Contents lists available atScienceDirect
Structural
Change
and
Economic
Dynamics
j o u r n a l h o m e p a g e :w w w . e l s e v i e r . c o m / l o c a t e / s c e d
Land
use
and
pollution
in
a
two-sector
evolutionary
model
Angelo
Antoci
a,
Simone
Borghesi
b,c,
Gianluca
Iannucci
d,∗,
Elisa
Ticci
c aDepartmentofEconomicsandBusiness,UniversityofSassari,ItalybFSRClimate,EuropeanUniversityInstitute,Florence,Italy
cDepartmentofPoliticalandInternationalSciences,UniversityofSiena,Italy dDepartmentofEconomicsandManagement,UniversityofFlorence,Italy
a
r
t
i
c
l
e
i
n
f
o
Articlehistory: Received7March2019
Receivedinrevisedform22May2019 Accepted2June2019
Availableonline6June2019 Keywords: Agriculturalsubsectors Evolutionarymodel Environmentalexternalities Vulnerabilitytopollution
a
b
s
t
r
a
c
t
Thispaperproposesanevolutionarydualmodelinordertostudyheterogeneityofagriculturefroman environmentalperspective.Instandardvisions,landusechangesaredrivenbyproductivity differen-tialsacrossagriculturalsubsectors.Ourmodeladdsothertwofactorswhichcanindirectlyaffectland allocationpatterns:differencesinenvironmentalimpactintensityandenvironmentalvulnerability.By includingthesetwodimensionsinaparsimoniousmodel,weshednewlightonconstraintsorability foraneconomytoreachasectorallandallocationwhichefficientlybalancesenvironmentalburden, environmentalconstraintsandproductivity.
Wefindthat,incaseoftrade-offbetweenthethreedimensions,farmers’welfaregrowsalongstructural changeswhichallocateincreasinglymorelandtotheagriculturalsubsectorwithlowerpollutionintensity regardlessitsresilienceandlandproductivityperformance.
©2019ElsevierB.V.Allrightsreserved.
1. Introduction
Theimportant role ofagriculture foroverall socio-economic
developmentandforpovertyreductionhasbeenlargely
acknowl-edgedbydevelopmenttheoryfordecades(JohnstonandMellor,
1961; Adelman, 1984; Vogel, 1994) and it has been recently
confirmed by further studies (De Janvry and Sadoulet, 2010;
Christiaensenetal.,2011;LigonandSadoulet,2018).Themostly
used conceptual framework compares agriculture with
non-agriculturalactivitiesevenifagricultureisnotamonolithicsector.
Indeed,dualismintheagriculturesectorisnotanewtopicbut,all
overtheworld,agriculturehasbeenexperiencingimportant
evolu-tionswhichgobeyondthestandarddichotomybetweentraditional
and mechanized modern farming. Heterogeneity of agriculture
bothinhighandlow incomecountriesinvolvesseveral
dimen-sions,fromtypeoforganizational models,degreeofintegration
ininternationalmarketstotechnologicalcontent.Empirical
stud-iesshowthatheterogeneityacrossagriculturalsubsectorsmatters
sincenotallagriculturalactivitieshavethesamepotentialforthe
economicdevelopmentofcountries.Diaoetal.(2012),forinstance,
showthatcultivationoffoodstaplesisusuallymoreeffectivethan
exportagriculture at promoting economic growth and poverty
∗ Correspondingauthor.ViadellePandette9,50127Firenze,Italy. E-mailaddresses:antoci@uniss.it(A.Antoci),simone.borghesi@unisi.it
(S.Borghesi),gianluca.iannucci@unifi.it(G.Iannucci),ticci4@unisi.it(E.Ticci).
reduction.Otherauthorshaveinvestigatedthewelfareeffectof
dif-ferentorganizationalmodels,suchascontractfarmingcomparedto
independentsmallholderfarming(Bellemare,2012)oroutgrower
schemescomparedtoplantations(Arndtetal.,2010).
Farmingpracticescandifferalsointermsofresiliencetoshocks,
demandofnaturalresourcesandcreationofenvironmental
dam-age,butourunderstandingonagriculture’sheterogeneityfroman
environmentalviewpointislessadvanced,thoughnotlessrelevant.
Inacontextofgrowingpollution,resourcedepletionandclimate
changemanifestations,thesuccessofdevelopmentisconditional
onitsenvironmentalimpact(DeJanvryandSadoulet,2017).Thus,
theenvironmentalperspectivecannotbeoverlookedand
agricul-tureispartofthisdebatesincethissector,notonlyhasabigpower
for povertyreduction and economicdevelopment,but is alsoa
majoruser(ormisuser)ofnaturalresources.
However,thedistinctionofagriculturesubsectorsby
environ-mentalburdenorconstraintsisanintrinsicallydifficultexercise
furthercompoundedbylackofdata.Inabsenceofrepresentative
datasetandevidence,theoreticalmodels,incombinationwithcase
studies,canbeeffectiveatdelineatingpossibledynamicregimes
emergingintheinextricablenexusbetweenagriculture
composi-tion,environmentandeconomicdevelopment.Thisistheaimof
thiswork.Wecontributetothedebateondifferentialanddynamic
effectsonagriculturalsubsectorsbyconcentratingon
environmen-tallinkages.Thisfocusisthefirstnoveltyofthisworkbutacaveat
isrequired:themodeldoesnotsubstitute,itcomplements
analy-seswithbackwardandforwardeconomiclinkageswhichhereare
https://doi.org/10.1016/j.strueco.2019.06.001
excludedforreasonsofanalyticaltractability.Secondly,wefocus
oncoordinationproblemsinacontextofenvironmental
external-ities.Despitetheconsensusontheimportanceofenvironmental
regulationandvaluationofnatureandecosystemservices,markets
forenvironmentalqualityinagricultureareusuallyincompleteor
lacking.Manynaturalresourcesandecosystemserviceshavethe
characterofpublicgoods(airquality,rivers,freeaccessforests,fish
stocks,geneticdiversity,environmentalregulatingservices)and,
formanyenvironmentalresources,thecreationandenforcement
ofclearpropertyoruserightsisverydifficult.Asaconsequence,
choiceprocessesinfarmingareoftentakeninacontextofshallow,
nonexistentorincompletemarketswithpervasiveexternalities.
Farmers’decisionsusuallydonotfullyconsiderthe
environmen-talimpactofagriculturalpractices.Forinstancetheyrarelypayfor
dischargeofpollutantsandsedimentintotheenvironmentorfor
soilerosion,degradationorsalinizationduetopoormanagement
practices. These environmental damages do not come without
economicconsequencesonagriculturalactivitiesthemselves.
Pes-ticides,herbicides,fertilizersandotheragrochemicals,forinstance,
cangeneratealonglistofdetrimentaleffectsonproductivityof
either“polluting”farmsorother“victim”farms.Examplesinclude
destructionofnaturalenemiesofpests(Lichtenberg,2002;Pelletier
andTyedmers, 2010),developmentofpesticideresistance, crop
pollinationproblems,honeybeelosses,biodiversity1loss(Baudron
and Giller,2014)that deterioratethestability and resilienceof
agriculturalsystems(see,e.g.,Brittainetal.,2013),orevenlabour
productivitylossduetotheimpactonfarmworkers’health.This
feedback effects can bring about mechanismsof perverse
self-reinforcingsectorspecializationandcrowdingouteffects.Tofix
ideas,wecanmentiontwoexamples,aglobalandalocalone.Let
usconsiderthecoexistenceofsustainableforestryactivitiesand
agriculture.Theimpactofclimatechangeonagriculture
productiv-ityispredominantlynegative,particularlyinlow-incomecountries
thathavehigherclimatevulnerabilityandloweradaptationcapital
stocks,whichhinderstheirprospectsfordevelopment(Bretschger
andValente,2011;BretschgerandSuphaphiphat,2014).However,
themainoptionsthatthissectorusestocounteracttoit–
inten-sificationorland-usechange–furtherincreasesgreenhousegas
emissions.Thisprocesswithself-reinforcingnature(Bajˇzeljand
Richards,2014)canbeassociatedwithcrowdingoutofthesector
lessresponsibleforclimatechangesinceagriculturalland
expan-sionislikelytohappenattheexpenseofforestryactivities.Another
example ofa welfare-reducing specializationand crowding-out
mechanism is related to the ecology of pollinators. Crop
rota-tion,organicfarming (Gabriel andTscharntke, 2007; Bengtsson
etal., 2005), patcheswithhighplantdiversity withinfarmland
(Gigante Carvalheiroet al.,2011)havebeneficialeffectson
pol-linators.However,farmers rarelyadoptthese practices,instead
preferringconventionalfarmingandlarge-scaleagricultural
inten-sification,removingnaturallyoccurringplants.Theexpansionof
theseagriculturalpracticesreducestheproductivityinallsectors
dependingonpollinationservicesandmaygiverisetoan
ineffi-cientspecializationandproductivitylosses.Otherexampleswill
bediscussedlater.
Basedonthisbackground,weproposeatwo-sector
evolution-arymodelinwhicheconomicagentshavetoallocatelandbetween
two agricultural sectors, Aand B. For both sectors, land is the
onlychoicevariableandproductionisdamagedby
environmen-taleffectsgeneratedbytheagriculturalactivitiesthemselves.At
thesametime,sectorsAandBdifferbyproductionelasticitywith
respecttoland,degreeofenvironmentalburdenandby
vulnera-1Theimportanceofbiodiversitymanagementisdiscussedinseveral
contribu-tionsineconomicliterature(see,e.g.,RauscherandBarbier,2010;Vardasand Xepapadeas,2010).
bilitytoenvironmentaldegradation.FollowingIPCC(IPCCGlossary,
2014,p.218),vulnerabilitycanbedefinedasthe“propensityor
pre-dispositiontobeadverselyaffected”,amultidimensionalnotion
which“encompassesavarietyofconceptsincludingsensitivityor
susceptibilitytoharmandlackofcapacitytocopeandadapt”.To
betterfocustheconceptandapplyitinthepresentanalysis,by
‘vulnerability toenvironmentaldegradation’we willmeanhere
theadverseimpactthathigherenvironmentaldegradation
(mea-suredbypollutioninthemodel)hasontheproductionlevelofeach
sector.2
The effects of environmentalimpactare not internalizedby
themarket(i.e.byprices).Themodelisthusveryessentialbutit
generatesmultipleenvironment-sectorcomposition-development
patternsprovidingnontrivial,evenunexpected,results.In
partic-ularweshowunderwhatconditionsthereallocationchoicesof
landendowmentfromonesectortotheotheronemaygiveriseto
awelfare-reducingspecializationcharacterizedbyareductionin
farmers’averagerevenuesandbyuniformityoflandscape.
Therestofthepaperisorganizedasfollows.Section2presents
themodel,Section3carriesouttheanalysisofstabilityproperties
ofstationarystates,whileSection4proposesaclassificationof
pos-sibledynamicregimesproducedbythemodel.Section5performs
someexercisesofcomparativestaticsonparametersrepresenting
twodimensionsofinterest,namelyvulnerabilitytopollutionand
landproductivity.Section6discussesthesocio-economicrelevance
oftheanalyticalresultsandSection7concludes.
2. Themodel
Wemodelasmallopeneconomywithtwoagriculturalsectors,
AandB,inwhichallpricesareexogenouslyset.Landendowment,
measuredbytheparameter ¯L>0,isfixed;LAandLB,LA+LB= ¯L,
indicatetheamountofland(measured,e.g.,inhectares)devotedto
productionactivitiesofsectorAandB.Aggregateoutputsofsectors
AandBaregivenrespectivelybytheconstantreturnsfunctions:3
YA=˛LA
YB=ˇLB
(1)
where the parameters ˛>0 and ˇ>0 measure the production
elasticitieswithrespecttoland(i.e.theyareindicatorsofland
pro-ductivity)insectorsAandB,respectively.Tosimplify,weassume
thatthepricesofthegoodsproducedinsectorsAandBareboth
equal tounity.SoYAand YB alsorepresentthemarketvalueof
aggregateoutputsofsectorsAandB,respectively.4
Indicatingwiththevariablex∈[0,1]theshareofland
endow-ment ¯L usedbysectorA(i.e.,LA=x¯L)andwith1−xtheshareof
2Foradeeperdiscussionontheexistingdefinitionsofvulnerabilityseeweadapt.
org.
3WecanconsiderthefollowingproductionfunctionsasderivingfromaLeontief
functionofthetypeY=min (aL,bK,cW ),whereKandWrepresentphysicalcapital andlabor,whilea,b,c>0areparameters.Supposingthatphysicalcapitalandlabor arenotconstrained(namely,landistheonlyscarcefactor),thenKandWarechosen tosatisfyaL=bK=cW,fromwhichK=aL/bandW=aL/c.Assumingthatbothinputs prices,r(physicalcapital)andw(labor),andoutputpricepofsectorAareconstant andexogenouslygiven(smallopeneconomyhypothesis),thentheaggregate prof-itscanberewrittenas:=paL−r
a/b−wa/c=ap−r/b−w/cL.Setting ˛=ap−r/b−w/c,consideringthenegativeeffectofpollutionandapplyingthe sametosectorB,weobtainfunctions(1).4Theresultsofthemodelholdtrueevenifwerelaxtheassumptionofequal
goods’pricesinthetwosectors.Infact,˛andˇcanbeconsideredascomposite parametersthatmeasurepossibledifferencesbetweensectorsAandBinbothland productivityandprices.
Fig.1. Dynamicregimes.Legend:•sinks,䊐saddlepoints.
¯LusedbysectorB(i.e.,LB=(1−x)¯L),theproductionfunctions(1)
canberewrittenasfollows:
YA=˛x¯L
YB=ˇ(1−x)¯L
Theproductionactivitiesofbothsectorsdeterminethetime
evolu-tionofthevalueofapollutionindex,P∈[0,+∞),accordingtothe
equation:
˙P=ε˛xL+ˇ(1−x)L−P (2)
where ˙PisthetimederivativeofP,theparametersε≥0and≥0
measuretheimpactonthepollutionaccumulationprocessofthe
aggregateoutputs˛x¯L andˇ(1−x)¯L ofsectorsAandB,respectively.
Finally,theparameter>0representsthedecayrateofP.
Followingpreviouscontributionsintheliterature(e.g.Ikefuji
andHorii,2012; Rezaietal., 2012;Hackett andMoxnes, 2015; Bretschger,2017;Daoetal.,2017;BretschgerandPattakou,2019),
weassumeanegativeimpactofpollutionontheoutputofthe
econ-omy.Inparticular,weassumethatashareoftheaggregateoutputs
mustbeusedasdefensiveexpenditurestorepairthedamagesdue
topollutionP,andthatthenetaggregateoutputsaregivenby:
A(P)·YA
B(P)·YB
(3)
whereA(P)andB(P)aretheso-called“damagecoefficients”:5
A(P)= 1 1+P B(P)= 1 1+ıP (4)
Theparameters>0andı>0measurethevulnerabilityto
pol-lution ofsectors A and B,respectively. Notice that thedamage
coefficientsarea decreasingfunctionof thepollution level:the
higheristhepollutionlevel,thelowerthelevelofthesecoefficients,
andthereforetheloweralsotheoutputandincomelevelofthe
cor-respondingsectornetofthedefensiveexpenditures.Thelatter(i.e.
thequantitiesoftheoutputsthatarenotactuallyavailablefor
con-sumptionand/orinvestmentbeingusedasdefensiveexpenditures)
areobviouslygivenbythedifferencebetweentheaggregate(gross)
5Suchcoefficientsarecommonlyusedintheliteratureonclimatechange(cf.,for
instance,GolubandToman,2016;BretschgerandPattakou,2019)tomeasurethe shareofoutputthatisactuallyavailableoncetheenvironmentaldamagesaretaken intoaccount.
outputofeachsectorandthenetoutputdescribedabove,namely, [1−A(P)]·YAand[1−B(P)]·YB,where: 1−A(P)= P 1+P 1−B(P)= ıP 1+ıP
Weassumethatthedynamicsofthesharexoflandusedinsector
Adependsontheaverage(net)productivitiesoflandemployedin
sectorsAandB: A(x,P)= A(P)·YA xL¯ =1+˛P B(x,P)= B(P)·YB (1−x)L¯ = ˇ 1+ıP
andisgivenbythewell-knownreplicatorequation(see,among
others,HofbauerandSigmund,1988;Weibull,1995):
˙x=x
A(x,P)− (x,P)(5)
where ˙xindicatesthetimederivativeofx,while:
(x,P)=xA(x,P)+(1−x)B(x,P) (6)
measuresaveragelandproductivityoftheeconomy.Accordingto
(5),thesharexoflandallocatedinsectorAincreasesiftheaverage
productivityA(x,P) insectorAishigherthantheeconomy-wide
averageproductivity ¯ (x,P).6Viceversaiftheoppositeholds.Itis
easytocheckthatEq.(5)canberewrittenas:
˙x=x(1−x) [A(x,P)−B(x,P)] (7)
Accordingto(7),thevalueofxincreases(decreases)whenA>B
(A<B),whilexremainsconstantwhenA=B.This
specifi-cationmirrorsthefactthat,asintherealworld,profitabilityand
productivityarethemaindriversoffarmers’landusechoices.
VariationsinthesharexaffectthepollutionlevelP,while
vari-ationsinPaffecttherelativeperformanceofsectors,andtherefore
thetimeevolutionofx,accordingtothesystem:
˙x=x(1−x)
˛ 1+P − ˇ 1+ıP ˙P=ε˛xL+ˇ(1−x)L−P (8)definedintheset:
={(x,P):0≤x≤1, P≥0} (9)
3. Stationarystatesandglobaldynamics
Thestationarystatesofthedynamicsystem(8)aregivenbythe
intersectionpoints,belongingtotheset (see(9)),betweenthe
straightline(22),where ˙P=0andoneofthestraightlinesx=0,
x=1,and(19),where ˙x=0(seeAppendix).Foragraphical
repre-sentationseeFig.1.Forsimplicity,weshalllimitouranalysistothe
casesinwhich˛ı−ˇ =/ 0andε˛−ˇ=/ 0hold.Inthiscontext,
thefollowingpropositionholds:
Proposition 1. In the context in which ˛ı−ˇ =/ 0 and
ε˛−ˇ=/ 0hold,thedynamicsystem(8)admitsatmostthree
sta-tionarystates:
6Verysimilarqualitativedynamicscanbeobtainedbysubstitutingthereplicator
equation(7)witheverypayoff-monotonicdynamics(seeWeibull,1995).
1.the point (0,P0)=
0,ˇ ¯L
, where the land endowment ¯L is
entirelyallocatedtosectorB;
2.the point (1,P1)=
1,ε˛
¯L
, where the land endowment ¯L is
entirelyallocatedtosectorA;
3.the point
˜x, ˜P= (ˇ−˛ε)¯L ˛−ˇ ˛ı−ˇ+ˇ¯L, ˛ı−ˇˇ−˛
, where
bothsectorsAandBcoexist.
Thestationarystates (0,P0) and (1,P1) alwaysexist,whilethe
stationarystate
˜x, ˜Pexistsifandonlyifthefollowingtwocondi-tionshold:
1. ˜P >0,thatis,eithercondition(20)orcondition(21)issatisfied;
2.1> ˜x >0,thatis,eitherP0< ˜P andP1> ˜P (inthecontextof
condition(23))orP0> ˜P andP1< ˜P (inthecontextofcondition
(24))hold.
Thefollowingpropositiondealswiththestabilitypropertiesof
thestationarystates(0,P0),(1,P1),and
˜x, ˜P
.Proposition2. Accordingtothedynamicsystem(8),thestationary
state(0, P0)islocallyattractiveif:
˛
1+P0−
ˇ
1+ıP0
<0 (10)
whileitisasaddlepoint(withstablemanifoldlyinginthestraightline
x=0)iftheoppositeofcondition(10)holds.
Thestationarystate(1,P1)islocallyattractiveif:
−
˛ 1+P1 − ˇ 1+ıP1 <0 (11)whileitisasaddlepoint(withstablemanifoldlyinginthestraightline
x=1)iftheoppositeof(11)holds.
Thestationarystate
˜x, ˜Pislocallyattractiveif:ε˛−ˇ
˛ı−ˇ<0 (12)whileitisasaddlepointiftheoppositeof(12)holds.
Proof. TheJacobianmatrix ofthesystem(8),evaluatedatthe
stationarystate
˜x, ˜P,canbewrittenasfollows:J
˜x, ˜P=⎛
⎜
⎝
0 ˜x(1− ˜x)ˇı 1+ı ˜P2 − ˛ 1+ ˜P2 ε˛−ˇ¯L −
⎞
⎟
⎠
where: TrJ˜x, ˜P=−<0 DetJ˜x, ˜P=−˜x(1− ˜x)ˇı 1+ı ˜P2− ˛ 1+ ˜P2 ε˛−ˇ¯L (13)
Taking into account that, at
˜x, ˜P, it holds ˛/1+ ˜P−ˇ/
1+ı ˜P=0,andtherefore1+ı ˜P/1+ ˜P=ˇ/˛,wecanwrite ˇı
1+ı ˜P2− ˛ 1+ ˜P2 = ˇ 1+ı ˜P ı 1+ı ˜P− ˛ 1+ ˜P 1+ ˜P = ˇ 1+ı ˜Pı 1+ı ˜P− 1+ ˜P =
ˇ 1+ı ˜P2 ı− 1+ı ˜P 1+ ˜P =
ˇ 1+ı ˜P2 ı−ˇ˛ (14) Accordingto(14),wehave:
sign
DetJ˜x, ˜P=sign−ε˛−ˇ˛ı−ˇTherefore,
˜x, ˜Pislocallyattractiveifε˛−ˇ˛ı−ˇ<0,whileitisasaddlepointiftheoppositeinequalityholds.The
Jaco-bianmatrixevaluatedat (0,P0) is:
J (0,P0)=
⎛
⎝
˛ 1+P0− ˇ 1+ıP0 0 ε˛−ˇ¯L −⎞
⎠
witheigenvalues−<0(indirectionoftheP−axis)and 1+P˛
0 −
ˇ 1+ıP0.
Analogously,theJacobianmatrixevaluatedat (1,P1) is:
J (1,P1)=
⎛
⎜
⎝
− ˛ 1+P1 − ˇ 1+ıP1 0 ε˛−ˇ¯L −⎞
⎟
⎠
with eigenvalues −<0 (in direction of the P-axis) and
−
˛ 1+P1 − ˇ 1+ıP1.䊐
Notethatcondition(10)holdsifP0< ˜P,inthecontext˛ı−ˇ>0,
andifP0> ˜P,inthecontext˛ı−ˇ<0(see(19)and(21)).
Anal-ogously,condition(11)holdsifP1> ˜P,inthecontext˛ı−ˇ>0,
andifP1< ˜P,inthecontext˛ı−ˇ<0.
Thefollowingproposition dealswiththeglobal dynamicsof
system(8).
Proposition3. Everyset⊂ :
={(x,P):0≤x≤1, ¯P≥P≥0}
with ¯P >max
P0,P1,ispositively invariantunderthe dynamic
system(8).Furthermore,everytrajectorystartingoutsideitentersit
infinitetime.
Proof. Toprovethisproposition,rememberthat ˙x=0holdsfor
x=0andx=1,thereforethesidesofwithx=0andx=1are
invari-ant.Furthermore,everypoint(x, ¯P)liesabovetheisocline ˙P=0
(andconsequently ˙P<0at(x, ¯P))whileeverypoint(x,0)liesbelow
theisocline ˙P=0(andconsequently ˙P >0at(x,0)).Thisprovesthe
positiveinvarianceoftheset.Sincein −nostationarystate
exists,thenbythePoincaré–BendixsonTheorem,everytrajectory
startingin −entersinfinitetime.䊐
Theexistenceoflimitcyclesaroundtheinternalstationarystate
˜x, ˜P
isexcludedwhenitisasaddlepoint(accordingtotheIndextheory,seee.g.,Lefschetz,1977),whileitcannotbeexcludedwhen
˜x, ˜P
islocally attractive,inthatthedivergence ∂∂x˙x+∂˙P∂P is not
alwaysnegativeintheset(see,e.g.,Giné,2014).
4. Dynamicregimes
Wecannowidentifyallpossibledynamicregimesthatmaybe
observedandwecandiscusstheconditionsunderwhicheachof
thememerges.Weexcludetrivialcasesinwhichtheinternal
sta-tionarystate
˜x, ˜Pdoesnotexistand,then,either(0,P0)or(1,P1)isgloballyattractiveintheinterioroftheset .Moreprecisely,the
stationarystate(1,P1)(thestationarystate(0,P0))withcomplete
specializationinsectorA(B)isgloballyattractivewhensectorA
(B)is,atthesametime,less(more)vulnerabletoenvironmental
degradationandmore(less)productivethanB(A),namelywith
˛>ˇ(ˇ>˛)and<ı(>ı).
Movingontothemoreinterestingcasescharacterizedbythe
existenceoftheinternalstationarystate
˜x, ˜P,theanalysisoftheisoclines ˙x=0, ˙P=0ofAppendixandstabilityanalysisofSection
3allowsustointroducethefollowingtaxonomy:
• Case(i):sectorAislessvulnerableandmorepollutingthan
sec-torB;thiscaseoccursifconditions(20)and(23)hold.Inother
words,themainweaknessofsectorAisalowproductivity,but
itcanrelyonotherstrengths.Moreprecisely,sectorAissubject
tolowenvironmentalconstraintsanditexertsstrongcrowding
outpressureonsectorBthroughitsenvironmentalimpact.
• Case(ii):sectorAislessvulnerableandlesspollutingthan
sec-torB;thiscaseoccursifconditions(20)and(24)hold.Theonly
differencewithcase(i)isinthatexpansionofsectorAdoesnot
ledtoanetincreaseinpollutionandthereforeitdoesnotcreate
acrowdingouteffectonsectorB.
• Case(iii):sectorAismorevulnerableandmorepollutingthan
sectorB;thiscaseoccursifconditions(21)and(23)hold.Thisis
theoppositetocase(ii).
• Case(iv):sectorAismorevulnerableandlesspollutingthan
sec-torB;thiscaseoccursifconditions(21)and(24)hold.Thisisthe
oppositetocase(i).
InCases(i)and(iv),illustratedinFig.1(a)and(d),respectively,
thestationarystates(0,P0)and(1,P1)arelocallyattractive,while
theinternalstationarystate
˜x, ˜Pisasaddlepoint.Thestableman-ifoldof
˜x, ˜P,representedinblue,separatesthebasinsofattractionof(0,P0)and(1,P1).Therefore,bistableregimesareobservedandthe
economytendstospecialiseeitherinAorinsectorB,accordingto
thestartingpoint (x(0),P(0)).InCases(ii)and(iii),thetwosectors
tendtocoexist(Fig.1(b)and(c)).7 Morespecifically,the
station-arystates(0, P0)and(1, P1)aresaddlepoints,whiletheinternal
stationarystate
˜x, ˜Pisattractive.Fig.1illustratesnumericalsim-ulationsofdynamicsincases(i)–(iv),respectively.Inthesefigures,
attractivestationarystatesaremarkedbyfulldots(•)andsaddle
pointsbysquares(䊐).
4.1. Averagelandproductivityoftheeconomyinthescenarios
(i)–(iv)
Inthissectionwecomparetheaveragelandproductivityofthe
economy(see(6)):
¯
(x,P)=xA(x,P)+(1−x)B(x,P)
7Noticethatsectorcoexistencewouldbemorelikelytooccurifvariableprices
anddecreasingreturnstoscalewereassumedsincethemarginalproductivityof landinagivensectorwoulddecreaseanditspricewouldincreaseastheeconomy movestowardfullspecializationinthatsector,thuspushingthesystembacktoward theoppositesector.However,evenundertheseassumptions,thedynamicsofthe modelcanstillgeneratefullspecialization.Indeed,theonlywaytoensuresector coexistenceisbyassumingInadaconditionssothatlandproductivitygoestoinfinity aslandusegoestozero.
Fig.2.Case(i):basinsofattractionforlow(a)andhigh(b)valueof˛,andlandaverageproductivity(c)ofboundarystationarystates.Parametervalues:ˇ=2,=1,ı=3, ε=3.5,=0.75,=2.5,L=1.Legend:•sinks,䊐saddlepoints.
evaluatedatthestationarystates(0,P0),(1,P1),and
˜x, ˜P: ¯ (0,P0)=B(0,P0)= ˇ 1+ıP0 ¯ (1,P1)=A(1,P1)= ˛ 1+P1 ¯ ˜x, ˜P=A ˜x, ˜P=B ˜x, ˜P= ˛ 1+ ˜P= ˇ 1+ı ˜P Fromwhich ¯ (0,P0) < ¯˜x, ˜P
< ¯ (1,P1) ifandonlyif:ˇ 1+ıP0 < ˛ 1+ ˜P = ˇ 1+ı ˜P < ˛ 1+P1 (15) and ¯ (0,P0) > ¯
˜x, ˜P
> ¯ (1,P1) ifandonlyif:ˇ 1+ıP0 > ˛ 1+ ˜P = ˇ 1+ı ˜P > ˛ 1+P1 (16)
Condition(15)holdsifP0>P1;conversely,condition(16)holdsif
P0<P1.Thefollowingpropositionsummarizestheseresults.
Proposition4. InCases(i)and(iii),wherecondition(23)holds,the
stationarystatesarerankedbytheinequality:
¯
(0,P0) > ¯
˜x, ˜P
> ¯ (1,P1) (17)InCases(ii)and(iv),wherecondition(24)holds,thestationarystates
arerankedbytheinequality:
¯
(0,P0) < ¯
˜x, ˜P
< ¯ (1,P1) (18)The sectoralland allocationwhich ensures thehighest level
ofaveragelandproductivity(andthereforealsothehighesttotal
valueoutput)istheoneassociatedwithlowesttotalpollution
bur-den.Inotherwords,thestationarystates(0,P0),(1,P1),and
˜x, ˜P
canbe orderedby averagelandproductivityaccording totheir
inverseorderbylevelofpollutionP.Thehighestland
productiv-ityisreachedwhentheeconomyisabletospecializeintheclean
sector(Aincases(ii)and(iv)orBincases(i)and(iii)).
5. Simulations
5.1. Changeinoutputelasticitywithrespecttoland
Thissection assesses theimpactof an exogenous changein
parametersrepresentingoutputelasticitywithrespecttoland(˛
insectorAandˇinsectorB)onstationarystates,theirbasinsof
attractionandaveragelandproductivity.Theaimistounderstand
howtheusuallypositiveeffectsofincreasedproductivitychange
onceenvironmentaldimensionsaretakenintoaccount.Cases(i)
and(iv)aresymmetrical,aswellallcases(ii)and(iii).Forthesake
ofsimplicity,wenarrowtheanalysisoncases(i)and(iii),inwhich
sectorAcanbelabelledas“dirty”agriculturesubsector.Cases(ii)
Fig.3. Case(iii):basinsofattractionforlow(a)andhigh(b)valueof˛,andlandaverageproductivity(c)ofinnerstationarystate.Parametervalues:ˇ=1,=3,ı=1,ε=2, =1,=2.5,L=1.Legend:•sinks,䊐saddlepoints.
IfthedirtysectorAexperiencesanexogenousgrowthinoutput
elasticitywithrespecttoland˛underthebistabledynamicregime
(i),theeffectisanexpansionofbasinofattractionofthe
station-arystate(1,P1)wherelandendowmentisentirelyallocatedtothe
dirtysectorA(seeFig.2(a)and(b)).Inotherwords,theeconomyis
morelikelytofollowawelfare-reducingspecialization
character-izedbylowerfarmers’averagerevenues(seeFig.2(c))thaninthe
alternativeattractivestationarystate(0,P0)(0, P0).
Fig.3showstheeffectofanexogenousgrowthinoutput
elas-ticitywithrespecttoland˛incase(iii),namelywhensectorAis,
notonlymorepolluting,butalsomoreproductiveandmore
envi-ronmentallyvulnerablethansectorB.Inthisscenario,theeffect
isashiftoftheinternalgloballyattractivestationarystate
˜x, ˜PtowardsalargerlandshareallocatedtothedirtysectorA.Despite
theexogenousproductivitygain,alsointhiscasetheresultisa
declineinoverallfarmers’revenueasillustratedinFig.3(c)
report-ingareductioninaveragelandproductivity.
Oppositeresultsareproducedbyanexogenousincreaseinˇ
whichrepresentstheoutputelasticitywithrespecttolandinsector
B,namelythe“clean”sectorunderthedynamicregimes(i)and(iii)
(seeFigs.4and5).
5.2. Changeindegreeofvulnerabilitytoenvironmental
degradation
Wecannowgiveacloserlookattheroleofvulnerabilityto
pol-lution,akeydriverofagriculturedevelopmentinterritoryexposed
toenvironmentalexternalities.Wefocusagainondynamicregimes
(i)and(iii)inwhichthesectorAischaracterizedbyahigher
pollu-tionintensitythansectorB.Iftheeconomyisundermonostable
dynamicregime (case(iii),seeFig.6(c)and (d)),aslongasthe
cleansectorbecomeslessresilienttopollution (i.e.ıincreases),
thegloballyattractiveequilibrium
˜x, ˜Pshiftsandthecorrespond-ingtransitionisassociatedwithanincreaseinthepollutionstock
andintheshareoflandusedinthedirtysector.Iftheeconomy
belongstoabistabledynamicregime(i),asshowninFig.6(a)and
(b),anexogenousgrowthofvulnerabilityofthecleansectorleads
toashrinkingbasinofattractionofthePareto-superiorstationary
state.Inbothcases,thefinaloutcomeisawelfareloss.
6. Interpretationoftheresults
Theresultsoftheanalysisprovideinterestinginsights.Inorder
togivemoresubstancetotheresults,weorganisethediscussion
inaquestion–answerformat.
Outputvalueispositivelyassociatedwithoutputelasticitywith
respecttolandandnegativelyassociatedwithenvironmental
vul-nerability.Specializationinfarmingactivitieswithhighelasticity
withrespecttoland(i.e.highlandproductivity)andlowsensitivity
toenvironmentalpressure would betheideal landuse.
Unfor-tunately,farmingsubsectorsrarelypresentthesetwofeaturesat
thesametime.Incaseoftrade-offbetweenlandproductivityand
resilience(asinallconsidereddynamicregimes(i)–(iv)),should
sec-Fig.4.Case(i):basinsofattractionforlow(a)andhigh(b)valueofˇ,andlandaverageproductivity(c)ofboundarystationarystates.Parametervalues:˛=1,=1,ı=3, ε=3.5,=0.75,=2.5,L=1.Legend:•sinks,䊐saddlepoints.
torortowardsthemostresilientone?Theansweris“itdepends”.
Ourresultsshowthatanystructuralchangecharacterizedbyan
increaseinlandshareallocatedtothecleanestsubsectorleadsto
anincreaseinaveragelandproductivityandthisistrueinall
sce-narios(i)–(iv).Letconsideragaincases(i)and(iii):inbothregimes,
Aismore pollutingthan B.In case (i),sector Ahasthe
advan-tageofalowenvironmentalvulnerabilityandthedisadvantageof
alow productivity.Thedynamicregimeis bistableandthe
sta-tionarystate(0,P0)(0, P0)withacomplete specializationinthe
cleanersectorBensuresahighertotaloutputvaluethanthe
sta-tionarystate(1,P1)withacompletespecializationinsectorA.In
case(iii),sectorAhastheadvantageofahighproductivityandthe
disadvantageofahighvulnerabilitytopollution.Inthisregime,
theinternalstationarystate
˜x, ˜Pisglobally attractive.Alsointhiscase,thestationarystate(0,P0)outperformstheother
station-arystatesintermsofoutputvalue,butit isunstable.Structural
changescanoccurwhenvariationsinparametervaluesmake
inter-nalstationarystate
˜x, ˜Pmove.Simulationsonparameter˛areanexample:anincreasein˛generatesastructuralchangetowards
alargerlandshareofsectorAandtheresultisaloweraverage
landproductivityindicating thefarmers’welfare wouldinstead
improvealong a shifttowardstheclean sectorB.These results
clearlyindicatethatthefirstcriterion inlandallocationchoices
should be the minimization of environmental impact, namely
movinglandallocation towardsthesectorwithlowerpollution
intensity.
In many cases, territorial development tends to landscape
uniformityandspecialization.Inprinciple,analternativeand
suc-cessfullandusepatternwouldbeabalancedcoexistencebetween
moreproductiveandpollutingagriculturalactivitieswithless
pro-ductivebutcleanerones.Whydoesthisscenariorarelyoccur?Inour
model,thisdynamicregimeisadmissibleonlyincases(ii)and(iii),
thatiswhenenvironmentalimpactintensityispositivelyrelatedto
pollutionvulnerability.Intherealworld,thisconditionrarelyholds
and,asresult,anontransientandstablecoexistenceoffarming
sec-torswithdifferentenvironmentalburdenandconstraintsisquite
infrequent.Taketheexampleoforganicandconventionalfarming:
inabsenceofastablepolicysupport,organicfarmingstrugglesto
gainmarketshares.Organicagricultureisoverallmore“integrated”
insurroundingecosystemsfromwhichitderivesseveralnatural
resourceinputsandenvironmentalservices.Itistherefore,notonly
lesspollutingbutalsomoresensitivetopollutionthanconventional
farmingwhich reliesmore onchemical andman-made
“substi-tutes”.Theinteractionsbetweenorganicandconventionalfarming
arethereforebetterdescribedbythedynamicregime(i)or(iv)than
(ii)and(iii).ThesameobservationappliestoGMOandGMO-free
crops.GMcropsgenerateheavyexternalitiesonGMO-free
culti-vations,inparticularonorganicproduction,whichareexposedto
theriskof“contamination”.Alsoconventionalfarmerscanbe
dam-agedincaseofcontamination,especiallyiftransitiontoGMseedsis
accompaniedbyachangeinfarmingpractices.Thesocalled
Fig.5. Case(iii):basinsofattractionforlow(a)andhigh(b)valueofˇ,andlandaverageproductivity(c)ofinnerstationarystate.Parametervalues:˛=2,=3,ı=1,ε=2, =1,=2.5,L=1.Legend:•sinks,䊐saddlepoints.
mid-1990swiththeintroductionofthetransgenicRoundupReady
(RR)soybeantogetherwithatechnologicalpackage ofchemical
fertilizationandintensiveuseoftheherbicideglyphosate(thenew
GMsoyvarietyisresistanttoit)withheavydetrimentalimpactson
humanhealthoflocalpopulation,soilquality,biodiversityand
for-estcoverage(Leguizamón,2014;PhélinasandChoumert,2017).
Theintroductionof GM soybeanseemstoportraytheeffect of
asuddenincreaseinlandproductivityunderdynamicregime(i)
(ratherthanunderregime(iii))whichleadstheeconomytowards
thespecializationinthesectorwithhigherenvironmentalimpact
(seeparagraphonsimulations)andtowardsanoverallwelfareloss.
CultivationofGMsoybeans,infact,hasexpandedattheexpense
ofcattle,maize,sunflower,andwheatproductionanditsgrowth
hasbeensorampantthatnowitaccountsfor60%oftotalland
cul-tivatedinthecountry(PhélinasandChoumert,2017).However,
despitetheircurrenteconomicsuperiorityintermsofprofitsand
productivitycomparedtonon-GMO,environmentalimplications
ofGMsoybeanmakeeconomicandenvironmentalsustainability
ofthisprocessofspecializationlesscertain,ifnotillusory.
Whatistheroleforpolicy?Wecangiveonlyanindirectanswer
aspolicyinstruments arenot includedin themodel. However,
theresultsoftheanalysisandofsimulationsproduceinteresting
insights.Agentstendtochooselanduseallocationmerely
look-ingatproductivitywithoutfullyconsideringenvironmentalburden
andconstraintsgeneratedbythechoicestakenbyallagents.Thus,
uncoordinatedagents’choicesareunlikelytoconvergetotheland
usecompositioncorrespondingtotheParetosuperiorstationary
state.Thisequilibriumis unstable(cases(ii)and(iii))orcanbe
reachedonlyiftheeconomystartsfromasituationinwhichthe
cleanersectoralreadyaccountsforasufficientlyhighlandshare
(cases(i)and(iv)).Thefirstnormativeimplicationisthat,inorder
toavoidwelfare-reducingandPareto-dominatedlandallocation
configurations,policyshouldfocusonincentivestoinvestinlow
impactfarmingactivities,evenwhentheyarecharacterizedbya
lowlandproductivity.Forthispurpose,severalpolicyinstruments
canbe used dependingonthe specificcase and corresponding
dynamicregimetakenintoaccount.Forinstance,ifthetwosectors
coexistattheequilibrium(i.e.thereisagloballyattractiveinner
stationarystate),adifferentiatedtaxrateontheproductionofthe
twosectors maymodifytherelativepayoffsofthetwosectors,
reducingtherelativeprofitsofthemorepollutingsectorandthus
shiftingeconomicactivitytowardsthecleanersector.If,onthe
con-trary,abistabledynamicregimeemergesfromtheanalysisleading
tofullspecializationinonesector,thenpolicy-makersmight
con-siderinterveningontheinitiallandallocationbetweenthetwo
sectors(e.g.establishingthemaximumshareoftotalavailableland
thatcanbeallocatedtotheclean/dirtysector)sothattheeconomic
systemliesintheattractionbasinofthesociallyoptimalstationary
state.Otherpossiblepolicyinstrumentsthatmaydrivethe
eco-nomicpathwaytowardsaPareto-superiorequilibriumarepublic
investmentsinthecleanersectorthatreduceitsvulnerabilityto
environmentaldegradationand/orincreaseitslandproductivity.
Secondly, policy makers should prevent sudden exogenous
Fig.6.Vulnerabilities.Legend:•sinks,䊐saddlepoints.
bringingitalonganinefficientandself-reinforcingspecializationin
pollutingagriculturalsubsector.Interestinglythismayoccuralso
asconsequenceofpositiveeconomicshocks,asinthecaseofan
increaseinlandproductivityofthedirtysector(seetheexampleof
the“soybeanization”ofArgentina).
Anegativereversaloflandusepatterncanbecausedalsoby
othertypeofshockssuchasanincreaseinvulnerabilityof
agri-culturalactivitieswithlowerenvironmentalimpact.Inthiscase,
anillustrativereal-worldcaseisrepresented,tosomeextent,by
therapidgrowthofcommercialshrimpculture,experiencedby
southwesterncoastalareasofBangladeshoverthelast30years.
Shrimpfarmingexpansionhasbeendrivennotonlybygrowing
demandandpolicysupport,butalsobyitsgreatersuitabilityto
changingenvironmentalecosystems.Theconstructionofseveral
mega-projectswhich havetransformedwaterresourcesystems,
togetherwithsealevelriseandstormsurges,havedramatically
modifiedenvironmentalconditions(Pouliotteetal.,2009).
Land-basedcropshavebecomemorevulnerabletosaltwaterintrusions.
Productionsysteminseveralvillageshaveundertakenatransition
fromaspecializationinriceandothertraditionalcropstosaltwater
shrimpfarmingwhich,inturns,hasseveralenvironmental
impli-cations,fromdestructionofmangroves,increasedsalinizationand
intensiveuseof chemicals(Islamand Yasmin, 2017).Using our
modelwording,cropproductionandshrimpculturecanbe
rep-resented,respectively, assectorBand sectorA. Theeconomyis
characterizedbythebistabledynamicregime(i)assectorBisless
pollutingandmorevulnerablethansectorA.This“bluerevolution”,
asoftenreferredto,inourmodelcanbeinterpretedastheresult
ofasuddenincreaseinparameterı8sothattheeconomy,
start-inginthebasinofattractionofstationarystate(0,P0),endsupinto
thebasinofattractionof(1,P1)withcompletespecializationinthe
dirtysectorA.Inotherwords,thisexogenousshockmadethe
econ-omy“jump”ontrajectoriesapproachingadifferentstationarystate
andradicallychangedlandusepatternfollowingaprocessof
wel-farereduction,self-reinforcingspecializationinpollutingactivities
andcrowdingoutoftraditionalcropfarming.Indeed,despitethe
immediateeconomicbenefitsofspecializationinshrimpfarming,
increasingconcernshavebeenexpressedonenvironmentaland
socio-economicsustainability(Deb,1998;Pouliotteetal.,2009;
PaulandVogl,2011)ofshrimpingcultureitselfandofoverall
ter-ritorialdevelopmentofBangladesh’scoastalareas.
7. Conclusions
Agriculturaldevelopmentusuallymeanschoosingthebest
per-formingagricultureactivityintermsoflandproductivity.Wehave
8Thisinterpretationobviouslydoesnotneedtoexcludetheroleofother
deter-minantssuchaspolicyactions,growinginternationaldemandforshrimps,big investors’interestforprofitopportunitiesinexportmarkets.
revisedthisapparenttautologybyintroducingtwomainelements
inaevolutionarymodelofsectorallandallocation:
1.environmentalconstraintsthat, in turn,dependon pollution
intensityandvulnerability.
2.interactionsbetweendifferentfarmingactivities.Each
individ-ual’s decision onthe preferred agriculturalactivitydoes not
occurinanimpermeablesetting.Incontrast,itisinfluencedby
landusechoicesofallfarmers.
Weshowthat multipledynamic regimesarepossible.
How-ever, conditions for the existence of bistable dynamic regimes
seemtobemoreconsistentwithrecurrentfeaturesofreal-world
interactionsbetweenagriculturalsubsectors.Wefindthatinthis
context,theeconomy is atrisk of followinga land usepattern
associatedwithincreasingenvironmentaldegradationandwelfare
declineevenifthisdevelopmentpathoccursalongaspecialization
inthesectorwithhigherlandproductivityorevenifthe
transi-tionispromptedbyapositiveshocksuchasanincreaseinland
productivity.
Ifpolicygoalistoapproachtheeconomytothestationarystates
atwhich well-being is greater,policy action needsto promote
thecleanersectorinordertoheadlandusesectoralcomposition
towardslowlevelsofpollution.Possibleinstrumentsforthis
pur-poseincludedifferentiated(sector-based)taxes/subsidies,landuse
planningestablishingminimum/maximumlandquotasthatcanbe
devotedtodifferentsectorsandpublicinvestmentsinadaptation
activitiesreducingthevulnerabilityofcleansectorsto
environmen-taldegradation.Theseandothersector-specificmeasurescanbe
veryeffectiveindrivingstructuralchange,asshownbytherecent
increaseinorganicfarmingintheEuropeanUnionwhereitis
esti-matedthat56percentofproducersbenefitedfromvarioussupport
measuresbytheEuropeanCommonAgriculturalPolicy(European
Commission,2013,2019).
Thepresentmodeldeliberatelyproposesaverysimple
analyt-icalframeworktoidentifya fewpossiblecausallinks thatmay
generateundesirableoutcomes.Futureresearch,however,should
examinewhetherandhowresultsmaydifferbyrelaxingsomeof
theunderlyingsimplifyingassumptions.Forinstance,itwouldbe
interestingtoseehowresultsmaychangeassumingdifferentand
variablewillingnesstopayforthegoodsproducedbyeach
sec-tor.Indeed,afewpeoplemayinitiallyhavehigherwillingnessto
payfororganicfarmingthanforconventionalfarmingwith
pes-ticides.However,individualwillingnesstopayandtheshareof
environmental-friendlyconsumersmaybeendogenouslyaffected
bytheotherconsumers’preferencesand/orbypolicyinterventions
(e.g.abetterinformationcampaignonhealthconsequencesof
dif-ferentproducts).Thisendogenousmechanismwouldnotprobably
alterthemaindynamicregimesobservedinthemodel,butitcould
generatepricechangesovertime,affectingthevalueofthe
station-arystateandtheirbasinsofattraction.Finally,whileinthemodel
wefocusonauniquekindofpollutant,itwouldbeinterestingto
investigatewhatwouldhappenifweassumethatdifferentsectors
maygeneratedifferentpollutantsand/ordifferentkindsof
environ-mentaldegradation.Weleavetheseanalysestofutureextensions
ofthemodel.
Appendix
Isoclines ˙x=0and ˙P=0
Accordingto(8), ˙x=0holdsforx=0,1andfor:
P= ˜P= ˇ−˛
˛ı−ˇ (19)
if˛ı−ˇ =/ 0,9where ˜P >0ifeithercondition:
˛−ˇ<0 and ˛ı−ˇ>0 (20)
orcondition:
˛−ˇ>0 and ˛ı−ˇ<0 (21)
holds. Notice that condition(20)may besatisfied onlyif <ı,
namelyifsectorAislessvulnerabletopollutionthansectorB.This
meansthatinacontextofheavypollution,thesector(inthiscase
A)whichislesssensitivetoenvironmentalpressureisabletoreach
strongerprofitabilityperformancecomparedtheotherone(B)even
itexhibitslowerlandproductivity.Whencondition(20)applies,
thenabove(below)thestraightline(19),intheplane(x,P),itholds
˙x >0( ˙x <0).Thismeansthattheshareoflandallocatedtosector
Atendstoincreaseforhighlevelsofpollution(foragraphical
rep-resentationseeFig.1reportingdifferentdynamicregimeswhich
willbediscussedlaterinSection4).
Conversely,condition(21)maybesatisfiedonlyif>ı,namely
ifsectorAismorevulnerabletopollutionthansectorB.When
con-dition(21)applies,thenabove(below)thestraightline(19),inthe
plane(x,P),itholds ˙x<0( ˙x>0).Inthiscontext,theshareofland
allocatedtosectorAdecreasesforhighlevelsofpollutionP.
Analogously,accordingto(8), ˙P=0holdsfor:
P=ˇ¯L
+(ε˛−ˇ)
¯L
x (22)
Itholds ˙P <0abovethestraightline(22),while ˙P >0belowit.
Thestraightline(22)haspositiveslope(i.e.,alongit,Pincreasesif
xincreases,seeFig.1(a)and(c))if:
ε˛−ˇ>0 (23)
whileithasnegativeslope(seeFig.1(b)and(d))if:
ε˛−ˇ<0 (24)
Wecanobservethatε˛andˇrepresenttheenvironmentalimpact
ofonelandunitemployedinsectorAandsectorB,respectively.
Thusifcondition(23)holds,thenshiftingtheuseofonelandunit
fromsectorAtosectorBresultsinanetdecreaseinthepollution
stock.
Moreover,forx=0,Eq.(22)gives:
P=P0=
ˇ
¯L>0 (25)
while,forx=1,itgives:
P=P1=
ε˛
¯L>0 (26)
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