University of British Columbia Okanagan

Munich Personal RePEc Archive

Stakeholder Engagement in Land Development Decisions: A Waste of Effort?

Janmaat, Johannus A.

University of British Columbia Okanagan

6 December 2007

Online at https://mpra.ub.uni-muenchen.de/6147/

MPRA Paper No. 6147, posted 07 Dec 2007 00:25 UTC

Deisions: A Waste of Eort?

John Janmaat

∗

Eonomis, IK Barber Shoolof Arts and Sienes

University of British ColumbiaOkanagan

john.janmaatub.a

Deember 6,2007

Abstrat

Currently,managementdevolutionandengagementofloalstakehold-

ers - expeted to have better information - is seen as key to eetive

environmentalmanagement. Often,the abseneoflear property rights

and/orsupportingmarketinstitutionsleavesmanagement deisionstoa

politial proess. Whereundevelopedlandprovidesapubligood,when

to halt further development is modelled as a repeated lobbyingontest

betweenindustryand households. Lobbying eortaets the ontinua-

tionprobability. Dependingonhowstakeholdersareengaged,theremay

belittle impatonnaloutomes,or alobbyingwaranbe stimulated.

Overallwelfareisseldomenhaned.

Keywords: Stakeholderengagement,lobbyingontest,publigood,water

onservation,landdevelopment

JEL:Q24,Q25,R14,R52

1 Introdution

Powerto thepeople isamantrathat hasbeomeanimportantthemein the

environmentalmovement. Arangeofbooks andartiles,([33,36℄forexample)

arguethatloal environmentalstewardshipisthemeansbywhihourenviron-

mentalproblemsmustbeaddressed. Bothgovernmentalandnon-governmental

organizationsareoftenstronglypromotingsuhapproahes,whileritialanal-

ysis of these approahesare sare, and are so far at best inonlusiveabout

∗

FundingforthisresearhwasprovidedbytheCanadianSoialSienesandHumanities

Researh Counil. I am grateful to omments provided at the 2007 CanadianEonomis

Assoiation meetings and the 2007 European Assoiation of Environmental and Resoure

Eonomismeetings. Remainingerrorsandoversightsaremine.

island useplanning. Often,planninginvolvesdeidingwhetherornotaparel

ofopenspaeisgoingtobedeveloped. Developmentandiretlyonsumeare-

sourethatproduesaloalpubligood,suhasopenspae,ormoreindiretly,

suhasleadingtohangedowsinloalstreams. Inthispaperasituationloser

tothelatterismodelled. Aregulatorretainsnalauthorityoverwhetherornot

toallowfurtherdevelopment,whileapro-andanti-developmentlobbyattempt

toinuenewhendevelopmentwillbehalted.

Althoughonsumption ofopen spaebydevelopmentisprobablythe most

publiizedimpatofsprawl,itisnotobviousthat substitutionofalandsaped

suburbanyardforanagriulturaleldis destrutionofapubligood. Inon-

trast,wheredevelopmentonsumeswaterthatwouldotherwisemaintainstream

ows, the destrution of the publi good is moreapparent. We fous on this

type of situation here. Some eorts have been made to value instream ows

(examplesinlude [9, 12, 11, 28℄), oftenusing ontingentvaluation. A general

result of all this literature is that below a ertain level, redutions in stream

owreduethepubligoodvalueofthestream. Thistypeofpubligoodisthe

fousoftheurrentanalysis.

Anotherbranhofliteratureexaminesmehanismsthatanbeusedtoseure

instreamows([17,6,32,16,8℄amongothers),while[25℄doumentsafewases

whereinentivebasedapproaheshavebeenatuallyapplied. Game theoreti

approahesinthisliteraturehavelargelybeenrestritedtobargainingmodels,

whereatleastonedimensionofthebargaininginludesinstreamows[1,38,7℄.

Dynamisaregenerallyrestritedtoelementsofthephysial proesses. These

models are mostly built to inform poliy makers, rather than analyzing the

proessitself.

Although enabling orforing stakeholders to diretly engage eah other is

relativelynovel,stakeholdershavetraditionallybeeninvolvedinwaternegotia-

tionproesses.Theireetivenessatpromotingtheirinterestsisrelatedtotheir

eort, suintly ommentedon by [29, p343℄ ... only those with suiently

onentratedostsorbenets,whoattendhearingsandommitteemeetingsor

makelargeampaignontributionswillbeheard. AsLoomisargues,valuation

studiesareonewaytomeasuretheimpatsonthosenotativeintheproess.

However,manyarguethat engagementis preferableto valuationstudies. Par-

tiipation should therefore bemade less ostly, orfailure to partiipatemade

moreostly. `Stakeholderengagement','partiipatorymanagement,'andother

suhapproahesareperhapsbestinterpretedaseortstohangetheostsand

benetsofinvolvementinthedeisionproess. Theresultsoftheratherlimited

analysisofsuhapproahesismixed[3,26,42,23,30,39℄. Partiipantsexpress

agreaterappreiationfor others' situation,and suggesttheyare morewilling

to ooperate. However, thereis littleevidene of behaviourhange, and some

suggestionthatpeopleengageintheproesstodelayregulatoryhange,rather

than to partiipate in shaping that hange. Inthe model below, twoaspets

ofthe partiipationproessare onsidered,the eetiveness oflobbying eort

andtheresponsivenessoftheregulatortothateort. Greatereetivenessand

responsiveness are akin to inreasing the potential benet of partiipation to

Therelationshipbetweenhouseholdsanddevelopershasbeenexplored.Fis-

hel[13,14℄arguesthatloalpolitisisheavilyinuenedby'homevoters'who

partiipateoutoffearthatthevalueoftheirmostimportantasset,theirhome,

may derease. Hendersonand Beker[19℄reviews anumber ofmodelsof ity

development, and deides that the most appropriate has ities rst built by

developmentrmsand then turnedoverto agovernment. Managingdevelop-

mentto maximizeitizenwelfare onlyhappensafterthere areitizenspresent.

Lubellet al.[31℄ disussesseveral models, partiularly theontrast betweena

propertyrightsmodel-wheresaritydrivesademandforpropertyrightsover

that whih is sare - againstinterest groupmodels - the'Growth Mahine' -

and the politial market - where interests try to buy the regulator. Suess

inahievingonservationobjetivesdependsonboththepowerof theinterest

groupsand the institutional form. As evidene, onservation is generally less

where developersare themost powerful,while it is greatestwhere population

pressuresarehigher.

Muh researh has looked at the role of lobbying in government deision-

making. Inwhatfollowswefousonapartiularstream ofthisliterature, the

rentseekingontestmodelstartedbyTullok[40,41℄. Tullokisreditedwith

being the rstto oneptualize lobbyingas investing to aet the probability

of apturing aprize. In thestati ase with Tullok's speiation, theNash

equilibriumalwaysinvolveswastefulspendingonlobbying. Linster[27℄showed

thatwhentheontestisinnitelyrepeated,thisneednotbetrue. Dijkstra[10℄

found that interest groups may prefer regulation over a nanial instrument

if lobbying over use of revenues exhausts potential payouts. Graihen et al.

[15℄ showed that it may be optimal for rms to improvetheir environmental

behaviourifit reduesthelikelihoodthat anenvironmentallobbyanbeome

asubstitute. Ironially, environmental and onsumerlobbies may be working

in opposite diretions in suh situations. This paper implements a Tullok

stylelobbyinggameinadynamilanddevelopmentontext,wheredevelopment

onsumesapubligood,akintoinstreamow.

2 Model

Weonsideramodelwhereommunitymembers-households-andrmsboth

anpartiipatein anegotiationorlobbyingproess. Partiipationis ostlyto

both households and rms. Although the terms 'lobbying' and 'negotiation'

have almost ontraditory normative onnotations, for our purposes the key

issue is that engagement is ostly, but engagement does inuene outomes.

Thetermswillthereforebeusedsomewhatinterhangeably. Thenegotiationis

overwhetherornottoallowmoreofasareresoureessentialforommunity

growth - land or instream water - to be developed. Undeveloped, the sare

resoure produes a publi good. When used, this developed land provides

aommodationfor membersof the ommunity. Thus, development inreases

thesizeoftheommunity,andtherebythemarginalpubligoodvalueoffurther

Tobespei,let

w

^{bethetotalamountoftheresourethatanbedevel-}

oped,

z t

^{theamountleft}undevelopedat

t

^,and

q t

⁽

q it

^{foreahrm)theamount}

thatisdevelopedin

t

^{. Thepubligoodandpopulationarebothnormalizedto}

thesameunits as

z t

^{,sothatatthebeginningofaperiod, populationis}

w − z t

^.

Developmentoursatthebeginningoftheperiod,afterwhihthepubligood

is enjoyed. Thus, thepopulation in period

t

^{, after}

q t

^{units of land are devel-}

oped,is

w − (z t − q t )

^{. This isthepopulationableto enjoythe publigood in}

thatperiod, andwillbelabelled

m t

^{whenthisisonvenient. Attheendof the}

period, rmshoose an amount

x it

^{to devote to the} negotiation proess, and householdshooseanamount

y jt

^{. The}regulator'sdeisionproessisprobabilis- ti,asinaTullokgame,withtheprobabilityofahaltinfurtherdevelopment

givenby

π(x t , y t )

^,with

x t

^and

y t

^{beingthetotal}negotiationeortforrmsand households. It is assumed that

π 1 < 0

^and

π 2 > 0

^{, where subsripts indiate}

partialderivativearguments. Onedevelopmentoftheresourestops,itnever

resumes.

Thereare

n

^{identialrms,withperiodprotgivenby}

p t (m t )q it − c t (q it ) − x it

⁽¹⁾

where

p t ()

^{isthepriethataunitoftheresoureommandsand}

c t (q t )

^istheost

tothermofdeveloping

q t

^{units. Thedemandurvesatises}

p ^′ _t < 0

^and

p ^′′ _t ≥ 0

^,

whiletheostfuntion satises

c ^′ _t > 0

^and

c ^′′ _t > 0

^{. Theresoureisdurable, in}

thateah onsumeronlyonsumesoneunit,whih providesindenite servie.

Demandthereforedependsontotaldevelopment(population,

m t = w−(z t −q t )

^),

not period development (immigration,

q t

^{). This is onsistent with land, or}

annual rights to a nite renewable resoure like water. For eah household,

periodutilityisgivenby

u(z t , Y i − y it )

⁽²⁾

where

Y i

^isanexogenouslygiveninomeforhousehold

i

^{. Standard}assumptions aresatised, with

u 1 > 0

^,

u 11 < 0

^,

u 2 > 0

^and

u 22 < 0

^{. Note that this is the}

utilityofaresidentwhoownsahouse,withthepriepaidforthehousetreatedas

asunkost. Forsimpliity,thedemandforhousesisassumedtobeindependent

oftheleveloftheloalpubligoodsuppliedbyundevelopedland. Houseprie

and the utility of residents is therefore independent - we are onerned with

utility of residents after purhasing a house. A visual representation of the

gameisshownin gure1.

Determiningtheoptimaldevelopmentpathandstoppingpointrequiresa-

ounting for rm prots and household utility. If prots of the development

industryleavetheommunity,sothataountingforthemonsistsofignoring

them,thentheoptimalommunitysizeandpubligoodlevelarefound,forany

initial

z t

^,bysolving

[β/(1 − β )] max

q t

{u(z t − q t , Y i )m t }

⁽³⁾

the present value of an annuity generating

u(z t − q t , Y i )m t

^{aggregate utility}

indenitely, with disount fator

β

^{. The rst order ondition is}

u 1 = u/m t

^,

F

H

F

N

0 ≤ x t ≤ R t − C t

x t

0 ≤ q t ≤ z t

q t

y t

0 ≤ y t ≤ Y i

1 − π t

π t

" T

X

t=0

β ^t ( R t − C t − x t ) ,

T

X

t=0

β ^t U t + β ^{T +1} 1 − β U T

#

Figure 1: Game Tree. Firm payo when the game ends is the present value

ofprotsfrom housesales,lesslobbyingost, tothe pointwheredevelopment

ends. Forhouseholds, payo is the present valueof the utility stream earned

whiledevelopmentours,andthepresentvalueofthepermanentlevelofutility

earnedafterdevelopmentstops.

ormarginal utility equals averageutility. Thus, not surprisingly, theoptimal

ommunitysize is that whih maximizes average utility. The dynami nature

oftheproblem isirrelevant, asthe driverforan optimalpathovertime is the

ost funtion. This is borne by the rms, and therefore ignored in this ase.

Theutilitymaximizing solutionis tosimply set theommunityat itsoptimal

sizeimmediately. Theonlydependeneontheurrentlevelofdevelopment,

z t

^,

isthat if

z t

^{is smallerthantheoptimal} undevelopedresourelevel, nofurther developmentours.

The polar opposite is to onsider only rm prots and ignore household

utility. We are then foused only on the rm, whih seeks to maximize the

presentvalueofprotsfromdevelopment. Intheformofareursiverelationship,

thevalueofarmis

V t (z t ) = max

q {p t (w − (z t − q t ))q it − c t (q it ) + (1 − π)βV t +1 (z t − q t )}

⁽⁴⁾

where

π

^{isanexogenous}probabilitythatfurtherdevelopmentwillnotbepermit- tedafter theurrentperiod. Inperiod

t

^,theequilibrium (assumingsymmetri rms)onditionis

(q t /n)p ^′ _t + p t − c ^′ _t = (1 − π)βV _t ^′ +1

⁽⁵⁾

Firms equate the marginal benet of urrent development to the disounted

expeted marginal benet of delay. Inreasing the numberof rms generates

moredevelopmentin

t

^(reallthat

p ^′ _t < 0

^).

utilityandprots. Ifweletrmsbeownedbyhouseholds,and,in thespiritof

theHartwikrule[18℄,protsanbeinvestedtogenerateapayoinperpetuity

(nodepreiation),athirdoptimization anbeperformed. FollowingBellman's

prinipleofoptimality[4℄,andassumingthatallprotsaredistributed equally

amonghouseholds, the reursiveequation that haraterizesthe optimalpath

is

U (k t , z t ) = max

q t

{u(z t − q t , Y i + (1 − β)k t /m t )m t + βU (k t +1 , z t +1 )}

⁽⁶⁾

where

z t+1 = z t − q t

^,and

k t+1 = p t (m t )q t − c t (q t ) + k t

^{. Thenewstatevariable,}

k t

^{, is the aumulated prot from} development ativities, whih generates a return at

(1 − β)

^{that is sharedequally among the population}

m t

^{. The rst}

orderonditionis

u t − u 1,t m t − (1 − β)(k t /m t )u 2,t = β(p ^′ _t q t + p t − c ^′ _t )U 1,t+1 − βU 2,t+1

⁽⁷⁾

where with two subsripts, the rst indiates argument of derivative and the

seond the time period at whih the arguments are evaluated. The marginal

benetofinreasingdevelopmentinperiod

t

^{istheutilityearnedbytheaddition}

tothepopulation,lessthepubligoodlossandapital dilutionimpats. This

issetequaltothepresentvalueofthemarginalbenetofdelay,whihinludes

theimpatsof thehigherprieand protnextperiodand thegreater levelof

thepubligood.

Introduinglobbyingornegotiationdemands that householdsandrmsbe

onsidered simultaneously. Further, if either type of agent is to lobby, there

must be a benet to doing so. Here, this is the impat on the probability

development stops after the urrent period,

π(x t , y t )

^{, where}

x t = P

x it

^and

y t = P

y jt

^{arethetotallobbyingeortsof thehouseholdsandrms. Thetwo}

reursiveequationsthatharaterizethissystemare

V (z t ) = max

q it ,x it

{p t (w − (z t − q t ))q it − c t (q it ) − x it

+(1 − π(x t , y t ))βV (z t − q t )}

⁽⁸⁾

U (z t ) = max

y jt

{u(z t − q t , Y j − y jt )

+π(x t , y t )β ² /(1 − β)u(z t − q t , Y j ) + (1 − π(x t , y t ))βU (z t − q t )

⁽⁹⁾

Twokeypointsarehighlightedinthesereursiverelationships. First,ifdevelop-

mentstops,thenthermearnsnofurtherprots. Seond,forthehousehold,if

developmentstops,householdsearnthepresentvalueof

u(z t − q t , Y j )

^,aonse-

queneofthefatthatthepubligoodlevelremainsat

z t − q t

^{forever,andthat}

nofurtherspendingonnegotiationisrequired. Theannuityfatoris

β/(1 − β)

^.

Some basi results of this formulation an be explored by examining the

rstorderonditions. Therstorder onditionsfor

x it

^and

y jt

^denethebest

responsefuntionsof thetwotypesofplayers. Theseare

−1 − π 1,t βV t+1 = 0

⁽¹⁰⁾

−u 2 ,t + π 2 ,t β [β/(1 − β)u t − U t +1 ] = 0

⁽¹¹⁾

the marginallobbing ost,

1

^{. For}households, urrent marginalutility loss is equated to marginal probability saled net benet if development stops, the

dierene between

u t = u(z t − q t , Y i )

^and

U (z t − q t )

^{. A lobbying warours}

whentheresultant

x t

^and

y t

^{valuesarelargerthanthehangeinwelfarerelative}

totheequilibriumthatwouldourwithoutlobbying.

For bothtypesof agents,twofores interatto inuene whether andhow

muh itisworthengagingin negotiations. Forrms,these arethesizeof

V t+1

and the marginal impat on the probability. If the rm value is large, then

thevalueof negotiating to allowfurther developmentis high. Likewise, if the

impatontheprobabilityislarge, thenthevalueofnegotiating ishigh. With

housingadurablegood, itfollowsthat

V _t ^′ +1 < 0

^{. Asmorehousingissold, the}

prieofhousing, and thereforefuture prots,falls. This impliesthat industry

lobbyingeortwilldelineovertime,asthestokofhousinggrows(asthestok

ofthepubligoodshrinks).

Forhouseholds,themarginalimpaton

π

^{interatswiththeexpetedutility}

impatof future development,

β/(1 − β)u t − U t +1

^{. A greater}probability im- pat,the moreit isworthspending. Likewise,the greatertheexpetedutility

impat- due tofuture redutionsin the publigood, themoreeortput into

negotiations. Therefore, if the publigood has diminishingmarginalvalue to

households,thenhouseholdlobbingeortwillinreaseovertime,astheamount

ofremainingpubligoodshrinks. Takentogether,thisimpliesthatasthegame

proeeds, industry lobbying delines and householdlobbying inreases. Thus,

theprobabilitythatthegameendsaftertheurrentperiodinreaseswithtime.

Theendofperiod lobbyinggameNashequilibrium generatestwofuntions

x ^∗ _t (q t )

^and

y _t ^∗ (q t )

^{. Assumingperfet} information, these funtions areinluded inthermshoieof

q t

^{atthebeginningoftheperiod. Therstorderondition}

forthisoptimizationleadstotheequilibrium ondition

p ^′ _t q t /n + p − c ^′ _t

| {z }

− x ^∗′ _t /n

| {z }

= (1 − π)βV _t+1 ^′

| {z }

+ (π 1 x ^∗′ _t + π 2 y _t ^∗′ )βV t+1

| {z }

M N R M L M F C M LI

(12)

withsymmetryassumed. Thefouromponentsofthisrelationareherelabelled

marginalnet revenue (

M N R

^{), marginallobbying (}

M L

^{), marginalfuture ost}

(

M F C

^{)andmarginallobbyingimpat(}

M LI

^{). Witha}probability

π

^thatdevel-

opmentwillendaftertheurrentperiod,andnolobbyinggame,

q t

^ourswhere

M N R = M F C

^{. Howthisoutomeisshiftedbythelobbyinggamedependson}

how

M L

^and

M LI

^{interat. Thisdependsonthebehaviourof}

x ^∗ _t

^and

y ^∗ _t

^,and

howthatinteratswith

π

^,where

π 1 < 0

^and

π 2 > 0

^.

Sineboth

x ^∗ _t

^and

y ^∗ _t

^{anbeeither dereasingorinreasing,there arefour}

possibleombinations(see table 1). Absent the

M LI

^{eets, when}

x ^∗′ _t > 0

^,

q t

isredued, as rmsredue developmentto redue the resultinglobbyingost.

When

M LI

^{ispositive,whihoursforasuientlylargeandpositive}

y _t ^∗′

^,this

eetisenhaned. Development,

q t

^{falls asrmsareseekingto avoidengaging}

inalobbyingwar,rms'fold'. Forallremainingvaluesof

y ^∗′ _t

^,

M LI

^isnegative,

and

q t

^{isinreased. Forlargeandnegativevaluesof}

y _t ^∗′

^{,theinreasein}

q t

^auses

Table1: NegotiatingGame Equilibria. Households(H) hoose

y

^andrms(F)

hoose

x

^{. In}equilibria,either householdsorrmsfold,orthesystemmovesin thediretionofalobbyingwar. Withintwoells,theoutomeisindeterminate

asitdependsonthepreiserelationships,notsimplythesigns.

y _t ^∗′ ≪ 0 y ^∗′ _t < 0 y _t ^∗′ > 0 y ^∗′ _t ≫ 0 x ^∗′ _t < 0 q t ↑

^{,H fold}

q t ↓

^,towar

q t ↓

^,indet.

q t ↓

^,Ffold

x ^∗′ _t > 0 q t ↑

^{,H fold}

q t ↑

^,indet

q t ↑

^,towar

q t ↓

^,Ffold

alargerdropin

y _t ^∗

^{thantheinreasein}

x ^∗ _t

^,essentiallyhouseholds'fold'. When

y _t ^∗′

^{issmallinabsolutevalue,inreasing}

q t

^{maymovethesysteminthediretion}

of alobbing war. Thisis ertain for

y ^∗′ _t > 0

^{, and analso be saidto our if}

y _t ^∗′ < 0

^but

x ^∗′ _t + y _t ^∗′ > 0

^{. Thehoieof}

q t

^{induesaninreaseintotallobbying}

eort. Notethatsinethesearemarginaleets,whetherrmsandhouseholds

areatuallyengagedinawastefullobbing warannotbedeterminedfrom the

signsalone.

When

x ^∗′ _t < 0

^{, and no}

M LI

^{, then rms inrease urrent} development in order to redue lobbying expenditures. With

M LI

^{negative, this eet is en-}

haned. Thisourswhen

y ^∗′ _t

^{is negativeandlargeenough(in absolutevalue).}

Oneagain, householdsfold. Likewise, when

y ^∗′ _t

^{is largeandpositive,}

q t

^{is re-}

dued. Lobbyingeortbyrmsdoesinrease,butthedelinein

q t

^issuiently

satisfyingtothehouseholdsthattotallobbyingfalls,andweagainsaythatrms

fold. With intermediate valuesfor

y ^∗′ _t

^,

q t

^{falls and industrylobbing inreases.}

When

y _t ^∗′ < 0

^{, householdlobbing also inreases, andthe systemmovesin the}

diretionof alobbyingwater. With

y ^∗′ _t > 0

^{, whetherornotthesystemmoves}

towardsalobbyingwardependsonwhether

x ^∗′ _t + y _t ^∗′ < 0

^.

A key poliy question is whether government has a role. At present, the

roleis often seenasfailitating negotiationby bringing stakeholders together.

Itisunlearwhethersuh failitationaets

π(x t , y t )

^{. Itislikelytoredue the}

ostof partiipationfor thestakeholders,whih, allother thingsequal, would

inreasestakeholderresouresdevotedtonegotiation. Insofarasthisinrease

inresouresdoesnothangetheoutome,suh eortsaredoublywasteful. At

therstlevel,governmentresouresaredevotedtoaproessthataomplishes

nothing. Atthe seond level,these governmentresouresleveragestakeholder

resoures,whih againaomplishnothing.

Thus, this suggests that government should not be devoting resoures to

failitatingthenegotiationproess. Rather,resouresshouldbediretedatun-

derstandingtherelativestrengthintheurrentproess,andlookingforwaysto

shiftthatbalanewhihinreasesthelikelihoodofinreasingaggregatewelfare.

The objetivetherefore is to hange

π(x t , y t )

^{. This may involvefunding tar-}

getedat strengtheningommunitygroups-thehousehold lobby in themodel.

Funding should diretlyaddresswherethe weakness isin the householdinu-

eneon

π(x t , y t )

^{-overomingthefreeriderproblem,supportingloalresearh,}

providingexpertise,et. Unfortunately,itisexpetedthatanysuhshiftswould

3 Numerial Example

Anumerialexampleisdevelopedin R[34℄. Funtiondenitionsare

u t (y jt , z t ) = Az _t ^α (Y j − y jt ) ^β

⁽¹³⁾

π(x t , y t ) = a y y t + b x

(a x x t + b x ) + (a y y t + b y )

⁽¹⁴⁾

p t (q t , z t ) = B(w − (z t − q t )) ^γ

⁽¹⁵⁾

C(q it ) = Cn ^{δ − 1} q ^δ _it

⁽¹⁶⁾

with all parameters exept

γ

^{assumed positive, and for} diminishing marginal utility,

0 < α, β < 1

^{. Equation 14 is a ontest suess funtion frequently}

usedfor lobbyinggames, militaryontests, and similarsituations. It isgener-

allyattributedto Tullok[40,41℄,withtwodierentaxiomizationpresentedin

Kooremanand Shoonbeek[24℄ andin Skaperdas[37℄. Theostfuntion de-

nition,equation16,hasasalingfatordependenton

n

^{. Withthis}adjustment, theaggregate osturveremains onstant asthe numberof rmsis hanged.

Thus, hangesinostsarenotdrivingresults.

The ontest suess funtion used is the ratio form. As pointed out by

Hirshleifer [20℄, this hasthe property that beause of the high marginal gain

from lobbying when total lobbying is near zero, a Nash equilibrium without

somelevel of wasteful lobbying annot exist. In the situation modelled here,

theagentthat has'theearoftheKing'likelygetstherewayifthereisnobody

elsewhispering. Assuh,theratioform istakento beappropriate.

Identiationofequilibriawasestimatedthroughabakwardindution im-

plementationof numerialdynami programming(See forexample 2). Ave-

torof 50disrete valueswasusedfor eah statevariable, generatingthe value

funtion(s)at 50 spei points. Quadrati interpolationwasusedto approx-

imatevaluefuntion levels betweenthe spei points. As for thetheoretial

development,symmetry wasimposed ontherstorder onditionsto establish

equilibriumrelations. ToloatetheNashequilibrium,asearhwasthenusedto

identifyapairofnegotiationexpendituresthatmutually zeroedtherespetive

relations. Thederivatives

x ^∗′ _t

^and

y _t ^∗′

^{werenumeriallyestimatedbyperturbing}

thevalueof

q t

^{that dened theNE. Thethus alulated}derivativeswere part ofthezerorelation thatdened theequilibrium

q t

^{level. Thiswasiteratedon}

untiltheeulideandistane betweenvaluefuntion vetorsforsuessiveperi-

odswaslessthan

10 ^{− 10}

^{orthenumberofiterationsexeeded100. Forthease}

omparisons, the onvergene threshold was

10 ^{− 10}

^{, with a maximum number}

ofiterationsat40. Inalargemajorityofases,theonvergene thresholdwas

attained. However,someasesenteredstableosillationsinvaluefuntionlevel.

Thesewereterminated afterthemaximumnumberofiterations.

The analytial development foused on asingle period, examining the in-

entivesgoverningthe amount ofdevelopmentin aperiod, and theamountof

0 10 20 30 40 50

0 5 10 15 20

Optimal Resource Use

z t

q t

Utility Profit Hartwick q _t Hartwick k _t = 0 Hartwick k _t

0 500 1000 1500 2000 k t

Figure2: Optimalresoureuse,forutilitymaximizationignoringprot,prot

maximization ignoring utility, and Hartwik style utility optimization, where

protsareinvestedintoaapitalstokthatontributestohouseholdinome. All

urvesexeptthatforHartwik

k t = 0

^{ase(grey)plotonleftaxis. Numerial}

onvergeneproblemsresponsiblefor'bumpiness'.

lobbyingeort. Thenumerialresults areillustrated by linking a sequeneof

periods together, and examining the development paths, as well as expeted

totaldevelopment, totallobbying, and time till developmentstops, asseenat

thestartofthegame. Figure2showsthestatedependentresoureusefuntion

forthreealternativeoptimalityonditions. Ifrmprotsareignoredandonly

household utility is maximized, then no development ours if

z t

^{is lessthan}

8.3333,andfor

z t > 8.3333

^{,itisoptimaltohoose}

q t = z t −8.3333

^{. Inontrast,}

ifhouseholdutilityisignoredandthepresentvalueoftheprotofamonopoly

ownermaximized,alloftheresoureisused. However,spreadingostsleadsto

amoregradualdevelopmentpathovertime. Priortoanydevelopment,

z t = w

^,

where,inthisase,

w = 50

^.

AthirdoptimizationistheHartwikstylease,wherereturnsfrominvested

protareaddedtohouseholdinome. When

z t

^{issmall,thereismoredevelop-}

mentthanwithamonopolist,asthatdevelopmentinreasesommunitypopula-

tionandaggregateutility. However,developmentfalls morerapidlyhittingthe

z t

^axisoinidentally loseto the point where aggregateutility is maximized.

As

z t

^falls,

k t

^{inreases, inreasing household inome, and themarginal value}

ofthe(normal) publi good. Relativetothe pathwhere apitalaumulation

beginswhen

z t = w

^{,that forapitalaumulationbeginninglaterisuniformly}

higher,anddevelopmentishaltedwithasmaller

z t

^{value. Withoutanyapital,}

Although notexplored in detail, theoptimalityquestion highlightsan im-

portant aspet of deentralization. Even if full ownership of the resoure is

providedto aommunity, thereisnoguaranteethat theenvironmentwill fare

better. Ifloalsareabletoapturethebenetsofdevelopment,theymayhoose

moredevelopment. Twofeatures of the urrent model would leadto suh an

eet. First,ifthebenetsofdevelopmentarelarge,relativeto theloal value

ofthepubli good, then greaterdevelopmentis likely. Seond, ifloalinome

is low, making the marginalvalueof the inome ontribution of development

large,then greater developmentis likely. If theresourein questionhas large

aggregatevaluebeyondtheloalommunity,deentralizingontroltotheloal

levelmaybeworseforaggregatewelfarethanmaintainingentralontrol.

Foromparisonpurposes,protmaximizingresoureuseandrmvalueare

shown in gure3. Not surprisingly, rmprot is inreasingin the amountof

resoureremaining. Theimpat of hangingthe probabilityis also onsistent

withexpetations, inthat thegreatertheprobabilitythat theresourewill be

availableforusenextperiod,themoreoftheresourermsarewillingtoleave

tonextperiod. What ismoreinterestingis thefat that thevaluefuntion is

notonave. Rather,whenthereismorethanonerm,itispieewiseonave.

Thisisaonsequeneoftheinterationbetweenthedisretetimenatureofthe

optimization and the prisoner's dilemmagame that the rmsare engaged in.

Disrete time implies that ations takeplae at preise points in time. Here,

a spei quantity of resoure is used in eah period, with all the remaining

resoureused upin some nal period. Onetherefore does nothaveasmooth

onsumption path over time, but a sequene of distint quantities. This is

responsibleforthekinksor disontinuitiesintheurves.

Theprisoner'sdilemmabetweenimperfetlyompetitiverms,inthisase,

hasthermsusingmorethantheoptimalamountoftheresoure,astheyaim

to apture it before their rival does. In panel (b), this manifests itself in the

fatthatthepointatwhihtheindustrynolongeronsumesalloftheresoure

intherstperiodoursforalarger

z t

^{thegreaterthenumberofrms. Thisis}

markedbythepointwheretheresoureuseurversthasakink. Fortherst

segmentafterthekink,theremainderoftheresoureisonsumedintheseond

period. However,onernsaboutbeing'beat'totheresoureintherstperiod

are no longer drivers. As

z t

^{is inreased, a point is reahed where the rms}

nolonger use all the remainingresoure in the seond period. This produes

a downward shift in the optimal resoure use, a onsequene of the drop in

the slope of the value funtion. The quadrati interpolation used smoothed

thekink in thevaluefuntion thatorrespondsto thehangein resoureuse,

distorting the graphsomewhat. In panel (a), for the

π = 0.0

^{ase, the value}

funtion didnotonverge,but ratherentered aylialpattern fortwoof the

50

z t

^levels,representedbythesawtoothjustbelow

z t = 40

^{. Asthe}probability thatdevelopmentwill takeplaenextperiod inreases,panel(a), thedistane

betweentheslopehangesandbetweenthedisontinuitiesdelines,andthesize

ofthedownwardstepsinreases.

Figure 4illustrates the impat of hangingthe eetiveness of negotiating

q t 0 5 10 15 20 25

a) Use by Probability, n = 2

π = 0.0 π = 0.2 π = 0.5 π = 0.8 π = 1.0

b) Use by Concentration, π = 0.5

n = 1 n = 2 n = 4

0 10 20 30 40 50

0 200 400 600 800

z t

V t ( z t )

c) Value by Probability, n = 2

π = 0.0 π = 0.2 π = 0.5 π = 0.8 π = 1.0

z t

0 10 20 30 40 50

d) Value by Concentration, π = 0.5

n = 1 n = 2 n = 4

Figure3: Resoureuseandrmvalueasfuntionsofresoureremainingunused.

Panels(a)and(b)showtheamountoftheresoureusedintheurrentperiod,

giventhe amount remaining. Panels() and (d) report thevalueof the value

funtion,whih isthepresentvalueoftheoptimal pathfromthe urrentdate

forward. Inpanels (a) and (), grey segment for

π = 1.0

^{indiates alternate}

resoureuseandvaluefuntionforvaluefuntionyle. Inpanel(d),greylines

marktotalindustryvalue,whileblaklinesmarkindividualrmvalue.

eort(

a x

^and

a y

^)andtheresponsivenessoftheregulator(

b x

^and

b y

^{). Inreasing}

theeetiveness orrespondsto making iteasier forstakeholders to engage in

negotiation,astheeterusparibus impatofmorenegotiationeortisgreater.

Inreasingtheregulatorresponsiveness(reduing

b x

^and

b y

^{)reduesthestrength}

oftheregulator'sbias. Resultsareallbasedonaninitialpubligoodlevel

z 0 = w

^{. Thegraphsshowtheexpetednumberofperiodsduringwhih}development oftheresouretakesplae,expetedpubligoodlevelwhendevelopmentends,

andpresentvalueofindustryandhouseholdexpendituresonnegotiationeort.

Allresultsarerelativetothemonopolistasewith

a x = a y = 1

^and

b x = b y = 1

^.

Panelsa,,andeshowtheimpatofhangingtheeetivenessofnegotiation

eort. Inreasing thesize of

a i

^{inreasestheimpatofadditional}expenditures onnegotiation eort foragent type

i

^{. Inreasing the eetiveness of industry}

lobbying inreases the duration of development ativity and redues the ex-

petednal publigoodlevel,foreahindustryonentrationlevel. Inreasing

rmnumberstendstoreduethedurationofdevelopment,whileinreasingthe

expetednalpubligoodlevel. Twofreeridingeetsontributetothis. First,

withmorerms,eahseekstofreerideontheotherslobbyingeort. Seond,the

openaessnatureoftheresourerightsresultsininreasingdevelopmenteah

period. Takentogether,householdlobbyinginreasesmorerapidlyin response

tofasterdevelopment,andrmsareunable tooordinateonounteratingit.

Negotiationeortsfollowamoreinterestingpattern. When

n = 4

^,household

eort is greatest when the eetiveness levels are approximatelyequal. This

eortis suientto overpowertheindustrylobbyingeort,protetingafairly

high level of the publi good. Inreasing the eetiveness of the household

lobbying inreases the expeted nal publi good level and redues the Nash

equilibriumnegotiationeorts. Likewise,reduinghouseholdnegotiationeort

eetiveness redues the NE negotiation eorts, andresults in equilibria with

lowernalpubligoodlevels.Inthemostextremease,thereisalmostnopubli

goodleft, but rmstakealongtimeto developalltheresoure. When

n = 2

^,

the greatest household expenditure on lobbying takes plae when households

aresomewhatmoreeetivethanrmsintheirlobbying. Otherwise,theeets

are similar. When

n = 1

^{, there is evidene of a lobbying war. When}

a y

^is

somewhat larger than

a x

^{then both industry and household lobbying eorts}

are high. However,there is notmuh dierene in the outome than what is

observedwithmorethanonerm.

Whenhangesintheresponsivenessoftheregulatorareonsidered,expeted

nalpubligoodlevelsaregenerallyinreasingwiththenumberofrms,while

durationtends to deline. Forany partiular numberof rms, both duration

and expeted nal publigood level are not very responsive to hanges in

b x

and

b y

^{. Thisissomewhat}surprising,sinetheregulator'sdefault(absentlobby- ing)probabilityofendingfurtherdevelopmentrangesfromapproximately0.01

(

0.1/10.1

^)toapproximately0.99(

10.0/10.1

^{). Theindustryandthehouseholds}

respond in suh a way that the bias is oset. Notie that as the bias shifts

to favourone type of player - inreasing

b x

^{favours rms -} negotiation eort from that type of playerfalls. Thisours forboth playertypes, but is more

pronounedfor thehouseholds. The freeriding eet on industrynegotiation

T z

x y

0.2 1.0 5.0

a) Effectiveness, n = 1

a y 0.2 1.0 5.0

c) Effectiveness, n = 2

a y

0.2 1.0 5.0

0.2 1.0 5.0

e) Effectiveness, n = 4

a x

a y

T z

x y

0.1 1.0 10.0

b) Responsiveness, n = 1

b y 0.1 1.0 10.0

d) Responsiveness, n = 2

b y

0.1 1.0 10.0

0.1 1.0 10.0

f) Responsiveness, n = 4

b x

b y

Figure4: Expetedduration(

T

^{),expetednalpubligoodlevel(}

z

^),expeted

PV of rm (

x

^{) and household (}

y

⁾ negotiation eort, for various expenditure eetivenessand regulatorresponsivenessand

z 0 = w

^{. Radius ofirlesetion}

measuresvariablerelativeto monopolyasewith

a x = a y = 1

^and

b x = b y = 1

^.

Graydashedirleinpanels()through(f)enablereferenetomonopolyase.

14

Eorts to inrease stakeholder engagement are analogous to hanging ef-

fetiveness andresponsiveness. Changingresponsivenesshasalmost noimpat

onexpeted time to developmentessation,nor onexpeted remainingpubli

good. Responsiveness is analogous to a regulator ontributionto lobbyingef-

fort,substitutingforhouseholdorrmlobbyingeortandleavingtheoutome

unhanged. It doesnot hange the marginalvalue of lobbying, and therefore

doesnotenouragemuh ofahange. Inontrast, hangingeetivenessdoes

hangethemarginalimpat. Whatstandsouthereisthat symmetrihanges

in eetiveness,suh asaregulatoropeningtheproessin anequalwaytoall

stakeholders,doesalmostnothingtohangetheoutome. Theoutomeisonly

hangedifengagementfavoursoneparty. However,eventhenitmayresultina

largeinreasein expetedlobbyingandamoveawayfrom theeientlevelof

thepubligood. Inreasingstakeholderengagementmayhavelittleimpaton

outomes, and mighteven makethings worse. Thus, whilepriniples of good

governanemaybeonsistentwithinreasingpartiipation,itisfarfromertain

thatitwillimprovetheeonomieienyoftheoutomes.

Figure5showstheeetofhangingtheutilityfuntionparametersandone

demandfuntion parameter. Whenhangingtheutilityfuntion,theelastiity

parameters were restrited to satisfy

α + β = 1

^{. In panels (a) through (),}

theexpeted nal publigood level inreasesasboth

α

^and

Y i

^{are inreased,}

while duration falls. This is aonsequene of the fat that inreasing

α

^and

inreasing

Y i

^{eah inrease the marginalutility of the publi good relative to}

residual inome. Thus, the marginal benet of lobbying inreases, leading to

aninreaseinthisativitybythehouseholds. Inreasingrmnumbersredues

lobbying or negotiation eort by the rms. However, the response patterns

dierforeahindustryonentrationlevel. Whendevelopmentismonopolized,

thermrespondstoinreasedhouseholdlobbingbyinreasingitsownlobbying

eort. Forthelower

α

^and

Y i

^{levels,thiseetisalsopresentforthe}oligopolisti industry. However,when

α = 0.5

^and

Y i = 50

^{,industrylobbyingeorthasfallen}

relativetotheaseswhere

α = 0.25

^and

Y i = 50

^or

α = 0.5

^and

Y i = 10

^{. Forall}

asesinpanel (b),household lobbying eortisgreaterthanin panel(a). Free

riding by therms inreasesthe marginalprodutivity of household lobbying

eort,whih for large

α

^and

Y i

^{is suessful in further driving down industry}

lobbying. Although dominated bythe free riding eet,in panel () industry

lobbyingagain falls for the highest

α

^and

Y i

^{levels. For low}

α

^and

Y i

^levels,

householdsinreaselobbying, relativeto the

n = 2

^{ase. However,the ability}

ofhouseholdlobbyingtodrivedownindustrylobbyingisstrongenoughwhen

α

and

Y i

^{arelargethathouseholdlobbyingatuallyfallsrelativetothe}

n = 2

^ase.

Whenthepubligoodisvaluableenoughtothehouseholds,andhouseholdshave

enoughinome, rms essentially apitulate in the lobbying game, whih then

reduesthehousehold'sneedtolobby. Notsurprisingly,wealthyneighbourhoods

gettheirwayatlowerostthanlesswealthyneighbourhoods.

Aninterationbetweenthefreeridingeetonlobbyingandthefreeriding

eetondevelopmentisalso evidentin panel(d). When

γ

^{issmall,inreasing}

n

^{redues durationandinreasesthenalpubli good level. This isdrivenby}

inreasedlobbyingfromhouseholds,leadingtoashiftinontinuationprobabili-

tiesfavouringthehouseholds. Thus,theexpetednalpubligoodlevelishere

inreasing in the number of rms. When

γ = −0.5

^{, rms} essentially give up onanydevelopmentafter therstperiod. Consequently,theydonotinvest in

negotiationeort,makingitunneessaryforhouseholdstoinvestmuh. Redu-

ingrmonentrationnowredues thenal publigood level,aswithgreater

onentration,rmsreduerstperioddevelopmenttoinreaserentsaptured.

4 Disussion

Mostalloationdeisionsaroundniteresouresarenotmadebyanomnisient

regulator. In general, the regulator is inuened by the aeted parties, the

stakeholders,in some way. At one extreme, stakeholders may diretly or in-

diretly tryto bribetheregulator. Theunfavourableonnotation to theterm

lobbyingseemsto reetthissomewhatshadysideoftryingtoinueneareg-

ulator'sdeision. Atpresent,inresponse toawidelyhelddisillusionmentwith

theonventionalproess,manyareenouragingstakeholderstodiretlyengage

eah other. This proess may appear dierent, but fundamentally it still re-

quires stakeholders to expend resouresin an eort to inuene the resoure

managementdeisionintheirfavour. Now,ratherthandiretlybuyingfavours,

theyhavetoshowthattheyareooperatingwithotherstakeholdersinresolving

theresouresharingonit.

Hereinwehaveonsideredasimplemodelofaresouremanagementprob-

lem,wherethemanagementdeisiononsistsofhaltingallfurtherdevelopment

of theresoure. Theresoureis bothnite and durable, onsistentwith land

orrightstoanannualalloationofwater. Bothpro-andanti-developmentlob-

bies attempt to inuene the deision of aregulator with nal authorityover

whether further developmentours. Fouroutomesare identied, aseswith

limitedlobbying,those where thepro-developmentlobbyoverpowerstheanti-

developmentlobby,theonverse,andalobbyingwar.Thislatteraseisperhaps

themostdisturbing,asitsuggeststhatlobbying,whetherastraditionallyenvi-

sioned,ornowas'stakeholderengagement'mayhavelittleimpatonthenal

outome. Assuh,lobbyingissimplyawasteofresoures,engagedin beause

partiipantsare involvedin aprisoner's dilemma. Inpartiular, iflobbyingis

madeeasier forstakeholders to engage in by governmentfailitating meetings

and other forms of interations, losses may be exaerbated. In therst ase,

governmentspendsmoneytolowertheostofinvolvementintheproess. The

redutioninthemarginalostofinueningtheregulatorinduesstakeholders

to spend moreonthis ativity. In theend, theoutome maybeno dierent,

butoverallostshaveinreased.

These resultsalso suggestthat ompensation paymentsfor habitat prote-

tionmaybesensitivetoindustrystruture. Thepreseneorabseneofompen-

sationhas beenshownto aet therateof development, withunompensated

takings hastening development and full ompensation slowing it [5, 21, 35℄.

T z

x y

0.1 0.2 0.5

2 10 50

a) ∆α and ∆ Y _i , n = 1

α Y i

0.1 0.2 0.5

2 10 50

b) ∆α and ∆ Y _i , n = 2

α Y i

0.1 0.2 0.5

2 10 50

c) ∆α and ∆ Y _i , n = 4

α Y i

T z

x y

−0.10 −0.25 −0.50

1 2 4

d) ∆γ

γ

n

Figure5: Variationsin utilityfuntion parametersand demandelastiity. For

panels(a) to (),

α

^and

Y i

respetively measureutility elastiity ofthepubli good and residual inome. In panel (d),

γ

^{measures the prie elastiity of}

demand. Quarter irles have been lipped to prevent overlap with adjaent

graphobjets.

good value [22℄. Although ompensation is not the fous of our model, our

resultsdospeakto this issue. Inpartiular, ifthepurpose ofompensationis

to pay rmsthe present valueof the assetbeingtaken, our resultsshow that

industry struture an play an important role in determining the size of the

presentvalue-thelessonentratedtheindustry,thelowerthepayment. Thus,

althoughthemonopolistmaybethefriendoftheonservationist,intermsofthe

rateofdevelopment,themonopolistdoesnotlettheonservationistoheaply

ifdevelopmentistobehalted.

The ineienies highlighted here are a onsequene of the lak of lear

propertyrights. In thease of land, ownersdo nothavean exlusiverightto

deidehowto usetheirproperty. Therightto apartiularuse-development-

mustbeatedupon before theregulatordeidesthat enoughsuhrightshave

been atedon. With land, suh 'takings' themselvestypiallyleadto aset of

legalbattlesaboutwhetherornotthepropertyownerdidown adevelopment

right-requiringompensation-ornot. Forwater,inontrast,rightsaretypi-

allyusufrutory,andonlyalloatedwhenaneedisdemonstrated. Thus,water

rightsarenotowneduntil developmentthatanuseithastakenplae. When

property rights to waterare vested with the user, then arrangementssuh as

leasingorpurhaseanprotetpublivaluesfrominstreamows. Inbothases,

thekeypropertyrightisessentiallyopenaess. Clarityofthelegalrighttode-

veloppropertyortoaesswater,independentofwhenthoseusesour,would

reduetheinentiveproblems analyzedin thispaper.

The roleof rmsize also bears somereetion. As modelled, there areno

eonomies of sale related to development osts aptured by the rms. This

is likelya reasonablereetionof the onstrution industry, where thetrades

(eletriians,plumbers,arpenters)aregenerallyharaterizedbyalargenum-

ber of small rms. The benets of size in the model ome from a redution

infreeriding inentivesbothin lobbyingandin thenal market. Theurrent

trend towards relatively large developments, with multiple year development

plans,maybeameansofpre-emptingthelobbyingproess. Firmsareableto

seuretheirdevelopmentrightsbeforetheoupantsarrive,whomaydesireless

development. An interesting empirial analysis would beto searh for arela-

tionship betweendevelopmentprojetsize (units, area, oryears tobuild) and

perunit publi spae. Iflargerprojetsarepre-empting thelobbyingproess,

thenpublispaeshouldbesmaller.

5 Conlusion

Astylizedlanddevelopmentindustrywhihonsumesapubligoodgenerating

resoure(openspae,surfaewater)ismodelledinteratingwithommunityo-

upantsinalobbyinggame. Householdsandtheindustryarelobbyingtoaet

whether further development is allowed. Lobbying eortinvested depends on

therelativepoweroftheagents,withsomeombinationsresultingin alobby-

ingwar. Inreasingtheeetiveness oflobbying,akintoreduingthemarginal

outomewhenbothinterestsareaetedsymmetrially. Thissuggeststhatthe

urrentlypopularstakeholderengagementeorts may dolittle to hange out-

omes. Iftheseinitiativesareostlytoimplement,andiftheyenouragegreater

lobbyingeortbythestakeholders,thentheyarewasteful. Ifitisknownwhih

aetedpartyisdisproportionatelypowerless,thentheeienyoftheoutome

anbeimprovedbyequalizingthepowerbalane. However,insodoing,thereis

theriskthatawastefullobbyingwarandevelop. Further,suhshiftingofthe

powerbalanepresupposesthattheregulatorknowsinwhihdiretionthee-

ientamountofdevelopmentis,apossibleproblem. Theresultsofthisanalysis

alsosuggestthat trendstowardslargerdevelopmentprojetsandonentrated

developmentrmsmayin partbearesponseto thethreatoflobbying.

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