Social Common Capital, Imputed Price, and Sustainable Development

Transcription

1 DBJ Reseh Cene on Globl Wing ECONOMIC ANALYSIS No 4 Deebe 2009 Soil Coon Cpil Ipued Pie nd Susinble Deelopen Hioui Uw RESEARCH INSTITUTE OF CAPITAL FORMATION DEVELOPMENT BAN OF JAPAN -9-3 OTEMACHI CHIYODA-U TOYO JAPAN gw@dbjjp

2 In his ppe we poe in es o he pooype odel o soil oon pil h he opiu ondiions o susinble poesses o pil uulion inoling boh pie pil nd soil oon pil oinide peisely wih hose o ke equilibiu wih he soil oon pil es ein speii es unde he siony epeions hypohesis onening he uue shedule o ginl poduiiy o pil o ll kinds eywods: Soil oon pil Pooype odel o soil oon pil Susinble poesses o pil uulion Soil oon pil Ipued pie Siony epeions hypohesis

3 Inoduion Soil oon pil inoles inegeneionl equiy nd jusie Alhough he onsuion nd inenne o soil oon pil equie he use o subsnil poions o se esoues boh hun nd non-hun puing signiin buden on he uen geneion bu he people in uue geneions will benei gely i he onsuion o soil oon pil ied ou by he uen geneion is popely nged In his ppe we eine he pobles o he uulion o soil oon pil piily o he iewpoin o he inegeneionl disibuion o uiliy Ou nlysis is bsed on he onep o susinbiliy inodued in Uw nd we eine he ondiions unde whih poesses o he uulion o soil oon pil oe ie e susinble The onepul ewok o he eonoi nlysis o soil oon pil deeloped in Uw 2005 is eended o del wih he pobles o he ieesibiliy o poesses o he uulion o soil oon pil due o he Penose ee The onep o he Penose ee ws oiginlly inodued in Uw in he one o o-eonoi nlysis nd ws eensiely uilied in he dyni nlysis o globl wing s in deil desibed in Uw The pesenion o he heoy o susinble poesses o pil uulion in his ppe lgely epodues he one inodued hee The eisene o he susinble ie-ph o onsupion nd pil uulion sing wih n biily gien sok o pil is ensued when he poesses o uulion o ious kinds o pil e subje o he Penose ee h ehibis he lw o diinishing ginl es o inesen In wh ollows we oule he onep o susinbiliy wihin he heoeil ewok o he eonoi nlysis o soil oon pil in suh nne h i y be onsuled in deising insiuionl ngeens nd poliy esues in eliing he siony se in he sense inodued by John Su Mill in

4 his lssi Piniples o Poliil Eonoy Mill 848 piully in he hpe eniled O he Siony Se The siony se s enisioned by Mill is inepeed s he se o he eonoy in whih ll o-eonoi ibles suh s goss doesi podu nionl inoe onsupion inesens wges nd el es o inees ein siony whees wihin he soiey indiiduls e iely engged in eonoi soil nd ulul iiies new sienii disoeies e inessnly de nd new podus e oninuously inodued while he nul enionen is being peseed he susinble se Ou nlysis is oused upon he ole o he ipued pies o he sok o ious oponens o pil boh pie pil nd soil oon pil in he poesses o susinble eonoi deelopen The ipued pie o eh kind o pil piul ie epesses he een o whih he ginl inese in he sok o h kind o pil ie indues he ginl inese in unis o ke pies in he wele leel o eh ouny in unis o ke pies inluding hose o ll uue geneions The ipued pie eins siony ie ; i e whee 0 ie is he susinble leel ie i i ees o he ie deiie wih espe o he ie o he iul pil ke ie A ie-ph o he uulions o eh kind o pil is deined susinble i he ipued pie is he susinble leel ll ies Beuse he susinbiliy o he ipued pie is deined wih espe o he iiious ie o he iul pil ke ie he susinbiliy o he ipued pie does no neessily iply he sioniy o he ipued pie s indeenly sed in Uw All he poliy nd insiuionl onlusions obined hee howee ein lid wih egd o he onep o he susinbiliy o ie-phs o he poesses o pil uulion boh pie pil nd soil oon pil s inodued in his ppe 2

5 2 Susinbiliy in he Aggegie Model o Cpil Auulion The bsi peises o he nlysis o susinbiliy e h he ineepol peeene odeing peiling in he soiey in quesion is independen o he ehnologil ondiions nd poesses o pil uulion We onside n ggegie odel o pil uulion whose behiol heisis e desibed by hose o he epesenie onsue nd podue We is onside he siple se in whih only one kind o goods sees boh o onsupion nd inesen uiliy union whee The insnneous leel o he uiliy u u u eh ie is epesened by is he quniy o goods onsued by he epesenie onsue ie We ssue h he uiliy union u u is deined o ll nonnegie 0 is oninuous nd oninuously wie-dieenible nd sisies he ollowing ondiions: We denoe by u > 0 u > 0 u < 0 o ll > 0 he sok o pil ie nd by onsupion nd inesen ie Then we he whee is he poduion union espeiely 0 The poduion union epesses he goss nionl podu podued o he gien sok o pil We ssue h poduion union is deined oninuous nd oninuously wie-dieenible o ll 0 h ginl podu is lwys posiie nd poduion poesses e subje o he lw o diinishing ginl euns: > 0 > 0 < 0 o ll > 0 The e o pil uulion ie is gien by he dieenil 3

6 equion o µ 0 2 whee is he Penose union eling he e o pil uulion o inesen nd he sok o pil pil nd µ is he e o depeiion ie o is he iniil sok o The Penose union epesses he goss e o pil uulion; hus we y ssue h he pil deiie o wih espe o is lwys posiie whees wih espe i is lwys negie: 0 > 0 < 0 The Penose ee is epessed by he ondiions h he Penose union is one nd sily qusi-one wih espe o : < 0 o ll < 0 The ollowing ondiion is usully ssued o he Penose union : < 0 The onep o he Penose ee ws oiginlly inodued by Penose 959 o desibe he gowh poesses o n indiidul i I ws le olied by Uw in he one o eynesin nlysis o o-eonoi poesses o dyni equilibiu o eluide he ee o inesen iiies on he poesses o pil uulion 2 Mginl Eiieny o Inesen A piully ipon onep ssoied wih he Penose union is ginl eiieny o inesen whih plys uil ole in he nlysis o dyni poesses o pil uulion nd eonoi gowh Mginl eiieny o inesen epesses he een o whih he ginl inese in inesen indues he ginl inese in goss nionl podu in he uue The ginl eiieny o inesen is oposed o wo oponens 4

7 The is oponen is he ginl inese in goss nionl podu diely indued by he ginl inese in he sok o pil due o he ginl inese in inesen ; h is whee is he ginl podu o pil The seond oponen esues he een o he ginl ee on uue poesses o pil uulion due o he ginl inese in he sok o pil ody ; h is s Thus he ginl eiieny o inesen y be epessed The ginl eiieny o inesen is deesing union o boh inesen nd he sok o pil : < 0 whee < 0 < 0 In he sndd neolssil heoy o inesen he Penose ee is no eognied; h is Then o ll 0 > 0 0 < 0 o ll 0 > 0 22 Ipued Pie o Cpil nd Susinbiliy The ipued pie o pil ie is he disouned pesen lue o he ginl ineses in oupus in he uue esued in unis o he uiliy due o he 5

8 ginl inese in he sok o pil ie The ginl inese in oupus uue ieτ in unis o he uiliy is gien by eiieny o inesen uue ie τ : τ τ whee τ is he ginl 3 Thus he ipued pie o pil ie τ τ τ τ τ τ τ τ τ e δ µ τ τ τ is gien by dτ 4 By dieeniing boh sides o 4 wih espe o ie we obin he ollowing dieenil equion: δ µ 5 Dieenil equion 5 is nohing bu he Eule-Lgnge dieenil equion in he lulus o iions In he one o he heoy o opiu pil uulion i is oen eeed o s he Rsey-eynes equion The eonoi ening o he Rsey-eynes equion 5 y be bough ou bee i we ewie i s δ µ 6 We suppose h pil is nsed s n sse on he iul pil ke h is peely opeiie nd he ipued pie is ideniied wih he ke pie ie Conside he siuion in whih he uni o suh n sse is held o he sho ie peiod [ ] > 0 The gins obined by holding suh n sse e oposed o "pil gins" nd "enings" ; h is On ohe hnd he os o holding suh n sse o he ie peiod [ ] onsiss o "inees pyen" δ nd "depeiion hges" µ whee he soil e o disoun δ is ideniied wih he ke e o inees Hene on he iul pil ke hese wo ouns beoe equl; h is δ µ By diiding boh sides o his equion by nd king he lii s 0 we obin elion 6 6

9 The ipued el nionl inoe ie H is gien by H u [ µ ] 7 The opiu leels o onsupion nd inesen ie e obined i ipued el nionl inoe onsins Whee H ie is iied subje o he esibiliy Le he Lgngin o be gien by L u [ µ ] p [ ] p is he Lgngin unknown ssoied wih onsins The opiu ondiions e whee he lue o Lgnge unknown u p 8 p 9 p is hosen so h esibiliy ondiion is sisied p y be inepeed s he ipued pie o he oupu ie Equion 8 ens h he opiu leel o onsupion ie is obined when ginl uiliy u is equed wih ipued pie ie p Equion 9 ens h he opiu leel o inesen ie is obined when he lue o he ginl podu o inesen elued he ipued pie o pil is equed wih he ipued pie o he oupu ie The ipued pie eins siony ie ; i e whee p is deined o be he susinble leel ie i i 0 ie ees o he ie deiie wih espe o he ie o he iul pil ke ie Fo he bsi dieenil equion 6 he ipued pie π is he susinble leel ie i nd only i he ginl eiieny o inesen is equl o he su o he soil e o disoun nd he e o depeiion; i e δ µ ie 0 A ie-ph o pil uulion is deined susinble i i is he susinble leel ll ies 7

10 8 23 Susinble Poesses o Cpil Auulion Fis we would like o see i he leels o onsupion nd inesen he susinble ie-ph [ ] e uniquely deeined To see his he ondiions o susinbiliy e pu ogehe s ollows: µ 2 µ δ 3 whee he ie sui is oied By king dieenil o boh sides o elions 2 nd 3 we obin dδ d d d 0 0 whee 0] [ 0 0 < < < Hene δ dδ d d d d d < > < > δ δ Thus he leels o onsupion nd inesen he susinble ie-ph e uniquely deeined In ddiion we he 0] 0 [ 0 0 < > < µ µ Hene he dieenil equion hs uniquely deeined siony se nd i is globlly sble ppohing he long-un siony se idenil wih h o he dynilly opiu leel Thus we he esblished he ollowing poposiion

11 Poposiion Fo n eonoy wih only one kind o pil he susinble poesses o pil uulion e obined i nd only i he ginl eiieny o inesen is equl o he su o he soil e o disoun nd he e o depeiion ll ies ; ie δ µ ll ies The leels o onsupion nd inesen long he susinble e-ph e uniquely deeined o ny gien sok o pil > 0 Along he susinble ie-ph he lge he sok o pie pil highe is he leel o onsupion nd he lowe is he leel o inesen highe he e o disoun δ he highe is he leel o onsupion is he leel o inesen A he susinble ie-ph he sok o pil o he The nd he lowe ppohes s ie goes o ininiy he long-un siony se * h is dynilly opiu Fo he sndd se o he neolssil wold we he o ll 0 Hene h sisies susinbiliy ondiions 3 does no genelly eis 3 The Pooype Model o Soil Coon Cpil The nlysis o susinble poesses o onsupion nd pil uulion we he inodued in he peious seion y be edily pplied o he pooype odel o soil oon pil s inodued in Uw 2005 In he pooype odel o soil oon pil inodued in Uw 2005 we onside piul ype o soil oon pil --- soil insuue suh s 9

12 publi uiliies publi nspoion syses pos nd highwys We onside he genel iusnes whee os o poduion h e neessy o he poessionl poision o seies o soil oon pil e eihe piely owned o nged s i pie owned Seies o soil oon pil e subje o he phenoenon o ongesion esuling in he diegene beween pie nd soil oss Theeoe o obin eiien nd equible lloion o se esoues i beoes neessy o ley es on he use o seies o soil oon pil The pies hged o he use o seies o soil oon pil eeed by he es he pies pid o soil insiuions in hge o he poision o seies o soil oon pil One o uil pobles in he eonoi nlysis o soil oon pil is o eine how he opiu es o he seies o ious oponens o soil oon pil e deeined The nue o seies o soil oon pil ies o suh signiin degee h i is eeely diiul o oule uniying heoy onening he deeinion o he opiu es on seies o soil oon pil The pooype odel o soil oon pil inodued in his ppe inopoes soe o he oe slien eues o soil oon pil nd he nlyil ppuses nd insiuionl nd poliy ipliions egding he pooype odel o soil oon pil y see s guidelines o he nlysis o he speii ypes o soil oon pil 3 Bsi Peises o he Pooype Model o Soil Coon Cpil Alhough he bsi peises o he odel ein idenil wih hose o he pooype odel o soil oon pil in Uw 2005 we us epliily ke ino oun he inesen iiies in boh pie is nd soil insiuions in hge o soil oon pil Fo he ske o eposioy beiy we ssue h only ied os o poduion e liiionl in he poduion poesses o boh pie is nd soil insiuions in hge o soil oon pil The ollowing nlysis y be esily 0

13 eended o he genel se in whih ible os suh s lbo nd enegy inpu e essenilly equied in he poduion poesses We onside n eonoy onsising o n indiiduls pie is nd s soil insiuions in hge o soil oon pil Indiiduls e geneilly denoed by n pie is by nd soil insiuions by s Goods podued by pie is e geneilly denoed by j J Fied os o poduion e geneilly denoed by F whees hee is only one kind o soil oon pil 32 Indiiduls The uiliy o eh indiidul is dinl nd is epessed by he uiliy union u u ϕ whee is he eo o goods onsued nd is he oun o seies o soil oon pil used boh by indiidul whees is he ol oun o seies o soil oon pil used by ll ebes o he soiey: whee is he oun o seies o soil oon pil used by pie i The ip inde union ϕ epesses he een o whih he uiliy o indiidul is eed by he phenoenon o ongesion wih espe o he use o seies o soil oon pil The ip oeiiens τ o soil oon pil deined by ϕ ' τ > 0 ϕ e ssued o be idenil o ll indiiduls nd sisies he ollowing ondiions: τ > 0 τ > 0 The uiliy union u is ssued o sisy he ollowing ondiions:

14 U u is deined posiie oninuous nd oninuously wie-dieenible wih espe o o ll 0 U2 u > 0 u > 0 o ll 0 U3 Mginl es o subsiuion beween ny pi o onsupion goods nd seies o soil oon pil e diinishing o oe speiilly u is sily qusi-one wih espe o U4 u is hoogeneous o ode wih espe o 33 Pie Fis Poesses o poduion in pie is e lso eed by he phenoenon o ongesion egding he use o seies o soil oon pil We ssue h in eh pie i he iniu quniies o os o poduion h e equied o podue goods by nd he se ie o inese he sok o ied os o poduion by wih he use o seies o soil oon pil he leel µ e speiied by he ollowing eo-lued union: ϕ ϕ whee ϕ is he ip inde wih egd o he een o whih he eeieness o seies o soil oon pil in poesses o poduion in pie i is ipied by ongesion Fo pie i he ip oeiiens τ o soil oon pil o be deined by ϕ ' τ ϕ e ssued o be idenil o ll pie is idenil o hose o indiiduls ; ie τ τ o ll The poduion possibiliy se o eh pie i T is oposed o ll obinions o eos o poduion nd inesen nd use 2

15 3 o seies o soil oon pil h e possible wih he ogniionl ngeens ehnologil ondiions nd gien endowens o os o poduion in i I y be epessed s { : T 0 ϕ } whee he ol oun o seies o soil oon pil used by ll ebes o he soiey is ssued o be gien pee The ollowing neolssil ondiions e ssued: T e deined posiie oninuous nd oninuously wie-dieenible wih espe o T < > > T 3 e sily qusi-one wih espe o T 4 e hoogeneous o ode wih espe o 34 Soil Insiuions in Chge o Soil Coon Cpil In eh soil insiuion he iniu quniies o os o poduion equied o poide seies o soil oon pil by nd he se ie o engge in inesen iiies o uule he sok o ied os o poduion by wih he use o podued goods by j e speiied by eo-lued union: ] [ Fo eh soil insiuion he poduion possibiliy se T is oposed o ll obinions o poision o seies o soil oon pil inesen nd use o podued goods h e possible wih he ogniionl ngeens ehnologil ondiions nd he gien endowens o os o poduion in soil insiuion Th is i y be epessed s { : T 0 } The ollowing neolssil ondiions e ssued:

16 T e deined posiie oninuous nd oninuously wie die dieenible wih espe o o ll 0 T 2 > 0 > 0 < 0 o ll 0 T 3 e sily qusi-one wih espe o o ll 0 T 4 e hoogeneous o ode wih espe o 35 Cpil Auulion in he Pooype Model o Soil Coon Cpil The uulion o he sok o pil goods in pie i is gien by he ollowing dieenil equion 4 µ 0 o whee is he eo speiying he leels o inesen in pil goods in pie i ie nd µ is he e o depeiion Siilly he uulion o he sok o pil goods in soil insiuion is gien by he ollowing dieenil equion 5 µ 0 o whee is he eo speiying he leels o inesen in pil goods in soil insiuion ie nd µ is he e o depeiion 4 Ipued Pies nd Susinble Poesses o Cpil Auulion in he Pooype Model o Soil Coon Cpil Ely s in he ggegie odel o pil uulion he ipued pie o pil in he pooype odel o soil oon pil is deined The ipued pie 4

17 in unis o he uiliy o eh kind o pil ie is he disouned pesen lue o he ginl ineses in ol uiliy in he uue due o he ginl inese in he sok o pil o h kind ie When we denoe by τ he ginl inese in he ol uiliy uue ie τ he ipued pie ie by is gien δ µ τ τ e dτ 6 By dieeniing boh sides o 6 wih espe o ie we obin he ollowing dieenil equion: δ µ 7 As in he se o he ggegie odel o pil uulion we suppose h pil is nsed s n sse on iul pil ke h is peely opeiie nd he ipued pie is ideniied wih he ke pie ie Conside he siuion in whih he uni o suh n sse is held o he sho ie peiod [ ] > 0 The gins obined by holding suh n sse e oposed o "pil gins" nd "enings" ; h is On ohe hnd he oss o holding suh n sse o he ie peiod [ ] onsis o "inees pyens" δ nd "depeiion hges" µ whee he soil e o disoun δ is ideniied wih he ke e o inees Hene on iul pil ke hese wo ouns beoe equl; h is δ µ By diiding boh sides o his equion by nd king he lii s 0 we obin elion 7 We deine h he ipued pie eins siony ie ; i e whee i y be einded h 0 ie o he iul pil ke ie is he susinble leel ie i i ees o he ie deiie wih espe o he ie 5

18 Fo he bsi dieenil equion 7 he ipued pie susinble leel ie i nd only i is he δ µ ie whee is he ginl inese in ol uiliy due o he ginl inese in he sok o pil o h kind ie Wih espe o he pooype odel o soil oon pil he ipued pie o pil in pie i ie is he susinble leel ie i nd only i δ µ ie 8 whee is he ginl inese in ol uiliy due o he ginl inese in he sok o pil in pie i ie Siilly he ipued pie o pil in soil insiuion ie is he susinble leel ie i nd only i δ µ ie 9 whee is he ginl inese in ol uiliy due o he ginl inese in he sok o pil in soil insiuion ie A ie-ph o pil uulion is deined susinble i he ipued pies o ll kind o pil boh pie pil nd soil oon pil e he susinble leels ll ies i e 8 nd 9 hold ll ies 4 Susinble Poesses o Consupion nd Inesen We pesue h he ipued pies o pil goods in pie is nd soil insiuions in hge o soil oon pil ll ie e gien espeiely by nd Then he ipued el nionl inoe in unis o he uiliy ie is 6

19 7 gien by µ µ ϕ u H whee is he eo o onsupion nd e espeiely he eos o inesen in he pil o pie i nd soil insiuion ll ie The opiu leels o onsupion nd inesen ie e obined s he soluion o he ollowing iu poble Miu Poble Miie he ipued el nionl inoe in unis o he uiliy ie H subje o he esibiliy onsins: ϕ whee e espeiely he ouns o seies o soil oon pil used by indiiduls nd pie is is he oun o seies o soil oon pil poided by soil insiuions nd is he ol oun o seies o soil oon pil ll ie Le L be he Lgngin o o his iu poble: µ µ ϕ u L π θ p [ ] [ ] ϕ

20 8 whee π θ p e espeiely he Lgngin unknowns ssoied wih onsins nd 24 The opiu ondiions e heied by he ollowing ginliy ondiions in ddiion o he esibiliy ondiions 20-24: u ϕ p od 25 u ϕ ϕ θ od 26 p ϕ od 27 ϕ od 28 θ [ ] ϕ ϕ od 29 ϕ od 30 π od i 3 od i 32 p [ ] od 33 od 34 τ τ τ π τ π θ 35 Lgnge unknowns p θ π y be inepeed espeiely s he ipued pies o he oupu he pies o he use o soil oon pil nd he pies pid o he poision o seies o soil oon pil nd nd i e espeiely he ipued ens o pil in pie i nd soil insiuion whees nd e espeiely he ipued pies o el he pil in pie i nd soil insiuion ll ie esued in unis o he uiliy A siple lulion shows h he ipued ens o pil in pie i nd soil insiuion nd i e espeiely he ginl ineses in ol uiliy due o he ginl ineses in he sok o pil in pie i nd soil insiuion boh ie Hene he susinble poesses o onsupion nd inesen in he pooype odel o soil oon pil y be obined when he ipued pies o pil in pie i nd soil insiuion ie

21 nd e espeiely equl o he disouned pesen lues o he ipued ens o pil in pie i nd soil insiuion ssuing h he ipued ens o pil ein siony; i e he ollowing elions hold o ll pie is nd soil insiuions ll ies : δ µ 36 δ µ The elions 36 en h he siony epeions hypohesis holds ue s egds he uue shedule onening ginl eiieny o inesen o ll kind o pil pie pil nd soil oon pil 42 Susinble Poesses o Cpil Auulion nd Mke Equilibiu The opiu ondiions o he susinble poesses ie s obined boe e idenil wih hose o ke equilibiu ie when he ipued pies o pil in pie i nd soil insiuion nd e espeiely egded s he ke pies o pil in pie i nd soil insiuion espeiely ll ies ssuing h he siony epeions hypohesis holds ue s egds he uue ginl eiieny o inesen o ll kind o pil nd he soil oon pil es e leied upon he use o seies o soil oon pil Indeed he opiu ondiions ogehe wih he esibiliy ondiions peisely oespond o he ondiions o he ke equilibiu in he odel o soil oon pil ie : i Eh indiidul hooses he obinion o onsupion nd he use o seies o soil oon pil u ϕ is iied subje o he budge onsin p θ y so h he indiidul s uiliy 9

22 whee y is he inoe o indiidul ii Eh pie i hooses he obinion o poduion inesen h ne pois e iied oe nd he use o seies o soil oon pil p T θ in suh nne iii Eh soil insiuion hooses he obinion o he poision o seies o soil oon pil podued goods e iied oe i in suh nne h ne pois π T p inesen nd he use o A he pies p ol dend o goods e equl o ol supply: A he pies o he poision nd he use o seies o soil oon pil π nd θ he ol ouns o he poision nd use o seies o soil oon pil e equl: i Soil oon pil es he e τ e leied upon he use o seies o soil oon pil; i e θ π τ π τ τ τ ii The epeions onening uue ginl poduiiy o pil o ll kinds e siony ie whee nd δ µ δ µ e espeiely he ipued pies nd he enl pies o 20

23 he pil goods uuled in pie i nd soil insiuion The disussion boe y be suied s Poposiion 2 In he pooype odel o soil oon pil he opiu ondiions o he susinble ie-ph o onsupion nd uulion o pie pil nd soil oon pil oinide peisely wih hose o ke equilibiu wih he ollowing ssupions: i The soil oon pil es he e τ e leied so h θ π τπ τ τ τ whee π θ e espeiely he pie pid o he poision o seies o soil oon pil nd he pie hged o seies o oon pil nd τ is he ip oeiien wih espe o he use o seies o soil oon pil ii The epeions onening uue ginl poduiiy o pil o ll kinds e siony Thus he susinble poesses o onsupion nd pil uulion inluding boh pie pil nd soil oon pil e obined solely in es o he se o he eonoy eh oen in ie independen o he hypoheses onening he uue shedules o ginl eiieny o inesen in pie pil nd soil oon pil On he ohe hnds he dynilly opiu poesses o onsupion nd pil uulion inluding boh pie pil nd soil oon pil e obined only he hypohesis o pee oesigh onening he uue shedules o ginl eiieny o inesen in ll kinds o pil s in deil disussed e g in Uw Rek: I y be noed h he nlysis o susinble poesses o pil 2

24 uulion o he pooype odel o soil oon pil deeloped in he pesen ppe holds ue o he genel iusnes in whih he elen unions suh s uiliy unions poduion unions nd Penose unions y hnge oe ie 22

25 Reeenes Mill J S 848 Piniples o Poliil Eonoy wih Soe o Thei Appliions o Soil Philosophy New Yok: D Appleon [5h ediion 899] Penose ET 959 The Theoy o he Gowh o he Fi Ood U:Blkwell Uw H 968 The Penose ee nd opiu gowh Eonoi Sudies Quely 9-4 Uw H 969 Tie peeene nd he Penose ee in wo-lss odel o eonoi gowh Jounl o Poliil Eonoy Uw H 2003 Eonoi Theoy nd Globl Wing New Yok: Cbidge Uniesiy Pess Uw H 2005 Eonoi Anlysis o Soil Coon Cpil New Yok: Cbidge Uniesiy Pess 23