1

WP 2016-14 September 2016

Working Paper The Charles H. Dyson School of Applied Economics and Management Cornell University, Ithaca, New York 14853-7801 USA

Demystifying RINs: A Partial Equilibrium Model of U.S. Biofuels Markets

Christina Korting, David R. Just

2

It is the policy of Cornell University actively to support equality of

educational and employment opportunity. No person shall be denied

admission to any educational program or activity or be denied

employment on the basis of any legally prohibited discrimination

involving, but not limited to, such factors as race, color, creed, religion,

national or ethnic origin, sex, age or handicap. The University is committed

to the maintenance of affirmative action programs which will assure the

continuation of such equality of opportunity.

Demystifying RINs: A Partial Equilibrium Model of U.S. Biofuels Markets

Christina Kortinga,b,∗, David R. Justa

aDyson School of Applied Economics and Management, Cornell University, USAbWarren Hall, 137 Reservoir Avenue, Ithaca, NY 14850

Abstract

We explore four fundamental channels of mandate compliance available under current U.S. bio-fuels policy: increased ethanol blending through E10 or E85, increased biodiesel blending, and areduction in the overall compliance base. Simulation results highlight the interplay and varyingimportance of these channels at increasing blend mandate levels. In addition, we establish howRIN prices are formed: The value of a RIN in equilibrium is shown to reflect the marginal costof compensating the blender for employing one additional ethanol-equivalent unit of biofuel. Thiscontrasts with existing research equating the price of RINs to the gap between free-market ethanolsupply and demand at the mandate level. We demonstrate the importance of this distinction incase of binding demand side infrastructure constraints such as the ethanol blend wall: as percent-age blend mandates increase, the market for low-ethanol blends may contract in order to reducethe overall compliance base. This has important implications for implied ethanol demand in theeconomy.

Keywords: Biofuels, Renewable Fuels Standards, blend mandateJEL: H23, Q21, Q42

1. Introduction

U.S. biofuels policy has reached a criticaljunction. By lowering the final 2014-2016 blendmandate requirements in December 2015, theEPA has acknowledged the difficulty of com-plying with the original 2010 renewable fueltargets due to important demand side bottle-necks. To gauge the intensity of the feasibilitydebate currently raging in the biofuels space,it suffices to look at the number of commentsreceived on proposed rulemakings by the EPA:23 in 2011, 488 in 2012, 94 in 2013, and 344,947in 2014 1.

∗Corresponding authorEmail addresses: cmk272@cornell.edu (Christina

Korting), drj3@cornell.edu (David R. Just)1see www.regulations.gov, dockets EPA-HQ-OAR-

2010-0133-0001 for 2011, EPA-HQ-OAR-2010-0133-

Given the current state of the market, itis more important than ever to understandthe available compliance mechanisms, their im-pacts and limitations. Important groundworkin this context was laid by De Gorter and Just(2009) and Lapan and Moschini (2012) who an-alyze the general market effects and incidenceof a blend mandate. Pouliot and Babcock(2014) provide estimates of potential demandfor high-ethanol blends given current infras-tructure constraints, which Pouliot and Bab-cock (2015) integrate into a short term partialequilibrium model accounting for existing mar-ket rigidities. Forthcoming work by Lade et al.(2015) explores the dynamic nature of the man-date.

0102 for 2012, EPA-HQ-OAR-2012-0546-0001 for 2013,EPA-HQ-OAR-2013-0479-0037 for 2014

1

We contribute to this discussion by extend-ing the existing literature in two importantways: First, we make explicit which compliancechannels are available under the current biofu-els policy and when they are employed. Todo so, we propose a partial equilibrium modelwhich takes into account the nested mandatestructure of the RFS2. As market pressuresincrease due to higher total renewable man-dates in the presence of ethanol infrastructureconstraints, our simulation results provide ev-idence for two important compliance channelsnot usually emphasized in the literature: over-age from nested mandate categories and a con-traction of the market for low-ethanol blendfuels such as E10 in order to reduce the overallcompliance base.

Second, we let the exchange of RINs enterthe model endogenously as an additional de-cision variable for non-integrated blenders andrefiners. This allows us to conclusively estab-lish how RIN prices are formed and what theyrepresent. Contrary to most of the existing lit-erature, we find that the core value of a RIN inequilibrium reflects the marginal cost of com-pensating the blender for employing one addi-tional ethanol-equivalent unit of biofuel2. Pre-viously, this core value was usually equatedto the gap between free-market ethanol sup-ply and demand at the mandate level (e.g.McPhail et al. (2011), Whistance and Thomp-son (2014) and Markel et al. (2016)). Figure 1illustrates this idea. While the two definitionsof RIN prices are conceptually very similar, weemphasize the importance of this distinction by

2RIN prices are usually broken down into three com-ponents: (i) the core value, or cost of complying withthe mandate, (ii) the marginal value of transferringphysical blending opportunities from high-cost to low-cost blenders, and (iii) the real option value of meetingbinding mandates in the future thanks to the (limited)bankability of RINs. Our model focuses on the firstcomponent since it tends to dominate RIN prices whenmandates are binding. However, our model could beextended to a dynamic setting including heterogeneouscost structures for blenders in order to capture the re-maining RIN price components.

Gallons

Price per gallon

Demand

Supply

Mandate

RIN price

Figure 1: Proposed RIN Price Formation in ExistingLiterature; Market for Ethanol

showing the strong dependence of the notion ofimplied ethanol demand on prevailing percent-age mandate levels. Our RIN price formulatherefore provides a more concise and reliableway to explain the price of RINs.

2. Renewable Fuel Standards

The Renewable Fuel Standards of 2005(RFS1) and 2007 (RFS2), passed as part ofthe Energy Policy Act (EPAct) and the En-ergy Independence and Security Act (EISA) re-spectively, mandate the use of specific amountsof biofuels in the transportation sector. Thereasons for promoting the use of biofuels aremanifold: (a) protecting against rising fossilfuel prices; (b) reducing emissions from thetransportation sector; (c) promoting energy se-curity by reducing the dependency on fossilfuel imports; and (d) increasing farm income(Rajagopal and Zilberman (2007); McCarl andBoadu (2009)). The Renewable Fuel Standardsshare many of their environmental goals withother existing energy policies such as fuel taxesand fuel efficiency standards3.

The RFS2 imposes a series of annual vol-umetric targets which are subsequently con-verted into blend mandates for the year aheadusing forecast gasoline and diesel consumption

3For more details about the RFS, please see Ap-pendix A

2

TotalRenewable

Advanced

BBD

Cellulosic

Figure 2: Nested Mandate Structure under the RFS2

levels. The obligated parties are refiners andimporters of fossil fuels who often do not di-rectly control the final blend of consumer mo-tor fuels. Compliance is therefore monitoredthrough financial instruments called Renew-able Identification Numbers (RINs) which rep-resent one ethanol-equivalent unit of biofuelblended. RINs are generated at production orimport of a biofuel, and become detached andseparately tradable at blending.

The RFS2 is designed to be ‘technology forc-ing’, governing both the pace and the intensityof the shift to more environmentally friendly fu-els using a nested mandate structure. For thisreason, four nested categories were establishedunder the RFS2: both cellulosic biofuels andbiomass-based diesel (BBD) are nested underthe advanced biofuels category, which requiresa greenhouse gas emissions (GHG) reductionof at least 50% compared to the fossil fuel be-ing replaced; the advanced biofuels mandate inturn is part of the total renewable fuels cate-gory (TR) which requires GHG savings of atleast 20%. Figure 2 provides a graphical rep-resentation of this nested structure.

The residual part of the total renewable fuelsmandate not met through advanced biofuels isoften referred to as conventional biofuels. Itis usually filled using U.S. corn-based ethanol

or biodiesel which did not meet the advancedbiofuel GHG savings requirements4. However,overage from the advanced biofuels categorycould equally be used for compliance towardsthe overall mandate. It is therefore importantto note that the RFS2 does not impose explicitethanol volume requirements.

At the end of each year, every obligatedparty has to comply with all four sub-categoriesof the RFS2. For instance, a pure gasoline im-porter would still have to provide BBD RINs tothe EPA in order to meet his renewable volumeobligation (RVO). Table 1 highlights some vol-umetric and percentage blend targets by cate-gory and introduces the labeling convention forRINs. For example, cellulosic biofuels generateD3 RINs. The nested mandate structure leadsto an implicit pricing relationship between thecategories since any D3 or D4 RIN can also beused to comply with the advanced or total bio-fuels mandate: the prices must always satisfypD3, pD4 ≥ pD5 ≥ pD6. These pricing rela-tionships will hold with equality if the widermandates become binding and there is a needto attract overage from some of the nested sub-categories.

2013 was the first year when BBD and con-ventional RIN prices approached parity. Thefundamental driver behind this convergencewas the attainment of the so called ethanolblend wall : ethanol is corrosive and there-fore risks damaging engines and fuel tanks atconcentrations of more than 10% in cars thatare not specifically equipped to use it. In2013, most motor gasoline was already soldwith a 10% ethanol share. There are currently

4Based on data from the EPA Moderated Trans-action System (EMTS), 252mn D6 RINs weregenerated from biodiesel or renewable diesel in 2013(https://www.epa.gov/fuels-registration-reporting-and-compliance-help/2013-renewable-fuel-standard-data). We maintain a single biodiesel supply curvefor simplicity in this model. It may be interesting toanalyze the dichotomy between D4 and D6 biodieselinputs and the resulting market dynamics in futurework.

3

Table 1: RFS2 Mandates by Category

2015 2022

Mandate Category LabelVolumetricMandate(bn GAL)

PercentageMandate

VolumetricMandate(bn GAL)

Cellulosic biofuel D3 0.123 0.069% 16Biomass-based diesel D4 1.73 1.49% TBDAdvanced biofuel D5 2.88 1.62% 21Renewable fuel D6 16.93 9.52% 36

Volumetric mandates are shown in billion gallons of ethanol-equivalent exceptBBD which was originally introduced as a diesel standard and is therefore repre-sented on a biodiesel-equivalent energy basis under the RFS. All percentage blendmandates, including D4, are shown in ethanol-equivalent terms.Source: EPA (2010) and EPA (2015)

four distinct ethanol-gasoline blends sold in theU.S.: (i) E0 which contains no ethanol, (ii) E10which contains up to 10% ethanol and can beused in all cars, (iii) E15 which contains upto 15% ethanol, is approved for use in modelsnewer than 2001, but does not meet some carmanufacturer warranties and is not currentlywidely available, and (iv) E85 which containsbetween 51-83% ethanol. E85 is designated foruse in so called flexible-fuel vehicles (FFVs)that can run on higher blends but currentlyrepresent a small percentage of the U.S. fleet.We focus on E10 and E85 as the two dominantblends in the U.S. market5.

3. Methodology

3.1. Model

Like Pouliot and Babcock (2015), we pro-pose a short term model of the U.S. biofuelsmarket which explicitly captures the rigidities

5The most recent EPA final rule document for 2014-2016 predicts E15 consumption of about 320mn GALin 2016 assuming an optimistic rate of growth in retailavailability. However, the relatively higher ethanol con-tent in E15 is expected to be roughly offset by smallamounts of E0 sales. Their most favorable infrastruc-ture scenario for E85 would lead to an estimated 400mnGAL consumed in 2016. As a reference point, 2014 con-sumption is estimated at 150mn GAL (EPA (2015), pp.77460-4)

imposed by demand side infrastructure con-straints. However, our framework extends theirsetting in two important ways: First, we modelthe creation of RIN prices more directly byallowing blenders and refiners to choose thequantity of RINs endogenously, and to thentrade RINs between each other subject to amarket clearing constraint. Second, we capturethe nested structure of the U.S. biofuels man-date by explicitly modeling the biodiesel spaceand allowing for strategic overage of biodieselRINs in order to meet the total renewable man-date.

Generally, existing models of RIN prices andthe RFS2 can be differentiated along four di-mensions: (i) short vs. long term approaches(e.g. considering the blend wall or abstractingaway from current infrastructure constraints)(ii) link to agricultural markets and trade vs.closed economy, fuel-only models (iii) nestingvs. ethanol only and (iv) static vs dynamicsettings. In order to obtain a parsimonious yetmeaningful representation of the core value ofRIN prices, and to study all available chan-nels of mandate compliance, we have chosen astatic, closed economy model considering onlyfuels, but taking the nested mandate structureand short term infrastructure constraints intoaccount. An explicit distinction between con-ventional and flex-fuel vehicle drivers differen-

4

tiates our approach from Christensen and Sid-diqui (2015) who largely abstract away fromthe ethanol consumption bottleneck by assum-ing a perfectly inelastic motor gasoline demandwhich can be arbitrarily split between E10 andE85.

Based on our model choice, the refiner (R)solves the problem of maximizing revenue fromrefined product sales minus the cost of refin-ing (CR), subject to meeting the BBD man-date requirement as well as the residual to-tal renewable requirement not met by BBDoverage. Throughout this paper, motor gaso-line (MG) denotes finished gasoline includ-ing ethanol blending components, while dieselfuel (DF ) refers to finished diesel includingbiodiesel for transportation. G and D on theother hand symbolize gasoline and diesel de-rived from crude oil. RFS2 percentage blendmandates are denoted by κ, which representsthe ratio of required renewable to fossil fuels6.All quantities and prices are denoted as q◦ andp◦ respectively, where ◦ stands for a genericsubscript. An exhaustive list of variable de-scriptions is provided in Appendix C.

max{qG, qD, qRD4, q

RD6}

ΠR =

pGqG + pDqD − CR(qG, qD)

− pD4qRD4 − pD6q

RD6

s.t. qRD4 ≥ κBBD(qG + qD)

and qRD4 + qRD6 ≥ κTR(qG + qD)

(1)

The first constraint specifies that the quan-tity of D4 RINs retired has to be at least com-mensurate with the BBD percentage mandaterequirement (κBBD) multiplied by the totalamount of fossil fuels consumed in the econ-omy. Given the nested mandate structure, D4

6Note that the blend wall is a physical limitationwhich relates to the amount of ethanol relative to theoverall fuel quantity instead. We will therefore some-times convert mandate amounts into these terms forillustration

RINs also count towards the total renewablemandate. The second constraint therefore im-poses that the sum of D4 and D6 retirementshas to exceed the TR percentage mandate ap-plied to the total compliance base.

In stating the blender’s problem (B), we willassume that E85 always has an ethanol contentof 74%. This assumption is in line with the av-erage E85 specifications reported by the EPAand used in the literature (e.g. Knittel et al.(2015)). The E10 ethanol content on the otherhand, represented by θE10, is allowed to varybetween zero and 10% . This permits blendersto use less than 10% ethanol at low mandatelevels and thereby implicitly captures the phys-ical reality of E0 sales. The biodiesel blend ra-tio in diesel fuel (θDF ) is allowed to vary freelysince there are no blend wall constraints in thebiodiesel market. Biodiesel blends up to 5%require no separate labelling at the pump, andblends up to 20% do not require engine modi-fications and are commonly used in the U.S.

max{qE10, qE85, θE10

qDF , qBD4, q

BD6, θDF }

ΠB =

qE10(pE10 − tMG) + qE85(pE85 − tMG)

+ qDF (pDF − tDF )

+ pD6qBD6 + pD4q

BD4 + θDF qDF tcBD

− ((1− θE10)qE10 + 0.26qE85)pG

− (θE10qE10 + 0.74qE85)pE

− (1− θDF )qDF pD − θDF qDF pBD− CBMG(qE10, qE85)− CBDF (qDF )

s.t. qBD4 ≤ 1.5θDF qDF

and qBD6 ≤ θE10qE10 + 0.74qE85

and θE10 ≤ 0.1

(2)

The blender generates revenue by sellingE10, E85 and diesel fuel and incurs a cost ofblending denoted by CB. The ethanol con-tent in E10 as well as the biodiesel content indiesel fuel are endogenous to his decision. Theblender’s constraints represent the process of

5

RIN generation: the number of units gener-ated has to be proportional to the amount ofbiofuels blended.

All percentage blend mandates, and there-fore all RIN quantities, are set in ethanol-equivalent terms by the RFS. The first con-straint for the blender, which represents D4RIN generation, therefore applies an equiva-lence value of 1.5 in order to account for thehigher energy content of biodiesel compared toethanol. The second constraints reflects thegeneration of D6 RINs through motor gaso-line sales. The last constraint effectively im-poses the blend wall, constraining the maxi-mum ethanol content in E10 to 10%.

The blender has to deduct gasoline and dieselfuel taxes, tMG and tDF , on every gallon sold,but receives a 1 USD/GAL biodiesel blendertax credit, tcBD, on the amount of biodiesel heblends7. CMG

B and CDFB represent the blendingcosts for motor gasoline and diesel fuel respec-tively.

All supply and demand functions are as-sumed to be of the constant elasticity form

q = Apε

with an elasticity of ε and a scaling fac-tor of A. Throughout this paper, subscriptsare used to differentiate between cost, supplyand demand functions (C, S,D), and then in-dicate the relevant product. To model the con-sumer choice between E10 and E85, we adopta neo-classical approach: first, consumers aresplit into flexible-fuel vehicle (FFV) ownersand conventional vehicle (C) owners. Ratherthan allowing for heterogeneous preferencesfor environmental quality and hence gradualswitching behavior, we assume that all FFVdrivers will switch from E10 to E85 when-ever E85 prices become equally or more at-tractive on an energy-equivalent basis. We de-note the demand functions for E10 and E85

7This tax credit has recently been extended to De-cember 2016 through House of Representatives Bill2029, Section 185

by D◦(pE10, pE85), but will drop the price ar-guments going forward for notational conve-nience. Denoting by λ the energy-equivalencefactor between E10 and E85, we therefore ob-tain the following piecewise demand functions:

• Case 1: pE85 > λpE10

No E85 will be consumed and all FFVdrivers will choose to consume E10 instead

DE85 = 0

DE10 = ADFFVpεDMGE10 +ADC

pεDMGE10

• Case 2: pE85 = λpE10

FFV drivers are indifferent between E10and E85 and will therefore consume anyquantity of E85 between zero and their to-tal fuel demand. Any residual demand willbe consumed in the form of E10.

DE85 ∈ [0, ADFFVpεDMGE10 ]

DE10 = ADFFVpεDMGE10 +ADCp

εDMGE10 −DE85

• Case 3: pE85 < λpE10

FFV drivers exclusively use E85

DE85 = ADFFV

(1

λpE85

)εDMG

DE10 = ADCpεDMGE10

The equilibrium in our model is governed bythe interplay of first order and complementaryslackness conditions for blender and refiner aswell as market clearing equations. The full listof equations is provided in Appendix B. Beforepresenting the simulation results for this modelin section 4.3, we will first discuss the data weuse in calibrating the model to market.

3.2. Data and Calibration

The scale parameters A◦ for the fuel demandfunctions are calibrated to annual price andquantity data from 2015. Table 2 below high-lights the elasticity estimates from the litera-ture that were chosen for our calibrations:

6

Table 2: Elasticity Estimates from the Literature

Variable Description Value Source

Supply Elasticities

εSEEthanol 2 Lee and Sumner (2010)

εSBDBiodiesel 2 (at 1.2b GAL) Babcock et al. (2013)

Demand Elasticities

εDMGMotor Gasoline -0.25 Pouliot and Babcock (2014)

εDDFDiesel Fuel -0.07 Dahl (2012)

In order to calibrate the motor gasoline de-mand functions, we use E85 demand estimatesfrom Figure 7 of Pouliot and Babcock (2014).Based on current infrastructure limitations, theE85 demand at a price of 1 USD/GAL in thisfigure is at around 1.2 bGAL. While Pouliotand Babcock (2014) allow for gradual switch-ing behavior from E10 to E85, the 1 USD/GALprice level is far enough below the assumedenergy-equivalent E10 price to suppose thatvirtually all switching would have occurred.Any further consumption increases beyond thispoint can therefore be attributed to increaseddriving demand at low fuel prices. The mo-tor gasoline demand of conventional drivers inour model is calibrated to the residual of totalmotor gasoline demand minus FFV demand.

In order to calibrate the cost functions, werely on the perfect competition assumption andchoose the scale parameter A which equalizesmarginal cost and marginal revenue (price) in2015. In this case, this is equivalent to impos-ing a zero profit condition. Table C.3 highlightskey data sources as well as the correspondingrealizations for 2015.

4. Results

4.1. Compliance Channels

Using a sequence of simulation results atchanging mandate levels, we are able to estab-lish the existence of four distinct channels formandate compliance in our model:

1. Increasing the blend ratio of ethanol inE10 (up to 10%)

2. Increasing E85 sales

3. Increasing the biodiesel share in diesel fuelbeyond the BBD mandate

4. Decreasing the overall compliance base byselling less diesel fuel and/or motor gaso-line

The first two compliance channels rely onincreased ethanol blend ratios in motor gaso-line (which could also be viewed as a decreasein E0 sales). The third channel makes use ofthe nested mandate structure, calling on RINsgenerated through biodiesel overage to complywith the total renewable mandate. To illus-trate how the fourth compliance channel oper-ates, consider an economy in which only motorgasoline is sold (i.e. there is no diesel fuel mar-ket), and the maximum E85 demand by FFVdrivers is fixed at 1 bn GAL. A mandate levelof κTR = 11.11% in this economy implies anethanol blend ratio of 10%, i.e. a blend ratiojust at the blend wall. In this case, any amountof motor gasoline sales would be feasible un-der the mandate. If the mandate was raised toto κTR = 12% instead, the mandate would ef-fectively impose a cap on total motor gasolinesales. To see this, consider the requirement

qEqG

=0.1qE10 + 0.74 ∗ 1

0.9qE10 + 0.26 ∗ 1≥ 12% (3)

Solving for qE10, we find a maximum of 89.6bn GAL of E10 sales in order to ensure man-date compliance. This fourth channel, whichis rarely mentioned in the existing literature,plays a key role in practice since other chan-nels grow more costly as mandates tighten.

7

In a model without nesting in which surplusbiodiesel RINs cannot be used to overcome theblend wall, this channel becomes the only op-tion for compliance once the blend wall hasbeen hit and E85 demand has been exhausted.

Our simulation results in section 4.3 provideevidence for the existence of all four channels.They also highlight the interplay of the differ-ent compliance channels as blend mandates in-crease given the 2015 market environment.

4.2. The Price of RINs

Based on the behavioral equations outlinedin Appendix B, we derive the pricing formulafor D4 RINs given in equation 5. The term

∂CDFB∂qDF

= ABCDFεBCDF

q(εBCDF

−1)DF (4)

represents the marginal cost of blendingdiesel fuel. The ‘core value’ of a D4 RINthus represents the marginal cost of compen-sating the blender for employing one addi-tional ethanol-equivalent unit of biodiesel. Theblender faces the input costs for the two blend-ing components, incurs a marginal cost ofblending, and is able to sell the final productat the diesel fuel price minus tax. If the costsof generating an additional unit of diesel fuelare higher than the price which can be achievedin the market, the blender demands a positiveRIN price as compensation for blending sincehe is not himself obligated under the RFS.

Similarly, for D6 RINs we find the pricingrelationship outlined in equation 6 assumingboth fuel blends are sold in equilibrium. Theinterpretation of terms in these equations isequivalent to the diesel fuel case.

By establishing these concise pricing formu-las, we provide an alternative to the widely es-tablished simplification equating the price ofRINs to the gap between ethanol supply anddemand at the mandated level. Beside the ob-vious abstraction away from the nested man-date structure, there are two key problems withthis notion:

• Implied ethanol demand is not well de-fined: The ethanol demand schedule isusually defined as the implied demand forethanol through E10 and E85 as ethanolprices vary. However, due to the existenceof the four different compliance channels,and the potential reduction of low-ethanolblends at high mandate levels in particu-lar, the notion of implied ethanol demandis highly sensitive to the prevailing per-centage mandate levels. Figure 3 illus-trates this effect by showing simulated de-mand schedules for different total renew-able blend mandates (κTR =0%, 9% and11%). Clearly, for any given ethanol vol-ume, the free-market supply demand gapis substantially different from the supply-demand gap given a binding mandate8.

• Equilibrium ethanol quantities do notequal volumetric mandates: Even assum-ing a well defined implied ethanol demandschedule and ignoring the fact that theRFS2 does not impose any direct man-dates for ethanol, the implied volumet-ric ethanol mandate is not a meaningfulquantity to consider to assess the price ofRINs. Percentage mandate requirementsare calculated using forecast motor gaso-line consumption which will not usually befulfilled exactly as predicted.

This description of RIN prices therefore rep-resents an inaccurate and highly impracticalrepresentation of the core value of RINs. How-ever, the notion of the supply-demand gap ishighly correlated to the more accurate pricingformula we provide: both are a function of theelasticity of ethanol supply as well as the poten-tial ethanol demand given the blend wall. For

8At 0% and 9% mandate levels, we first see increaseddemand thanks to higher ethanol blend ratios in E10,and finally a jump in demand as ethanol becomes cheapenough to induce E85 sales. The 11% demand sched-ule only features one kink when channel four starts todominate and the market contracts

8

pD4 =1

1.5θDF︸ ︷︷ ︸Scaling Factor:

Diesel Fuel to D4 RINs

(1− θDF )pD + θDF pBD +∂CDFB∂qDF︸ ︷︷ ︸

Marginal Cost of Blending oneAdditional Unit of Diesel Fuel

− (pDF − tD)︸ ︷︷ ︸Marginal Revenue from Selling one

Additional Unit of Diesel Fuel

(5)

pD6 =1

θE10︸ ︷︷ ︸Scaling Factor:E10 to D6 RINs

(1− θE10)pG + θE10pE +∂CMG

B

∂qE10︸ ︷︷ ︸Marginal Cost of Blending one

Additional Unit of E10

− (pE10 − tMG)︸ ︷︷ ︸Marginal Revenue from Selling one

Additional Unit of E10

=1

0.74︸︷︷︸Scaling Factor:E85 to D6 RINs

0.26pG + 0.74pE +∂CMG

B

∂qE85︸ ︷︷ ︸Marginal Cost of Blending one

Additional Unit of E85

− (pE85 − tMG)︸ ︷︷ ︸Marginal Revenue from Selling one

Additional Unit of E85

(6)

10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 15

Ethanol Quantity (bnGAL)

0

1

2

3

4

5

Eth

an

ol P

rice

(U

SD

/GA

L)

Free-Market Ethanol Supply and Implied Demand

Freemarket Demand

Demand given kappaTR=90bps

Demand given kappaTR=110bps

Ethanol Supply

Figure 3: Implied Ethanol Demand Schedules at Differ-ent Mandate Levels

example, the D6 equilibrium RIN price in equa-tion 6 depends negatively on pE85. This meansthat if the price of E85 has to adjust down-wards faster due to demand side bottlenecks,the RIN price will increase faster as mandatesrise.

In order to reinforce this idea and to studythe evolution of equilibrium pricing relation-ships at varying mandate levels, we pro-vide comparative static results for a simplifiedmotor-gasoline-only model (see Appendix Dfor a detailed model description). By calcu-lating the comparative statics results based onthis reduced framework, we can solve for up-per bounds on κTR which guarantee that pE85

declines with mandate levels as would be ex-pected. The corresponding bounds are pro-vided in equation 7.

The bound on pE85 is a function of the scaleddistance to the blend wall (0.10.9 in an ethanol-only world) plus an additional term which de-pends on the quantity of low-ethanol blendsales (qE10). The resulting expression will be-

9

dpE85

dκTR≤ 0 ⇔ κTR ≤

0.1

0.9

(pE

εSEpD6

+ 1

)+

qE10

0.9pD6BDC

(7)

come small if the imposed blend mandate re-quires a heavy reliance on channel four withqE10 sales declining in order to lower the com-pliance base and pD6 exploding. In a very ex-treme scenario in which motor gasoline marketseffectively shut down, we could thus encounterE85 prices that rise with the mandate level.Otherwise, pE85 is guaranteed to depend nega-tively on the prevailing mandate level.

Appendix D provides a similar formula foran upper bound on mandate levels which guar-antees increasing RIN prices as a function ofpercentage standards. Our comparative stat-ics results therefore show that under ’normal’market environments, RIN prices will increasewith blend mandate levels while E85 pricesdecrease. This implies the negative correla-tion between RIN prices and the price of high-ethanol blends pointed out above. However,under very extreme circumstances, the fourthcompliance channel may become so dominantthat these natural relationships are no longerguaranteed to hold.

4.3. Simulation Results

Figure 4 shows the impact of an increasingκTR mandate in the market for consumer fu-els. Throughout these simulations, we hold thebiomass-based diesel mandate fixed at its 2015level of around 1.5%. The first row of graphsrepresents quantity changes, while the secondrow highlights changes in equilibrium prices. Itis important to note that these graphs do nothave a time component, but rather representthe market outcomes if a given mandate levelwas imposed in a market environment similarto the U.S. in 2015.

The quantity of E85 jumps up sharply inresponse to the blend wall9. This change of

9As noted previously, the blend wall occurs in the

consumption is induced by a drastic reductionin E85 prices which incentivizes FFV driversto switch to the cheaper fuel. As some con-sumers abandon E10 for E85, the E10 pricedrops, thereby enabling an increase in E10 con-sumption by conventional vehicle owners. Thisphenomenon explains the small uptick in E10consumption in the first panel of Figure 4.

The E10/E85 switching corresponds to com-pliance channel two in action: more ethanol isblended into motor gasoline in order to meetthe mandate. Overall motor gasoline use in-creases as low prices induce more E85 con-sumption by FFV drivers. We also find clearevidence for the fourth compliance mechanism:as the mandate tightens and the inducementof additional E85 consumption becomes morecostly, total motor gasoline consumption be-gins to decline again as shown in Figure 5. Be-cause we are modelling E85 demand using aconstant-elasticity function, the expansion inE85 here dominates the curtailment of E10.However, if we were to impose a cap on E85consumption, we would expect overall motorgasoline use to decline as channel four wouldbegin to dominate once channel two has beenexhausted.

Looking at the diesel fuel market as shownin the right hand side panels of Figure 4, itbecomes evident that the dominant compli-ance channel in our model is an increase in thebiodiesel blend ratio, accompanied by increas-ing diesel fuel prices. The decrease in diesel fuelsales is thus driven by a supply shock in theform of increased marginal costs due to higher

ethanol-only model whenever EG

becomes larger than10%, which corresponds to an ethanol-only mandate of11.11%. However, in a market with both motor gasolineand diesel, κTR = E+BD

D+Gwhich is why the blend wall

now occurs before the salient level of 11.11%

10

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Total Renewable Percentage Mandate κTR

120

125

130

135

140

q (

bn G

AL)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

qE

85 (

bn G

AL)

Gasoline Quantities

qE10

qG

qE85

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Total Renewable Percentage Mandate κTR

38

39

40

41

42

43

44

45

q (

bn G

AL)

Diesel Quantities

qDF

qD

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Total Renewable Percentage Mandate κTR

0.5

1

1.5

2

2.5

p (

US

D/G

AL)

Gasoline Prices

pE10

pG

pE85

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Total Renewable Percentage Mandate κTR

1.6

1.8

2

2.2

2.4

2.6

2.8

3

p (

US

D/G

AL)

Diesel Prices

pDF

pD

Figure 4: Price and Quantity Changes for Consumer Fuels. All Prices are Shown in USD/GAL. All Quantities areShown in bn GAL.

Motor Gasoline Quantities

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Total Renewable Percentage Mandate κTR

136

136.5

137

137.5

138

138.5

q (

bn

GA

L)

0

0.5

1

1.5

qE

85 (

bn

GA

L)

qMG

qE10

qE85

Figure 5: Quantity Changes in Motor Gasoline (bnGAL)

biodiesel use.The important role which biodiesel plays in

overcoming the blend wall is also evident inthe choice of blend ratios. Our calibratedethanol supply curve leads to ethanol pricescheap enough to encourage full use in E10, butnot cheap enough to also encourage the pro-duction of E85 at low mandate levels. The E10blend ratio is therefore stable at 10% regard-less of the percentage blend mandate10. Thediesel fuel blend on the other hand changessignificantly beyond the blend wall, increasingfrom around 3.7% to 7.8% as shown in Figure6. This change is purely driven by ethanol de-mand constraints as the BBD mandate level it-self remains fixed at 1.5% throughout our sim-ulations.

Finally, Figure 7 depicts the changing equi-

10The free-market blend ratio which refiners wouldchoose in the absence of a blend wall in our model is12.5%

11

Biofuels Blend Ratios as a Function of the Overall Mandate

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Total Renewable Percentage Mandate κTR

0

5

10

15

Pe

rce

nta

ge

Ble

nd

Ra

tio

θE10

θDF

Figure 6: Changes in Fuel Blend Ratios (Percent)

libria in the biofuels market11. The increasein ethanol and D6 RIN quantities is effectivelycapped due to the blend wall. The increase inbiodiesel and D4 RIN quantities on the otherhand is unconstrained and progresses in linewith the increasing biodiesel blend ratio we ob-served in the previous figure. The differencebetween biodiesel and D4 quantities is due tothe 1.5 equivalence value applied in biodieselRIN generation.

As noted in section 2, the nested mandatestructure leads to an implicit pricing relation-ship between D4 and D6 RINs: the prices mustalways satisfy pD4 ≥ pD6. This relationshipholds with equality when the wider mandatebecomes binding and needs to attract overagefrom the nested sub-category. This effect be-comes evident in the second panel of Figure 7.

We also observe a sharp increase in biodieselprices compared to ethanol prices due to thedemand constraints in E85. This suggests thatthe diesel market, and hence the transportationsector, carries a large part of the economic bur-den imposed by the ethanol consumption bot-

11The erratic behavior of D6 RIN quantities belowthe blend wall is due to over-blending of ethanol at lowmandate levels. Given a zero RIN price and no banka-bility, the chosen quantity in our model oscillates freelyas neither blender nor refiner have an incentive to ex-change the superfluous RINs. Once the mandate startsbinding and RIN prices become positive, the quantitiesof ethanol and generated D6 RINs in our model con-verge as expected

tleneck.

5. Conclusion

We propose a parsimonious partial equilib-rium framework which demonstrates the avail-able compliance channels under current U.S.biofuels policy. Our simulation results provideevidence for a strong reliance on both biodieseloverage and a reduction in low-ethanol motorgasoline blends in order to meet the total re-newable mandate given a binding blend wall.Since heavy trucks and trains account for mostof the diesel consumption in the U.S., this sug-gests important general equilibrium ramifica-tions as the higher cost of transportation willlikely be passed on in the form of higher con-sumer prices. In addition, assuming limitedbiodiesel production capacity in the short term,we expect the fourth compliance channel toplay an increasingly important role going for-ward. This implies significant welfare losses fordrivers of cars without flexible-fuel capacity.

We also present a concise formula for the corevalue of RINs. The value of a RIN in equilib-rium is shown to reflect the marginal cost ofcompensating the blender for employing oneadditional ethanol-equivalent unit of biofuel.Previous research had often represented RINprices as the gap between free-market ethanolsupply and demand at the mandate level. Oursimulation results highlight the important ap-proximation error induced by this notion ofRIN rices by showing the strong dependenceof implied ethanol demand on the prevailingblend mandate requirements.

Future work will focus on establishing thefeasibility of the proposed RFS mandate pro-gression under different infrastructure scenar-ios. If the technology forcing potential of theRFS2 cannot be realized as expected, it is im-portant to understand which additional pol-icy tools could be employed in order to over-come the current bottleneck in ethanol con-sumption. Our model provides a convenientstarting point to explore the effect of additional

12

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Total Renewable Percentage Mandate κTR

0

5

10

15

q (

bn G

AL)

Biofuels and RIN Quantities

qE

qBD

qD6R

qD4R

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Total Renewable Percentage Mandate κTR

0

1

2

3

4

5

6

7

p (

US

D/G

AL)

Biofuels and RIN Prices

pE

pBD

pD6R

pD4R

Figure 7: Price and Quantity Changes for Biofuels. All Prices are Shown in USD/GAL. All Quantities are Shown inbn GAL.

incentive structures such as increased biodieseltax credits.

Acknowledgements

The authors would like to thank Prof. Harryde Gorter and Dr. Anthony Radich for theirvaluable suggestions and helpful commentswhich have greatly enhanced the quality of thispaper. Any remaining errors are, of course, theauthors’.

We gratefully acknowledge the financial sup-port received for this research from (i) theNational Research Initiative of the NationalInstitute of Food and Agriculture, US De-partment of Agriculture (USDA; Washington,DC, USA; Grant No 2014-67023-21820 underthe Agricultural and Food Research Initiative(AFRI)).; and (ii) USDA Cooperative Agree-ment 58-0111-15-018; and (iii) Cornell Univer-sity Agricultural Experiment Station federalformula funds (project no. NYC-121-7444) re-ceived from the Cooperative State Research,Education and Extension Service, USDA. Anyopinions, findings, conclusions, or recommen-dations expressed in this publication are thoseof the authors and do not necessarily reflect theview of the U.S. Department of Agriculture.

References

Bruce A Babcock, Marcelo Moreira, Yixing Peng, andothers. Biofuel taxes, subsidies, and mandates: Im-pacts on US and Brazilian markets. Center for Agri-cultural and Rural Development, 2013.

13

Antonio M. Bento, Richard Klotz, and Joel Landry.Are There Carbon Savings from US Biofuel Policies?The Critical Importance of Accounting for Leakagein Land and Fuel Markets. Energy Journal, 36(3):75–109, July 2015. ISSN ISSN 0195-6574.

Adam Christensen and Sauleh Siddiqui. A mixed com-plementarity model for the us biofuel market withfederal policy interventions. Biofuels, Bioproductsand Biorefining, 9(4):397–411, 2015.

Carol A Dahl. Measuring global gasoline and dieselprice and income elasticities. Energy Policy, 41:2–13, 2012.

Harry De Gorter and David R Just. The economics ofa blend mandate for biofuels. American Journal ofAgricultural Economics, 91(3):738–750, 2009.

Harry De Gorter, David R. Just, and Dusan Drabik.The Economics of Biofuel Policies - Impacts on PriceVolatility in Grain and Oilseed Markets. PalgraveMacmillan, April 2015. ISBN 978-1-137-41484-7.

EPA. 2010 Final Rule, March 2010.EPA. Renewable Fuel Standard Program: Standards

for 2014, 2015, and 2016 and Biomass-Based DieselVolume for 2017; Final Rule, December 2015.

Carlisle Ford and Benjamin Senauer. How biofuelscould starve the poor. Foreign Affairs, www.foreignaffairs. org/20070501faessay86305/c-ford-runge-benjamin-senauer/how-biofuels-could-starve-the-poor. html, 2007.

Stephen P. Holland, Jonathan E. Hughes, Christo-pher R. Knittel, and Nathan C. Parker. UnintendedConsequences of Carbon Policies: TransportationFuels, Land-Use, Emissions, and Innovation. EnergyJournal, 36(3):35–74, July 2015. ISSN 01956574.

Christopher R. Knittel, Ben S. Meiselman, andJames H. Stock. The Pass-Through of RIN Pricesto Wholesale and Retail Fuels under the RenewableFuel Standard. Working Paper 21343, National Bu-reau of Economic Research, July 2015.

Gabriel E Lade, C-Y Cynthia Lin, and Aaron Smith.Policy Shocks and Market-Based Regulations: Evi-dence from the Renewable Fuel Standard. Technicalreport, CARD Working Paper [16-WP 565], 2015.

Harvey Lapan and GianCarlo Moschini. Second-bestbiofuel policies and the welfare effects of quantitymandates and subsidies. Journal of EnvironmentalEconomics and Management, 63(2):224–241, 2012.

Hyunok Lee and Daniel A Sumner. International tradepatterns and policy for ethanol in the united states.In Handbook of bioenergy economics and policy, pages327–345. Springer, 2010.

Evan Markel, Burton C English, and Dayton Lam-bert. Thresholds and regime change in the marketfor renewable identification numbers. Technical re-port, Agricultural and Applied Economics Associa-tion, 2016.

Bruce A. McCarl and Fred O. Boadu. Bioenergy and

U.S. Renewable Fuels Standards: Law, Economic,Policy/Climate Change and Implementation Con-cerns. Drake Journal of Agricultural Law, 14:74,2009.

Lihong McPhail, Paul Westcott, and Heather Lutman.The renewable identification number system andUS biofuel mandates. ERS Report BIO-03, USDA,November, 2011.

NERA. Effects of Moving the Compliance Obligationunder RFS2 to Suppliers of Finished Products. FinalReport, July 2015.

Sebastien Pouliot and Bruce A Babcock. The demandfor e85: Geographical location and retail capacityconstraints. Energy Economics, 45:134–143, 2014.

Sebastien Pouliot and Bruce A. Babcock. CompliancePath and Impact of Ethanol Mandates on RetailFuel Market in the Short Run. American Journal ofAgricultural Economics, December 2015. ISSN 0002-9092, 1467-8276.

Deepak Rajagopal and David Zilberman. Review of en-vironmental, economic and policy aspects of biofuels,volume 4341. World Bank Publications, 2007.

Randy Schnepf and Brent D Yacobucci. Renewable FuelStandard (RFS): overview and issues. In CRS Reportfor Congress, October 2010.

Timothy Searchinger, Ralph Heimlich, Richard AHoughton, Fengxia Dong, Amani Elobeid, JacintoFabiosa, Simla Tokgoz, Dermot Hayes, and Tun-Hsiang Yu. Use of US croplands for biofuels increasesgreenhouse gases through emissions from land-usechange. Science, 319(5867):1238–1240, 2008.

P Verleger. Renewable Identification Numbers. Pre-sentation to Agricultural Advisory Committee: Com-modity Futures Trading Commission, 2013.

Jarrett Whistance and Wyatt Thompson. A criticalassessment of rin price behavior and the implica-tions for corn, ethanol, and gasoline price relation-ships. Applied Economic Perspectives and Policy,page ppu012, 2014.

Brian Wright. Global Biofuels: Key to the Puzzle ofGrain Market Behavior. The Journal of EconomicPerspectives, 28(1):73–97, 2014. ISSN 0895-3309.

Brent D Yacobucci. Intermediate-Level Blends ofEthanol in Gasoline, and the Ethanol Blend Wall.In CRS Report for Congress, October 2010.

14

Appendix A. Additional Informationon the RFS

The RFS2 is implemented as a set of an-nual volumetric mandates for the 48 contiguousstates and Hawaii that are subject to final re-view by the EPA12. In order to apportion theserequirements to the obligated parties, the man-dates are transformed into percentage blendobligations by dividing the required amount ofrenewable fuel for the year ahead by the to-tal forecast amount of gasoline and diesel con-sumption. The forecasts are obtained from theNovember issue of the Short-Term Energy Out-look13 preceding the mandate year. The RFS2thus effectively operates as a blend mandate forbiofuels.

Compliance is monitored through so calledrenewable identification numbers (RINs).RINs represent an accounting mechanism inwhich a unique 38 digit tracking number isassigned to every gallon of biofuel produceddomestically or imported into the U.S. Oncethe underlying gallon has been physicallyblended for final consumption in the trans-portation sector, the RIN becomes detachedfrom the renewable fuel it accompanies andturns into an independently tradable financialinstrument. The advantage of this mechanismis that the obligated party can be a step re-moved from the physical blending process: thenecessary amount of RINs for compliance canbe procured through the blending of biofuels,purchases in the RIN market or a combinationthereof. Similar to a cap-and-trade scheme,RINs therefore allow for efficiency gainsthrough strategic over- and under-blendingby obligated parties with heterogeneous coststructures.

In fact, the RFS places the percentage blendobligations on refiners and importers of fossil

12Alaska, Hawaii and non-contiguous U.S. territoriesare exempted from the program unless they opt in. Un-like Hawaii, Alaska has not yet chosen to exercise thisoption.

13http : //www.eia.gov/forecasts/steo/outlook.cfm

fuels rather than blenders. This distinctionis important since, as highlighted in NERA(2015), around 40% of US refiners in 2015 wereneither integrated with blenders nor retailers14.The original justification for the choice of obli-gated party was to minimize regulated partiessince the number of importers and refiners atthe time was lower than the number of blendersusing ethanol. However, due to the increasedmandate levels under the RFS2, virtually allblenders now purchase some amount of ethanoland have therefore become regulated, thoughfor the most part not obligated, parties.

The U.S. biofuels environment has been an-alyzed from a multitude of different angles. In-troductions to the regulatory framework as wellas the nature of RINs can be found in McCarland Boadu (2009), McPhail et al. (2011) andVerleger (2013)15.

A number of papers have challenged thenet environmental benefits of the RFS2.Searchinger et al. (2008) were the first to raisethe concern that the use of corn-based ethanolmight actually increase global greenhouse gaslevels due to indirect land use change. A gen-eral equilibrium study by Bento et al. (2015)cautions that the RFS in its current form in-creases emissions due to significant leakages inboth land and fuel markets. This result isalso underlined by Holland et al. (2015) whoexplore unintended consequences of the RFSand find that land-use costs from erosion andhabitat loss under the RFS2 could be as high

14Percentage based on the number of active firms inthe market rather than throughput

15The Department of Agricultural and ConsumerEconomics at the University of Illionois at Urbana-Champaign (http : //farmdocdaily.illinois.edu) andthe Center for Agricultural and Rural Develop-ment at Iowa State University (CARD) (https ://www.card.iastate.edu/policy briefs) provide regularmarket commentary and policy briefs to discuss changesto the regulation or market environment. Similarly,Congressional Research Service reports to congresssuch as Schnepf and Yacobucci (2010) and Yacobucci(2010) provide valuable insights into current discussionsaround the RFS2.

15

as $693 million while a cap-and-trade systemwould add virtually zero costs of this type.

Another source of concern is the effect of bio-fuels policies on food prices. De Gorter et al.(2015) explore the nature of the link betweencrop and fuels markets which U.S. biofuels pol-icy has shaped. They note that agriculturalcrops such as corn and soybeans can effectivelylock on to oil prices through the fundamen-tal pricing relationships implied by blending.These insights help to inform the debate onbiofuels’ potential to exacerbate famine duringfood price booms such as in 2007/2008 (Fordand Senauer (2007), Wright (2014)).

Appendix B. Nested Model

The blender and refiner cost functions arerepresented by constant elasticity functions. Inthis case, we require ε > 1 in order to ensureconvexity of the cost function, and hence con-cavity of the profit function. We allow for syn-ergy effects such as benefits from shared stor-age infrastructure in the production of gasolineand diesel, as well as in the blending of E10and E85 by letting both products feed into onejoint cost function. Motor gasoline blendingand diesel fuel blending on the other hand aretreated as separate. The proposed cost func-tions are therefore of the form highlighted inequation B.1.

In total, the model consists of 25 equationsin 25 unknowns:

• Nine quantities: qE10, qE85, qG, qDF , qD,qRD4, q

BD4, q

RD6, q

BD6

• Nine prices: pE10, pE85, pG, pDF , pD, pBD,pD4, pD6, pE

• Five Lagrange multipliers: γRD4, γRD6, γ

BD4,

γBD6, γBE10

• Two Blend Ratios: θE10, θDF

The full set of behavioral equations is shownin the set of equations B.2.

Appendix C. Data and Calibration Re-sults

Throughout this paper, the symbol ◦ standsfor a generic subscript. The capital letters D◦,C◦ and S◦ represent demand, cost and supplyfunctions respectively. Quantities are alwaysdenoted by q◦ while p◦ represents prices. Thesuperscripts B and R designate variables per-taining to the blender or refiner respectively.

Table C.3 highlights key data sources aswell as the corresponding realizations for 2015.Quantities are shown in billion gallons (bGAL)and prices in USD per gallon or USD per RIN.

Most of the data is collected from the EIAMonthly Energy Review Beta website16, whilethe quantity of E85 is calculated as the sum ofconventional gasoline blended with fuel ethanolfor blends higher than 55%17 and renewablefuel and oxygenate plant net production of fin-ished motor gasoline18. Ethanol prices wereobtained through Bloomberg while RIN priceswere purchased from OPIS. We are using theB99/B100 biodiesel prices from the DOE Alter-native Fuels Data Center as a proxy for whole-sale biodiesel prices.

Relevant motor gasoline and diesel fuel taxrates were obtained from the EIA. Includingfederal and average state taxes, the tax ratesfor 2015 were at 44.89 USc/GAL and 51.64USc/GAL respectively. Based on the outlinedparametric assumptions and elasticity choiceswe obtain the calibration results shown in tableC.4.

Using these calibrated inputs, we apply a se-quential quadratic programming procedure tosimulate market equilibria for different man-date levels. Additional notation is summarizedin table C.5.

16http://www.eia.gov/beta/17EIA Weekly Refiner and Blender Net Production

update18EIA Petroleum and Other Liquids report

16

Refiner: (ARCGqG +ARCD

qD)εRC

Blender (MG): (ABCE10qE10 +ABCE85

qE85)εBCMG

Blender (DF): ABCDFqεBCDFDF

(B.1)

Appendix D. Reduced Model: MotorGasoline Only

Refiner’s Problem (linear cost of blending,cR):

max{qG, qRD6}

ΠR =

pGqG − cRqG − pD6qRD6

s.t. qRD6 ≥ κTRqG

(D.2)

Blender’s Problem (linear markups forblending, (mE10,mE85)):

max{qE10, qE85, q

BD6}

ΠB =

qE10(pE10 −mE10 − tMG)

+ qE85(pE85 −mE85 − tMG)

+ pD6qBD6

− (0.9qE10 + 0.26qE85)pG

− (0.1qE10 + 0.74qE85)pE

s.t. qBD6 ≤ θE10qE10 + 0.74qE85

(D.3)

Linear Demand Functions:

• Case 1: pE85 > λpE10

DE85 = 0

DE10 = ADFFV+ADC

− (BDFFV+BDC

)pE10

• Case 2: pE85 = λpE10

DE85 ∈ [0, ADFFV−BDFFV

pE10]

DE10 = ADFFV+ADC

− (BDFFV+BDC

)pE10 − qE85

• Case 3: pE85 < λpE10

DE85 = ADFFV− BDFFV

λpE85

DE10 = ADC−BDC

pE10

Upper bound on κTR to ensure that the priceof D6 RINs rises with increasing mandate levelsprovided in equation D.1.

17

First Order Conditions

FOC Refiner pg −∂CR

∂qG− γRD4κBBD − γRD6κTR = 0

FOC Refiner pD −∂CR

∂qD− γRD4κBBD − γRD6κTR = 0

FOC Refiner pD4 − γRD4 − γRD6 = 0

FOC Refiner pD6 − γRD6 = 0

FOC Blender pE10 − tMG −∂CMG

B

∂qE10− (1− θE10)pg − θE10(pE − γBD6) = 0

FOC Blender pE85 − tMG −∂CMG

B

∂qE85− 0.26pg − 0.74(pE − γBD6) = 0

FOC Blender pDF − tDF −∂CDFB∂qDF

− (1− θDF )pD − θDF (pBD − 1.5γBD4) = 0

FOC Blender pD4 − γBD4 = 0

FOC Blender pD6 − γBD6 = 0

FOC Blender qE10(pG + γBD6 − pE)− γBE10 = 0

FOC Blender qDF (pD + 1.5γBD4 − pBD) = 0

Market Clearing

MC Motor Gasoline qE10 −ADCpεDMGE10 = 0

MC Motor Gasoline qE85 −ADFFV

(1

λpE85

)εDMG

= 0

MC Diesel Fuel qDF −ADDFpεDDFDF = 0

MC Gasoline qG − (1− θE10)qE10 − 0.26qE85 = 0

MC Ethanol SE(pE)− θE10qE10 − 0.74qE85 = 0

MC Diesel qD − (1− θDF )qDF = 0

MC Biodiesel SBD(pBD)− θDF qDF = 0

MC D4 RINs qBD4 − qRD4 = 0

MC D6 RINs qBD6 − qRD6 = 0

Complementary Slackness

CS Refiner γRD4(qRD4 − κBBD(qG + qD)) = 0

CS Refiner γRD6(qRD4 + qRD6 − κTR(qG + qD)) = 0

CS Blender γBD4(1.5θDF qDF − qBD4) = 0

CS Blender γBD6(θE10qE10 + 0.74qE85 − qBD6) = 0

CS Blender γBE10(0.1− θE10) = 0

(B.2)

18

Table C.3: Data SourcesVariable Description 2015 Units Source

qG Gasoline in Transport. excl. Ethanol 124.72 bGAL EIAqE Ethanol in Transport 13.38 bGAL EIAqE10 E10 Consumption 138.02 bGAL CalculatedqE85 E85 Consumption 0.07 bGAL EIAθE10 Implied E10 Ethanol Content 9.65% Percent Calculated

qD Diesel Fuel in Transport. excl. Biodiesel 43.17 bGAL EIAqBD Biodiesel in Transport. 1.48 bGAL EIAqDF Distillate Fuel Oil in Transport. 44.65 bGAL EIAθDF Implied Biodiesel Content 3.31% Percent Calculated

pG Refiner Price of Motor Gasoline for Resale 1.72 USD/GAL EIApE Prompt Month Denatured Ethanol Futures 1.51 USD/GAL BloombergpE10 Regular Motor Gasoline, All Areas 2.43 USD/GAL EIApE85 E85 Prices 1.96 USD/GAL e85prices.com

pD Refiner Price of No. 2 Diesel Fuel for Resale 1.66 USD/GAL EIApBD U.S. Retail Fuel Prices B99/B100 3.65 USD/GAL DOE AFDCpDF On-Highway Diesel Fuel Price 2.71 USD/GAL EIA

κTR Final Percentage Standards: Renewable Fuel 9.52% Percent EPAκBBD Final Percentage Standards: BBD 1.49% Percent EPApD6 Ethanol RINs (D6) 0.55 USD/RIN OPISpD4 Biodiesel RINs (D4) 0.72 USD/RIN OPIS

Table C.4: Calibration ResultsVariable Description Value

ARCGCost Refiner (Gasoline) 0.623

ARCDCost Refiner (Diesel) 0.655

ABCE10Cost Blender (E10) 0.243

ABCE85Cost Blender (E85) 0.175

ABCDFCost Blender (Diesel Fuel) 0.270

ASESupply Ethanol 2.541

ASBDSupply Biodiesel 0.065

ADCDemand Motor Gasoline, Conventional Cars 177.177

ADFFVDemand Motor Gasoline, FFVs 1.200

ADDFDemand Diesel Fuel 47.348

19

Table C.5: Additional NotationVariable Description

γRD4 Refiner Lagrange Multiplier Refiner (D4 RINs)γRD6 Refiner Lagrange Multiplier Refiner (D4+D6 RINs)γBD4 Blender Lagrange Multiplier Refiner (D4 RINs)γBD6 Blender Lagrange Multiplier Refiner (D6 RINs)γBE10 Blender Lagrange Multiplier Refiner (E10 blend ratio)

tMG Motor Gasoline TaxestDF Diesel Fuel TaxestcBD Biodiesel Tax Credit

λ Energy-equivalence Factor between E10 and E85

CR(·) Refiner Cost FunctionCBMG(·) Blender Motor Gasoline Cost FunctionCBDF (·) Blender Diesel Fuel Cost Function

κTR ≤εSE

(0.1 ∗ 0.9λBDC+ 0.26 ∗ 0.74BDFFV

) + pEqE

qGpD6

(0.12λBDC+ 0.742BDFFV

) + λεSE

qGpD6

εSE(0.92λBDC

+ 0.262BDFFV) + pE

qEBDC

BDFFV(0.1 ∗ 0.26− 0.74 ∗ 0.9)2

(D.1)

20

WP No Title Author(s)

OTHER A.E.M. WORKING PAPERS

Fee(if applicable)

Rural Wealth Creation Impacts of Urban-based Local Food System Initiatives: A DelphiMethod Examination of the Impacts onIntellectual Capital

Jablonski, B., Schmit, T., Minner, J., Kay,D.

2016-13

Parents, Children, and Luck: Equality ofOpportunity and Equality of Outcome

Kanbur, R.2016-12

Intra-Household Inequality and OverallInequality

Kanbur, R.2016-11

Anticipatory Signals of Changes in CornDemand

Verteramo Chiu, L., Tomek, W.2016-10

Capital Flows, Beliefs, and Capital Controls Rarytska, O., Tsyrennikov, V.2016-09

Using Unobtrusive Sensors to Measure andMinimize Hawthorne Effects: Evidence fromCookstoves

Simons, A., Beltramo, T., Blalock, G. andLevine, D.

2016-08

Economics and Economic Policy Kanbur, R.2016-07

W. Arthur Lewis and the Roots of GhanaianEconomic Policy

Kanbur, R.2016-06

Capability, Opportunity, Outcome - -andEquality

Kanbur, R.2016-05

Assessment of New York's PollutionDischarge Elimination Permits for CAFO's: ARegional Analysis

Enahoro, D., Schmit T. and R. Boisvert2016-04

Enforcement Matters: The EffectiveRegulation of Labor

Ronconi, L. and Kanbur, R.2016-03

Of Consequentialism, its Critics, and theCritics of its Critics

Kanbur. R2016-02

Specification of spatial-dynamic externalitiesand implications for strategic behavior indisease control

Atallah, S., Gomez, M. and J. Conrad2016-01

Networked Leaders in the Shadow of theMarket - A Chinese Experiment in AllocatingLand Conversion Rights

Chau, N., Qin, Y. and W. Zhang2015-13

Paper copies are being replaced by electronic Portable Document Files (PDFs). To request PDFs of AEM publications, write to (be sure toinclude your e-mail address): Publications, Department of Applied Economics and Management, Warren Hall, Cornell University, Ithaca, NY14853-7801. If a fee is indicated, please include a check or money order made payable to Cornell University for the amount of yourpurchase. Visit our Web site (http://dyson.cornell.edu/research/wp.php) for a more complete list of recent bulletins.