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'WORKING PAPERS
International
Trade
International
Economics
Department
TheWorldBank
November
1992
WPS1024
An ExactApproach
for Evaluatingthe Benefits
from Technological
Change
Will Martin
and
Julian M. Alston
How a modified trade expenditurefunction can be used to
measure the welfare costs and benefits from technological
change- in a modelthat allowsfor multiplemarketdistortions
and generalequilibriumfeedback.
PolicyReaarch WodzingPaper5disaminatethefindingsof workin pgness andencowagetheexchangeof ideasamnongBank
staffand
allotsinrei
sed in developmtiasues. Thesepapes disnbutedbytheRearchAdvisoiy Staff,canythenamnesof
theauthors.reflect
onlytheirviews,andshouldbe usedandcitedaccordingly.
Thefindings.interpretations,and
conclusionsasetheauthors'own.They
should
not be attnbutedto the WorldBank.its Boardof Directo itsinanagcnient. or any of itsmaer countries.
t
PolleyResearch|
Trade
International
WPS1024
Thispaper-aproduct of theIntemationalTradeDivision,IntemationalEconomicsDepartment-is part
of a larger departmentalstudy of how distortionsin commoditymarkets affect the benefits front, and
incentivesfor undertaking,agriculturalresearchand developmentprojectsin developingcountries. The
study was funded by the Bank's ResearchSupportBudgetunder researchproject "AgriculturalPolicy
Reformfor DevelopingCountries"(RPO 676-11).Copiesof this paperare availablefree from the World
Bank, 1818 H Street NW, Washington,DC 20433. Please contact Dawn Gustafson, room S7-044,
extension33714 (November1992,31 pages).
It is commonlybelievedthat taxingagricultural
commoditiesin developingcountries,and
subsidizingagriculturalcommoditiesin industrial countries,reducesincentivesin the developingcountriesfor both currentproductionand
longer-term investments in capital, knowledge,
modelsbetter measurethe implicationsof tradedistortingpolicies.Martin and Alstondescribe
how to hamess these approachesto evaluatethe
benefitsand costs of technologicalchanges.
They show that a modified trade expenditure
technology,and infrastructure.It is arguedthat
distortionsin agriculturalmarketshavekept
investmentsin researchand development,and
productivityrates, low in agriculturein developing countries.
function can be used to measurewelfarechanges
exactly,with a modelconsistentwith the optimizingbehaviorof both producersand consumers. They do so in a general settingthat allows
for multiplemarket distortionsand multiple
paths of generalequilibriumfeedback.
Martinand Alstonlay the theoreticalfoundation for empiricalstudies of how such distortions
affect returns to agriculturalresearchand developmentin developingcountries.Earlierstudies
of the benefits fromtechnologicalchangehave
typicaUyused partial equilibriummodelswith
MarshaUianwelfaremeasures.Such modelshave
not allowedfor a general set of market distortions and marketinteractions.
Theyillustratethis approachusing a quadratic form for a profitfunctionthat is a componentof the trade expenditurefunction.They spell
out, in principle,how to applythis approachwith
minimalrequirementsfor additionalinformation,
usingthe resultsfrom a computablegeneral
equilibriummodel.Theyprovide a diagramto
illustratethe applicationof the technique.
Techniquesrecentlydevelopedfor evaluating welfarein the context of generalequilibrium
The PolicyResearchWorkingPaperScriesdisseminatesthefindingsof workunderwayin theBank.Anobjectiveof the series
is to get these findingsout quickly,even if presentationsare less thanfuDypolished.The findings,interpretations,and
conclusionsin thesepapersdo notnecessarilyrepresentofficialBank policy.
Producedby the Policy ResearchDisseminationCenter
AN EXACT APPROACHFOR EVALUATINGTHE BENEFITSFROM
TECHNOLOGICALCHANGE
Wdi Martin and JulianM. Alston"
WorldBank and the Universityof Califomia,Davise
Tableof Contents
The Welfare Formulation
3
The Specificationof TechnicalChange
6
Direct Incorporationof TechnicalChange Variables
Output- or Input-Augmenting TechnicalChange
A Varying-ParameterApproach
Comparisons of Types of TechnicalChange
8
9
11
13
Implications of FunctionalForm
13
Interpreting the Measuresof the WelfareEffectsof TechnicalChange
16
Relationshipto ConventionalMeasures
21
EmpiricalIssues in Implementing the Approach
24
Conclusion
27
References
30
FOR EVALUATINGTHEBENEFITSFROM
AN EXACTAPPROACH
CHANGE
TECHNOLOGICAL
Giventhe centralroleof technicalchangein agriculturaldevelopment,the highandrising
pressureon agriculturalresearchbudgets,and the need to allocatescarce researchresources
efficienty, a frameworkfor the analysisof benefitsfrom researchand technicalchangeis
required. The task is complicatedby the widevarietyof formsof technicalchangethat affect
agriculture. An extensiveliterature on the evaluationof benefitsfrom researchhas now
developed(e.g., seethe surveyby Nortonand Davis, 1981). Thisliteraturehasprovidedmany
insightsinto the effects of differenttypes of technicaladvanceon the welfareof particular
groups,and in the presenceof particulardistortions(e.g., Edwardsand Freebairn,1981;Alston,
Edwardsand Freebairn,1988). However,it has proveddifficultto generalizetheseinsightsto
situationsinvolvingmorethan one technicalchangeor morethan one distortion,especiallyin
aes wheremorethan onepriceis endogenousso that thereis morethanone sourceof general
equilibriumfeedback(e.g., see Thurman, 1991b,and Alston, 1991, pp. 41-46). In most
countriesagricultureis characterizedby differentialdistortionsamongclosely-linkedmarkets,
so that a methodologythatcannotdeal with new technologyin a distortedmulti-marketsetting
is of limitedapplicability.
In addition, there are some other problemswith the state of the art of evaluating
technologicalchange. For the most part, the analysishas relied upon standardMarshallian
to the
consumerandproducersurplusmeasureswhichcan, at best,provideonlyapproximations
truewelfareeffects,are not amenableto generaliztion,and do not exploitthe manyadvantages
offeredby a modem,dual formulation.With the simplead hoc supplyfunctionsusedin most
2
analyses,it has frequentlybeen difficultto distinguishbetweenfixedand variableprices, and
to specifyexactlywhichshadedareaswere the appropriatemeasuresof welfarechange,in the
commoncase of multi-output
productionpossibilities(e.g., see Rose, 1980).
The purposeof this paperis to put forwarda generalapproachto evaluatingthe effects
of technicalchangethat will provideexact measuresof the welfareconsequencesof technical
changeand will allow the incorporationof multipledistortionsand multipleinteractionsin a
generalequilibriumsetting. At the same time, the approachis able to take advantageof the
many insightsprovidedby the previousliterature. By using Taylor-seriesexpansions,it is
possibleto obtainapproximatemeasureswhichallow an intuitiveinterpretationof the results
obtainedusing the exact evaluationproceduresand which bear a clear relationshipto the
traditionalconsumerand producersurplusmeasures.Thesemeasuresallowthe theoreticalbasis
of the taditional surplusmeasuresto be evaluatedand the importanceof the approximations
on
whichthey are basedto be assessed.
The basicformulationof the welfaremeasuresto be utilizedis givenin the nextsection
of thepaper. Followingthat, threealternativerepresentations
of technicalchangeare described
and compared,the choice of particular forms of technical change is discussed, and the
relationshipbetweenthe form of technicalchangeand the functionalform of the net revenue
function,is illustrated. Then, in order to providean understandingof the effectsof important
typesof technicalchange,and to illustratethe relationshipbetweenthe exactapproachand the
conventionalmethodsin the literature,approximatemeasuresof welfareeffectsare derived.
After that, someempiricalissuesin implementatingthe approachare discussedwith a
w to
maing clear how the approachmaybe usedin practice. A finalsectionconcludesthe paper.
3
The WelfareFormulation
The welfaremeasuresproposedin this paperare basedon a modificationof the distortedtrade
expenditure
fiuition or balanceof tradefiuction widelyutilizedin the trade literature(e.g.,
Vousden,1990;Lloyd and Schweinberger,1988;Andersonand Neary, 1992)to evaluatethe
effects of trade and exogenousshocks. The basic form of the modifiedtrade expenditure
functionused in this paper is definedfor a single-household
economyas:'
(1)
H' = e(p, w, d) - g(p, w. v, .0 - (p - PP'm(p, W vJ -f
andthe money-metric
measureof totalwelfarein the economy(Hr)is basedon four components:
(a) the minimumexpenditurenecessaryto obtaina givenlevelof utilityfrom consumption;(b)
benefitsin the form of incometo ownersof factorsof production;(c) benefitsin the form of
governmenttaxationrevenuesfrom tradetaxes;and (d) net transfersfrom abroad. Thesefour
componentsare obtainedas follows. The fimctione is the net expenditurefunctionof a
representativehouseholdfor a givenvectorof domesticprices,p, and a level of utilitywhich
is exogenouslyspecifiedat leveli/ sincethis measureis baseduponthe Hicksianmoney-metric
measuresof welfarechange. The functiong definesthe (maximized)
net revenuegeneratedfrom
productionin the economyfor givendomesticpricesof outputs,pricesof endogenously
supplied
t Althoughthe dcussion
in this paporis pedominantlycouchedin trm of dualfunctions,thmeis no need
for the functionalspecification
used in any paticular ampiricalanalysisto be specifieddirty in termsof these
functions.Thetechnologymay,instead,be specifiedusingpdmalproductionor transfonraionfunctionssuchu
theCobb-Douglsor CMS.Whenthenecessayandsufficientconditions
for optimizalicn
aresatisfied,thoresuting
supplyand demandfunctionsare consistenwith an appropriaterevenuefunctionsafying al of the theoretical
requirements.Similarly,theconsumption
strhcturemaybe specifiedusinga primalspecification
suchas the laoinRubinutilityfimctionwhichwideliosthepopularlinear ExpenditureSystem
4
factors,w, a vector'F fixedfactors,v, and a vectorof technologyvariables,r, representingthe
state of the availabletechnology. For a vector of world prices,pw, the second-lastterm in
equation(1) is the governmentrevenuegeneratedby .ariffs (or spent on exportsubsidies). It
and the
is calculatedas the innerproductof the vectorof tradetaxeson eachcommodity(p-pW)
vectorof importlevels,m, whichare determinedby productand factorpricesand the resource
endowment. In this standard formulation,it is assumed that these tariff revenues are
redistributedcostlesslyto the consuminghousehold. Finally,f, is the financialinflow from
abroad,in the form of net transfers,net factorincomeflows,or foreignborrowings.
The significantmodificationmade here-to the standard trade expenditurefunction
appearingin the trade literature(e.g., Vousden)-is the use, whencalculatingtariff revenues,
of the actual level of imports rather than the quantity of imports that would result if
compensationhad been madeto hold utlity at d. This approachhas a numberof advantages
overthe usual formulation.Firstly,and as arguedby Mayshar(1990),it is consistentwiththe
assumptionof hypotheticalcompensationon whichall of thesemeasuresare based-the use of
a compensated
importdemandfunctionwouldbe appropriateonlyif compensationwereactually
paid, rather than being purely hypothetical. Secondly,this approachprovidesestimatesof
welfarechange that are consistentwith the measuresobtainedby direct evaluationof the
expenditurerequiredto achievethe changein welfareoccurringin a fully specifiedgeneral
equilibriummodel. If preferred,the actualimportdemands-m(p, w, v)-in equation(1) can
be replacedwith the compensated
demandsso as to providea welfaremeasurebasedon actual,
ratherthan hypothetical,compensation.
S
The use of the expenditurefunctionapproachalso meansthat moneymeasuresof the
compensation
requiredto maintaina particularlevelof utilityare deri ld in a consistentmanner,
avoidingthe discrepanciesthat can arise whencompensationis conisidered
one marketat a time
(see Thurman,1991a,p. 1513;Huethand Just, 1991,pp. 15-18).
The modifiedtrade expenditurefunctionpresentedin equation(1) can be generalizedin
a numberof ways. Firstly, it can be extendedfrom a single householdto any numberof
householdssimplyby identifyingthe expenditureand revenuefunctionsassociatedwith each
householdor householdgroup. Similarly,verticalmarketlinkagesthroughintermediateinputs
can be incorporatedby identifyingseparatenet revenuefunctionsfor the input-supplying
and
input-usingsectors. Domestictaxationon production,consumptionor factorreturns can be
incorporatedby distinguishing
betweenthe pricespaidby demandersand receivedby suppliers
and by accountingfor the resultinggovernmentrevenuesin the sameway that tariff revenues
are incorporated.The assumptionthat factorreturnsare redistributedcostlesslycan be relaxed
by specifyingthat a proportionof the governmentrevenuesis lost to costssuchas administration
or rent seeldng(Andersonand Neary).
An exact money-metricmeasureof the welfarechangeresultingfrom technicalchange
can be obtainedfromequation(1) simplyby comparingthe net expendituresrequiredto achieve
a givenlevel of utility, d, underthe initialtechnology,Tr, and underthe new technology,TI.
The compensatingvariationversion of the measureis defined with the utility level in the
expenditurefunctionlieldconstantat u°':
(2)
Ri - BO= H(pj p. W,,
wv, vI., J - Hpo, pot we. v,
top).
7,
6
The equivalentvariationversionof the welfaremeasureis exactlyt;hesameas that definedin
equation(2), exceptthat utilityis heldat u' ratherthan u°.
The Specificationof TechnicalChange
An importantinsight from the traditionalliteratureon the evaluationof the benefits from
technicaladvancein agricultureis the impoktance
of the particularformof technicalchangefor
the size and distributionof benefits. In particular,a parallelshiftof supplyhas been shownto
benefitproducersregardlessof the demandelasticity(unlesssupplyis perfectlyelasticwhen
there are no benefitsor coststo producers)whilea proportionalsupplyshiftwill surelyreduce
producerwelfarewhendemandis inelastic(e.g., Scobie,1977). Thechoiceof assumptionabout
the natureof the research-inducedsupplyshift has been dictatedto a great extent by a prior
choice of functionalforms for supply and demand functions,combinedwith a desire for
convenience. In particular,multiplicativeshifts typicallyhave been usedin conjunctionwith
constantelasticitymodelsand parallelshiftstypicallyhavebeenusedwithlinearmodels. There
are other, lessdramaticbut still potentiallyimportant,implicationsfor the sizeand distribution
of researchbenefitsfrom othercombinationsof assumptionsabout functionalformsof supply
and demand,elasticitiesof supplyand demand,and the natureof the research-induced
supply
shift(see,for example,Duncanand Tisdell,1971;LindnerandJarrett, 1980;Rose;and Norton
and Davis). By analogy,thechoiceof functionalform for a profitor revenuefunctionwill have
implicationsfor whichformsof technicalchangeare analyticallytractableand the combination
of thosechoicesmightwellhave implicationsfor the sizeand distributionof the benefits.
7
Giventheseinsights,it is desirablethatthe formof technicalchangespecifiedwiNhin
the
moregeneralspecificationproposedin this paper shouldat leastbe able to capturethe broad
types of technicalchange identifiedin the earlier literature. An importantadvantzgeof
specifyingtechnicalchangein termsof the revenue1-nctionis that this also makesexplicitthe
need to remainconsistentwiththe basicrequirementsof a revenue(or profit)function. In the
earlierliterature,the impactof the specifiedtechnicalchangeson the satisfactionof theoretical
requirements by the profit function characterizing the production side of the
economy-monotonicity,homogeneityof degreeone and convexityin prices, symmetry,and
adding-up-weresimplynot considered.An advantageof explicitlyusingthe revenuefunction
approachis that theserequirementsfrom theorycan assuredlybe satisfied.
The formsof technicalchangeconsideredin thispaperare disembodiedtechnicalchanges
involvingvariousformsof biases. Thereare threewaysin whichdisembodiedtechnicalchange
canbe introducedintoa profitfunction:(a) the directincorporation
of technicalchangevariables
in the function(Binswanger,1974;Kohli, 1991),(b) the use of a distinctionbetweenactualand
effectivequantitiesand prices, and output-or input-augmenting
technicalchange(see Dixon,
Parmenter,Suttonand Vincent,1982)for very extensiveapplicationsof this approach);and (c)
the use of a varying-parameter
specificationin which the coefficientsof a static model are
2 In generalform thesethree specifications
themselvesfunctionsof technicalchange.
may be
representedas:
(a) Xr = g(p,w,v,r I a),
2 FulginiiandPerrin(1972)
(b)
X=
gfp(r)^wvI a),
(c)
gg(P.w,VI
a(r)),
providean exampleof thistypeof approachin a primalspecification
in whichthe
paamets of a Cobb-Douglas
productionfunctionthemselves
ar functionsof technological
changevariables.
8
where X is variable economicprofit (i.e., the total return to the fixed factors), all of the
variablesare as previouslydefined,and a is a vectorof parametersof the profitfunction. The
consequences
of thesethreetypesof technicalchangeare consideredbelowusinga second-order
Taylor-seriesexpansionto approximateany - .itrary functionalform for the revenuefunction.
For simplicityand concreteness,a quadraticprofit functionis specified.
Direct Incorporationof TechnicalChange Variables
The first specificationof technicalchangeis wellknownfrom the empiricalliteratureon
the estimationof flexiblefunctionalforms(seeBinswanger).Underthisapproach,the technical
changevariable(s)enter theprofitfunctionin the samewayas a quasi-fixedfactorwould,except
thatbeing "public"goodsthey receivea zero factorreturnat the level of the firm. In this case,
the technicalchangecan be thoughtof as an increasein the supplyof nonrivalgoodswhichare
providedfree to individualproducers. Using the quadraticprofit %unction
to illustratethis
approachyields:
(3)
whereP = [p' w' v'I''
s= a+c*'P+
*P'AP
is an n x 1 vectorof outputprices,inputprices, fixedfactors,and
technologyvariables, ao is an intercept parameter, ae' = cvl,...
, atJ is a 1 x n vector of
parameters,and A is an n x n matrixof parameters,av,,.Typically,only a smallnumberof
indexesof technicalchange(Tdwillbe required,and a popularspecificationinvolvesthe use of
only one suchvariable,the time index. Give-nthe choiceof a qjadratic form in equation(3),
thesevariableswill enter the profit functionquadratically.
9
By Hotelling'slemma,differentiationof the profit functionwith respectto the output
prices yieldsthe outputsupplyfunWtions.The inputdemandfunctionsfor the variableinputs
are obtainedby differentiating
withrespectto theirprices,whileinverseinputdemandfunctions
for the fixedfactorscanbe obtainedby differentiating
withrespectto the quantitiesof the fixed
factor inputs. For the quadraticfunctionrepresentedin equation(3), this will result in the
technologyvariablesenteringthe outputsupply and input demand functionsas linear shift
variables. A typicaloutputsupplyor inputdemandfunctionarisingfrom this specificationis:
(<4)
x;
=a, + a av, + m
pi
r1l
.tel
q
a+
h-I
Clcarly,the speci.5cation
representedby equation(4) alows onlyfor parallelshiftsin theoutput
supplyor inputdemandequations,sincethe effectof Thon x, does not dependon either the
outputor the price level.
Output-or Input-Augmenting
TechnicalChange
Anotherspecificationwhichhas been used widelyin modelingtechnicalchangeis the
distinctionbetweenactualand effectivequantitiesandprices utilizedby Dixonet al. Underthis
approach,technicalchangeis thoughtof as somethingthat increasesthe effectivequantityof a
goodassociatedwitha givenphysicalquantity. An importantfeatureof this specification
is that
there is a correspondingchangein the effectiveprice of the good. An increasein the effective
quantityof a goodprovidedby eachphysicalunit will reducethe effectiveprice relativeto the
price of the physicalunits.
10
Technicalchangeof this naturemaycomeaboutin manyways,suchas an improvement
in the physicalqualityof the good,or fromimprovedinformationor managementwhichallows
the goodto be utilizedmoreefficiently.Usi-crthis approach,the relationshipbetweenphysical
and effectivequantitiesof a particulargood (i.e., inputor output),xi, can be representedby x,
= x,.71,
wherex4 is the physicalquantityof the good;x; is the effectivequantityof the good
and 74 is the levelof output-augmenting
or input-augmenting
technicalchangefor good i. The
1
correspondingrelationshipbetweenactualand effectiveprices is pA= p,he,
wherep, is the
effectiveprice of the good;pAis the actualprice and Tt is the augmentation
factor. Whenxi is
an input, input-savingtechnicaladvanceis representedby a declinein
T1,
whichreducesthe
physicalquantityof the inputrequiredfor one effectiveunitand also lowersthe effectiveprice
relativeto the actualprice. Whenxiis an output,an increasein i, representsoutput-augmenting
technicalchange: an increaseraises the physicalquantityassociatedwith a given effective
quantityand raisesthe effectivepricefor a givenactualprice.
Underthisspecification
of technicalchange,producersare representedas optimizingover
effectivequantitiesand prices, ratherthanactualquantitiesand prices. This causeschangesin
the quantitiesof goodschosen,and hencein the revenuesgenerated. Oncethe quantitieshave
beenchosen,however,the revenuesmaybe calculatedby simplemultiplication
usingeitherthe
actualor the effectivequantitiesand prices sincethe e zermswill cancelundermultiplication.
Theprofitfunction,incorporatingtechnicalchange,is definedby replacingthe variables
in equation(3) with the correspondingeffectivevaluesof thosevariables,and eliminatingthe
terms involvingthe directtechnicalchangevarables, as can be seenin equation(3').
(3')
-r = CO+ ar
+ % P"AP",
11
whereF = Lj ' w ' v' j.
Considering,for simplicity,technicalchangeaffectingonly the
variable output quantitiesx, and the correspondingprices, p, output supply or input demand is:
n
x=
(5)
q
m
ag+E a%P, +, alr Wr+E aiVk,
J.1
r.l
k-I
where thex, andp, variablesare as defined above. Substitutingthe definitionsof p and x into
equation (5) yields a behavioral function in the actual price and quantity variables:
(6)
(6)
Xi =T [ af + Sn
J-1
(P4)m
frr
p7)+
E a.
w, +E aJt ]k.
r-I
k.1
From inspection of equation(6), a technicaladvance of this form for commodityi gives rise to
a divergentsupplyshift whichis morethan proportionate--acombinationof a parallel shift (from
the impact on the intercept) and a pivotal shift (the impact on the slope is quadratic in -,).
A Varying-ParameterApproach
A third way of incorporatingtechnlicalchange is to allow all of the parameters of the
profit function to be expressed as functionsof a scalar technologyindex, f.
In this approach
it is important that the functions that define the parameters are chosen so that the desired
parametric restrictions hold over the region of interest. In equation (3), after discarding the
vector of technologyindexes (7) so that P = Lo' w' v'l', the parameters may be defined as a
function of the technologyindex. For example, assuminga linear relationship:
of
= a°o + lo 7p;
of = a° + flrp;
ag, = Oag + #'rp-
12
Thenthe supply(inputdemand)functionsmaybe expressedas:
(7)
XI a°+
i ,li 7p +E (Cao+J P)pJ + E (ask+
J-l
7p)W,, + E (alok+PMP) Vt
r l
&El
wherethe variablesare as definedabove. Clearlythis specificationpermitsany combinationof
slope and interceptchangesso that the shiftsof supplyinducedby technicalchangecould be
parallel,convergent,or divergent,anda divergentshiftcouldbe proportionaleitherin the price
direction(i.e., a pivotalshift in Lindnerand Jarrett's terminology)or in the quantitydirection
or it couldbe nonproportional.Thusanysuchshiftsare, in principle,compatiblewitheconomic
theoryunderthe assumptionof a quadraticprofit function.
To seethis moreclearly,differentiating(7) withrespectto the technologyindexyields:
x / alp- # + flyPP+E P.Wr+E
(8)
J-l
r,1
V
kal
A numberof specialcases can be seenby settingsomeof the technology-changing
parameters
a,
(i.e, a's) in equation(8) equalto zero. For instance,if all of the parametersexcept are zero,
the supplyof xi shiftsin parallel,a resultthat was obtainedearlierby incorporatingtechnical
changedirectlyinto the profit function. Alternatively,if all of the parametersof this equation
a,,
except are zero, we have a proportionalshiftof the supplyof
a,in the price direction.
It is also usefulto considerdirectlythe implicationsof this type of specificationfor the
effectof technicalchangeon the valueof theprofit function.Differentiatingtheprofit function
withrespectto rP yields:
13
(9)
air/dt = 0 + p'P + * PtBP
Companson of lypes of Technical Change
The three approachesabove providegreat flexibilityin the specificationof technical
changewhilemaintainingconsistencywith the requirementsimposedby economictheory. As
of technologyvariablesin the revenuefunction
wasdemonstratedabove,the directspecification
leadsto parallelshiftsin the resultingsupplycurveswhilethe use of the effectivequantity/price
approachleads to (morethanproportional)divergentshiftsin these functions. A combination
of the two approachescouldbe usedto generateany typeof shiftin a particularoutputsupply
or inputdemandfunctionbelievedconsistentwith observedchangesin the technology. For
example,a convergentshiftin an outputsupplycurvecouldbe generatedthrougha combination
technicalchangeand a negativeoutput-augmentation.
of a positivedirectlyoutput-increasing
Altematively,incorporatingtechnicalchangeas an adjustmentof parameters-ratherthanas an
argumentof the profit functionor a modificationof its arguments-maybe used to represent
exactlythe types of supplyshiftsthat have beenpositedin the previousliterature.
Implicationsof FunctionalForm
The quadraticprofit functionleads to linear equationsfor output supply and input
demand. Using the quadraticform, differentwaysof introducingtechnicalchangemay have
differentimplicationsfor the shiftsin the functions. However,it is relativelystraightforward
to representtechnicalchangesin waysthatare consistentwithboththevariousadhoc treatments
in the literatureand the restrictionson the profit functionthat are impliedby the theory.
14
In theliteratureon benefitsfromtechnicalchange,typicallyparallelshiftshavebeenused
in conjunctionwith linear supplyfunctionsand multiplicative(proportional)shifts have been
used with constantelasticityfunctions,primarilyfor convenience. In the approachproposed
here, the approximatingfunctionfor the modelis definedat the level in whichwe are primarily
interested(the money-metricof welfarechange)ratherthan at the level of its derivativeswith
respectto price (i.e., at the levelof supplyand demandfunctions).Thusthe effortand potential
problemsinvolvedin integratingback to computewelfareare avoided.
To illustratethis point, considerthe translogprofit functionthat has been widelyused
in recent years. Since the translogis a quadraticform in logarithmsof variables,we can
interpret equation(3) as a translogby redefiningthe variablesas logarithms,and we can
introducethe alternativetypesof technicalchangeas for the quadraticprofitfunction. Thatis,
In ir = ao + a' enP + * enP'A InP,
(3")
where en P = (tn p' fn w' env' r 'I' The applicationof Hotelling'slemmato the translog
form suchthat
profit functionyieldsoutputsupply(inputdemand)equationsin share-dependent
Si
=
pi/t
= atnT/8anp1.
The directintroductionof technicalchange(e.g., as by Binswanger)is reflectedin a set
of additionallineartermsin the shareequationsas follows:
n
(10)
Si= a,+
m
Ea,npJ+Ea,,
j1l
v1
q
s
nw,+Eakinv+ E&
t-l
.
hlaw
In this equation,MSl/.Th= cO,is a constantand the profit share of the fh output(or input)xi
changesby a constantamountin responseto a unit changein the technologyindex, vh. The
15
natureof the impactof technicalchangeon the supplyfunctionexpressedin the levelsof the
variables(ratherthan sharesand logarithms)is difficultto see in this case.
Kohli (p. 105) showedthat an input-augmenting
technicalchangein a translogcost
functionwouldlead to a changein the interceptsof the share equationsfrom the cost function.
A similarresult holds for output-augmenting
technicalchangein the translogprofit function.
If we define fnx; = enxlrexp(7ipIj
= Efnxj-7
and fnp; = inpj+ej and substitutefor the quantities
and pricesin the translogprofitfunction,the impliedshareequationsfor outputsand inputsare:
n
(11)
m
q
n
kal
J.1
Si =a, + , a. inp, +E cq,in w,+E Xken V,t+ ot7
J-1
r-I
The similaritybetweenthis result and that in equation(10) illustratesthe point that alternative
formsof technicalchangethat have differentimplicationsfor net revenuesmay appearsimilar
in the contextof the derivedshare or supplyequations;in otherwords,a numberof different
specificationsof the underlyingtechnical change might be consistentwith a particular
specificationof outputsupply. In thiscase twodifferentspecifications
of the natureof technical
changeled to additiveeffectsin share equationsthat can be distinguishedonlythroughthe fact
that in equation(10) the coefficientson technicalchange(aq) are free while in equation(11)
they are equalto the correspondingprice coefficients.
Finally,the moregeneralvarying-parameter
approachcouldbe appliedin the sameway
as for the quadraticcost function. Whileit is not donehere, in the interestof savingspace,it
wouldbe straightforward
to applythe typeof approachusedfor derivingequation(7)to the case
of the translogor someother functionalform.
16
Interpreting the Measuresof the WelfareEffects of TechnicalChange
The measuresof the gains from technicalchangeproposedin this paper require some
interpretationif theiruseis to be accepted. Fortunately,a second-orderTaylor-seriesexpansion
allowsthemto be interpretedin an intuitivemannerthat convenientlydemonstratesthe linkages
betweenthesemeasuresand the diagrammatic,partialequilibrium,treatments.
Considerthe followingfunctionthat correspondsto that in equation(3) but with the
vectorof technologicalchangevariables(7)enteringin a generalform, excludingnet transfers,
and using morecompactnotationso thatp representsall prices of outputsand variablefactors
and quantities of fixed factors and the speciJictariffs (t) are defined so that t = p - pv:
(12)
H = e(p, u) - gfp, t) -t'm(p) = z(p, u, t) -t'm(p).
wherez(p, u,
7)
=
e(p, u) - g(p, 7) is the expenditurefunctionfor imports. Thus z, is the
vector of compensatedimport demands(in which utility levels are constant) whereas n
representsthe vectorof uncompensated
importdemands(in whichutilitylevelsare endogenous).
Supposetechnologychangesfrom -r to rl so that the changein welfare,definedas the
compensatingvaiation for the changein technology,may be representedas:
(13)
Hz - Ho = feip,,u - e(po.
ua)J- (g(p,Ov - g6Pe,
rdl - t'[m(p) - m(p)J,
wherep, is the vectorof prices underthe new technology,7t. Here we can see that the total
welfarechangeis equal to (a) the compensatingvariationfor the changein consumerwelfare
due to the price changeinducedby the technologicalchange(the first termin squarebrackets),
17
minus(b) the increasein producerprofitdue to the new technology(thesecondtermin square
brackets),minus(c) the changein govemmenttariffrevenuesdue to the new technology(the
last termin squarebrackets).Considerthe casewherechangesin technologycanbe represented
by changesin a scalarindex, r (corresponding
either to ?' in equation(8) or to changesin a
particulartechnologicalvariable,r; in equation(4)). A second-orderapproximationto the
welfareeffectsis:
(14)
H1 -H
HI-0
==87 ,HAr + I a 2H (Ar)
2
2
Thecomponentsof this equationare obtainedby differentiating
equation(13) withrespectto r.
Takingthe first derivativeof H withrespectto 7-at the initialpointof approximation-yields:
(15)
H,
= [e'
-
-gp'-t'm,J(dp/d) - g, -tm
1z;- t'mJ(dp/d7) - g&- t'(2j,crgJs
wherecy is the effectof a changein incomeon the vectorof quantitiesconsumed.
In equation(15), the first term representsthe welfareeffectsassociatedwith responses
to price changes,the secondrepresentsthe effecton profit (holdingprices constant),and the
third representsthe effectson tariffrevenuewhenimportschange(holdingprices constant).
In the secondline of equation(15), the uncompensatedimport demand responseto
changesin technologyhas beendecomposedintoa shiftof the compensated
importdemandand
an incomeeffectusinga type of Slutskyequationin whichCyis the vectorof incomeeffectson
consumer(andhenceimport)demandswhichis usedto capturethe incomeeffectsof changes
18
in technology(throughgj). These incomeeffects measurethe shifts in the uncompensated
importdemandfunctionsin responseto any changesin incomeinducedby the new technology,
a generalequilibriumeffectthattypicallyis not takenintoaccountin partialequilibriummodels
of benefitsfrom technicalchange.
Consider a small open economy,with protectionprovidedby tariffs, so that both
domesticprices and the world prices are unaffectedby technologicalchange in the home
country. In such a case, with exogenousprices, changesin technologyaffect compensated
importdemandonly throughthe outputeffect(z,, = gF,)and equation(15) reducesto
8H187
- g, - t'm,
H,
=
=
_ g, _ tt(z,,-Cyg,)
= - & - 'gcrgj
so that the welfareeffect is simplythe increasein producerprofit plus the changein tariff
3 The secondderivativemaybe writtenas
revenue.
H2l/a7,2=
H
=
=
-
g,, - t',
-
e
g-
crg,).
Substitutingthesecomponentsinto (14)yields:
(16)
HI - Ho
=
=
gA
+ '
g,,(sA
_ [gA7 + %A
g,&./)2
2
+ t'mA
+ % t'm(Ar) 2 J1
2 1.
+ tI(gP,-_cgd)Ai + % t'(g,,-Cyg,(ft&r)
31ncreases
in tariffstrickenimportsgeneratea welfar gainwhiloincreasesin subsidizedimportsor exports
cause welfare losses. This term is zero in the absence of distortions but a first-order, and hence potentially
important,term in the presenceof distortions.For a sufficientlylargetariff, it is conceivabletbat the welfare
consequec of a productivityincreasecouldbe negative,as demonstrated
graphicallyby Johnson(1967).
19
The first two termsof equation(16) are the welfaregainsin termsof increasedproducerprofit
and the secondtwo termsare the welfarelossesdue to reducedtariff revenue.
With technicalchangeof the type representedby rP in equation(7), and exogenous
prices, there are no second-ordereffectsto considerbecausethe secondderivativesvanish(g,
= 0 and g.,
=
0, as can be seen from equation(9) and the fact that g., = a2x/&9)and
thereforeHZ- Ho = - [g, +
t9'(-ccyg)j]r.
Thismeasureincludesthe effectsof changesin the
technologyindex on all of the equationsof the systemof outputsuppliesand factor demands
derivedfromthe profitfunction,and the effectsof changesin tariffrevenuesarisingfromshifts
of the uncompensated
importdemanddue to changesin both outputand income. Even with
moregeneraltypesof technicalchange,the omissionof suchhigher-ordertermsseemsunlikely
to lead to serious errors in most cases.
If (a) onlyone output,x,, wereaffectedby changesin the technologyindex,(b) the only
distortionin the economyis a tariffon importsof that commodity,and (c) therewereno income
effectsin importdemand(i.e., m, = a,m/ar = -axl/ar),the welfarechangewouldbe equalto
(17)
HI - Ho = - gAr + t,(ax,/a)Ar .
And,if there were no distortionsin the marketfor that good (i.e., t, = 0), the welfarechange
wouldbe simplyHI - Ho = - gA-r.4 For instance,with the quadraticprofit function(linear
supply)and a changein technologythat shiftsonly the supplyfunctionfor one output(x) in
parallelas shownin equation(7), g&will equalAA (i.e., j3 > 0 and P4= 0 for al in). Since
the change in output is Ax, = P Ar, the welfare changeis AH = -p,&x,+ t,Ax, = -(i, - t,)Ax,
40ncedistortionsare introduced,thewelfarechangealsoinvolvesthe secondterm in (17),
20
= -p,Axi,where an increasein welfareis a negativenumberbecauseit correspondsto the
reductionin net expendituresrequiredto achievea givenlevelof utility. Thus, in thisextremely
simplecase,the appropriateapproachinvolvesevaluatingthe quantityincreaseat worldprices,
a widelyusedrule of thumbfor measuringresearchbenefits.
Evenfor this particulartype of technicalchange,this rule of thumbbreaksdownwhen
any of the specialassumptionsthat underlieit are relaxed. In particular,whenother markets
are distorted,and thereare inducedchangesin quantitiesof othergoods,therewillbe additional
effectson governmentrevenuesto consider. Suchinducedchangesin quantitiesmightcome
from linkagesin supplyor demand.
For instance,even wherepricesare exogenous,manyformsof technicalchangecan be
expectedto changethe supplyof morethanonecommodity.An output-augmenting
productivity
increasein corn is likely to draw resourcesaway from competingcrops such as soybeans,
affectingthe volumeof tradein bothcorn and soybeansand, assumingthereare distortionsin
both markets,the governmentrevenuesfrom trade taxes or subsidiesin both markets. The
incorporationof this type of technicalchangerequiresa furthergeneralization. equation(17)
to includeeffectson tax revenuesacrossall commodities
(18)
HI - Ho = - g]iT + [
tj(813r) ]AT
lj .
In addition,as can be seenin the equationsabove, even when new technologyhas its
direct impactonly on one commoditysupplyfunction,and prices are exogenous,the faUin
importdemandis not equalto the increasein outputfor the goodwhosesupplyhas shifted(i.e.,
ar.4187• -axlar), and not equal to zero for othergoods(i.e., m1/7 •d 0, for j
wei),
unless
21
incomeeffectsare zero. In general,incomechangeswill cause shiftsin the import demand
equationsboth for the commodityin questionand for othercommodities,leadingto additional
impactson tariff revenueswhen the goods are subjectto tariffs. These generalequilibrium
effectsmeanthat the morecompletemeasureof the welfarechangeis equal to
(19)
H - Ho = - gAr + [ E t,(aXat) ]Ar +
t E t, c. g, ]At
wherecR7
is thej' elementof the vectorcr of incomeeffectson demand,measuringthe income
effect on demandfor goodJ. In this equationthe last term representsthe additionaltariff
revenuechangesarisingfrom incomeeffectsin importdemand. Thus, the rule of thumbhas
beenextendedto allowfor effectson productionor consumption
of othergoodsthat are subject
to distortions. However,equation(19) still maintainsan assumptionof exogenousprices.
Relaxingthatassumptionwouldadd significantcomplexity.Whileextensionssuchas these-in
goingfromequation(17)to equations(18)and(19)or beyond-involvemajorcomplications
and
ambiguitiesin the traditionaldiagrammaticapproach,they are very straightforwardwith the
approachproposedin this paper.
Relaonship to Conventional
Measures
Thegeneralmeasuresof the totalwelfareimpactandits distributionare closelyanalogous
to those that wouldbe obtainedin a conventionalpartialequilibriumanalysisof technological
change(exceptthat a Hicksianratherthana Marshallianmeasureof consumerwelfareis being
used), and are exactlythe sameas the partialequilibriummeasureswhenthe assumptions
22
underlyingthepartialequilibriummodelare valid. Thatis, the measurefromthe modifiedtrade
expenditurefunctioncontainsthe conventionalmeasuresas specialcases.
For instance,considerthe caseshownin figure1 of a smallcountrywitha technological
changefor an i nportedgood that is subjectto a tariff, but with no other distortionsin the
economy.Undextheseassumptionsbothdomesticandworldpricesare exogenousand thereare
no shiftsof supplyand demanddue to endogenousprice changes. A shiftin supplyfromS0 to
Sz has noeffecton consumerprices(Ae = 0), althoughit doesaffectthe levelof actualspending
and, hence, import demand. The benefitto producers,measuredas the changein producer
surplus,is equal to the shadedarea betweenthe two supplycurves (4oablz)belowthe tariffridden domesticprice, po
=
pi
=
p, and this benefit is equal to Ag from equation (13). The
decreasein govemmenttariff revenueis equal to the importtariff multipliedby the changein
imports(measuredusingthe uncompensated
demand)-areaabcd = (m,-mo)Xp-p)
as measured
by the last term in equation(13). However,as noted above, this measurewill only be an
approximation
becauseendogenousincomeeffectsmeanthatuncompensated
demandhasshifted
demandis D, reflectingan
from its initialposition,Do. !i figure 1, the Pewuncompensated
increasein demand(as wouldarise if the goodwere normaland new technologyhad izd to an
increasein income). The incomeeffectleadsto an increasein importsof this goodrelativeto
mz (to m2) and the decreasein tariffrevenuein this marketis reducedto area abcd-efgh=
(M2 -
If other marketsare subjectto tariffs, then there will be additionalchangesin tariff
revenuesin thesemarketsto be considered,as is clear from equation(17). These changesin
23
revenuesreflect firstly the direct effects of the technicalchangeon the supply of the other
and secondlythe incomeeffectson demand,and henceimportdemand,in the other
commodities
Figure 1: Welfare Impacts of Technological Change in a
Small Country with a Tariff
Price
So
1
~~I
~
I
mlI
MI~
o
x1
O
Ax
l |< . . I I
I
I
Co
C1
Quantity
24
distortedmarkets. Theseeffectscannotbe incorporatedin a singlepartialequilibriummarket
diagram, although they can be illustratedin a separatediagram. This can be seen by
reinterpretingfigure 1 as representingthe marketfor a secondgood, s^y y, subjectto a tariff
equal to p-pP.
Then, shiftsfrom SOto SI and fromDoto Di can be interpretedas the shiftsof
supplyand demandfor goody resultingfrom technicalchangein the marketfor x. For the
welfareevaluation,when importsof y increasefrom mOto m2, the additionaleffect on tariff
revenuesis (m2-mo)(p-p).
As greater generalityis allowed in the partial equilibriummodel-in the form of
endogenousprices, multipledistortions,and multiplesourcesof generalequilibriumfeedback
of price changes into shifts of cetens panibus supply and demand functions-it becomes
increasinglydifficultto identifymeaningfulmeasuresof welfarechange;and evaluatingmultiple
exogenousdisplacementsis even moredifficult(e.g., see Thurman,1991band Alstonfor an
applicationto researchbenefits).However,meaningful,precise,and tractablemeasures,of both
the sizeof researchbenefitsand theirdistribution,are availableusingthe approachproposedin
this paper.
Empiricai Issues in Implementingthe Approach
The approachproposed greatly expands the problems for which accurate welfare
evaluationcan be undertaken-inmanycases,withoutrequiringany data or parametersbeyond
thoserequiredfor the traditionalgiaphicalapproach. To clarifythe issuesinvolved,we list the
stepsinvolvedin implementingthe approach.
25
The first requirementis the constructionof a behavioralmodelof consumerdemand,
producerrevenuesand governmenttaxationreceipts. It is most desirablethat this modelbe
consistentwith the restrictionsimposedby economictheoryand correspondexactlywith the
functionalformsfor theexpenditureandrevenuefunctionsusedfor the welfareevaluationstage.
Once a specificfunctionalform has been selected,the requirementof theoreticalconsistency
imposesno informationalneedsbeyondthoseof the traditionalpartialequilibriumapproach-the
5
own-and cross-priceelasticitiesof demandand supply,and the incomeelasticitiesof demand.
These parametervalues, for the commoditiesof interest,are sufficientto calibratecomplete
second-orderflexible consumer expenditureand producer revenue functions under the
assumptionof separabilitybetweenthe commoditiesof interestand all other commodities.
If the technicalchangeunderconsiderationis sufficientlysmallthat it will not resultir.
an incomechangelargeenoughto affectthe pricesof nontradedgoodsin the economy,thenthe
analysiscan proceedin a similarfashionto traditionalpartialequilibriumanalyses. Assuming
weakseparability,all commoditiesotherthan thecommoditiesdirectlyaffectedby the technical
changecan be aggregatedinto a compositegood whichservesas the numeraire.' Onlyif the
technicalchangeis sufficientlylarge that the resultingincomeeffectswill causechangesin the
price of nontradedgoodswillan explicitgeneralequilibriumapproachbe required. Eventhen,
however, the general equilibriummodel can be relatively simple, requiring little more
informationthan the traditionalpartialequilibriumapproach.
5 Theconventional
approachusingMarshallanconsumersurplusdoesnot requireincomeelasticitiesbutthese
arn requiredin theparial equilibriumapproachfor Hickslanmeasus of consumerwelfare.
6An equivalentassumption
is implicitunderthe traditionalpartialequilibrium
approach.
26
A behavioralmodel,constructedas describedabove,may be usedto solvefor a baseline
anda perturbedsolutionfor theprice, quantity,expenditureand revenuevariablesin the model.
With the modifiedtrade expenditurefunctionapproach,the welfareevaluationis causally
posteriorto the solutionof the model, with the compensateddemandfunctionsplayingno
explicitrole in the determinationof the equilibriumsolution. This is an importantoperational
advantageof the mnodledtradeexpenditurefunctionapproach,sinceempiricalimplementation
of thestandardtradeexpenditurefunctionapproachrequiresthatthe behavioralmodelbe solved
a second time to compute the hypotheticalgovernmentrevenuesthat would have arisen if
consumerswere actuallycompensatedfrom outsidethe system.
Recallthat the tradeexpenditurefunctionhas threecomponents:conlsumerexpenditure,
producerrevenues,and governmenttax revenues.Of these,changesin governmenttax revenues
are probablythe most straightforwardto calculatesince these can be read directlyfrom the
modelsolutions. Changesin producernet revenuescan be computedby usingthe valueof the
revenuefunctionusedto generatethe supplyanddemandfunctions(whichwillbe equivalentto
calculatingchanges in payments to fixed factors in the model). Thus, only consumer
expenditurenecessarilyinvolvesan explicitadditionalspecification:the consumerexpenditure
functionwhichunderliesthe consumerdemandequationsof the behavioralmodel.
Once a generalequilibriummodelhas been used to computethe prices and quantities
undertheold andnew technologies,the totalwelfarechangeand eachof its componentscan be
computed. If the supplyand demandcurves used to generatethe prices and quantitiesare
denveddirectlyfromthe underlyingpreferencesand technology,thenthe welfaremeasureswill
be exact. This wouldbe so, for instance,if the equationsrepresentingthe demandsideof the
27
modelwerederivedexplicitlyfroman integrableconsumerexpenditurefunction(e.g., an almost
idealdemandsystem)and the supplysideof the economywere derivedexplicitlyfrom a profit
function(suchas the translogor the quadraticform shownearlier).7
In sharpcontrastwith the traditionalapproach,multiplesourcesof generalequilibrium
feedbackpresent no problemsfor the calculationand interpretationof exact measuresof the
welfareeffectand its distributionat any levelof aggregation.Theproceduresidentifiedabove
in thepresenceof multiplesourcesof pricechangeand
withoutmodification
canbe implemented
endogenouslydeterminedprices. Thus, the seeminglyintractableproblems identifiedby
Thurman(1991b)are resolved.
Conclusion
In modelingand measuring the total benefit from research and its distribution,
approach. In doingso they
agriculturaleconomistshave madeextensiveuseof a single-market
have leant heavilyon the resultsof Just and Hueth(1979)and Just, Hueth and Schmitz(1982)
who establishedconditionsunderwhich single-marketwelfaremeasureswouldbe meaningful
8 However,one of the key conditionsfor validityof the single-market
measures
and accurate.
(as emphasizedby Harberger(1971)and discussedby Just, Huethand Schmitzpp. 196-99and
7 Tbisexpenditure
utilityindexthatis not involvedin the solutionof the
functioninvolvesthe unobservable
model,but whichmustbe heldconstant(ateitherits initialor perturbedvalue)for thewelfareevaluation.Thetrick
holdingutilityconstant. For example,if the abnost idealdemand system
is to calibratetheexpenditurefunmtion
(AIDS)functionalformwereused,theexpenditurefunctioncouldbe expressedas follows(DeatonandMuellbauer,
of thisequationfor thevalueof utilityat, say, theinitial
1980,p. 75): In e(u,p) = a(p) + ub(p). Transformation
17ne0 - a(pdJ/b(pd whichmaybe usedto eliminatethe
a(p)Jlb(pd
e(uo,p,)
u
=
an
levelof prices,Po,yields 0
changein the valueof the expenditurefunction(in
Thus
the
calculations.
the
from
utility
index
unobservable
- In eo.
eo
a(p.Jb(p)/b(pd
+
[In
logarithms)wouldbe CV = a(pd
8 Thurman
(199la,b)providesa usefulintuitivediscussionof the issueand somefurtherresults.
28
AppendixD) is the absenceof distortionsin other markets. Given the pervasivenature of
distortionsin agriculturalmarkets,andthe stronglinkagesin productionandconsumption
among
individualagriculturalcommodities,the validityof single-marketmeasuresof researchbenefits
is open to question. The absenceof tractablealternativesto the single-marketapproachmay
haveaccountedfor its continuedusein spite of its clear deficiency.
We have shownthat it is feasibleto relatethe welfaregains from technologicalchange
to the formaltheoryof welfareevaluation,ratherthanrelyingsimplyupongraphicaltechniques.
The approachthat has been suggestedin this paper permitsa theoreticallysoundmodelto be
applied consistentlyin the estimationof underlyingfunctions,in the simulationof market
displicementsin responseto newtechnologies,and in the evaluationof the changesin economic
welfare,and its distribution,associatedwith those marketdisplacements.
As well as beingan improvedway of analyzingand measuringthe welfareeffectsof
technicalchangein casesthathavebeen studiedusingad hoc methodsin partialequilibrium,this
approachcan be used to evaluatecaseswhere multimarketrelationshipsare importantand the
partia equilibrumframeworkhas provedinadequate. Particularlyimportantexamplesin this
regard include cases where: (a) there are importantinteractionsamong commoditieswith
multiplesourcesof generalequilibriumfeedbackof price changesfrom one marketto another
(e.g., products such as corn and soybeansthat are closelyrelated in both productionand
consumption);(b) it is of interestto disaggregatewelfareeffectsamongsuppliersof factorsof
productionand where,for that reason,thereare complicatedinteractionsamongthe marketsof
interest (e.g., in verticallyrelated markets);(c) a particularchangein technologyaffects a
numberof relatedmarkets(e.g., changesin feedgrainsupplyaffectingseverallivestock-feeding
29
industries,or developmentof improvedinputsapplcable in a numberof industria); and (d)
thereis interet in the impactsof muldplemarketdistortions(e.g., impactsof tade lib
on
on researchbenefits).
Otherdirecdonsin whichthisworkcouldbe extnded include:(a)cosidetion of policy
instrumentsother thanborder taxes;(b) considration of changesin productqualityassociated
with new technology(a problemthat has proved largely intracble in the ad hoc pardal
equilibriummodelsbut may be tctable in the trade expenditurefIucdon approach);and (c)
anaysis explainingagriculturalresearh investmentsin a politica economyframework,where
the size and distributionof benefits matter and where the simplifyiingasumpons of an
undisortedpartal equilibriummodelam
oae
30
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WPS1022 A NewApproachto EvaluatingTrade James E. Anderson
J. PeterNeary
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WPS1023Tariff Index Theory
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the Benefitsfrom Technological
Change
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Title
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