayer lablty from the blender s credt, $3.32 bllon. We do not model how much of ths welfare gan s retaned by the blenders and how much s passed through to retal gasolne consumers. However, Du and Hayes (2008) examne the effect of the ethanol ndustry on retal gasolne prces and fnd that ethanol producton has reduced retal gasolne prces by $0.29 to $0.40 per gallon dependng on the regon. Ths suggests that blenders pass at least some of the welfare gans on to retal gasolne consumers. So far the results are all postve concernng the ethanol subsdy; all groups consdered have enjoyed net welfare gans: taxpayers, farmers, and gasolne consumers or blenders. In our analyss, one group collectvely fnances ths transfer. The consumers 14

17 of agrcultural commodtes experence a large welfare loss of $26.9 bllon. The largest losers are foregn users of agrcultural commodtes. Consumers demandng corn, soybeans, and wheat for export had welfare losses of $10 bllon. Next, the domestc lvestock feedng ndustry loses $9.3 bllon n welfare, and the food processng ndustry loses $7.6 bllon. These enttes are ntermedate demanders of agrcultural commodtes, but, assumng these markets are compettve, these welfare losses are passed on to retal consumers. Ths results n an aggregate welfare loss of $597 mllon. We also are able to calculate dstrbutons over the net welfare change smulated n our model (see fgure 4); n our smulaton there s no mass over postve net welfare changes. Ths ndcates that n our model aggregate deadweght losses wll occur wth near certanty. Comparson wth the Exstng Lterature Separatng the welfare effects among producers, taxpayers, and the varous types of agrcultural consumers s a trcky undertakng, and several papers recently address the task. A sde-by-sde comparson of these studes s provded n table 4. The aggregate welfare change estmates range from -$5,733 to $1,281. De Gorter and Just (2008) calculate the welfare effects of the U.S. ethanol tax credt and note that water n the tax credt causes sgnfcant rectangular welfare losses. In ther modelng framework they nclude the corn market wth demand dsaggregated nto foregn and domestc producers, wth the excess supply of corn absorbed by the ethanol ndustry. They then model the fuel market to calculate the effect of ethanol n the domestc fuel market. The fnd net welfare losses from the ethanol tax credt. 15

18 Schmtz, Moss, and Schmtz (2007) calculate the welfare costs and benefts of U.S. ethanol producton, and fnd a postve aggregate welfare gan. The drver of ths result s that whle tax revenue s decreased because of the blender s tax credt, taxpayer labltes are reduced by more than ths amount because subsdes to corn farmers are reduced, but the authors use a determnstc model. They separate out the welfare effects to non-ethanol users of corn between food, alcohol, and ndustral use verses feed and resdual use. Du, Hayes, and Baker (2008) perform welfare analyss focusng on the fuel markets for both gasolne and ethanol on an energy-equvalent bass and the market for corn. They fnd the net welfare effect of ethanol producton to be negatve. Babcock (2008) uses a determnstc model of the ethanol and corn markets, dstngushng demand for corn as comng from feed, food, and exports. A later pece wrtten smultaneously wth ths one by McPhal and Babcock (2008) uses a smlar model but ncorporates uncertanty n corn yelds, corn demand, and ethanol demand. Ths study does not consder cross-market effects wth soybeans and wheat. Gardner (2007) uses a determnstc model of the ethanol market, ncludng corn producers, users of corn ncludng ethanol, feed and exports, taxpayers, ethanol producers, and ethanol consumers. Our study s the only one of those studes consdered here to recognze that a reducton n farm program payments causes a reducton n farmer surplus as well as a decrease n taxpayer cost because the farm program payment s effectvely an opton farmers own and the taxpayer s oblgated to honor. In an aggregate welfare analyss, we 16

19 should nclude ths reducton of farmer surplus from the decreased value of the defcency payment optons they hold before we add back n the beneft that famers receved from hgher prces. Notce also that f we dd not subtract ths decreased opton value from the farmer s surplus change we would calculate a net welfare gan from the ethanol tax credt of $2.5 bllon. Our study s also the frst to nclude the ndrect effect on the nterlnked markets of soybeans and wheat. The range of estmates among these artcles llustrates how senstve welfare studes are to model assumptons partcularly to the structure mposed. A model that assumes a market functonng n solaton wll yeld quanttatvely dfferent results than a model that ncludes market nteracton n a rcher set of lnked markets; every pece left out dstorts the pcture of where transfers are gong, the sze of aggregate transfer, and deadweght loss. For example, notce n our analyss that the sze of transfer from consumers to producers s larger than n the other artcles. Ths s because gnorng the soybean and wheat market effects understates the sze of the dstorton. Even when a gan by one group s a loss n the same amount by another group, t s mportant to record these transfers because of ther mplcatons for polcy decsons. Concluson The U.S. ethanol polcy results n a transfer from consumers of agrcultural commodtes to producers (farmers). Consumers of retal fuel also receve welfare gans, but ths amount s dwarfed by the sze of transfer from consumers to producers caused by the ncrease n equlbrum market prces. Also, we fnd a modest ncrease n taxpayer outlays under the ethanol tax credt. We compare our study wth a survey of several 17

20 recent welfare analyses. Prevous studes left out one or more salent features of these markets; e.g., lnkages among commodty markets n both producton and consumpton and uncertanty n commodty yelds. Includng lnkages among commodty markets s mportant because wth scarce fertle crop ground, ncentves mplemented ncreasng the equlbrum prce of one crop ncreases the equlbrum prce of all crops competng for acreage. We nclude corn, soybeans, and wheat to capture these lnked market effects, and our measure of farmer gan and consumer loss s larger than n the welfare studes to whch we compare our work. Includng multple crop markets also gves a more realstc estmate of the effect to taxpayers through the reduced defcency payment labltes. Also, ncludng uncertanty n crop yelds allows us to better quantfy the reducton n the defcency payment lablty to the taxpayer. 18

21 Endnotes 1 Avalable at Parameters are calbrated to the most recent estmates avalable (2006 crop year). We use fertlzer cost as a proxy for ncreasng margnal cost, κ, and all other operatng costs as constant margnal cost, a. 2 We assume yelds follow a lnear trend. We estmate the trend from yeld data (per harvested acre) for the years 1980 through Avalable at t t t μ = t, μ = t, μ = t corn soybean wheat 3 We estmate the var-cov matrx of the crop yelds from the hstorcal data above as well. 4 The amount of bofuel of type n operaton s gven by n t n bllon gpy. Therefore, δ 0 represents the amount of feedstock used annually by the ndustry. 5 We estmate the relatonshp between the prce of soy ol and soybeans from daly nearest contract prces on the CBOT from Oct. 17, 2005, to Sept. 14, For soybean meal we use daly nearest contract prces of soybean meal and soybeans on the CBOT from Aprl 30, 2007, to March 3, Soy Ol Prce t = t p sb 0.009, R 2 = Soybean Meal Prce t t = ( psb 100), R 2 = The loan rates for corn, soybeans, and wheat are $1.95, $5.00, and $2.75, respectvely (see 19

22 7 In 2007 there were 1.87 bllon bushels of wnter wheat, and 0.55 bllon bushels of sprng wheat produced n the U.S. (see 8 Informaton about the countercyclcal payment program s avalable at Target prces for corn, soybeans, and wheat are $2.63, $5.80, and $3.92, respectvely. 9 Ethanol producton was 6.5 bllon gallons per year n 2007, so n our model we smulate the prce changes from an ncrease to ths producton level. 10 Actual average government expendtures for all support and related programs was $3,437 ml for corn, $384 ml for soybeans, and $2,160 for wheat for the years (see 20

23 References Babcock, B. A Dstrbutonal Implcatons of U.S. Ethanol Polcy. Revew of Agrcultural Economcs 30(3): de Gorter, H., and D. R. Just The Welfare Economcs of Bofuel Tax Credt and the Interacton Effects wth Prce Contngent Farm Subsdes. Amercan Journal of Agrcultural Economcs, n press. Du, X., and D. J. Hayes The Impact of Ethanol Producton on U.S. and Regonal Gasolne Prces and on the Proftablty of the U.S. Ol Refnery Industry. CARD Workng Paper 08-WP 467, Center for Agrcultural and Rural Development, Iowa State Unversty, Aprl. Du, X., D. J. Hayes, and M. L. Baker A Welfare Analyss of the U.S. Ethanol Subsdy. CARD Workng Paper 08-WP 480, Center for Agrcultural and Rural Development, Iowa State Unversty, November (revsed). Gardner, B Fuel Ethanol Subsdes and Farm Prce Support. Journal of Agrcultural and Food Industral Organzaton 5(4). Larson, R., R. Hosteltler, and B. Edwards Multvarable Calculus, 7th ed. Edted by J. Shra. Boston, MA: Houghton Mffln Company. Mas-Colell, A., M. Whnston, and J. Green Mcroeconomc Theory. New York, NY: Oxford Unversty Press. 21

24 McPhal, L. L., and B. A. Babcock Short-Run Prce and Welfare Impacts of Federal Ethanol Polces. CARD Workng Paper 08-WP 468, Center for Agrcultural and Rural Development, Iowa State Unversty, June. Schmtz, A., C. B. Moss, and T. G. Schmtz Ethanol: No Free Lunch. Journal of Agrcultural and Food Industral Organzaton 5(3). Searchnger, T., R. Hemlch, R. A. Houghton, F. Dong, A. Elobed, J. Fabosa, S. Tokgoz, D. Hayes, and T.-H. Yu Use of U.S. Croplands for Bofuel Increases Greenhouse Gases through Emssons from Land Use Change. Scencexpress 319(5867):

25 Table 1. Supply parameters used n Monte Carlo smulaton Corn Soybeans Wheat κ a Table 2. Demand parameters used n Monte Carlo smulaton Corn Soybeans Wheat α α α β β γ γ δ Note: Unts of demand equatons are bllon bushels. 23

26 Table 3. Results for 2007 crop year (mllons of dollars) Corn Soybeans a Wheat Totals Ag Producers Market (+) $8, $8, $9, $26, Lost CCP (-) ($392.60) ($105.19) ($44.00) ($541.79) Lost LDP (-) ($474.23) ($1,206.00) ($948.98) ($2,629.22) Total $7, $7, $8, $23, Ag Consumers Feed (-) ($6,777.74) ($2,608.32) ($9,386.06) (+) $43.80 $43.14 $86.94 total ($6,733.94) ($2,565.18) ($9,299.12) Food (-) ($1,251.92) ($596.66) ($5,785.93) ($7,634.51) Export (-) ($1,702.65) ($4,480.28) ($ ) ($10,004.26) Total ($9,688.51) ($7,642.12) ($9,607.26) ($26,937.89) Gasolne Cons/ Blenders Taxpayers (+) $3, CCP (+) $ $ $44.00 $ LDP (+) $ $1, $ $2, Blender s Credt (-) ($3,315.00) Total $ $1, $ ($143.99) Net Change ($597.25) a Welfare change n the crush market attrbuted to proporton of soybean meal (feed) and ol (food) comng from the soybean crush process 24

27 Table 4. Comparson of recent welfare studes (mllons of dollars) Babcock 2008 Baker 2008 (current study) a de Gorter & Just 2008 Du, Hayes, & Baker 2008 Gardner 2007 McPhal & Babcock 2008 Schmtz, Moss, & Schmtz 2007 Ag Producers Market $14,393 $26,341 $1,484 $14,050 $425 $1,581 $1,154 Lost CCP ($542) Lost LDP -- ($2,629) ($3,508) Total $14,393 $23,170 ($2,024) $14,050 $425 $1581 $1,154 Ag Consumers Feed ($6,126) ($9,299) ($730) ($1,008) ($1,484) Food ($1,251) ($7,635) ($197) ($3,094) Export ($1,955) ($10,004) $ ($276) ($993) Total ($9,332) ($26,938) ($1,051) ($16,170) ($322) ($1,203) ($5,095) Gasolne Cons/ Blenders $2366 $3,315 $1,606 $1,150 $2406 $2,337 $3883 Taxpayers LDP -- $3,171 $3,508 $3, $4,084 Blender s Credt ($13,160) ($3,315) ($3,330) ($3,260) ($2,600) ($1,391) ($2,761) Total ($13,160) ($144) $178 $190 ($2,600) ($1,391) $1,323 Net Change ($5,733) ($597) ($1,291) ($780) ($91) ($568) $1,281 a Includes soybean and wheat market calculatons as well as corn, whereas the other studes only consder corn. 25

28 Q Q 0. 8 Q dsb, t dsb, t dsb, t crush ol l sbmeal sb α ( ) ( ) sb d 1 2 sb, t sb t t α l sbmeal = α 0 c sbmeal Q p p = + dsb, t t β ( ) 1 Q f ol = β 0 psbol Q = Q + Q dsb, t dsb, t dsb, t ol f ol e ol dsb, t dsb, t dsb, t sb, Q = Qcrush + Qx Q = δ n d t t e ol sb sb Q = γ γ ( p ) 1 sb dsb, t sb t x 0 sb Fgure 1. Relatonshp of aggregate soybean demand to all of ts components 26

29 + p c E p c NE D crush D export D crush Q E-export Q NE-export Q E-crush Q NE-crush Fgure 2. DWL n the soybean market dstorton and cross-market effects 27

30 $2.00 $1.80 $1.60 Payment to farmer $1.40 $1.20 $1.00 $0.80 $0.60 $0.40 $0.20 $0.00 $0.00 $1.00 $2.00 $3.00 $4.00 Market Prce of Commodty CCP LDP Total Payment Note: Corn market s depcted wth a $1.95 loan rate, $2.63 target trce, and $0.28 drect payment. The CCP s made on 85% of base acres, and LDP s made on actual producton. To make ths fgure we calculate the total payment usng on the same quantty of gran for CCP and LDP payments. Fgure 3. Defcency payments to farmer as a functon of market prces 28

31 Fgure 4. Dstrbuton of net welfare change from the ethanol blender s credt (mllons of dollars) 29