Research Division Federal Reserve Bank of St. Louis Working Paper Series

Transcription

1 Reearch Diviion ederal Reerve Bank of St. Loui Working Paer Serie Biofuel Subidie and International Trade Subhayu Bandyoadhyay Sumon Bhaumik and Howard J. Wall Working Paer B htt://reearch.tlouifed.org/w/2009/ df October 2009 Revied Setember 2012 EDERAL RESERVE BANK O ST. LOUIS Reearch Diviion P.O. Box 442 St. Loui, O The view exreed are thoe of the individual author and do not necearily reflect official oition of the ederal Reerve Bank of St. Loui, the ederal Reerve Sytem, or the Board of Governor. ederal Reerve Bank of St. Loui Working Paer are reliminary material circulated to timulate dicuion and critical comment. Reference in ublication to ederal Reerve Bank of St. Loui Working Paer (other than an acknowledgment that the writer ha had acce to unublihed material) hould be cleared with the author or author.

2 Biofuel Subidie and International Trade Subhayu Bandyoadhyay ederal Reerve Bank of St. Loui and IZA, Bonn Sumon Bhaumik + Aton Univerity, UK, and IZA, Bonn Howard J. Wall $ Lindenwood Univerity, O Setember 21, 2012 Abtract Thi aer exlore otimal biofuel ubidie in a general equilibrium trade model. The focu i on the roduction of biofuel uch a corn-baed ethanol, which divert corn from ue a food. In the mall-country cae, when the tax on crude i not available a a olicy otion, a econd-bet biofuel ubidy may or may not be oitive. In the large-country cae, the twin objective of ollution reduction and term-of-trade imrovement jutify a combination of crude tax and biofuel ubidy for the food exorter. inally, we how that when both nation engage in biofuel olicie, the term-of-trade effect encourage the Nah equilibrium ubidy to be oitive (negative) for the food exorting (imorting) nation. JEL Code: 1, H2, O1 Keyword: Biofuel Subidy, Pigouvian Tax, Pollution Externality Correonding author: Reearch Diviion, ederal Reerve Bank of St. Loui, PO Box 442, St. Loui, O , USA. bandyoadhyay@tl.frb.org; Tel: Economic and Strategy Grou, Aton Buine School, Aton Univerity, Aton Triangle, Birmingham B4 7ET, United Kingdom. .bhaumik@aton.ac.uk; Tel: $ Economic Deartment, Lindenwood Univerity, 209 S. Kinghighway, St. Charle, O 63301, USA. HWall@lindenwood.edu; Tel:

3 1. Introduction 1 The literature on trade and the environment ha roceeded largely along two ath. One trand of the literature ha examined the imact of trade itelf on ollution (ee Coeland and Taylor; 1994, 2003). It ha highlighted the fact that by fotering economic growth, trade can have two ooing effect on environmental quality. On the one hand, the higher outut reulting from trade would contribute to ollution (the cale effect). 2 On the other hand, higher income would reult in greater demand for a cleaner environment and might, therefore, reult in the adotion of ollution-reducing technologie (the technique effect). 3,4 A econd trand of the literature ha modeled trategic interaction between two trading artner. An imortant concluion drawn by thi line of inquiry i that, contrary to oular widom, it might not be otimal for a government to imoe weak environmental tandard on dometic indutrie to give them a cometitive advantage. Strict tandard might intead be otimal if firm comete in rice (Barrett, 1994). 5 A olicy iue that ha been central to environmental olicy in the United State, among other nation, relate to biofuel. The ue of cro uch a corn to make ubtance like bioethanol ha everal imlication, including reduced reliance on oil imort from otentially unreliable trade artner and a moving to cleaner ource of energy. While our analyi can be 1 We thank an anonymou referee for helful uggetion. The uual diclaimer alie. 2 If, however, ollution quota are enforced through the iuance of a fixed number of ollution ermit, the environmental imact of trade liberalization might be negligible. urther, it can be hown that if ollution taxe are adjuted to equate the marginal cot of ollution with the marginal benefit of the aociated roduction, the net imact on ollution i indeterminate (Loez, 1994; Raucher, 1997; Coeland and Taylor, 2003). 3 Emirical evidence ugget that the effect of riing income might be the tronger driver of the trade-environment relationhi, reulting in a oitive imact of trade on environment in higher-income countrie (rankel and Roe, 2005). 4 See Antweiler et al. (2001). 5 A related iue i trade in hazardou ubtance, which can have a direct negative imact on the environment of the imorting nation. A recent aer by Bagg (2009) rovide an emirical analyi of thi iue, where the focu i on country characteritic that determine trade in hazardou material. Alo, ee Dean (1992), for a urvey of iue that ertain to uch trade. 1

4 adated to addre the firt iue, in line with the trade and environment literature we chooe to focu on the econd. Thi i an imortant iue given the longtanding government uort for biofuel and the dramatically increaed diverion of the US corn cro into ethanol roduction (igure 1). In 1980, about one-half of a ercent of US corn roduction wa ued to roduce ethanol, but by 2009 thi hare wa 33 ercent, having rien more than five-fold between 2000 and ore recently, on October 13, 2010, the US Environmental Protection Agency (EPA) raied the 30-year-old ca of 10 ercent ethanol blend in fuel for ordinary car to 15 ercent (known a E15) for model 2007 onward (Power, 2010, and Wald, 2010). The imlementation of thi new rule ha coincided with riing corn rice and evere drought, which highlight how the effect of biofuel olicy do not occur in a vacuum. One of the central contribution of thi aer i to rovide a general equilibrium model that hel u to analyze uch linkage, which, in turn, hel to enlighten olicy. The ue of biofuel cannot be dicued in iolation from two related iue. irt, it i generally acceted that the growth of the biofuel indutry in all countrie excet Brazil, where it ha attained cale economie, i contingent on ignificant ubidy. 6 Second, given the energy inefficiency of biofuel, an aggreive trategy to romote it ue can lead to a ignificant increae in the world rice of food item. 7 Among other roblem, thi econd iue can be 6 In the United State, where bioethanol roduction i corn baed, the break-even rice for etroleum i $54 er barrel, and in Euroe, where bioethanol roduction i wheat baed, the break-even rice i $72 er barrel (Laron, 2008). The US government rovide a ubidy of 51 cent er gallon to roducer of bioethanol. In Germany, where the growth of the roduction and ue of biofuel wa among the fatet in EU member countrie, biofuel roducer not only enjoy a 35 ercent tax advantage vi-a-vi the roducer of traditional fuel, but the tate alo ubidize contruction of biofuel roduction unit u to 50 ercent. 7 or examle, corn-baed ethanol ha 57 ercent energy efficiency while etroleum ha 81 ercent efficiency. OECD (2006) etimate ugget that, to account for 10 ercent of vehicular fuel, ercent of the current cro area in the US, Canada, and the EU-15 countrie would have to be devoted to cro that can be ued to roduce ethanol. 2

5 quite devatating for the develoing nation. 8 Develoed countrie would be affected alo if, a rojected, there i a tee increae in the rice of tale item like corn and wheat. Such rojection clearly warrant a dicuion about the efficacy of oting for biofuel ubidie. 9 The uroe of thi aer i to rovide a benchmark to think about biofuel ubidie within the context of international trade and ollution, where trade olicie cannot be ued due to conflict with WTO rule. Pollution i treated here a a global ublic good becaue foil fuel contribute (arguably) to atmoheric change. To imlify the analyi we treat a homogeneou food item like corn to have two otential ue. The firt i direct conumtion a food. The econd i to ue a an intermediate inut in the roduction of energy. The other intermediate inut ued to roduce energy i crude oil. Energy itelf i treated a a non-traded commodity becaue of difficultie in hiing it acro large ditance. The focu of the analyi i on two nation, one of which (ay US) exort corn, while the other (ay China or Brazil) imort corn in exchange for manufacturing exort. The uly of crude come from a third nation (ay the iddle Eat), which i blackboxed here through the aumtion that the rice of crude i fixed Runge and Senauer (2007) have argued that by uhing u the rice of cro that are tale for the world oor oulation, by 2025 biofuel could nearly double the number of eole who are chronically hungry. 9 By contrat, the dicuion in the trade and environment literature largely involve olicie that either ca ollution through fiat and ermit or raie the cot of roducing the olluting good (ee Coeland and Taylor, 2004, for a dicuion). 10 Thi aumtion imlifie the analyi coniderably. or examle, even in a imle model like Bhagwati et al. (1983) where there are two good (and hence a ingle relative rice) and free trade, the introduction of a third, nonarticiant, nation can generate rice amlification and tranfer aradoxe that do not arie in two-country model. Our model, although not terribly comlicated, ha an additional traded intermediate inut (hence, two relative rice to be otentially determined by the world market), a non-traded good, and everal olicy variable. Endogenizing the rice of crude in even our imle tructure would add everal layer of comlexity. Given that the oint of our aer i to conider how biofuel olicie affect food rice, and not to analyze foil fuel rice, our aumtion i a tractable comromie. Of coure, one can alway look at the effect of foil fuel rice change in our model by conducting comarative tatic exercie. The outline of uch an analyi i reented in ection C of the aendix at the end of thi aer, for the cae of Laiez aire. inally, we refer the reader to an imortant aer by Laan and ochini (2009) which doe analyze multile relative rice. They ue ome functional earability aumtion and quai-linearity to achieve tractability, although their general equilibrium ectoral tructure i quite different from our. 3

6 Conequently, the term-of-trade that we conider i between food and manufacturing, where the latter i treated a the numeraire good. To kee the analyi imle, we aume that the ue of crude in energy roduction i olluting, while the ue of corn in making energy i not. 11 The analyi roceed in three art. In the firt, we conider a mall oen economy facing given rice of all the traded good. The only market failure here tem from the ollution externality created by crude ue in energy roduction, which can be corrected by an aroriate tax on crude. If the tax on crude i not available becaue of olitical economy conideration, the econd-bet olicy may be a tax rather than a ubidy on biofuel. Thi reult comlement and extend the finding of Vedenov and Wetztein (2008) and Khanna et al. (2008), who have alo noted thi oibility in other context. We dicu the difference between our analyi and their reective aer in the next ection. 12 At thi oint, it i alo worthwhile to note that the widom of biofuel ubidization ha alo been quetioned by Grafton et al. (2010). Uing a dynamic model, they how that biofuel ubidie may increae the rate of foil-fuel extraction, and thereby make otential climate-change damage more imminent. The econd art of thi aer deal with the cae where the term-of-trade for food i endogenou to the ytem. In thi context, we conider welfare-maximizing crude tax and biofuel ubidy combination for the food-exorting nation (the other nation i aumed to be aive). The tax on crude deart from the Pigouvian level, becaue in addition to targeting ollution it alo affect the term-of-trade of food by raiing the demand for corn to be ued a a ubtitute for crude in energy roduction. In addition, a biofuel ubidy i alo ued to 11 Thi aumtion kee the analyi clean without acrificing the baic thrut of our reult a long a crude ue i aumed to be more olluting than biofuel ue. The oint of thi aer i not to jutify bioethanol olicie, but to ugget that even if they are clean, they can till be miued comared to firt or econd-bet benchmark. Of coure, if they are more olluting than crude, then our argument about oible miallocation caued by uch olicie are trengthened. 12 Alo ee de Gorter and Jut (2010) in thi context. 4

7 comlement the term-of-trade imroving imact of the crude tax. 13 Effectively, in a world where beggar-thy-neighbor trade olicie cannot be ued becaue of WTO rule, a tax on crude and a biofuel ubidy may erve a imilar uroe. When the food exorting nation ue biofuel ubidy to imrove it term of trade, the food imorting nation uffer. However, the food imorting nation can alo ue it biofuel ubidy to counter thi advere term-of-trade movement. Thi trategic interdeendence of biofuel olicy ha not yet been analyzed in thi literature. Our aer i the firt to cat thi roblem in the context of a Johnon (1953) tye Nah olicy equilibrium, which i augmented to conider ollution a a global ublic good. Intead of uing imort tariff or exort taxe, the nation ue biofuel ubidie to target both ollution and term-of-trade. When a ubidy i warranted by the ollution motive, the term-of-trade motive comlement it for the food exorter. In contrat, for the food imorter, the term-of trade motive ull the biofuel ubidy below the level uggeted by the ollution motive. 2. The Benchmark Cae: A Small Oen Economy Let u conider a mall oen economy with rereentative conumer. Each conumer maximize utility given by U U(, E,, G), where, E,, and G are conumtion level 13 Laco and Khanna (2009) analyze term-of-trade effect of biofuel ubidie. However, their context i one of an ethanol imorting nation, where a biofuel ubidy lead to a term-of-trade lo. Of coure, in uch a etting there i no incentive to ubidize biofuel urely for term-of-trade reaon. In contrat, we want to highlight the gain of US corn farmer from a higher rice of corn in the world market. Hence term-of-trade gain i an integral motive of biofuel ubidization in thi aer. Laan and ochini (2009) alo analyze biofuel ubidie in a trade model. While thi aer comlement their analyi, we have ome imortant difference. irt, the functional earability aumtion in their aer eal off many of the interectoral linkage that we conider. Second, the fuel tax that they conider i a tax that dicourage ue of both foil fuel and ethanol (i.e., it i imoed on the blend). Thu, a rie in their fuel tax will reduce the demand for ethanol. In contrat, the burden of our foil fuel tax fall excluively on the ue of foil fuel a an inut in energy roduction. Thi caue ubtitution toward biofuel (a an inut in energy), and raie the demand for biofuel/corn. In turn, thi confer term-of-trade benefit to the food exorting nation. inally, a major difference between our model i that we conider a three nation context, where two nation imort crude from a third nation, and both of thee nation engage in biofuel olicy. The trategic interdeendence in biofuel olicy that arie in thi context i novel to the literature and comlement the aforementioned aer. 5

8 of food, energy, a manufactured good, and clean environment, reectively. i the numeraire good. If i the rice of food and q i the rice of energy, the exenditure function i ~ ~ ~ e(, q,1, u, G) in qe, ubject to u U(, E,, G), (1) which yield the uual Hickian demand function. In addition, e u 0 14 and e e U In thi economy, all commoditie are roduced uing contant return to cale (CRS). ood () i roduced uing labor ( L ) and land (T ). Auming that land i ecific to food and that it endowment i given, we have ( L, T) f( L ), where f (.) 0 and f (.) 0. (2) Cometitive rofit maximization enure that w f '(.), imlying that L L (, w). Similarly, the manufactured good i roduced uing labor ( L ) and energy ( E ): ( L, E ). (3) The rofit maximization condition are w ( L, E ) and q ( L, E ). Labor uly i given at L, uch that L E G u G L L L. 16 (4) inally, energy i roduced uing food for biofuel (B) and crude oil (R) our roxy for foil fuel. 17 All of R i aumed to be imorted at a given rice r: 14 Throughout the aer we ue the convention that unle ecified otherwie, i and ij are, reectively, the firtand econd-order artial derivative of any function ( x i, x j ). 15 Conider quai-linear reference and earability of G: U (, E ) ( G). The exenditure function aociated with thi utility function i: e(, q, u, G) (, q) qe (, q) u [ (, q), E (, q)] G, which imlie e (, q), e E(, q) q, eu 1, eg ( G) 0, and eu equ The roduction tructure in thi model i omewhat imilar to arjit et al. (2007), in that a olicy induced wage rie in the manufacturing ector mut have a negative effect on the landowner in the agricultural ector, who own an immobile fixed factor. 17 Biofuel B in our model i jut corn ued a an intermediate inut for roduction of energy E. The um of B and the conumtion demand for corn (food) i the total demand for corn in thi economy. Thu, corn can either be an exortable or an imortable in the mall oen economy cae, deending on the underlying roduction and conumtion arameter that define thi economy. In the large country cae analyzed later, we aume that the third 6

9 E E( B,R ). (5) The function E( B, R) i a tandard roduction function in the inut B and R, with diminihing marginal rate of ubtitution, uch that one can imerfectly ubtitute B for R along a given energy ioquant. We hould note that R i not directly conumed it i a ure intermediate inut in roducing energy. Thu, there i no direct relationhi between R and B in conumtion. However, energy and food are both conumed, and our exenditure function allow for ubtitutability or comlementarity. Thu, although there i no direct relationhi between B and R on the conumtion ide, their effect on food or energy rice will lead to cro-effect between food and energy conumtion. inally, we note that the rofit-maximization condition in the energy ector equate the net inut rice of B and R to the value of their marginal roduct. The environment here i treated a a global ublic good, where carbon emiion lead to global ollution. Carbon emiion occur at the energy roduction tage, and, conitent with a view of biofuel a being cleaner, we aume that crude i olluting but that biofuel i not. 18 Let R be the amount of crude ued in the foreign nation. Clean environment i a decreaing function of the amount of global crude ue, uch that G G R R, G. 0. (6a) urther, noting that in the mall country cae the amount of crude ued by the ret of the world ( R ) i taken a given by the dometic nation, (6a) reduce to country neither roduce nor conume corn. Thu, the firt two nation (Home and oreign) have to balance the world market for corn. Without lo of generality, we have aumed there that corn i an exortable for the home country and, thu, an imortable for the foreign country. 18 An alternative would be to rooe that global ollution i a function of biofuel and crude, with biofuel being relatively le olluting. Our olar aumtion coniderably imlifie the analyi without comromiing the baic meage that can be drawn from it. 7

10 G G R, G( R) 0. (6b) The exenditure-revenue identity for thi economy (equivalently, it trade balance equation) i e(, q,1, u, G) f ( L ) ( L, E ) qe( B, R) B rr qe. (7) Given the difficultie in trading energy in it final form over long ditance, we aume that E i a nontraded good with it rice determined by the zero rofit condition: q C(, r,1), (8) where C (.) i the unit cot of roducing energy. The aumtion of CRS imlie that qe B rr 0. Subtituting thi exreion in (7) and uing (8), total differentiation of (7) yield du eg G 0. (9) dr e u It i clear from Eq. (9) that the cometitive Laiez aire equilibrium i not ocially otimal in the ene that a mall reduction in R will raie the utility of the rereentative agent of thi mall oen economy. Thi i the tandard market failure outcome where energy roducer do not have to ay for the cot of ollution that they create. The next ection exlore the different olicy otion available to correct thi ditortion. 2.1 Otimal Subidy on Biofuel and an Otimal Tax on Crude Suoe that the government ubidize the ue of biofuel (B) uch that it inut rice in energy roduction, net of ubidy, i. Alo, aume that the government ue a tax t on crude, o the dometic rice of crude i r d r t. 19 Uing (8), 19 Given the roduction function decribed in Eq.(5), where we aume a diminihing marginal rate of ubtitution between the two inut, a rie in either t or will raie B and reduce R through the ubtitution effect, although the effect on outut effect will differ. rom (10) it i evident that the ubidy will reduce the rice of energy, while the 8

11 d B R q C(, r,1) q q(, t), q, and qt E E. (10) Under CRS, qe B rr B tr. Uing (7) and (10) we get u G edudb t eg dr, (11) where the firt term on the right-hand ide i the lo due to the ditortion in inut ue, and the econd term i the net benefit due to the reduction of crude ue. rom (11), the otimal ubidy condition i Uing (12), e u u 0 ot R ( t egg). 20 (12) B u RB t ot RBt eu ( teg G ) Rt 0t eg G 0, auming R t 0. (13) t B B Notice that eg G meaure the amount of the numeraire good that the conumer will need to be comenated for a unit rie in R (and hence ollution). Therefore, uing (12) and (13), it i clear that the otimal crude tax i the Pigouvian tax, which equal the marginal damage from ollution. Alo, when thi tax i in lace, the otimal biofuel ubidy i zero. In thi mall oen economy, the only ource of market failure i the environmental externality of crude roduction. An aroriate tax i enough to rectify thi failure, and no other intrument i neceary. Thi i a ueful benchmark for the analyi and reult below, where we extend the model to conider crude tax will raie the energy rice. A the crude tax raie the rice of energy, the quantity of energy demanded will fall, reducing the cale of roduction. Thi outut effect may or may not offet the rie in biofuel demand becaue of the ubtitution effect. However, demand for crude will urely fall. By analogou reaoning, the biofuel ubidy will urely raie the ue of biofuel, but may or may not raie crude ue. Thi iue i analyzed in detail in ection 2.2, where equation (19) through (22) rovide the relevant mathematical roof. 20 Part B of the aendix derive R, R t, B, and B t for both the mall- and the large-country cae uing a quailinear utility function that i alo earable in G. Thi rovide a tractable examle, and there i no lo in generality. Indeed, the analyi in the text i for general utility function. Detail of derivation for the general cae, which allow for income effect, are available from the author on requet. 9

12 ituation where either a tax i not available a an intrument or other externalitie exit (uch a a term-of-trade externality) that the tax intrument cannot addre fully. 2.2 Second-Bet Biofuel Subidy (when a crude tax i not feaible) A tax on crude might not be available a a olicy intrument, erha becaue of the country olitical economy. 21 On the other hand, the reence of a trong agricultural lobby can make biofuel attract olicy attention. Conider ethanol roduced from corn, which i mixed with crude to make the final fuel. Although the efficiency of making corn-baed ethanol i quetionable, it i quite oular in the United State becaue it i good for the corn belt tate like Iowa and inneota and draw uort from both the agricultural and ethanol roducing lobbie. 22 The analyi below decribe the biofuel ubidy a a econd-bet intrument. Uing t 0 in (11), e u u 0 SB R egg, (14) B where SB i the econd-bet biofuel ubidy. Note that R C (.) E dr C (.) de EC (.) d. (15) r r r Alo, total energy ue mut equal the amount ued a an inut in the manufacturing ector lu the amount ued directly in conumtion: 21 While ection 2.2 conider the olar cae where a tax on crude i not allowed, it i not difficult to adat it to cae where uch taxe are allowed but olitical comulion limit their level. In uch a cae, the tax may be retricted to not exceed a level t max, uch that t tmax egg. Uing Eq. (11) it i clear that in uch a cae a biofuel ubidy i otentially welfare imroving. The cae analyzed here i one where t max 0, and it facilitate exoition, without acrificing anything critical. urthermore, the aer doe conduct a careful analyi of the crude tax in ection 2.1 and 3.1. Although we do not urue an exlicit olitical economy analyi in thi aer, it i oible to do o along the line of redrikon (1997) and other. 22 See, for examle, Power (2010), which tate The caue of booting ethanol ue in car ha been trongly chamioned by Growth Energy, an ethanol trade grou led by Weley Clark, the retired army general and 2004 Democratic reidential candidate. 10

13 Uing (15) and (16), E e, q( ),1, u, G( R) E (, q) q 23 de e E dq e du e GdR. (16) qq q qu qg qq q r qg qu, where, CGe r qg de e E q EC e G d e du 1 1. (17) Uing (10), note that when t 0, q q() and q B E 0. Uing thi fact, along with (15) and (17), we have Aq Z d Ydu, dr (18) where A ( e qq Eq ) Cr 0, Z EC r 0, and Y equcr. 24,25 At the utility-maximizing, du 0 and R Aq Z. (19) ollowing a imilar et of te a above, we can comute the imact on food demand of a biofuel ubidy: A q Z d Y du, db (20) where A C ( e E ) 0, Z E( C e GC C ) 0, 26 and Y e C. Once qq q qg r again, at the utility-maximizing ubidy rate, du 0 and B A q Z 0. (21) Uing (19) and (21) in (14) (i.e., after taking into account the imact of the ubidy on the ue of crude and the demand for biofuel for energy roduction), the econd-bet ubidy i qu 23 The zero rofit condition in manufacturing i C ( w, q,1) 1. Thi imlie that w w( q) and that E w( q) L. Uing (2) and (4),, ( ) L L w q L (, q ). Thu, E E (, q ). e U e e U i mall. 24 It can be hown that A < 0 if < 0, which i the cae when 25 Note that in the two-inut cae, concavity of the cot function require that the cro effect i trictly oitive. 26 We aume here that the environment-generated income effect on energy demand (i.e., e qg ) i ufficiently mall, uch that the own-rice effect C dominate. qg G qu u Gq 11

14 Aq Z SB egg Aq Z 0 iff Aq Z R 0. (22) Prooition 1: In the abence of a tax on crude, the econd-bet olicy i to ubidize the ue of biofuel if and only if the cro inut ubtitution effect in energy roduction overcome the ubidy cale effect via a reduction in the rice of energy. The term Aq cature the cale effect of the ubidy on crude demand, while Z i the cro-ubtitution effect between the two inut in energy roduction. The latter effect i eay to undertand. The biofuel ubidy reduce the relative rice of biofuel, thereby roviding an incentive to ubtitute biofuel for crude in the roduction of energy. It magnitude deend on the elaticity of ubtitution between the two inut. Conider now the cale effect. The ubidy reduce the net inut rice of biofuel. Thi i aed on a a reduction in energy rice, which timulate the aggregate demand for energy, which in turn raie roduction (the cale effect). The net imact of thee two effect i ex ante ambiguou and i determined by demand-ide arameter and the aforementioned elaticity of ubtitution. If technology i Leontief tye, for examle, the cro-ubtitution effect will diaear altogether. In uch a cae, the demand for crude would unambiguouly increae with a ubidy, and a government that aim to imrove environmental quality hould tax biofuel rather than ubidize it. It i imortant to note that both Vedenov and Wetztein (2008) and Khanna et al. (2008) find imilar reult. The model analyzed by Vedenov and Wetztein (2008) i analogou to our ecial cae where technology i of the Leontief tye. Thi i becaue their equation (3 ) fixe the ratio in which ethanol mut be ued with foil fuel to cater to aggregate fuel conumtion, which rule out ubtitution between ethanol and foil fuel. In contrat, the rimary role of the 12

15 biofuel ubidy in our model i to reduce the relative rice of uing corn a an inut in energy roduction, which make the role of inut ubtitutability central to our analyi. Khanna et al. (2008) i cloer to our modeling. irt, they acknowledge the role of inut ubtitutability through a CES roduction function for energy, where the inut are gaoline and ethanol. Then they how that an ethanol ubidy may raie or reduce emiion, becaue the ubtitution toward ethanol may be offet by the increae in mile driven becaue of the rice reducing effect of inut ubidization. There are imortant difference between our analye. irt, we conider ue of energy not only for conumtion but alo a an inut in the manufacturing ector. Thi amlifie the cale effect, becaue cheaer energy not only ur conumer demand but alo make indutrie more energy intenive (thi how u a the term Eq in Eq. (16) and in the analyi following it). Another difference i an exlicit recognition of the feedback income/ollution effect of ubidization. or examle, the econd term on the right-hand-ide of Eq. (16) account for change in the demand for energy from direct income change (given ollution), while the third term relate to ollution induced change in demand (for a given u). inally, at the heart of our analyi i the dual ue of corn a inut into energy roduction and a final conumtion good (i.e., food). Thi allocation i affected when the biofuel ubidy affect the rice of food. While rooition 1 i derived under the aumtion of a contant food rice (mall oen economy aumtion), thi aumtion i relaxed tarting from the next ection. In uch a context, a rie in corn rice due to a greater demand for corn will move the relative rice of food againt dometic conumer. The reulting ubtitution in conumer demand toward energy will further amlify the harmful cale effect of the ubidy. Thee are all ditinct inight that comlement the exiting literature. 13

16 3. The Large-Country Cae The mall-country aumtion retained u to thi oint require that the rice for food (i.e., ) i given exogenouly by the world market. An imortant iue regarding biofuel ubidie i that they encourage alternate ue of food roduct, thu reducing the net availability of food and raiing it rice in the global market. Thi iue can be modeled in the context of a large oen economy where the food rice i endogenou. If the ubidy raie the net global demand for food, it international rice will rie, conferring term-of-trade gain to the foodexorting nation. In addition, following the logic of the reviou ection, uch a ubidy will alo affect ollution. Suoe that there are three nation: home, foreign, and the ret of the world (ROW). The home country exort food to the foreign country and imort a manufactured good from it. It alo imort crude from the ROW at a given term-of-trade r and ay in term of the manufactured good (the numeraire). Thu, the home trade balance require that the value of it food exort mut equal the value of it net imort of the manufactured good. The latter equal the um of home conumtion of the manufactured good and it ayment to the ROW for crude, net of home roduction of the manufactured good. Analogouly, the foreign country net exort of the manufactured good equal it roduction minu the um of it conumtion demand and ayment to the ROW (for crude). inally, the ROW i aumed to not have any dometic conumtion of crude, and it only role in the model i to rovide crude to the home and foreign countrie in exchange for the manufactured good. 27 Home and foreign trade balance condition are, reectively, X ~ ~ rr and X rr, (23) 27 Thi tructure lend tractability to the model. Admittedly, allowing for rice of crude to be endogenou and for the ROW to conume crude are realitic aumtion, but they come at the cot of comlicating an already-comlex analyi. The central oint that we make are intuitive and can be made without adding to the model comlexity. 14

17 where X f e B and X f e B are their net exort of food Otimal Policy: The One-Sided Cae Thi ubection conider otimal olicy choice for the home nation, where the foreign nation i aive (i.e., when t 0 ). In the reence of a home tax t on crude and a ubidy on biofuel, the home exenditure-revenue relationhi i e(, q,1, u, G) f ( L ) ( L, E ) qe( B, R) B rr qe. (24) Noting that in the large-country cae We differentiate (24) to get R i endogenou, (6) ha to be relaced by G G R R ( ). edu XddB teg dr egdr (25) u ( G ) G. Equation (25) i imilar to (11) in the mall oen-economy cae, with two imortant difference. The firt i the term-of-trade effect, which i catured by the firt term on the right-hand-ide of (25). Home utility will rie to the tune of a rie in the rice of food (i.e., d ) weighted by it level of food exort (i.e., X). The econd critical difference (comared with the mall-country cae) i that when the home country affect, it affect the foreign country net inut rice of biofuel a well. In turn, thi change aumed to be aive, R, and hence G. Given that the foreign government i edu X degdr and W u G R W R R, (26) where W R i global crude ue. 29 The market-clearing equation for food i f f e B e B X X 0, (27) 28 Note that roduction and conumtion tructure in both nation are the ame a in ection 2. The notation i imilar, excet that an aterik refer to the foreign country. 29 We relax thi aivity aumtion in the next ubection, where both nation may ue biofuel ubidie. 15

18 which imlie that (, t). 30 (28) Uing (25) and (28), the otimal ubidy and tax level are ot X e GR R ( e GR X ) R G t G t t BR RB t t, BRRB 0 ; (29a) t t t B e GR X. (29b) ot. ot t G t t egg Rt Prooition 2: A large oen-economy otimal tax on crude will deart from the tandard Pigouvian tax of the mall oen-economy cae. 31 Alo, even if an otimal tax on crude i in lace, the otimal biofuel ubidy may be nonzero. It i clear from an inection of (29a) and (29b) that even if an otimal crude tax i in lace, a biofuel ubidy i till required. Conider for exoitional uroe the cae where zero and i oitive. In thi cae, auming that oitive if and only if the term X i larger than B i oitive, 32 the otimal ubidy i G RS i egr. The term X i the tandard termof trade effect, while egr i home utility lo from increaed crude ue (and ollution) by G the foreign country, induced by a rie in the rice of food (and hence the rice of biofuel) due to home ubidization. Thee two effect are novel to the large-country cae and exlain why the 30 The term-of-trade effect are analyzed by uing a quai-linear utility function that i alo earable in G. Thi erve a a tractable examle and doe not comromie the generality of our reult. 31 Laan and ochini (2009, dicued earlier) alo how that a tax on fuel will deart from it Pigouvian level. However, the role that their fuel tax lay i quite different. Their tax imrove the nation term-of-trade in crude imort, and dicourage both ethanol and foil fuel ue. In contrat, we aume a fixed foil fuel term-of-trade, while our tax encourage ubtitution toward biofuel (a an inut into energy), and raie the demand for biofuel/corn, conferring term-of-trade benefit in term of food exort. 32 In the aendix we how that while B i necearily oitive in the mall-country cae, there i ome ambiguity in the current context. 16

19 otimal biofuel ubidy here deart from the zero level of the mall-country cae dicued earlier. In the mall-country cae, the only role of the biofuel ubidy i to target the dometic crude level ( R ). When an otimal crude tax i in lace, there i no reaon to ue the ubidy. Thi i not true in the large-country cae. Even if the effect of a biofuel ubidy on dometic crude ue i zero (i.e., if R 0 ), there are till gain from uing a biofuel ubidy. Turning to the otimal tax on crude, it i clear from (29b) that the exreion for the otimal tax here i different from eg G (which wa the otimal tax level in the mall-country cae). The exreion differ becaue the tax here ha three additional effect. irt, it affect the ue of biofuel and therefore the burden of the ubidy to the extent B t ot.. Second, by changing, the rice of crude relative to the net inut rice of B i affected in the foreign nation. If thi lead to an increae in foreign crude ue (i.e., if R 0 ), then home utility i reduced. t inally, if the tax raie the rice of food (i.e., if t 0 ), then the home nation gain to the tune of X t Nah Biofuel Subidie Here we conider a cenario in which a crude tax i unavailable a a olicy intrument, although home and foreign can both ue biofuel ubidie. 34 Each nation ubidy affect the net global demand for food and, hence the common international rice of food. Therefore, each 33 The exreion for t i in the aendix. Suffice it to note here that a tax affect the net global demand for food through variou channel, including the ubtitution of biofuel for crude in energy roduction when crude become more exenive. Thi effect by itelf will tend to raie demand and the rice of food, but there are countervailing effect. or examle, the tax raie the inut rice for energy roduction, in turn raiing the energy rice. Thi will tend to reduce energy demand, which will reduce the derived demand for biofuel. or detail, we refer the reader to the aendix. 34 Thi aumtion lend tractability and allow u to focu better on the role of interdeendence between nation in their choice of biofuel ubidie. Thi i a relatively mall acrifice to make, becaue the fundamental inight of uing a crude tax and biofuel ubidy combination have already been dicued. 17

20 country biofuel ubidy affect the other utility, raiing trategic conideration for both nation. We aume that the nation lay Nah in the ene that each take the other ubidy rate a given when chooing it own utility-maximizing ubidy. The market-clearing equation (27) yield Uing (24) and (30), (, ). (30) W eu X B egr. (31) u G Auming B 0 (ee the aendix for detail), the Nah utility maximizing ubidy i W X e GR 0, iff X B Nah G e GR. (32a) W G Analogouly, we can derive the foreign ubidy rule. In addition, uing X X, we get X e GR 0, iff X W Nah G B e GR (32b) W G The detail of the term-of-trade effect ( and ) are analyzed in the aendix. Suffice it to ay here that one of the rimary effect of a biofuel ubidy i to encourage the ue of biofuel intead of crude. Thi increae the demand for food (a biofuel) and raie it rice regardle of which country i roviding the ubidy. Thu, both and are likely to be oitive. On the other hand, there i an aymmetry in the term-of-trade effect on the utility of the two nation, becaue while home i an exorter of food (i.e., X > 0), foreign i an imorter (i.e., X X 0 ). irt, conider the cae where W R i negative. Home ubidization reduce global ollution, and thi benefit, couled with the term-of-trade gain, ugget that the Nah ubidy in (32a) i oitive. On the other hand, if the cale effect make W R oitive, the termof-trade motive and the ollution-reduction motive conflict and a ubidy might or might not be 18

21 jutified. Uing (32b) we can ee that analogou conideration ugget that the foreign country, which uffer from a term-of-trade lo when it ue a biofuel ubidy, will ubidize only if it W ubidy reduce ollution (i.e., only if R 0 ). The foreign country will chooe a ubidy if the aforementioned neceary condition i met, and if the ollution-reduction effect dominate the advere term-of-trade effect that the foreign nation imoe on itelf. It i eay to ee from the dicuion above that term-of-trade conideration might lead the home country to chooe a biofuel ubidy even when it increae ollution, and converely, the foreign country may chooe a tax even when it ubidy reduce ollution. It i obviou that uch an equilibrium i jointly ubotimal: the term-of-trade effect wah out between the two nation while the ollution increae reduce joint welfare. Thi i exlained below by adating equation (25) to the current context: W e du e du ( X X ) d db db ( e e ) GdR. (33a) u u G G Note that market clearing for food require that X X 0. Thu, (33a) imlifie to W edue du dbdb ( e e ) GdR. (33b) u u G G Evaluating (33b) at the nonintervention outcome ( 0 ), and normalizing marginal utility of income for both nation to unity at thi outcome: W du ( u) ( e e) GdR. (34) 0 G G It i clear that joint utility can rie only tarting from nonintervention if global crude ue fall, leading to le ollution. Therefore, any olicy intervention by either nation that lead to a net rie in crude ue i jointly ubotimal. 19

22 Prooition 3: If biofuel ubidy reduce global ollution, term-of-trade conideration imly that: (i) the Nah olicy for the food exorter i to ue a biofuel ubidy; and, (ii) the Nah olicy of the food imorter i a biofuel tax iff the term-of-trade motive dominate the ollutionreduction motive. Such a Nah equilibrium i jointly ubotimal, and may or may not dominate the free trade outcome. The dicuion receding the rooition rovide the roof. It i clear from (34) that the Nah ubidy equilibrium may be aociated with le ollution relative to free trade, which in turn imlie that Nah intervention may dominate free trade. On the other hand, a bad Nah W W equilibrium emerge when, for examle, R 0, R 0, and term-of-trade motive dominate for both nation, o that home imoe a biofuel ubidy while foreign imoe a biofuel tax. W W Becaue R 0 and R 0 in thi cae, the home ubidy and the foreign tax both raie ollution. Clearly, in thi cae, the Nah equilibrium i wore than free trade. The welfare ranking of other oible cae i not obviou, and one ha to roceed on a cae-by-cae bai. 4. Concluion The main contribution of thi aer i to rovide a tractable general equilibrium analyi of biofuel ubide (in the tradition of a neoclaical cometitive trade model) to rovide guidance on otimal olicie under certain contraint. Accordingly, mot of the olicie analyzed are of the econd-bet variety. In the firt art of the aer we outline the role of ooing cale and ubtitution effect of biofuel ubidization, keeing in mind different general equilibrium linkage on both the conumtion and roduction ide. Next, we extend the model to conider term-of-trade conideration, and exlore the link between the ue of corn a 20

23 an inut in roducing energy and it demand a a final conumtion good. In thi context, a combination of a tax on foil fuel and a biofuel ubidy i hown to be otimal to target ollution and term-of-trade. inally, we conider international interdeendence in biofuel olicy, and how that term-of-trade conideration will amlify the biofuel ubidy of the food exorting nation, while it will moderate the level of thi ubidy for the food imorting nation. The effect of uch Nah olicie on global ollution (tarting from a non-intervention outcome) i ambiguou. 21

24 Aendix A. Term-of-Trade Effect or tractability, we aume quai-linearity of reference and earability of G for thi aendix. Thee aumtion allow u to abtract from income effect, coniderably imlifying the dicuion, without changing the thrut of our analyi. The general cae i available on requet. Uing equation (27) and (28) from the text, it can be hown that N D, (A1) where D 0, becaue of the arhall-lerner condition, and N e C (.) E f L q EC. (A2) q q q Noting that the concavity of the unit cot function in ector enure that wq ( )[defined in footnote 24] i convex, we get E Eq eqq Eq 0 q becaue eqq 0 and E q w( q) 2 L w( q) 0. (A3) f ( L ) Alo, L q w( q) 0 f ( L ) E becaue w( q) 0 L and f (.) 0. (A4) inally, qc(, rt,1) q C 0. (A5) Uing (A3) through (A5) in (A2), and noting that C(.) i concave in inut rice, N e C (.) E f L q EC 0 if e 0. (A6) q q q q 22

25 (A6) rovide a ufficient but not neceary condition for the biofuel ubidy to raie the international rice of food. Indeed, even if e q i oitive (i.e., food and energy are Hickian ubtitute in conumtion), the rice of food will rie unle thi cro-ubtitution effect in conumtion overwhelm all the other effect. The rimary effect of the ubidy i to raie the ue of biofuel a an inut into energy at given rice. Thi i catured by the term 0. The ubidy alo reduce the rice of EC energy becaue of a reduction in the unit cot (i.e., q 0 ). The lower energy rice directly raie food demand if they are Hickian comlement (i.e., if eq 0 ). It alo boot the demand for energy for conumtion and a an inut in manufacturing, thereby raiing the demand for food a an inut in energy roduction: C e E q 0. inally, the lower energy inut qq q rice exand the manufacturing ector at the exene of the food ector, driving down food uly: fl q 0 becaue L 0. All thee effect contribute to a rie in the net demand for q food (unle e q i oitive and larger than the um of the other effect), raiing the rice of food. Thi confer a term-of-trade benefit to the home country a the exorter of food, and a lo to the foreign country. Similarly, t t N D t, (A7) where N e C (.) E f L q EC, (A8) t q q q t d r and 23

26 qt C (.) 0, C 0 r d d C r. (A9) r t Uing equation (A3) to (A6), e C (.) E fl 0 if e 0. (A10) q q q q Uing (A9) and (A10) in (A8), we ee that while the firt term on the right-hand ide of (A8) i negative, the econd term i oitive. Thu the ign of N t i ambiguou. Thi haen for the following reaon. irt, the tax raie the relative rice of crude a an inut and increae the inut demand for biofuel (and, therefore, for the food roduct) via the cro-ubtitution effect. On the other hand, the remaining effect all reduce demand for food a follow: (i) The crude tax raie the rice of energy, which reult in reduced conumtion demand for food, if food and energy are Hickian comlement in conumtion, (ii) The rie in the rice of energy reduce the demand for energy, reulting in a decline in the derived demand for biofuel in energy roduction, (iii) Since L 0, the rie in the energy rice raie home uly of food, reducing the exce demand for food. q If, in the final analyi, the effect of the induced change in energy rice are dominated by the rimary cro-ubtitution effect, then N 0 0. The analyi for i imilar to t t that for above. B. Effect of Policy Variable on Biofuel and Crude Ue that Noting that C(, r t,1) i the unit cot function in the energy ector, CRS enure BEC (, r t,1). (A11) 24

27 Under quai-linearity and earability in G, E e (, q) E. (A12) q Noting that w w( q), uing E L w( q) from (A4), and uing (2) and (4) [which yield L L (, w) ], we get E E (, q) L, w( q) w( q), (A13) where E w( q) L 0, and E 0 a hown in (A3). q Allowing for all the olicy variable conidered in thi aer to be reent, the market clearing equation for food dictate that t (,, ). (A14) Uing (A5), qc(, rt,1) q q(,, t), (A15) where q C 0, q C q 0, and q C 0. Uing (A12) through (A15), t r d E E(, t, ) eq (.), q (.),, t E (.), q (.),, t, (A16) where (.) t (,, ). Uing (A11) and (A16), B t Et C r t. (A17) (,, ) (,, ) ( (.),,1) Uing (A17) and imlifying, we get B C ( eq E ) C q ( eqq Eq ) EC (1 ). (A18) In the mall-country cae 0 and (A18) reduce to B C q ( e E ) EC 0, (A19) qq q 25

28 becaue q 0 and E 0 from (A3) and becaue of concavity of the cot and exenditure function. q Uing (A18), it i clear that in the large-country cae, if 1 0, then B 0 if the lat term on the right-hand ide of (A18) dominate or if eq 0 and dominate the negative term E. Similarly, uing (A17), t t d r t B E C C C E, (A20) where E ( e E ) ( e E )( q q ) 0, if 0 and e 0. In the mall-country t q t qq q t t cae, t 0 and (A20) boil down to t q B EC C E t d t, E ( t eqq Eq ) qt 0 r. (A21) The two term on the right hand ide of the firt equality in (A21) have ooite ign. Therefore, the ign of B t i ambiguou even in the mall-country cae. Uing (A20) we can infer that the ame i true in the large-country cae. Analogou to (A11), R EC (, r t,1). (A22) r d Uing (A16), we can differentiate (A22) to obtain: t d t d t d d r r r r R C E E C C, (A23) where E i defined in (A20) above. In the mall-country cae, t R C E EC C ( e E ) q EC 0. (A24) t d t d d d qq q t d d r r r r r r Uing (A23) and (A20) we can ee that there i ambiguity in the large-country cae, but Rt 0 if the term C d t 0 r i ufficiently mall and if eq 0. Uing (A22) and (A16), 26

29 R C E EC (1 ), (A25) d d r r where E eq E eqq Eq q eqq Eq q. In the mall-country cae, (A25) reduce to r qq q R C e E q EC. (A26) Since C e E q 0 r d d d qq q r and EC d 0, the ign of R i ambiguou even in the mallcountry cae. inally, conider foreign crude ue t 0, r r R. Analogou to (A22), and noting that R EC(, r,1). (A27) Like (A16), E E (, t, ) e (.), q (.), E (.), q (.), q, (A28) where where (.) t (,, ) E. Thu, R EC (, r,1) EC ZC EC, (A29) r r r r Z, Z e E e E q q q q q. It i clear from (A29) that in the mall-country cae R 0. In the large-country cae, the ign i ambiguou becaue Z 0 if q e 0. Similar derivation yield t r r t R ZC EC. (A30) R 0 in the mall-country cae, wherea it ign i ambiguou in the large-country cae. t 27

30 C. Effect of Crude Price on ood and anufacturing Outut (under Laiez aire) Uing the labor demand function in food defined following Eq. (2), and uing Eq. (8) and footnote 24, we get L L, w C, r,1. (A31) Differentiating (A31), L r L L wc L wc ; (A32) w r w r where, r, L 0, Lw 0, w 0, C 0, and Cr 0. r L In the mall country cae r 0 and, hence, (A32) imlie that 0. In thi cae, it r i clear from Eq. (2) that food outut mut increae when the rice of crude rie in the world market. In the large country cae, analyi along the line of Section A above ugget that r can take either ign. If it i oitive, (A32) ugget that food outut mut rie. If it i negative, the imact on food outut i ambiguou. Uing Eq. (4) and the (A32): L r L r 0 if r 0. (A33) Uing footnote 24, Eq. (8) and (A33), and noting that w q 0 E L E w q L w L wcr r r Thu, in the mall country cae, 0 L and E [exlained in Section A above]: if r 0. (A34) mut both fall a the rice of crude rie and, therefore, manufacturing outut fall. In the large country cae, a long a the rie in the crude 28

31 rice raie the food rice alo, manufacturing outut mut fall. If the food rice fall, then the effect on manufacturing i ambiguou. 29

32 Reference Antweiler, W., Coeland, B.R. and Taylor,.S. (2001). I free trade good for the environment? American Economic Review 91(4), Bagg, J. (2009). International trade in hazardou wate. Review of International Economic 17(1), Barrett, S. (1994). Strategic environmental olicy and international trade. Journal of Public Economic 54(3), Coeland, B.R. and Taylor,.S. (1994). North-South trade and the environment. Quarterly Journal of Economic 109(3), Coeland, B.R. and Taylor,.S. (2003). Trade and the Environment: Theory and Evidence. Princeton: Princeton Univerity Pre. Coeland, B.R. and Taylor,.S. (2004). Trade, growth and the environment. Journal of Economic Literature XLII, Dean, J.. (1992). Trade and the environment: A Survey of the literature. Background aer for World Develoment Reort World Bank working aer #WPS de Gorter, H. and Jut, D.R. (2010). The ocial cot and benefit of biofuel: The interection of environmental, energy and agricultural olicy. Alied Economic Perective and Policy, 32(1), rankel, J.A. and Roe, A.K. (2005). I trade good or bad for the environment? Sorting out the cauality. Review of Economic and Statitic 87(1), redrikon, P. (1997). The olitical economy of ollution taxe in a mall oen economy. Journal of Environmental Economic and anagement 33(1), Grafton, R.Q., Koma, T., and Long, N.V. (2010). Biofuel ubidie and the green aradox. CESifo working aer #2960. Johnon, H.G. (1953). Otimum tariff and retaliation. Review of Economic Studie 21, Khanna,., Ando, A.W., and Taheriour,. (2008). Welfare effect and unintended conequence of ethanol ubidie. Review of Agricultural Economic, 30(3),