We present designs for optimal contracts to solve the investment hold-up problem for perennial crops for the biofuel industry. A fixed-price contract is ex-ante efficient but renegotiation-proof for a limited range of discount parameters. A perfectly- indexed contract is both renegotiation-proof and ex-post efficient. Provided long-run land prices are stationary, the expected cost for both contracts converges to the long-run expected price of land for a risk-neutral farmer.Biofuels, Miscanthus, contract theory, industrial organization, renegotiation-proof contract, Marketing,

Alexander, Corinne E.

Rosch, Stephanie D.

Tyner, Wallace E.

Wu, Steven Y.

Yoder, Joshua

English

Research Papers in Economics

 
Making a market for Miscanthus: can new contract designs solve the 
biofuel investment hold-up problem? 
 
 
Steven Y. Wu*, Stephanie Rosch
1*, Corinne E. Alexander*, Wallace E. Tyner*, 
Joshua Yoder* 
 
*Department of Agricultural Economics, Purdue University 
403 West State Street, West Lafayette, IN 47906 
1 Corresponding author: srosch@purdue.edu, Ph: (765) 496-7318 
 
 
 
Poster prepared for presentation at the Agricultural & Applied Economics Association 2010 
AAEA,CAES, & WAEA Joint Annual Meeting, Denver, Colorado, July 25-27, 2010 
 
 
Keywords: Biofuels, Miscanthus, contract theory, industrial organization, renegotiation-proof contract 
 
 
 
 
 
 
 
 
 
Copyright 2010 by Steven Y Wu, Stephanie Rosch, Corinne E Alexander, Wallace E Tyner, and 
Joshua Yoder. All rights reserved. Readers may make verbatim copies of this document for non-
commercial purposes by any means, provided that this copyright notice appears on all such 
copies. fC C Making a Market for Miscanthus: Can New Contract Designs Making a Market for Miscanthus: Can New Contract Designs Making a Market for Miscanthus: Can New Contract Designs Making a Market for Miscanthus: Can New Contract Designs  gg
S l th Bi f l I t t H ld Pb l ? Solve the Biofuel Investment Hold up Problem? Solve the Biofuel Investment Hold-up Problem? Solve the Biofuel Investment Hold up Problem? p
St Y W St h i R h C i E Al d W ll E T J h Y d Steven Y Wu Stephanie Rosch Corinne E Alexander Wallace E Tyner Joshua Yoder Steven Y. Wu, Stephanie Rosch, Corinne E. Alexander, Wallace E. Tyner, Joshua Yoder
Principal’s Problem Abstract Ex Post Efficient Contract Principal s Problem Abstract Ex-Post Efficient Contract p
• For a two period contract: W t di f ti l tt t l th itt hl d bl • Since there is no existing market for these crops one strategy that is likely to • For a two period contract: We present designs for optimal contracts to solve the investment hold-up problem • Since there is no existing market for these crops, one strategy that is likely to  p g p p p
for perennial crops for the biofuel industry A fixed price contract is ex ante efficient be agreeable to both contracting parties is to construct an index from familiar for perennial crops for the biofuel industry. A fixed-price contract is ex-ante efficient be agreeable to both contracting parties is to construct an index from familiar  p p y p
but renegotiation proof for a limited range of discount parameters A perfectly commodities (such as corn wheat hay oil diesel etc) The indexed contract but renegotiation-proof for a limited range of discount parameters. A perfectly- commodities (such as corn, wheat, hay, oil, diesel, etc).  The indexed contract 
indexed contract is both renegotiation proof and ex post efficient Provided long run uses a consistent relationship between changes in the index price and changes indexed contract is both renegotiation-proof and ex-post efficient. Provided long-run uses a consistent relationship between changes in the index price and changes 
i th t t i th f ll t t i d h th t th t t i land prices are stationary the expected cost for both contracts converges to the in the contract price over the full contract period such that the contract price land prices are stationary, the expected cost for both contracts converges to the in the contract price over the full contract period such that the contract price 
l fl t th l f th t t d d ti t th li d t t long-run expected price of land for a risk-neutral farmer always reflects the value of the contracted good contingent on the realized state  long run expected price of land for a risk neutral farmer. yg g
of the world b of the world.   s, b, q ,, q
• A perfect index - where changes in the index price are completely reflected in A perfect index  where changes in the index price are completely reflected in 
the contract price without attenuation or amplification - maximizes ex-post
Motivation
the contract price without attenuation or amplification  maximizes ex post
li d l Motivation realized surplus. Motivation realized surplus.  
Bi f l h th l bi di l h t diti ll b f t d • Biofuels, such as ethanol or biodiesel, have traditionally been manufactured  ,, y
from annual crops such as corn or sugar The environmental benefits of these from annual crops such as corn or sugar. The environmental benefits of these  pg
crop sources is questionable (Schlarlemann & Laurance 2008) and diverting crop sources is questionable (Schlarlemann & Laurance 2008) and diverting 
food crops from human consumption can have real impacts on domestic food food crops from human consumption can have real impacts on domestic food 
prices (Abbott et al 2008) prices (Abbott et al. 2008) 
Wh
T h thl i t t ft b i fl f i l h
• Where: 
•The technology exists to manufacture biofuels from perennial crops such as  gy p p
switchgrass Miscanthus or willow None of these crops are presently grown at • s is a per-period fixed payment switchgrass, Miscanthus, or willow. None of these crops are presently grown at  • There is are no limits on the discount rate for this type of contract • s is a per-period fixed payment g, , p p y g
commercial scale however and the investment cost of a plant to process these
There is are no limits on the discount rate for this type of contract. 
b i i t i b df i d t h it l [ 0 1 ] commercial scale, however, and the investment cost of a plant to process these  • b is an incentive  bonus defined on the interval [0,1]
feedstocks is much greater than for a conventional corn fueled plant This leads
[,]
feedstocks is much greater than for a conventional corn-fueled plant. This leads  • q is a per-acre yield of the biofuel crop
to an investment hold-up problem: firms are unwilling to commit resources to
• q is a per-acre yield of the biofuel crop
to an investment hold-up problem: firms are unwilling to commit resources to 
Yi il d f t h id ( d t b ) build a refinery to process perennial crops without first insuring an adequate • Y is a per-acre yield of the index crop (assumed to be corn) build a refinery to process perennial crops without first insuring an adequate 
ff
p yp ()
supply of feedstocks. • P is the price of corn in each period supply of feedstocks. • P is the price of corn in each period
• Long term contracts between farmers and processors are one possible C() i i i t f ti • Long-term contracts between farmers and processors are one possible  •C() is an increasing, convex cost function
solution to the investment hold up problem In the absence of a traded market
C() s a c eas g, co e cost u ct o
solution to the investment hold-up problem.  In the absence of a traded market, 
• is the Arrow Pratt measure of risk aversion these contracts would establish (1) a price for the contracted good and (2) a Cl i
• is the Arrow-Pratt measure of risk aversion these contracts would establish (1) a price for the contracted good and (2) a  Conclusions it hd i t t method of adjusting that price (if need be) to long-run changes in either Conclusions • is the discount rate method of  adjusting that price (if need be) to long run changes in either 
f ’ ’lif i
is the discount rate
farmers’ or processors’ valuation functions. •A fixed-price contract is ex-ante efficient but renegotiation-proof for a limited • σ is the standard deviation of the distribution of corn prices (assumed to be farmers or processors valuation functions. A fixed price contract is ex ante efficient but  renegotiation proof for a limited  • σ  is the standard deviation of the  distribution of corn prices (assumed to be 
• Farmers’ long run valuation function for a biofuel feedstock is likely to be range of discount parameters. A perfectly-indexed contract is both stationary) • Farmers long-run valuation function for a biofuel feedstock is likely to be  range of discount parameters.  A perfectly indexed contract is both 
ti ti fd tf f i i tP i d d l ldi
stationary)
related to long run land values We assume corn prices approximate renegotiation-proof and ex-post efficient.  Provided long-run land prices are  related to long-run land values.   We  assume corn prices approximate  renegotiation proof and ex post efficient.  Provided long run land prices are 
tt i t h td t f bt h t t t t h l movements in land rental rates as evidenced by Du and co-author’s work in stationary, the expected cost for both contracts converges to the long-run  movements in land rental rates, as evidenced by Du and co-author s work in  y, p g g
expected price of land for a risk neutral farmer Iowa (Du et al 2009) expected price of land for a risk-neutral farmer. Iowa (Du et al. 2009).  pp
Ar i s kneutral processor’s valuation function will minimize cost subject to a • The fixed price contract provides complete insurance against absolute • A risk-neutral processor s valuation function will minimize cost subject to a  The fixed price contract provides complete insurance against absolute 
Ex Ante Efficient Contract
pj
target quantity of feedstock This target quantity will be specified by earnings losses, but no insurance against relative earnings losses. Relative Ex-Ante Efficient Contract target quantity of feedstock.  This target quantity will be specified by  earnings losses, but no insurance against relative earnings losses.  Relative 
i l it h f i t dt h f idi t t i
Ex Ante Efficient Contract
exogenously determined factors (such as transport costs of the feedstock from earnings losses are instances where profit under the fixed price contract is 
Fi k t t h tt i h i h i i t td exogenously determined factors (such as transport costs of the feedstock from  ea gs osses a e sta ces e e p o t u de t e ed p ce co t act s
l th th li d fit f th t id ti Fi d i t t l • For risk averse agents, the contract price which maximizes ex-ante expected 
the farm to the processing facility) less than the realized profit for the outside option.  Fixed price contracts also  g, p p
surplus is a fixed price contract the farm to the processing facility).     pp p
protect the agent against the risk of principal bankruptcy as the principal’s surplus is a fixed price contract.  
B th ti ill t t t l h t i ith d b tt
protect the agent against the risk of principal bankruptcy, as the principal s  pp
• Both parties will agree to contract as long as each party is either made better-
pg g p p p y p p
future liabilities are well specified ex ante On the other hand the perfect pg g p y
off (increased surplus) or indifferent (no change in surplus) This may be ex
future liabilities are well-specified ex-ante.  On the other hand, the perfect 
off (increased surplus) or indifferent (no change in surplus).  This may be ex- index completely insures the agent against relative earnings losses but does (p )( g p ) y
ante expected surplus or ex post realized surplus but there is no contract
index completely insures the agent against relative earnings losses, but does 
ante expected surplus or ex-post realized surplus, but there is no contract  not protect against principal bankruptcy or absolute earnings losses
specification which can simultaneously maximize both types of surplus
not protect against principal bankruptcy or absolute earnings losses.  
specification which can simultaneously maximize both types of surplus. 
A t i i diff t b t th t t t if d l if th li d • An agent is indifferent between these two contracts if and only if the realized  gy
index price exactly equals expected index price less the idiosyncratic risk index price exactly equals expected index price less the idiosyncratic risk  py q p p y
premium With heterogeneous agents there will be some set of agents who premium.  With heterogeneous agents, there will be some set of agents who 
are not indifferent between these contracts for any given ex-post index price References are not indifferent between these contracts for any given ex-post index price,  References
depending on the frequency of agent types in the population References
depending on the frequency of agent types in the population.
Abbott PC Hurt C & Tyner W E 2008 What’s driving food prices Abbott, P.C., Hurt, C. & Tyner, W.E., 2008. What s driving food prices, 
Jl July. July.
D X Henness D A & Ed ards W M 2009 Determinants of Io a Du, X., Hennessy, D.A. & Edwards, W.M., 2009. Determinants of Iowa  ,, y , , ,
Cropland Cash Rental Rates: Testing Ricardian Rent Theory Cropland Cash Rental Rates: Testing Ricardian Rent Theory.  gy
Unpublished Manuscript Dept of Economics Iowa State University Unpublished Manuscript. Dept. of Economics, Iowa State University.
Contact Author: Stephanie Rosch Department of Agricultural Contact Author: Stephanie Rosch, Department of Agricultural 
Economics Purdue University 403 W State St West Lafayette IN Schlarlemann J PW & Laurance W F 2008 Environmental science: Economics, Purdue University, 403 W. State St. West Lafayette, IN  Schlarlemann, J.P.W. & Laurance, W.F., 2008. Environmental science: 
47907 USA how green are biofuels? Science, 319(5859), 43. 47907, USA.  how green are biofuels? Science, 319(5859), 43.
srosch@purdue edu Tel: +1 765 496 7318;F a x+ 1765 494 9176 srosch@purdue.edu Tel: +1-765-496-7318; Fax +1-765-494-9176

depending on the frequency of agent types in the population.

Determinants of Io a

Stephanie Rosch Department of Agricultural Contact Author: Stephanie Rosch, Department of Agricultural Economics Purdue University 403 W State St West Lafayette

Making a market for Miscanthus: Can new contract designs solve the biofuel investment hold-up problem?

Making a market for Miscanthus: Can new contract designs solve the biofuel investment hold-up problem?

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