Human Capital, Innovation, and Climate Policy: An Integrated Assessment

Size: px
Start display at page:

Download "Human Capital, Innovation, and Climate Policy: An Integrated Assessment"

Transcription

1 Fodazio Ei Erico Mai Workig Paprs Huma Capial Iovaio ad Clima Policy: A Igrad Assssm Carlo Carraro Uivrsiy of Vic Fodazio Erico Mai CEP CESifo ad CMCC carlo.carraro@fm.i Erica Cia Fodazio Erico Mai ad CMCC Massimo Tavoi Fodazio Erico Mai ad CMCC Follow his ad addiioal works a: hp://srvics.bprss.com/fm commdd Ciaio Carraro Carlo; Cia Erica; ad Tavoi Massimo "Huma Capial Iovaio ad Clima Policy: A Igrad Assssm" April Fodazio Ei Erico Mai Workig Paprs. Papr 669. This workig papr si is hosd by bprss. Copyrigh 2012 by h auhors.

2 Carraro al.: Huma Capial Iovaio ad Clima Policy: A Igrad Huma Capial Iovaio ad Clima Policy: A Igrad Assssm Carlo Carraro Uivrsiy of Vic Fodazio Erico Mai CEP CESifo ad CMCC Erica Cia Fodazio Erico Mai ad CMCC Massimo Tavoi Fodazio Erico Mai ad CMCC Absrac This papr looks a h irplay bw huma capial ad iovaio i h prsc of clima ad ducaioal policis. Usig rc mpirical simas huma capial ad gral purpos ar iroducd i a igrad assssm modl ha has b xsivly applid o sudy clima chag miigaio. Our rsuls suggs ha clima policy simulas gral purpos as wll as cla rgy bu rducs h iciv o ivs i huma capial formaio. Huma capial icrass h produciviy of labour ad h complmariy bw labour ad rgy drivs is polluio-usig ffc dirc ffc. Wh huma capial is a ssial ipu i h producio of gric ad rgy ddicad kowldg h crowdig ou iducd by clima policy is miigad hough o complly offs idirc ffc. Th polluio-usig implicaios of h dirc ffc prvail ovr h idirc coribuio of huma capial o h craio of w ad clar kowldg. A policy mix ha combis ducaioal as wll as clima obcivs offss h huma capial crowdig-ou wih a modra shor-rm cosumpio loss. Huma capial is complm o all forms of iovaio ad a ducaioal policy simulas boh rgy ad gral purpos iovaio. This rsul has impora policy implicaios cosidrig h growig cocr ha ffciv clima policy is codiioal o solid coomic dvlopm ad hrfor i ds o b supplmd by ohr policy args. Kywords Clima Policy Iovaio Huma capial JEL Cods O33 O41 Q43 Publishd by Brkly Elcroic Prss Srvics

3 Fodazio Ei Erico Mai Workig Paprs Ar. 669 [2012] 1. Iroducio A icrasig umbr of igrad assssm modls usd i clima chag policy aalysis hav lookd a h dyamics of chical chag. Modls dscribig chical chag as a dogous procss mak i possibl o sudy h rlaioship bw clima policy ad chical chag ad o valua h implicaios of policy-iducd chical chag ITC o h macrocoomic coss of clima policy. A firs wav of sudis focusd o iovaio i h rgy scor h raso big h rlvac of rgy fficicy masurs ad dcarboisaio of rgy as miigaio sragis Nordhaus 2002 Popp 2004 Bosi al Ths modls assum ha chical chag is cssarily rgy-savig glcig ohr forms of iovaio or chical chag ha could acually hav a rgy-usig ffc s for xampl Maagi ad Kumar 2009 Carraro ad Cia This approach cours h risk of udrsimaig h coss of clima policy bcaus i ovrlooks h macrocoomic dyamics of chical chag ad cao rack how clima policy rdisribus rsourcs across diffr scors. A icrasig umbr of clima-coomy modls ow faurs boh rgy savig ad rgy-usig dogous chical chag Gouldr ad Schidr 1999 Su Wig 2008 Oo al Grlagh 2008 Carraro al Massi ad Nicia Ths modls shar h ida ha chology advacms i boh rgy- ad o-rgy scors ar driv by a spcific sock of kowldg. Thy all agr ha clima policy modifis o oly h dircio of chical chag bu also h oal lvl of iovaiv aciviy. Gouldr ad Schidr 1999 Su Wig 2008 ad Oo al mphasis how h gral quilibrium ffc du o h policyiducd icom rducio ca lowr h ovrall amou of rsourcs availabl for kowldg craio. Grlagh 2008 shows ha if a suffici amou of ivsms go o rgy-savig chical chag h hr migh b a rsarch dividd ad ovrall rsarch aciviy may icras. Carraro Massi ad Nicia 2009 Massi ad Nicia 2010 highligh ha h complmariy bw rgy ad o-rgy ipus drivs h dircio of iducd chical chag i li wih hory of dircd chical chag Acmoglu Guidd by h mpirical vidc o iducd iovaio Laouw ad Mody 1996 Jaff ad Palmr 1997 Nwll Jaff ad Savis 1999 ad Popp 2002 ad followig maisram growh hory.g. Arrow 1962 omr 1986 ad 1990 Grossma ad Hlpma 1991 Aghio ad Howi 1992 Acmoglu 2002 Acmoglu al mos clima-coomy modls assum ha h gi of chical chag is h accumulaio of kowldg or xpric. Ohr drivrs such as huma capial Lucas 1998 Blakau ad Simpso 2004 or rad Camro 2005 Maagi ad Kumar 2009 Carrao ad Cia 2009 hav b glcd. Th arrow focus o rgy 2 2

4 Carraro al.: Huma Capial Iovaio ad Clima Policy: A Igrad has boudd h applicabiliy of IAM o h sudy of cla iovaio i rlaio o clima chag. By omiig ohr gis of macrocoomic growh h cocios wih coomic dvlopm hav o b fully aalysd by h modllig liraur. Th aim of his papr is o xplor his likag ad provid som ovl isighs o h cocios bw clima chag ad coomic dvlopm wih a paricular focus o ducaio. Clima chag policy ad ducaio ca irac hrough svral chals. Firs of all a highr lvl of huma capial ca mak miigaio policis mor ffciv. Huma capial is a ssial ipu i h craio of w kowldg ad w producs ad hrfor i is bhid rgy-savig iovaio as wll. Br skills ca b xpcd o lad o a fasr dvlopm of chologis ha ca rplac or rduc h us of fossil fuls. Som sudis do suppor h xisc of a posiiv rlaioship bw iovaio ad huma capial bu a h aggrga lvl Griffih ddig ad Va 2000 Tixira ad Forua To our kowldg hr ar o mpirical works ha hav lookd a h rlaioship bw kowldg ad huma capial i h cox of clima-rlad iovaio. By simulaig labour produciviy ad coomic growh xpdiur i ducaio ca icras h amou of rsourcs availabl for produciv usags icludig iovaio. Huma capial is posiivly rlad o h capabiliy of adopig clar chologis Nlso ad Phlps 1966 dvlopd udr h simulus of viromal policy. Educaio ca also b xpcd o improv h ffcivss of adapaio masurs. Th Third Assssm por of h IPCC idifid huma capial amog h drmias of adapiv capaciy. Accordig o Yoh 2001 huma capial o oly affcs h abiliy o rspod o clima variabiliy ad chag bu i is also a drmia of miigaiv capaciy. Fially ducaio is fudamal o icras h awarss of clima chag which i ur should icras h willigss of vors o suppor clima policy. Th achivm of uivrsal primary ducaio is o of h igh Millium vlopm Goals o b achivd by 2015 oghr wih susaiabl dvlopm. Th qusio w ask i his papr is whhr hr ar syrgis bw ducaioal ad clima chag policis ha go hrough h iovaio ad growh chals. Our sarig framwork is a igrad assssm modl wih a good characrisaio of dogous chical chag bu cofid o h rgy scor Bosi al W amd h macrocoomic producio srucur o accou for facor-augmig ffc of gral purpos ad huma capial. This iroducs a dirc lik bw huma capial ad coomic growh. I his sig h disribuiv ffcs of policy i diffr forms of xpdiur ad iovaio ca b fully characrisd. W also look a h idirc ffc ha huma capial could hav o chology absorpio ad iovaio hough as a xploraiv aalysis aimd a idifyig aras for fuur rsarch. Th papr proposs a comparaiv aalysis of clima policy Publishd by Brkly Elcroic Prss Srvics

5 Fodazio Ei Erico Mai Workig Paprs Ar. 669 [2012] udr hr modl varias ha abl us o valua how h iducd-chical chag hypohsis rspods o diffr rprsaios of chical chag. Th mor gral ram of dogous chical chag allow us broad h focus of h aalysis from h arrow clima policy-rgy-iovaio lik o h clima chag ad coomic dvlopm xus. Our rsuls idica ha clima policy simulas ddicad ivsms i rgy wihou rducig gral purpos iovaio. O h ohr had ducaio xpdiurs ar rducd palisig h formaio of huma capial. Wha drivs his rsul is h assumpio ha huma capial is polluio-usig bcaus i augms h produciviy of labour which is gross complm o rgy. Th crowdig-ou of clima policy o ducaio xpdiur is lssd if rsourcs allocad o ducaio ca fosr chology absorpio ad iovaio. W also fid ha huma capial is complm o all forms of iovaio. A policy ha susais ducaio xpdiur simulas boh rgy ad gric iovaio. This implis ha a policy mix ha combis a clima sabilisaio arg wih a ducaioal policy susaiig ducaio xpdiur could rduc h log-ru macrocoomic coss of h clima policy. Th addiioal coss of implmig h wo policis ar rasiory ad i h log-ru a scal ffc parly miigas clima chag policy coss. Th rs of h papr is orgaisd as follows. Scio 2 dscribs h rlaioship bw chical chag ad ipu subsiuio wh chical chag is facor-spcific. Facor-augmig chical chag driv by iovaio ad huma capial is h icorporad io a Igrad Assssm Modl. Policy scarios ar aalysd i Scio 3 ad 4. Scio 5 cocluds. 2. Facor-augmig chical chag ad IAMs 2.1 Facor-augmig chical chag ad ipu subsiuio Narly all IAMs dscrib producio usig Cosa Elasiciy of Subsiuio CES producio fucios. Cosidr h simpls xampl of CES producio fucio bw labour L capial K ad rgy EN 1 : Y σ 1 σ 1 σ 1 σ σ σ σ σ 1 = H A K + AL L + AEN EN K 1 whr σ is h lasiciy of subsiuio bw h hr ipus ad Y is h fial good producd i h coomy which ca b usd for cosumpio or ivsm. Facors of producio ar xprssd i fficicy uis. Th muliplicaiv cofficis A i rprs h produciviy of ipus. Nural chical chag is dscribd by h paramr H. 1 Th choic of a o-sd CES as opposd o a s CES bw a capial labour budl ad rgy is o rlva for h rsuls discussd i h papr. Wha ulimaly drivs h rsuls is ha o-rgy ipus capial ad labour ar gross complms o rgy. 4 4

6 Carraro al.: Huma Capial Iovaio ad Clima Policy: A Igrad Allowig for dogous diffrcs i h dvlopm of chology paramrs has a horical foudaio i h work o dircd chical chag Acmoglu Wh facoraugmig chical chag is dogous h ffc of chology drivrs ca b boh rgyusig or rgy-savig. Cosidr a dogous formulaio as simad i Carraro ad Cia 2009 whr capial ad rgy produciviy dpd o h sock of gric kowldg whil labour produciviy dpds o huma capial HK: A A A K EN L = A = A = A K 0 L 0 EN 0 HK L K χ χ χ EN 5 Wih gross complmariy bw facors of producio σ < 1 ad posiiv lasiciy of huma capial o labour produciviy χ L huma capial has a rgy-usig ffc: EN L HK σ σ χ L χ L 1 P L ALo HK ALo HK = 1- σ χ L > 0 if σ < 1ad χ L PEN AEN AEN > 0 6 As for h dirc impac o rgy dmad is gaiv.g. rgy-savig if h lasiciy of subsiuio is lss ha o. Howvr h idirc impac via capial produciviy is rgy-usig as i h cas of huma capial. Th ffc ulimaly dpds o h rlaiv siz of h lasiciy of capial ad rgy produciviy wih rspc o kowldg χ K ad χ EN. Carraro ad Cia 2009 fid ha ha χ K < χ EN suggsig ha ovrall gral purpos has a rgy-savig ffc. Th x scio dscribs how his formulaio of chical chag has b igrad i h igrad assssm modl WITCH. 2.2 Facor-augmig chical chag ad h WITCH modl Modl hacm Th WITCH modl Bosi al alrady provids a horough characrisaio of iovaio bu oly i h rgy scor. WITCH is a rgioal igrad assssm hard-lik hybrid modl. Is op-dow compo cosiss of a irmporal opimal 2 A horough dscripio ad a lis of rlad paprs ad applicaios ar availabl a hp:// Publishd by Brkly Elcroic Prss Srvics

7 Fodazio Ei Erico Mai Workig Paprs Ar. 669 [2012] growh modl i which h rgy ipu of h aggrga producio fucio has b xpadd o giv a boom-up lik dscripio of h rgy scor. Th modl accous for chological advacs ha ca occur i h rgy scor disiguishig bw h ivio/iovaio phas ad h procss of diffusio ad dploym. Th modl disiguishs ddicad ivsms for hacig rgy fficicy from ivsms aimd a faciliaig h compiivss of iovaiv low carbo chologis brakhrough chologis. Sarig from his s-up w iroduc dogous chical chag wih ipu-spcific chology drivrs. W compar hr modl varias ha diffr i h way of accouig h rol of huma capial. Th sarig s-up modl 1 oly cosidrs h dirc ffc of huma capial o labour produciviy followig h spcificaio simad i Carraro ad Cia Th firs varia modl 2 adds o h dirc ffc a idirc coribuio via chology diffusio. I his cas huma capial icrass h absorpiv capaciy. Th scod varia modl 3 xplors h rlaioship bw huma capial ad iovaio addig h coribuio of h idirc ffc of huma capial o kowldg formaio. All modl quaios ca b foud i h Appdix. I h rmaiig of his scio w dscrib modl hacm calibraio ad sig. Th macrocoomic producio srucur is modifid o accommoda for facor-augmig chical chag wih ddicad chology drivrs q. A4. I h modifid modl capial ad rgy produciviis dpd o a gric kowldg sock h sock of gral purpos xpdiur whras labour produciviy o huma capial h sock of ducaio xpdiur s q. A5. I addiio o h ffc of gral purpos ddicad rgy fficicy ca spcifically addrss improvms i rgy fficicy q. A5 or dvlop brakhrough chologis q. A11. Sic h dyamics of chical chag i all scors ar ow dogous rgy ivsms comp wih h rsourcs ha ar allocad o huma capial dvlopm ad gric. Th producio of boh huma capial ad kowldg is characrisd by irmporal spillovrs. Th sock availabl i ach rgio a a giv poi i im coribus o h craio of h fuur sock. Followig sa-of-h-ar liraur omr 1990 Jos 1995 Popp 2002 Glomm ad avikumar 1997 Blakau ad Simpso 2004 w assum ha huma capial is producd usig a Cobb-ouglas combiaio of h xisig sock of huma capial ad curr xpdiur i ducaio. q. A6 ad A7. I a similar way h availabl kowldg sock ad curr ivsms ar combid o produc w kowldg qs. A8 ad A9. Th craio of rgy kowldg is also iflucd by iraioal spillovrs s q. A10. Forig kowldg ca 6 6

8 Carraro al.: Huma Capial Iovaio ad Clima Policy: A Igrad impac domsic procss of kowldg craio dpdig o coury s absorpiv capaciy ad disac from h froir Bosi. al I h wo xdd vrsios of h modl hs quaios ar modifid o accou for h idirc coribuio of huma capial. Firs of all modl 2 huma capial icrass h abiliy o adop w chologis. This idas gos back o h modl of chology diffusio iroducd by Nlso ad Phlps Couris ca bfi from h world chology froir by icorporaig mor advacd chologis io hir coomy. Tchology adopio is a huma capial-isiv aciviy ha rquirs skill labour. Thrfor a largr sock of huma capial facilias h absorpio of w producs ad w discovris. Th ida ha succssful chology diffusio rquirs suffici absorpiv capaciy Coh ad Lvihal 1990 has b mpirically suppord by a umbr of sudis Bhabib ad Spigl 1994 Griffih ddig ad Va Mor rcly Luz al cofirmd ha huma capial acclras h covrgc owards h chological froir rprsd by h richs coury. W igra his ida io our modl modl vrsio 2 s abl 4 by assumig ha h absorpiv capaciy improvs o oly by h rgy kowldg sock bu also by buildig up huma capial s quaio A13 i h Appdix. I h scod modl varia modl vrsio 3 s abl 4 huma capial is a ssial ipu i h craio of boh socks of gric ad rgy kowldg s q. A14. Modl calibraio Educaio ad ivsms hav b calibrad usig h hisorical rgioal shars of xpdiur ovr Gross omsic Produc for ach rgio of h modl. World xpdiur o gric i 2005 is 2.17% of GWP global ducaio xpdiur 4.34%. As show i Tabl 1 OEC couris hav h largs shar i boh ducaio ad xpdiur. Tabl 1. ivsms ad ducaio xpdiur. Hisorical daa a h calibraio poi of 2005 % GP Hisorical daa Ergy IEA Gric WI Educaio WI WOL 0.03% 2.17% 4.34% OEC 0.03% 2.49% 4.55% NON-OEC.a. 0.93% 3.62% IEA: Iraioal Ergy Agcy WI: World vlopm Idicaors 3 Alhough i would b aural o characris spillovrs i h gral purpos scor w rfrai from doig so mosly bcaus of cosiscy wih h mpirical sudy ha is usd o calibra our modl which did o accou for spillovrs. I addiio prvious sudis s Bosi al 2008 show ha h coribuio of kowldg spillovrs is limid. Publishd by Brkly Elcroic Prss Srvics

9 Fodazio Ei Erico Mai Workig Paprs Ar. 669 [2012] Th hr facors of producio labour rgy ad capial ar modlld as gross complms bcaus mos coomric sudis suggs ha his i fac rflc h hisorical pars obsrvd i h daa. Carraro ad Cia 2009 usig yarly daa simad h lasiciy of subsiuio bw capial labour ad rgy qual o 0.3. Howvr i h modl a highr valu qual of 0.7 is chos for wo rasos. Firs h modl im sp is of fiv yars whras h simad valu is basd o yarly pal. Th lasiciy of subsiuio ovr fiv yars is highr ha h lasiciy ovr o yar as discussd i Pssoa al Scod h valu 0.3 is basd o h vidc from dvlopd coomis. I coras dvlopig couris ar characrisd by highr coomic growh ad largr subsiuio possibiliis. Bcaus w do o hav h daa o diffria dvlopd ad dvlopig couris w hav chos a commo valu ha mad i possibl o rplica rgioal coomic growh pars as i Bosi al I is impora o mio ha h simad lasiciis vary qui sigificaly from vry low o high valus v grar ha o s for xampl va dr Wrf Th ky drivr for h dircio of chical chag is whhr h lasiciy is grar or smallr ha o bu h acual valu dos o affc h dircio of h rsuls. Tabl 2 summariss h valus of ky paramrs. Tabl 2. Subsiuio lasiciy bw labour capial ad rgy σ ad facor lasiciy wih rspc o dogous chology drivrs σ 0.7 χ L HK 0.17 χ E 0.60 N χ K 0.26 A subsiuio lasiciy lss ha o implis ha ipus ca b subsiud wih ach ohr bu wih som rigidiy. Wh a ipu bcoms mor produciv ad hr is full mploym of rsourcs addiioal produciviy lads o addiioal oupu. This scal ffc pus a upward prssur o h dmad for ohr ipus as wll ad hus o rgy. As a cosquc assumig hr ar o chags i h rgy mix rgy-rlad missios would icras. This argum glcs h disicio bw skilld ad uskilld labour which would mak h discussio mor complicad. A rlaioship of complmariy bw labour ad ohr ipus capial is ypically foud wh skilld labour is cosidrd. Isad mpirical sudis foud ha capial d o b a subsiu for uskilld labour. As a cosquc h sock of huma capial drivs a form of chical progrss ha is rgy-usig. I coras h ffc of gric iovaio is rgysavig if i improvs rgy produciviy mor ha capial. 8 8

10 Carraro al.: Huma Capial Iovaio ad Clima Policy: A Igrad gardig h calibraio of idirc ffcs w mad h followig assumpios. I h firs varia modl 2 huma capial is simply addd o h rgy kowldg sock i h absorpiv capaciy compo of quaio A13. Th calibraio of h idirc coribuio of huma capial o kowldg formaio modl 3 is lss sraighforward du o h lack of clar mpirical guidac. A fw sudis sd h hypohsis ha iovaio is iflucd by h dowm of huma capial by simaig a Cobb-ouglas producio fucio i which oal facor produciviy is drmid by huma capial ad hir iracio. Boh Griffih ddig ad Va 2000 usig a pal of OEC couris ad Tixira ad Forua 2004 usig ims sris for Porugal foud a posiiv ad sigifica coffici associad wih h iracig rm idicaig a posiiv rlaioship bw iovaio ad huma capial. For h coribuio of huma capial o kowldg craio γ EU w choos a rag of valus bw 0.1 ad Th maximum valu xprimd corrspods o h cofficis simad by Griffih ddig ad Va 2000 ad Tixira ad Forua 2004 which ar clos o 0.4. I should b poid ou ha hs mpirical sudis cosidr h oi ffc of huma capial ad iovaio o oal facor produciviy growh. This approach is diffr from simaig a dirc rlaioship bw huma capial ad iovaio usig a iovaio producio froir which isad is h modllig approach adopd i his papr. Modl sig Bfor cosidrig h implicaios of clima policy w prform a ad-hoc xprim o s h macrocoomic ffcs of icrasig ducaio xpdiur. W impos a 10% xogous icras i ducaio xpdiur ad w compu h lasiciy of slcd variabls. For his sig xrcis w us h firs modl vrsio wih o idirc ffcs. As rpord i Tabl 3 h ΔY lasiciy of fial oupu o ducaio Δ I EU is largr ha zro idicaig a posiiv rlaioship bw ducaio xpdiur ad oupu growh. This rsul occurs wh ducaio is fiacd wih cosumpio axs Blakau ad Simpso I h WITCH modl ducaio xpdiur is fiacd ou of h budg cosrai ad hr ar o disorig axs o labour or capial. Addiioal ducaio xpdiur coms a h coss of lowr cosumpio bu oly i h shor-rm. Afr 2035 h growh ffc icrass cosumpio possibiliis as wll as idicad by h posiiv valu of h lasiciy. 4 I is rasoabl o xpc h ducaio ffc o kowldg o b lowr ha h ffc of boh ivsms ad capial sock. Th siz of his paramr is also cosraid by h valu of h ohr paramrs ad h rsricio ha h sum cao xcd 1. Paramrs i h iovaio producio froir hav b rcalibrad so as o yild h sam basli as i h basic modl. 9 Publishd by Brkly Elcroic Prss Srvics

11 Fodazio Ei Erico Mai Workig Paprs Ar. 669 [2012] Th xpasio of coomic aciviy has wo addiioal ffcs. Emissios icras bcaus coomic growh pus a upward prssur o rgy dmad. A h sam im coomic growh icrass h amou of rsourcs availabl for all forms of iovaio poiig a h complmariy bw kowldg ad huma capial. Boh gric ad ddicad rgy icras alhough h ffc o gric iovaio is slighly largr. Bcaus par of iovaio is rgy-savig i h mdium/log-rm his lads o a pak ad dcli afr 2050 of h lasiciy of missio o ducaio whras h lasiciis of oupu ad cosumpio coiu o icras ovr im. Tabl 3. Elasiciis o ducaio xpdiur wh his is icrasd by 10% ΔY Δ I EU ΔC Δ I EU ΔEMI Δ I EU Δ I ΔI EU Δ I ΔI EU Δ I EU % % % % This simpl xrcis illusras how ivsig i huma capial formaio affcs o oly coomic growh ad cosumpio bu also iovaio ad missios. I ligh of hs rsuls wha is h xpcd oucom of clima policy? O h o had huma capial is polluio-usig ad hrfor i may mak h achivm of a sabilisaio arg mor difficul. O h ohr had h posiiv ffc ducaio has coomic growh ad iovaio may parially compsa h coomic loss du o clima policy. Ths issus ar xplord i h x Scio. 3. Implicaio of sad-alo clima policis W ow ur o h implicaios of a clima policy o h accumulaio of kowldg huma capial ad ulimaly h dircio of chical chag. Tabl 4 summariss h diffrcs across h hr spcificaios of dogous chical chag cosidrd

12 Carraro al.: Huma Capial Iovaio ad Clima Policy: A Igrad Tabl 4. Th rol of huma capial i h hr modl vrsios cosidrd Huma capial hacs labour produciviy Huma capial hacs absorpiv capaciy Huma capial rs as ipu i h iovaio producio fucio dirc ffc Modl 1 Ys No No Modl 2 Ys Ys No Modl 3 Ys No Ys 3.1 Clima policy wh huma capial has a dirc ffc o labour produciviy modl 1 W cosidr a clima policy i which all rgios coopra o h sabilisaio of GHG cocraios a 550 CO2-q by which dfis h global cap o missios. A iraioal cap-ad-rad sysm allows rgios o buy ad sll prmis o h world mark so as o achiv h arg i h mos cos-ffciv way qualisig margial coss of abam across rgios 6. Th sig is ha of cos-ffcivss ad hrfor h macrocoomic coss of h policy do o cosidr h bfis du o rducd clima chag damags. Wh facig a clima policy cosrai ach rgio rshaps h opimal mix of ivsms o m h cosrai a h miimum cos. Th carbo pric sigal rallocas rsourcs owards low carbo chologis rwabl rgy coal quippd wih carbo capur ad sorag ad uclar rgy fficicy cla rgy ad subsquly o h dploym of h chologis brakhrough ar cla chologis ha rplac fossil fuls. I h modl h cos of brakhroughs is dogously driv by i h firs plac ad oc h chology is dployd by isalld capaciy followig a wo-facor larig curv s q. A11. Figur 1 shows ha clima policy simulas ddicad ivsms i rgy as wll as gral purpos iovaio. This is du o h fac ha gral purpos by raisig h produciviy of 5 I should b srssd ha h chos clima policy scario is oly illusraiv. Th goal of his papr is o udrsad h basic mchaisms bhid iducd iovaio wh hr is also huma capial. W hrfor absrac from scodbs cosidraios ad from h aalysis of mor ralisic policy scarios. 6 Prmis ar allocad o a qual pr capia basis. This allocaio schms d o favour dvlopig couris. Howvr h goal is o o provid a comprhsiv valuaio of diffr policy archicurs bu rahr o mphasis h rad-off ad/or h syrgis bw diffr policy goals a h global lvl. Publishd by Brkly Elcroic Prss Srvics

13 Fodazio Ei Erico Mai Workig Paprs Ar. 669 [2012] rgy mor ha ha of capial improvs rgy fficicy ad his is a cos-ffciv abam opio. Figur 1 also shows h allocaio of rgy bw rgy fficicy masurs ad brakhrough. Ergy iovaio is mosly dircd a rducig h coss of brakhrough chologis bcaus his will rduc h log-ru coss of dcarboisig h rgy sysm. I absolu lvls ad ovr h whol cury clima policy allocas a comparabl amou of rsourcs o rgy ad gral purpos. Thr is hough a diffrc i h im profil. Ergy icrass mosly i h shor-ru as a rspos o h aicipaio of a risig carbo pric. Gral purpos isad ovraks rgy afr Boh forms of iovaio rduc h rgy pr ui of oupu ad hrfor ar complms rahr ha subsius. This rsul diffrs from prvious fidigs ha cosidrd diffr programs bu glcd h rol of huma capial Gouldr ad Schidr 1999 Su Wig 2008 Carraro Massi ad Nicia 2009 Massi ad Nicia For xampl Carraro Massi ad Nicia 2009 ad Massi ad Nicia 2010 assum ha o-rgy is rgy-usig. Thrfor clima policy icras rgy bu rducs o-rgy. Our rsul is i li wih rc mpirical vidc which cofirmd ha crowdig-ou bw cla ad diry rgy migh xis bu o bw iovaio i h rgy ad o-rgy scor Popp ad Nwll Figur 1. Addiioal ivsms i various yps of kowldg i h clima policy wih rspc o h Busiss as Usual BaU gardig h rsuls o huma capial Figur 1 shows ha clima policy iducs a crowdig-ou o ducaio xpdiur. I absolu umbrs h rsourcs ha ar divrd away from h ducaio scor ar sigifica rachig abou 1 rillio US afr As alrady aicipad his is du o h fac ha huma capial is labour-augmig ad o h complmariy bw rgy ad labour. This is a rsul ha has b alrady foud i h 12 12

14 Carraro al.: Huma Capial Iovaio ad Clima Policy: A Igrad liraur o viromal policy ad huma capial. Wh polluio is likd o fial oupu viromal policy ca rduc ducaio xpdiur ad slow dow huma capial accumulaio Gradus ad Smuldrs 1993 Hich 1998 Paurl Clima policy wh huma capial has a idirc ffc o absorpiv capaciy modl 2 W ow ur o h ffc of clima policy wh huma capial has a idirc ffc o h capaciy o absorb forig kowldg. Our modl faurs iraioal spillovrs of rgy kowldg. Forig rgy kowldg ca coribu o h craio of a domsic sock of rgy kowldg providd h absorpiv capaciy is sufficily larg ad dpdig o h disac from h chology froir dfid as h sock of rgy kowldg i high-icom couris 7 Bosi. al Ivsig i rgy is a impora miigaio bcaus i icrass rgy fficicy masurs ad favours h larg scal dploym of zro-carbo chologis. Th kowldg sock ca b hacd by ihr ivsig domsically i rgy or by usig h idas ad oios alrady dvlopd i ohr couris. Howvr his lar opio is ffciv oly if couris hav h miimum capaciy rquird o xploi ohr rgios idas. W upgrad his faur by assumig ha huma capial ca coribu o improv o coury absorpiv capaciy which i h origial modl dpds oly o h rgy kowldg sock s quaio A13 i h Appdix. Huma capial big a ipu i h craio of w rgy kowldg has a idirc rgy-savig ffc hough of a small magiud compard o h mor dirc ffc o labour produciviy. Our rsuls idica ha addig huma capial as a drmia of absorpiv capaciy dos o sigificaly affc h dyamics of iovaio ad ducaio xpdiur s Tabl 5. Udr his modl spcificaio clima policy iducs a slighly rducd crowdig-ou a mos 12% smallr ha i h basic modl 1. Ergy ivsms ar lowr spcially durig h firs dcads bcaus huma capial icrass h capaciy o bfi from h pool of iraioal rgy kowldg hus rducig h rquirm i rms of domsic ivsms. Mdium- ad log-rm ivsms i gric slighly icras driv by h posiiv scal ffc o coomic growh. Th macrocoomic coss of h clima policy ar rducd from 1.37% o 1.32% of prs valu cosumpio. 7 High icom couris i h WITCH modl ar Uid Sas Wsr Europ Easr Europ Souh Kora Ausralia Caada Japa Nw Zalad. Publishd by Brkly Elcroic Prss Srvics

15 Fodazio Ei Erico Mai Workig Paprs Ar. 669 [2012] Tabl 5: Huma capial ad kowldg ivsms i h clima policy. Chag bw modl 2 ad modl 1 i rlaiv ad absolu rms 2005US Billio i parhsis Ergy Gral purpos Educaio xpdiur % % % % % % % % This xrcis idicas ha accordig o our modl spcificaio- h idirc ffc of huma capial o h capaciy o absorb forig kowldg i h cla rgy scor ca oly parly rduc h coracio of ducaio xpdiurs. Th limid rol of rgy spillovrs is i li wih wha origially foud by Bosi. al cofirmd a robusss aalysis of h paramr spac by mas of ssiiviy aalysis. 3.3 Clima policy wh huma capial has a idirc ffc o kowldg craio modl 3 Th rsuls rgardig h crowdig ou of clima policy o huma capial also follow from h assumpio ha huma capial dos o affc h procss of craio of w idas ad chological iovaios. To icorpora his mchaism io our framwork w iroduc modl 3 whr h iovaio froir of boh rgy ad gric is likd o h sock of huma capial s quaio A14 i h Appdix. Through his addiioal chal huma capial has a idirc impac o rgy ad capial produciviy. u o h lack of clar mpirical guidac w prform ssiiviy aalyss ovr a wid rag of lasiciis bw huma capial ad kowldg bw 0.1 ad Figur 2 shows h rsuls from his formulaio. Bcaus of h addiioal lik bw huma capial ad kowldg ducaio bcoms a ssial ipu i h producio of kowldg which has a rgy-savig ffc as discussd i Scio 2.1. For his spcificaio v wih a small lasiciy h crowdig-ou of ducaio xpdiurs is sigificaly miigad. This ffc is mor prooucd ha h absorpiv capaciy o dscribd 8 I is rasoabl o xpc h ducaio ffc o kowldg o b lowr ha h ffc of boh ivsms ad capial sock. Th siz of his paramr is also cosraid by h valu of h ohr paramrs ad h rsricio ha h sum cao xcd 1. Paramrs i h iovaio producio froir hav b rcalibrad so as o yild h sam basli as i h basic modl

16 Carraro al.: Huma Capial Iovaio ad Clima Policy: A Igrad i h prvious paragraph ssially bcaus of h modl formulaio. Huma capial rcivs a shar of 0.1 i h kowldg craio procss. Alhough iraioal kowldg gs a slighly largr shar qual o 0.15 h sock of forig rgy kowldg is much smallr ad i addiio oly par of ha is usd by h rcipi coury. Furhr icrasig h coribuio of huma capial.g. icrasig h lasiciy coius o rduc h crowdig-ou alhough by a smallr margi. Howvr h sig of h rlaio bw clima policy ad ducaio is vr rvrd for h various paramrisaio cosidrd ad ducaio is always crowdd ou. gardig iovaio ivsms i gric ar iiially rducd compard o h basic modl i which kowldg grows oly wih xisig kowldg sock bu afr hy bcom largr. Howvr h magiud of variaio is small a mos 1.16% i I coras rgy ivsms ar rducd mor sigificaly spcially durig h firs dcads. Lss ddicad iovaio is dd o m h sabilisaio arg bcaus h sock of huma capial adds a oabl coribuio o dvlop h rgy kowldg sock ha drivs rgy fficicy improvms ad rducs h cos of advacd carbo-fr chologis. Th macrocoomic coss of h clima policy ar rducd from 1.37% o 0.92% of prs valu cosumpio wh h shar o huma capial i kowldg producio is 0.1. Cosumpio losss fall furhr o 0.66% wh his shar is icrasd o 0.4. Figur 2. Educaio xpdiur i h clima policy chags wih rspc o BAU udr modl 1 ad hr paramrisaio of modl 3 γ EU = Publishd by Brkly Elcroic Prss Srvics

17 Fodazio Ei Erico Mai Workig Paprs Ar. 669 [2012] 3.4 Sum up of h implicaios of clima policy udr diffr modl spcificaios Th aalysis carrid ou wih h hr modl varias dscribd i h prvious Scios pois o similar coclusios. Clima policy icrass iovaio boh i rms of gric ad rgy bu crowds ou par of h ivsms i ducaio. Alhough modllig h idirc ffcs of huma capial o absorpio capaciy ad kowldg formaio is abl o lss h crowdig-ou iducd by clima policy h dirc rgy-usig ffc is show o prvail. A summary of hs rsuls is providd i Tabl 6. I should b srssd ha modllig rsuls ulimaly dpd o h simad lasiciis rpord i Tabl 2 which ar h cral valu simas. Th cofidc irvals of hos simas ar vry broad. This implis ha hr ar combiaios of h hr lasiciis for which h idirc ffcs of huma capial ca offs h crowdig-ou iducd by clima policy. This ca occur for xampl wh h lasiciy of labour produciviy o huma capial is s qual o h lowr boud of h cofidc irval 0.02 whil h ohr wo paramrs ar lf qual o h cral valu simas. I his cas h idirc ffc o absorpiv capaciy ad kowldg formaio assumig a coribuio qual o 0.1 prvails. Tabl 6: Impac of clima policy o iovaio ad huma capial dyamics: summary across modl spcificaios. Prcag chag of cumulaiv ivsms compard o BaU 2005US Trillio i parhsis Basic modl modl 1 Basic modl+ idirc ffc o absorpiv capaciy modl 2 Basic modl+ idirc ffc o kowldg craio modl 3 268% % % 9.2 Ergy 4.9% % % 12.8 Gral purpos -8.4% % % Educaio xpdiur Policy Coss iscoud Cosumpio loss -1.37% -1.32% -0.92% Th gral rsuls poi o a poial coflic bw policis o aai clima sabilisaio ad huma capial improvms. This implis ha h huma capial crowdig-ou ds o b addrssd by spcific policis. I h x Scio w valua a combiaio of clima ad ducaio policy

18 Carraro al.: Huma Capial Iovaio ad Clima Policy: A Igrad 4. Couplig clima ad ducaio policis Clima policy args ar likly o b addiioal o ohr policy commims. A xampl is giv by h EU aciv rol i clima policy as wll as is commim o susaiig ducaio ad iovaio. Aohr xampl is providd by h Millium vlopm Goals MGs which ar igh diffr obcivs ha hav b accpd by 189 couris ad ha should b achivd by Uivrsal primary ducaio ad susaiabl dvlopm which icluds clima chag miigaio ar wo of h igh Goals. Th Fourh Assssm por IPCC 2007 also mphasisd ha o b ffciv clima policy should b supplmd by gric socio-coomic dvlopm ad icrasd miigaiv capaciy. This suggss ha hacig ducaio a drmia of miigaiv capaciy Yoh 2001 is a policy obciv islf. Primary ducaio is almos uivrsal i all dvlopd couris ad may dvlopig couris ar o h righ rack o achiv h Millium vlopm Goals o-rack couris. Achivig uivrsal primary ducaio is paricularly challgig i poor couris such as Souh Asia SASIA ad Sub-Sahara Africa SSA. Agais his backgroud w aalys a combiaio of clima ad ducaio policy. W dsig h followig ducaio policy. Th Sub-Sahara Africa ad Souh Asia SSA ad SASIA rgios will icras ducaio ivsms so ha h fracio of populaio currly off-rack will b o-rack from 2015 owards 9. Th rmaiig rgios will maiai h pah of ducaio xpdiur fors i h o-clima policy cas as curr spdig is alrady cosis wih h achivm of h MG. I ordr o compu h addiioal spdig o ducaio i SSA ad SASIA w combid h prcag of populaio off-rack 10 from Glww al wih populaio procios form h WITCH modl. W also usd h simas of avrag spdig pr sud providd by Glww al which amous o US$ 46 Billio i SASIA ad US$ 68 Billio i SSA. Bw 2010 ad 2015 Sub-Sahara Africa ad Souh Asia icras ducaio xpdiur by US$ 100 Billio a yar which is comparabl o curr spdig o Official vlopm Assisac 11. Th macrocoomic ffcs of combiig ducaio ad clima policy ar show i Tabl 7. 9 Couris or populaio ar classifid o-rack i achivig uivrsal primary ducaio if coiuig o liar rds bw 1990 ad 2002 will rsul i a complio ra abov 95% by Off- rack mas ha h complio ra is procd o b blow 50% i 2015 sriously off rack or blow 95% modraly off rack. 10 Th implici assumpio is ha avrag spdig ad h prcag of populaio off-rack rmais cosa bw 2000 ad Afr 2015 SSA ad SASIA coiu o spd a las h avrag amou rquird o hav all populaio o-rack. Publishd by Brkly Elcroic Prss Srvics

19 Fodazio Ei Erico Mai Workig Paprs Ar. 669 [2012] Tabl 7 Global macrocoomic ffcs of oi clima ad ducaio policis. Basic modl wih oly dirc ffc modl 1. Prc chags compard o BaU 5% discouig for NPV. Educaio xpdiur Gric Ergy Oupu Cosumpio % 4.82% % -1.03% -1.13% % 6.39% % -2.09% -1.88% % 5.68% % -1.37% -1.41% NPV 1.13% 4.60% % -1.03% -1.12% NPV Clima policy oly -5.31% 4.15% % -1.37% -1.09% Addig h ducaio policy simulas furhr iovaio spcially gric which has a dirc impac o facor produciviis ad hus o coomic growh. Th icras i ducaio xpdiur also pus a upward prssur o missios as wll. This rsul is i par du o h lasiciis of oupu ad missios o ducaio ivsms show i Tabl 3. Th lasiciy of oupu is largr ha ha of missios ad hrfor h addiioal ffor rquird o comply wih h arg is limid. This is cofirmd by h almos gligibl impac o h margial abam coss. Th carbo pric icrass bu oly slighly a mos by 2% a h d of h cury ad h ffc o oupu growh parially compsas h coss of clima policy. I N Prs Valu clima miigaio coss ar lowr i rms of gross world oupu bu highr i rms of cosumpio. This rsul raiss h issu of h appropria mric o masur h coss of a policy Hourcad ad Ghrsi Whras oupu provids a masur of h macrocoomic ffcs cosumpio is a br idicaor of wlfar. I addiio prs valus ar aggrga figurs ha hid a rad-off bw shorrm ad log-rm cosumpio which is furhr aalysd i Figur 3. I h shor-rm ducaio policy absorbs addiioal rsourcs rducig cosumpio possibiliis. Howvr shorrm addiioal ducaio xpdiur pays off i h log-rm wh i icrass ovrall coomic growh ad ulimaly cosumpio

20 Carraro al.: Huma Capial Iovaio ad Clima Policy: A Igrad Figur 3. Cosumpio pah i wo policy scarios Basic modl wih oly dirc ffc modl 1. Prc chags compard o BaU. 0.50% 0.00% % chag wr BaU -0.50% -1.00% -1.50% -2.00% -2.50% -3.00% clima+ducaio policy clima policy From his xprim of combid policis w ca coclud ha h crowdig-ou ffc ha clima policy ds o hav o ducaio ca b corrcd a modra ad mporary wlfar coss. Tha is addig a policy goal argd a ducaio dos o opardis h achivm of h ohr obciv ha of sabilisig GHG cocraios i h amosphr. 5. Coclusios This papr has xplord h rlaioship bw iovaio huma capial ad clima policy by mas of a Igrad Assssm Modl. This approach is ma o advac h curr saus of clima chag coomics rsarch ad o clarify som of h cocios bw clima chag ad coomic dvlopm. To our kowldg his is a firs of is kid modllig assssm of h irplay bw wo impora drmias of coomic growh iovaio ad huma capial i h cox of clima policy. Firs w proposd a producio srucur wih dogous chical chag suppord by ad calibrad o h mpirical vidc ha pois a a dirc rlaioship bw huma capial ad labour produciviy. Usig his basic srucur w aalysd h idirc ffc of huma capial o chological absorpio ad xplord h rlaioship bw huma capial ad iovaio. Publishd by Brkly Elcroic Prss Srvics

21 Fodazio Ei Erico Mai Workig Paprs Ar. 669 [2012] Usig hs alraiv formulaios w aalys how clima policy affcs iovaio ad h accumulaio of huma capial. suls idica ha clima policy simulas ivsms i rgy wihou rducig hos i gric if hr ar complmariis bw h hs wo forms of ivsms. Alhough gric has a polluio-usig ffc hrough capial produciviy i also has a rgy savig ffc Wh oly h dirc ffc of huma capial is cosidrd advacms i labour produciviy hav a gaiv impac o h virom bcaus labour ad rgy ar gross complms. Thrfor clima policy dcrass ducaio ivsms by a mos 10%. This is du o h capial-skill complmariy assumpio mbddd i our producio srucur. Modllig h idirc ffc of huma capial o absorpiv capaciy miigas h crowdig-ou ffc of clima policy oly slighly. I his cas huma capial augms h abiliy o absorb forig kowldg ha ca b applid o improv rgy fficicy or o rduc h pric of advacd zro-carbo chologis. Howvr h idirc ffc is o abl o courbalac h dirc impac o labour produciviy. All i all h rgy-usig dirc ffc of huma capial always prvails ad hrfor h crowdig-ou iducd by clima policy ds o b addrssd by a spcific policy. Ispcio of a policy mix ha combis clima ad ducaio args shows ha h crowdig-ou o ducaio ca b limiad by icurrig i small addiioal coomic palis ad oly i h shor-ru. Icrasd huma capial simulas log-ru coomic growh which ulimaly rducs clima chag policy coss. This rsul has impora policy implicaios cosidrig h growig cocr ha ffciv clima policy is codiioal o solid coomic dvlopm ad hrfor i ds o b supplmd by ohr policy args. A xploraory ivsigaio of h irdpdc bw ad huma capial shows ha h crowdig-ou ffc iducd by h clima policy is lssd by a largr x wh ducaio coribus o kowldg producio. This xrcis is a prlimiary aalysis ma o suggs h imporac of addiioal mpirical work i his ara

22 Carraro al.: Huma Capial Iovaio ad Clima Policy: A Igrad frcs Aghio P. Howi P A modl of growh hrough craiv dsrucio. Ecoomrica Acmoglu ircd Tchical Chag. v. Eco. Sud Acmoglu. Aghio P. Burszy L. Hmous Th Evirom ad ircd Tchical Chag. NBE Workig Paprs No Barro.J. L W A w daa s of ducaioal aaim i h world NBE Workig Papr No Bhabib J. Spigl M Th rol of huma capial i coomic dvlopm: vidc from aggrga cross-coury daa. J. Moary Eco. 34: Blakau W. Simpso N Public ducaio xpdiur ad growh. J. v. Eco Bosi V. Carraro C. Galoi M. Massi E. Tavoi M WITCH: A World Iducd Tchical Chag Hybrid Modl. Th Ergy J. Spcial Issu Hybrid Modllig of Ergy Evirom Policis: cocilig Boom-up ad Top-dow Bosi V. Massi E. Tavoi M Th WITCH Modl. Srucur Basli Soluios. Fodazio ENI Erico Mai Noa di Lavoro Mila. Bosi V. Cia E. Sgobbi A. Tavoi M Th 2008 WITCH Modl: Nw Modl Faurs ad Basli. Fodazio ENI Erico Mai Noa di Lavoro Mila. Bosi V. Carraro C. Massi E. Tavoi M Iraioal Ergy Spillovrs Ad Th Ecoomics Of Grhous Gas Amosphric Sabilizaio. Ergy Eco Bovbrg A.L. Smuldrs S Eviromal qualiy ad polluio augmaio chological chag i a wo scor dogous growh modl. J. of Public Eco Camro G. J. Proudma ad S. ddig Tchological covrgc rad ad produciviy growh Europa Ecoomic viw Carraro C. Cia E Facor-augmig chical chag: a mpirical assssm. " Workig Paprs 2009_29 parm of Ecoomics Uivrsiy of Vic "Ca' Foscari". Carraro C. Massi E. Nicia L How os Clima Policy Affc Tchical Chag? A Aalysis of h ircio ad Pac of Tchical Progrss i a Clima-Ecoomy Modl. Th Ergy J Coh. Soo M Growh ad huma capial: good daa good rsuls. J. of Eco. Growh Coh W. Lvihal Absorpiv capaciy: A w prspciv o larig ad iovaio. Admiisraiv Sci. Quar Grlagh A clima-chag policy iducd shif from iovaios i carbo-rgy producio o carbo-rgy savig. Ergy Eco Publishd by Brkly Elcroic Prss Srvics

23 Fodazio Ei Erico Mai Workig Paprs Ar. 669 [2012] Glomm G. avikumar B Public vrsus priva ivsm i huma capial: dogous growh ad icom iqualiy. J. Pol. Ecoomy Gouldr L.H. Schidr S Iducd Tchological Chag ad h Aracivss of CO2 Abam Policis. sour. ad Ergy Eco Gradus. Smuldrs S Th rad-off bw viromal car ad log-rm growhpolluio i hr prooyp growh modls. J. Eco Griffih. ddig S. va J Mappig h wo facs of : Produciviy growh i a pal of OEC idusris. v. Eco. Sa Grimaud A. Tourmai F Why ca viromal policy ax promo growh hrough h chal of ducaio? Ecol. Eco Grossma G.M. Hlpma E Trad kowldg spillovrs ad growh. Europa Eco. v Hich F Growh ffcs of a rvu-ural viromal ax rform. J. Eco Hourcad J.C. Ghrsi F Irprig viromal policy cos masurs i: Bosi V. Grlagh. Schlichr S. Eds Modlig Trasiios o Susaiabl vlopm. Edwar Elgar Publishig Lodo. IPCC Clima Chag 2007: Miigaio. Coribuio of Workig Group III o h Fourh Assssm por of h Irgovrmal Pal o Clima Chag [B. Mz O.. avidso P.. Bosch. av L.A. Myr ds] Cambridg Uivrsiy Prss Cambridg Uid Kigdom ad Nw York NY USA. XXX pp. Jaff A.B. Palmr K Eviromal rgulaio ad iovaio: a pal daa sudy. v. Eco. ad Sa Jos C.I Basd Modls of Ecoomic Growh. J. of Poliical Ecoomy Jorgso. Fraumi B Ivsm i ducaio ad U.S. coomic growh. Scad. J. Eco. 94 S51-S70. Laouw J.O. Mody A Iovaio ad h Iraioal iffusio of Eviromally sposiv Tchology. s. Policy Lucas.E O h mchaics of coomic dvlopm. J. Moary Eco Lopz Th virom as a facor of producio: h ffcs of coomic growh ad rad libralizaio. J. Eviro. Eco. Maag Luz W. Cuarsma J.C. Sadrso W Th mography of Educaioal Aaim ad Ecoomic Growh. Scic Makiw N.G. omr. Wil.N A Coribuio o h Empirics of Ecoomic Growh. Quar. J. Eco Massi E. Nicia L Opimal Ivsms ad h Cos of GHG Sabilizaio wh Kowldg Spills across Scors. CESifo Workig Paprs No Nlso. Phlps E Ivsm i humas chological diffusio ad coomic growh. Amr. Eco. v

24 Carraro al.: Huma Capial Iovaio ad Clima Policy: A Igrad Nwll.G. Jaff A.B. Savis.N Th Iducd Iovaio Hypohsis ad Ergy- Savig Tchological Chag. Quar. J. Eco Nordhaus William Modlig Iducd Iovaio i Clima Chag Policy I A. Grublr N. Nakicovic ad W.. Nordhaus ds Modlig Iducd Iovaio i Clima Chag Policy sourcs for h Fuur Prss Washigo Oo V.M. Löschl A. llik Ergy biasd chical chag: A CGE aalysis. sour. Ergy Eco Paurl X Eviromal policy ducaio ad growh: A rappraisal wh lifim is fii. Fodazio ENI Erico Mai Noa di Lavoro Mila. Pssoa S. d Abru S. Pssoa M. ob Elasiciy of Subsiuio Bw Capial ad labour ad is Applicaios o growh ad vlopm. PIE Workig Papr Uivrsiy of Psylvaia. Popp Iducd iovaio ad rgy prics. Amr. Eco. v omr P. M Edogous chological chag. J. Poliical Ecoomy Popp. Nwll.G Whr dos rgy com from? Examiig Crowdig Ou from Eviromally-Fridly. NBE Workig Papr icci F Chals of rasmissio of viromal policy o coomic growh: A survy of h hory. Ecol. Eco Siasi B. va J Th rurs o ducaio: macrocoomics. J. Eco. Survys Smuldrs S. d Nooi M Th impac of rgy cosrvaio o chology ad coomic growh. sour. Ergy Eco Tixira A.A.C. Forua N Huma capial iovaio capabiliy ad coomic growh i Porugal Porugus Eco. J Yoh G Miigaiv capaciy: h mirror imag of adapiv capaciy o h missios sid. Climaic Chag Publishd by Brkly Elcroic Prss Srvics

25 Fodazio Ei Erico Mai Workig Paprs Ar. 669 [2012] Appdix: quaios ad variabls WITCH is a dyamic opimal growh modl op-dow wih a boom-up rprsaio of h rgy scor. I ca b classifid as a hybrid modl. Th gographical covrag is global ad world rgios ar groupd io wlv macro-rgios sharig coomic gographic ad rgy similariis. Ths rgios ar USA Uid Sas WEUO Wsr Europ EEUO Easr Europ KOSAU Kora Souh Africa Ausralia CAJANZ Caada Japa Nw Zalad TE Trasiio Ecoomis MENA Middl Eas ad Norh Africa SSA Sub-Sahara Africa SASIA Souh Asia CHINA Chia ad Taiwa EASIA Souh Eas Asia LACA Lai Amrica Mxico ad Caribba. Th WITCH modl icluds a rag of chology opios ha dscrib h us of rgy ad powr graio. iffr fuls ca b usd for lcriciy graio ad fial cosumpio: coal oil gas uraium ad biofuls. Elcriciy ca b grad usig ihr radiioal fossil-fulbasd chologis or carbo-fr opios. Fossil-ful-basd chologis iclud aural gas combid cycl NGCC oil ad pulvrisd coal PC powr plas. Coal-basd lcriciy ca also b grad usig igrad gasificaio combid cycl producio wih carbo capur ad squsraio IGCC+CCS. Carbo fr chologis iclud hydrolcric ad uclar powr wid urbis ad phoovolaic pals WidSolar ad a backsop chology. A scod backsop opio rprss a alraiv o oil i rasporaio such as hydrog or scod graio biofuls. Th modl faurs dogous chical chag i h rgy scor i h form of boh Larig-By-sarchig ad Larig-By-oig Th modl faurs a gam-horic s-up ha maks i possibl o capur h ocoopraiv aur of iraioal rlaioships. Clima chag is h maor global xraliy bu ohr coomic xraliis iduc fr-ridig bhaviours ad sragic iracios. Th modl ca produc wo diffr soluios. Th coopraiv soluio is globally opimal bcaus i maximiss global social wlfar ad i iraliss viromal ad coomic xraliis. I rprss a firs-bs opimum. Th dcralisd or o-coopraiv soluio is sragically opimal for ach giv rgio Nash quilibrium bu i dos o iralis xraliis. I rprss a scod-bs opimum. A irmdia soluio ha iraliss oly h viromal xraliy ca also b compud. Th Nash quilibrium is compud as a op-loop Nash quilibrium. I is h oucom of a o-coopraiv simulaous op mmbrship gam wih full iformaio. This rmaiig of h Appdix dscribs h mai quaios of h coomic modul of h modl. Th compl dscripio of all modl quaios ca b foud i Bosi al ad Bosi al I ach rgio idxd by a social plar maximiss h followig wlfar fucio: 24 24

26 25 [ ] { } = c L W log A1 whr ar 5-yar im sps ad h discou facor is giv by: [ ] = + = v v ρ A2 whr ν ρ is h pur ra of im prfrc ad L C c = is pr capia cosumpio. Th budg cosrai dfis cosumpio as oupu lss ivsms ad opraio ad maiac coss i diffr rgy chologis I ad OM ivsms i fial good I c ducaio xpdiur I EU ad ivsms i gric ad rgy I I E : I I I I I M O I Y C B E EU C i i = A3 Oupu is producd via a sd CES fucio ha combis capial labour ad rgy srvics: Y Y EN Y L Y K EN A L A K A H Y ρ ρ ρ ρ Ω = A4 Nural chical chag H volvs xogously wih im. Facor produciviy is dogous ad dpds o h sock of gric kowldg or huma capial HK. Ergy produciviy is also affcd by a ddicad sock of rgy kowldg E : L E K HK HK AL AL AE AE AK AK E E χ χ χ = + + = = A5 25 Carraro al.: Huma Capial Iovaio ad Clima Policy: A Igrad Publishd by Brkly Elcroic Prss Srvics 2012

27 Fodazio Ei Erico Mai Workig Paprs Ar. 669 [2012] Th producio of boh huma capial ad kowldg is characrisd by irmporal spillovrs as h sock availabl i h coomy a ach poi i im coribus o h craio of h fuur sock. Th w addiio o huma capial Z EU is producd usig a Cobb-ouglas combiaio of h xisig sock of huma capial HK ad h curr xpdiur i ducaio I EU. I a similar way h availabl kowldg sock ad curr ivsms I ar combid o produc h w kowldg capial Z. Th sum of h xpos is lss ha o o accou for dimiishig rurs o ducaio ad : Z Z E U whr β β EU = α = α + ϕ + ϕ EU EU < 1 < 1 I I β EU β EU HK ϕ EU ϕ A6 Th sock of boh kowldg ad huma capial dprcia ovr im. Followig Jorgso ad Fraumi 1992 h dprciaio ra of huma capial δ EU is lowr ha h dprciaio ra of kowldg δ 2% ad 5% pr yar rspcivly. Th fial laws of accumulaio rad as follows: HK + 1 = HK 1 δ EU + Z EU + 1 = 1 δ + Z A7 Ivsms i ha build up h sock i quaio A6 rprs h oal iovaiv aciviy of h coomy. Thrfor w also rfr o i as gric iovaio. Ivsms i rgy I ar combid wih h xisig sock of kowldg ad h kowldg of ohr couris SPILL o produc w ddicad rgy kowldg Z. Th modl spcifis hr diffr rgy kowldg socks rgy fficicy ad wo socks of brakhrough kowldg which ar dod wih h idx = ff brakhrough

28 27 1 whr < + + = d SPILL I Z d E ϕ β α ϕ β A8 wih h sadard accumulaio quaio: 1 1 Z + = + δ A9 Th coribuio of forig kowldg SPILL is o immdia bu dpds o h iracio bw wo rms Bosi. al 2008: h firs dscribs h absorpiv capaciy whras h scod capurs h disac from h chology froir which is rprsd by h sock of kowldg i rich couris USA WEUO EEUO CAJANZ ad KOSAU. omsic ivsms ar rquird i ordr o bfi from h iraioal pool of kowldg SPILL HI HI = A10 Th WITCH modl icluds wo backsop chologis c. Ths ar iovaiv zro carbo chologis currly o commrcialisd bcaus vry xpsiv. Thy cssia ddicad ivsms o bcom coomically compiiv ad dploym o bcom availabl o larg scal. Th coss of hs chologis ar modlld wih a wo-facor larig curv. Th ui cos of ach backsop chology c P volvs ovr im wih chology dploym c CC ad h accumulaio of a ddicad kowldg sock c : b c CC CC P P = 0 * A11 whr =brakhrough. sock accumulas wih h prpual rul ad wih h coribuio of iraioal kowldg spillovrs as i q. A8-A9 Equaios A1-A11 dscrib h basic formulaio of h modl. Sarig from his vrsio w cosidrd wo possibl variaios. Firs scio 3.2 huma capial has a idirc ffc o 27 Carraro al.: Huma Capial Iovaio ad Clima Policy: A Igrad Publishd by Brkly Elcroic Prss Srvics 2012

29 28 chological absorpio ad i coribus o icrasig h absorpiv capaciy i h rgy scor: HK SPILL HI HI + = A13 Scod scio 3.3 huma capial is a ipu i h craio of boh socks of gric ad rgy kowldg. Thrfor quaios A6 A8 ad A12 ar modifid as follows EU EU HK SPILL I Z HK I Z d γ ϕ β γ ϕ β α α = = A14 Wh huma capial is iroducd i h producio fucio of w idas h paramrs α ad ϕ ar rcalibrad so ha h dyamics of kowldg ad ducaio ivsms rplica hos i h modl vrsio 1 α α < ad ϕ ϕ <. 28 Fodazio Ei Erico Mai Workig Paprs Ar. 669 [2012]

1973 AP Calculus BC: Section I

1973 AP Calculus BC: Section I 97 AP Calculus BC: Scio I 9 Mius No Calculaor No: I his amiaio, l dos h aural logarihm of (ha is, logarihm o h bas ).. If f ( ) =, h f ( ) = ( ). ( ) + d = 7 6. If f( ) = +, h h s of valus for which f

More information

, then the old equilibrium biomass was greater than the new B e. and we want to determine how long it takes for B(t) to reach the value B e.

, then the old equilibrium biomass was greater than the new B e. and we want to determine how long it takes for B(t) to reach the value B e. SURPLUS PRODUCTION (coiud) Trasiio o a Nw Equilibrium Th followig marials ar adapd from lchr (978), o h Rcommdd Radig lis caus () approachs h w quilibrium valu asympoically, i aks a ifii amou of im o acually

More information

Research on the Decomposition of the Economic Impact Factors of Air. Pollution in Hubei Province in China

Research on the Decomposition of the Economic Impact Factors of Air. Pollution in Hubei Province in China d raioal Cofrc o ducaio, Maagm ad formaio cholog (CM 5) Rsarch o h Dcomposiio of h coomic mpac Facors of Air olluio i Hubi rovic i Chia Luo Jua, a, Aglia N.lchko, b, H Qiga, c Collg of Mahmaics ad Compur

More information

Response of LTI Systems to Complex Exponentials

Response of LTI Systems to Complex Exponentials 3 Fourir sris coiuous-im Rspos of LI Sysms o Complx Expoials Ouli Cosidr a LI sysm wih h ui impuls rspos Suppos h ipu sigal is a complx xpoial s x s is a complx umbr, xz zis a complx umbr h or h h w will

More information

Continous system: differential equations

Continous system: differential equations /6/008 Coious sysm: diffrial quaios Drmiisic modls drivaivs isad of (+)-( r( compar ( + ) R( + r ( (0) ( R ( 0 ) ( Dcid wha hav a ffc o h sysm Drmi whhr h paramrs ar posiiv or gaiv, i.. giv growh or rducio

More information

Numerical Simulation for the 2-D Heat Equation with Derivative Boundary Conditions

Numerical Simulation for the 2-D Heat Equation with Derivative Boundary Conditions IOSR Joural of Applid Chmisr IOSR-JAC -ISSN: 78-576.Volum 9 Issu 8 Vr. I Aug. 6 PP 4-8 www.iosrjourals.org Numrical Simulaio for h - Ha Equaio wih rivaiv Boudar Codiios Ima. I. Gorial parm of Mahmaics

More information

Part B: Transform Methods. Professor E. Ambikairajah UNSW, Australia

Part B: Transform Methods. Professor E. Ambikairajah UNSW, Australia Par B: rasform Mhods Profssor E. Ambikairaah UNSW, Ausralia Chapr : Fourir Rprsaio of Sigal. Fourir Sris. Fourir rasform.3 Ivrs Fourir rasform.4 Propris.4. Frqucy Shif.4. im Shif.4.3 Scalig.4.4 Diffriaio

More information

Modeling of the CML FD noise-to-jitter conversion as an LPTV process

Modeling of the CML FD noise-to-jitter conversion as an LPTV process Modlig of h CML FD ois-o-ir covrsio as a LPV procss Marko Alksic. Rvisio hisory Vrsio Da Comms. //4 Firs vrsio mrgd wo docums. Cyclosaioary Nois ad Applicaio o CML Frqucy Dividr Jir/Phas Nois Aalysis fil

More information

Web-appendix 1: macro to calculate the range of ( ρ, for which R is positive definite

Web-appendix 1: macro to calculate the range of ( ρ, for which R is positive definite Wb-basd Supplmary Marials for Sampl siz cosidraios for GEE aalyss of hr-lvl clusr radomizd rials by Sv Trsra, Big Lu, oh S. Prissr, Tho va Achrbrg, ad Gorg F. Borm Wb-appdix : macro o calcula h rag of

More information

What Is the Difference between Gamma and Gaussian Distributions?

What Is the Difference between Gamma and Gaussian Distributions? Applid Mahmaics,,, 85-89 hp://ddoiorg/6/am Publishd Oli Fbruary (hp://wwwscirporg/joural/am) Wha Is h Diffrc bw Gamma ad Gaussia Disribuios? iao-li Hu chool of Elcrical Egirig ad Compur cic, Uivrsiy of

More information

Fourier Series: main points

Fourier Series: main points BIOEN 3 Lcur 6 Fourir rasforms Novmbr 9, Fourir Sris: mai pois Ifii sum of sis, cosis, or boh + a a cos( + b si( All frqucis ar igr mulipls of a fudamal frqucy, o F.S. ca rprs ay priodic fucio ha w ca

More information

( A) ( B) ( C) ( D) ( E)

( A) ( B) ( C) ( D) ( E) d Smsr Fial Exam Worksh x 5x.( NC)If f ( ) d + 7, h 4 f ( ) d is 9x + x 5 6 ( B) ( C) 0 7 ( E) divrg +. (NC) Th ifii sris ak has h parial sum S ( ) for. k Wha is h sum of h sris a? ( B) 0 ( C) ( E) divrgs

More information

Mixing time with Coupling

Mixing time with Coupling Mixig im wih Couplig Jihui Li Mig Zhg Saisics Dparm May 7 Goal Iroducio o boudig h mixig im for MCMC wih couplig ad pah couplig Prsig a simpl xampl o illusra h basic ida Noaio M is a Markov chai o fii

More information

Which dual labour market model should we choose?

Which dual labour market model should we choose? Spmbr 2002 hich dual labour mark modl should w choos? By Mor Skak Dparm of Ecoomics Uivrsiy of Souhr Dmark Campusvj 55, DK-5230 Ods M Pho +45 6550 2111. Fax. +45 6615 8790 mos@sam.sdu.dk Absrac O way o

More information

Software Development Cost Model based on NHPP Gompertz Distribution

Software Development Cost Model based on NHPP Gompertz Distribution Idia Joural of Scic ad Tchology, Vol 8(12), DOI: 10.17485/ijs/2015/v8i12/68332, Ju 2015 ISSN (Pri) : 0974-6846 ISSN (Oli) : 0974-5645 Sofwar Dvlopm Cos Modl basd o NHPP Gomprz Disribuio H-Chul Kim 1* ad

More information

The Development of Suitable and Well-founded Numerical Methods to Solve Systems of Integro- Differential Equations,

The Development of Suitable and Well-founded Numerical Methods to Solve Systems of Integro- Differential Equations, Shiraz Uivrsiy of Tchology From h SlcdWorks of Habibolla Laifizadh Th Dvlopm of Suiabl ad Wll-foudd Numrical Mhods o Solv Sysms of Igro- Diffrial Equaios, Habibolla Laifizadh, Shiraz Uivrsiy of Tchology

More information

Note 6 Frequency Response

Note 6 Frequency Response No 6 Frqucy Rpo Dparm of Mchaical Egirig, Uivriy Of Sakachwa, 57 Campu Driv, Sakaoo, S S7N 59, Caada Dparm of Mchaical Egirig, Uivriy Of Sakachwa, 57 Campu Driv, Sakaoo, S S7N 59, Caada. alyical Exprio

More information

Mathematical Preliminaries for Transforms, Subbands, and Wavelets

Mathematical Preliminaries for Transforms, Subbands, and Wavelets Mahmaical Prlimiaris for rasforms, Subbads, ad Wavls C.M. Liu Prcpual Sigal Procssig Lab Collg of Compur Scic Naioal Chiao-ug Uivrsiy hp://www.csi.cu.du.w/~cmliu/courss/comprssio/ Offic: EC538 (03)5731877

More information

ELECTROMAGNETIC COMPATIBILITY HANDBOOK 1. Chapter 12: Spectra of Periodic and Aperiodic Signals

ELECTROMAGNETIC COMPATIBILITY HANDBOOK 1. Chapter 12: Spectra of Periodic and Aperiodic Signals ELECTOMAGNETIC COMPATIBILITY HANDBOOK Chapr : Spcra of Priodic ad Apriodic Sigals. Drmi whhr ach of h followig fucios ar priodic. If hy ar priodic, provid hir fudamal frqucy ad priod. a) x 4cos( 5 ) si(

More information

The Impact of Separate Processes on Asset Pricing

The Impact of Separate Processes on Asset Pricing Th Impac o Spara Procsss o Ass Pricig DECISION SCIENCES INSTITUTE Th impac o spara procsss o aggrga dividds ad cosumpio o ass pricig wih a ails (Full Papr Submissio) Jacky So Uivrsiy o Macau Uivrsiy o

More information

Chapter 3 Linear Equations of Higher Order (Page # 144)

Chapter 3 Linear Equations of Higher Order (Page # 144) Ma Modr Dirial Equaios Lcur wk 4 Jul 4-8 Dr Firozzama Darm o Mahmaics ad Saisics Arizoa Sa Uivrsi This wk s lcur will covr har ad har 4 Scios 4 har Liar Equaios o Highr Ordr Pag # 44 Scio Iroducio: Scod

More information

MAT3700. Tutorial Letter 201/2/2016. Mathematics III (Engineering) Semester 2. Department of Mathematical sciences MAT3700/201/2/2016

MAT3700. Tutorial Letter 201/2/2016. Mathematics III (Engineering) Semester 2. Department of Mathematical sciences MAT3700/201/2/2016 MAT3700/0//06 Tuorial Lr 0//06 Mahmaics III (Egirig) MAT3700 Smsr Dparm of Mahmaical scics This uorial lr coais soluios ad aswrs o assigms. BARCODE CONTENTS Pag SOLUTIONS ASSIGNMENT... 3 SOLUTIONS ASSIGNMENT...

More information

Economics 302 (Sec. 001) Intermediate Macroeconomic Theory and Policy (Spring 2011) 3/28/2012. UW Madison

Economics 302 (Sec. 001) Intermediate Macroeconomic Theory and Policy (Spring 2011) 3/28/2012. UW Madison Economics 302 (Sc. 001) Inrmdia Macroconomic Thory and Policy (Spring 2011) 3/28/2012 Insrucor: Prof. Mnzi Chinn Insrucor: Prof. Mnzi Chinn UW Madison 16 1 Consumpion Th Vry Forsighd dconsumr A vry forsighd

More information

ECEN620: Network Theory Broadband Circuit Design Fall 2014

ECEN620: Network Theory Broadband Circuit Design Fall 2014 ECE60: work Thory Broadbad Circui Dig Fall 04 Lcur 6: PLL Trai Bhavior Sam Palrmo Aalog & Mixd-Sigal Cr Txa A&M Uivriy Aoucm, Agda, & Rfrc HW i du oday by 5PM PLL Trackig Rpo Pha Dcor Modl PLL Hold Rag

More information

Modeling of Reductive Biodegradation of TCE to ETH. Adam Worsztynowicz, Dorota Rzychon, Sebastian Iwaszenko, Tomasz Siobowicz

Modeling of Reductive Biodegradation of TCE to ETH. Adam Worsztynowicz, Dorota Rzychon, Sebastian Iwaszenko, Tomasz Siobowicz Modlig of Rduciv Biodgradaio of o ETH Adam Worszyowicz, Doroa Rzycho, Sbasia Iwaszo, Tomasz Siobowicz Isiu for Ecology of Idusrial Aras Kossuha S., Kaowic, Polad l. (+-) 5, fax: (+-) 5 7 7 -mail: iu@iu.aowic.pl

More information

Some Applications of the Poisson Process

Some Applications of the Poisson Process Applid Maaics, 24, 5, 3-37 Publishd Oli Novbr 24 i SciRs. hp://www.scirp.org/oural/a hp://dx.doi.org/.4236/a.24.59288 So Applicaios of Poisso Procss Kug-Ku s Dpar of Maaics, Ka Uivrsiy, Uio, USA Eail:

More information

Log-periodogram regression with odd Fourier frequencies

Log-periodogram regression with odd Fourier frequencies Log-priodogram rgrssio wih odd Fourir frqucis Erhard Rschhofr Dparm of Saisics ad Opraios Rsarch, Uivrsiy of Via, Ausria Uivrsiässr. 5, Via, Ausria E-mail: rhard.rschhofr@uivi.ac.a Absrac I his papr, a

More information

High Speed Rail Transport Valuation

High Speed Rail Transport Valuation High Spd Rail Traspor Valuaio Pdro Migul Piml Uivrsiy of h Azors Busiss ad coomics Dparm, CAplA, R. Mã d Dus, 95 Poa Dlgada, Porugal, ppiml@os.uac.p José Azvdo-Prira ISG Uivrsidad Técica d Lisboa Dparm

More information

Recovery of Valuable Incompletely-Recorded Return- Stroke Current Derivative Signals

Recovery of Valuable Incompletely-Recorded Return- Stroke Current Derivative Signals Rcovry of Valuabl Icomplly-Rcordd Rur- Srok Curr Drivaiv Sigals Lakmii Prra Elcrical ad Compur Egirig Dparm Ryrso Uivrsiy Toroo, Caada lakmii.prra@ryrso.ca Ali M. Hussi Elcrical ad Compur Egirig Dparm

More information

Review Topics from Chapter 3&4. Fourier Series Fourier Transform Linear Time Invariant (LTI) Systems Energy-Type Signals Power-Type Signals

Review Topics from Chapter 3&4. Fourier Series Fourier Transform Linear Time Invariant (LTI) Systems Energy-Type Signals Power-Type Signals Rviw opics from Chapr 3&4 Fourir Sris Fourir rasform Liar im Ivaria (LI) Sysms Ergy-yp Sigals Powr-yp Sigals Fourir Sris Rprsaio for Priodic Sigals Dfiiio: L h sigal () b a priodic sigal wih priod. ()

More information

CHAPTER CHAPTER14. Expectations: The Basic Tools. Prepared by: Fernando Quijano and Yvonn Quijano

CHAPTER CHAPTER14. Expectations: The Basic Tools. Prepared by: Fernando Quijano and Yvonn Quijano Expcaions: Th Basic Prpard by: Frnando Quijano and Yvonn Quijano CHAPTER CHAPTER14 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 14-1 Today s Lcur Chapr 14:Expcaions: Th Basic Th

More information

ECE351: Signals and Systems I. Thinh Nguyen

ECE351: Signals and Systems I. Thinh Nguyen ECE35: Sigals ad Sysms I Thih Nguy FudamalsofSigalsadSysms x Fudamals of Sigals ad Sysms co. Fudamals of Sigals ad Sysms co. x x] Classificaio of sigals Classificaio of sigals co. x] x x] =xt s =x

More information

Poisson Arrival Process

Poisson Arrival Process Poisso Arrival Procss Arrivals occur i) i a mmylss mar ii) [ o arrival durig Δ ] = λδ + ( Δ ) P o [ o arrival durig Δ ] = λδ + ( Δ ) P o P j arrivals durig Δ = o Δ f j = 2,3, o Δ whr lim =. Δ Δ C C 2 C

More information

They must have different numbers of electrons orbiting their nuclei. They must have the same number of neutrons in their nuclei.

They must have different numbers of electrons orbiting their nuclei. They must have the same number of neutrons in their nuclei. 37 1 How may utros ar i a uclus of th uclid l? 20 37 54 2 crtai lmt has svral isotops. Which statmt about ths isotops is corrct? Thy must hav diffrt umbrs of lctros orbitig thir ucli. Thy must hav th sam

More information

On the Derivatives of Bessel and Modified Bessel Functions with Respect to the Order and the Argument

On the Derivatives of Bessel and Modified Bessel Functions with Respect to the Order and the Argument Inrnaional Rsarch Journal of Applid Basic Scincs 03 Aailabl onlin a wwwirjabscom ISSN 5-838X / Vol 4 (): 47-433 Scinc Eplorr Publicaions On h Driais of Bssl Modifid Bssl Funcions wih Rspc o h Ordr h Argumn

More information

WORKING PAPER SERIES. High Speed Rail Transport Valuation. CEEAplA WP No. 14/2008. Pedro Pimentel José Azevedo-Pereira Gualter Couto.

WORKING PAPER SERIES. High Speed Rail Transport Valuation. CEEAplA WP No. 14/2008. Pedro Pimentel José Azevedo-Pereira Gualter Couto. WORKING PAPR SRIS CAplA WP No. 4/8 High Spd Rail Traspor Valuaio Pdro Piml José Azvdo-Prira Gualr Couo Novmbr 8 Uivrsidad dos Açors Uivrsidad da Madira High Spd Rail Traspor Valuaio Pdro Piml Uivrsidad

More information

ON H-TRICHOTOMY IN BANACH SPACES

ON H-TRICHOTOMY IN BANACH SPACES CODRUTA STOICA IHAIL EGA O H-TRICHOTOY I BAACH SPACES Absrac: I his papr w mphasiz h oio of skw-oluio smiflows cosidrd a gralizaio of smigroups oluio opraors ad skw-produc smiflows which aris i h sabiliy

More information

Page 1. Before-After Control-Impact (BACI) Power Analysis For Several Related Populations (With Unknown Variance Matrix) Richard A.

Page 1. Before-After Control-Impact (BACI) Power Analysis For Several Related Populations (With Unknown Variance Matrix) Richard A. Pag Bfor-Afr Corol-Impac (BACI) Powr Aalysis For Svral Rlad Populaios (Wih Ukow Variac Marix) Richard A. Hirichs Spmbr 0, 00 Cava: This xprimal dsig ool is a idalizd powr aalysis buil upo svral simplifyig

More information

The geometry of surfaces contact

The geometry of surfaces contact Applid ad ompuaioal Mchaics (007 647-656 h gomry of surfacs coac J. Sigl a * J. Švíglr a a Faculy of Applid Scics UWB i Pils Uivrzií 0 00 Pils zch public civd 0 Spmbr 007; rcivd i rvisd form 0 Ocobr 007

More information

Midterm Examination (100 pts)

Midterm Examination (100 pts) Econ 509 Spring 2012 S.L. Parn Midrm Examinaion (100 ps) Par I. 30 poins 1. Dfin h Law of Diminishing Rurns (5 ps.) Incrasing on inpu, call i inpu x, holding all ohr inpus fixd, on vnuall runs ino h siuaion

More information

1. Inverse Matrix 4[(3 7) (02)] 1[(0 7) (3 2)] Recall that the inverse of A is equal to:

1. Inverse Matrix 4[(3 7) (02)] 1[(0 7) (3 2)] Recall that the inverse of A is equal to: Rfrncs Brnank, B. and I. Mihov (1998). Masuring monary policy, Quarrly Journal of Economics CXIII, 315-34. Blanchard, O. R. Proi (00). An mpirical characrizaion of h dynamic ffcs of changs in govrnmn spnding

More information

Poisson Arrival Process

Poisson Arrival Process 1 Poisso Arrival Procss Arrivals occur i) i a mmorylss mar ii) [ o arrival durig Δ ] = λδ + ( Δ ) P o [ o arrival durig Δ ] = 1 λδ + ( Δ ) P o P j arrivals durig Δ = o Δ for j = 2,3, ( ) o Δ whr lim =

More information

z 1+ 3 z = Π n =1 z f() z = n e - z = ( 1-z) e z e n z z 1- n = ( 1-z/2) 1+ 2n z e 2n e n -1 ( 1-z )/2 e 2n-1 1-2n -1 1 () z

z 1+ 3 z = Π n =1 z f() z = n e - z = ( 1-z) e z e n z z 1- n = ( 1-z/2) 1+ 2n z e 2n e n -1 ( 1-z )/2 e 2n-1 1-2n -1 1 () z Sris Expasio of Rciprocal of Gamma Fuctio. Fuctios with Itgrs as Roots Fuctio f with gativ itgrs as roots ca b dscribd as follows. f() Howvr, this ifiit product divrgs. That is, such a fuctio caot xist

More information

Practice papers A and B, produced by Edexcel in 2009, with mark schemes. Practice Paper A. 5 cosh x 2 sinh x = 11,

Practice papers A and B, produced by Edexcel in 2009, with mark schemes. Practice Paper A. 5 cosh x 2 sinh x = 11, Prai paprs A ad B, produd by Edl i 9, wih mark shms Prai Papr A. Fid h valus of for whih 5 osh sih =, givig your aswrs as aural logarihms. (Toal 6 marks) k. A = k, whr k is a ral osa. 9 (a) Fid valus of

More information

Session : Plasmas in Equilibrium

Session : Plasmas in Equilibrium Sssio : Plasmas i Equilibrium Ioizatio ad Coductio i a High-prssur Plasma A ormal gas at T < 3000 K is a good lctrical isulator, bcaus thr ar almost o fr lctros i it. For prssurs > 0.1 atm, collisio amog

More information

Physics 160 Lecture 3. R. Johnson April 6, 2015

Physics 160 Lecture 3. R. Johnson April 6, 2015 Physics 6 Lcur 3 R. Johnson April 6, 5 RC Circui (Low-Pass Filr This is h sam RC circui w lookd a arlir h im doma, bu hr w ar rsd h frquncy rspons. So w pu a s wav sad of a sp funcion. whr R C RC Complx

More information

The Science of Monetary Policy

The Science of Monetary Policy Th Scinc of Monary Policy. Inroducion o Topics of Sminar. Rviw: IS-LM, AD-AS wih an applicaion o currn monary policy in Japan 3. Monary Policy Sragy: Inrs Ra Ruls and Inflaion Targing (Svnsson EER) 4.

More information

UNIT #5 EXPONENTIAL AND LOGARITHMIC FUNCTIONS

UNIT #5 EXPONENTIAL AND LOGARITHMIC FUNCTIONS Answr Ky Nam: Da: UNIT # EXPONENTIAL AND LOGARITHMIC FUNCTIONS Par I Qusions. Th prssion is quivaln o () () 6 6 6. Th ponnial funcion y 6 could rwrin as y () y y 6 () y y (). Th prssion a is quivaln o

More information

Economics 302 (Sec. 001) Intermediate Macroeconomic Theory and Policy (Spring 2011) 4/25/2011. UW Madison

Economics 302 (Sec. 001) Intermediate Macroeconomic Theory and Policy (Spring 2011) 4/25/2011. UW Madison conomics 302 (Sc. 001) Inrmdia Macroconomic Thory and Policy (Spring 2011) 4/25/2011 Insrucor: Prof. Mnzi Chinn Insrucor: Prof. Mnzi Chinn UW Madison 21 1 Th Mdium Run ε = P * P Thr ar wo ways in which

More information

Themes. Flexible exchange rates with inflation targeting. Expectations formation under flexible exchange rates

Themes. Flexible exchange rates with inflation targeting. Expectations formation under flexible exchange rates CHAPTER 25 THE OPEN ECONOMY WITH FLEXIBLE EXCHANGE RATES Thms Flxibl xchang ras wih inlaion arging Expcaions ormaion undr lxibl xchang ras Th AS-AD modl wih lxibl xchang ras Macroconomic adjusmn undr lxibl

More information

A MATHEMATICAL MODEL FOR NATURAL COOLING OF A CUP OF TEA

A MATHEMATICAL MODEL FOR NATURAL COOLING OF A CUP OF TEA MTHEMTICL MODEL FOR NTURL COOLING OF CUP OF TE 1 Mrs.D.Kalpana, 2 Mr.S.Dhvarajan 1 Snior Lcurr, Dparmn of Chmisry, PSB Polychnic Collg, Chnnai, India. 2 ssisan Profssor, Dparmn of Mahmaics, Dr.M.G.R Educaional

More information

2 Dirac delta function, modeling of impulse processes. 3 Sine integral function. Exponential integral function

2 Dirac delta function, modeling of impulse processes. 3 Sine integral function. Exponential integral function Chapr VII Spcial Fucios Ocobr 7, 7 479 CHAPTER VII SPECIAL FUNCTIONS Cos: Havisid sp fucio, filr fucio Dirac dla fucio, modlig of impuls procsss 3 Si igral fucio 4 Error fucio 5 Gamma fucio E Epoial igral

More information

Phys463.nb Conductivity. Another equivalent definition of the Fermi velocity is

Phys463.nb Conductivity. Another equivalent definition of the Fermi velocity is 39 Anohr quival dfiniion of h Fri vlociy is pf vf (6.4) If h rgy is a quadraic funcion of k H k L, hs wo dfiniions ar idical. If is NOT a quadraic funcion of k (which could happ as will b discussd in h

More information

THE SHORT-RUN AGGREGATE SUPPLY CURVE WITH A POSITIVE SLOPE. Based on EXPECTATIONS: Lecture. t t t t

THE SHORT-RUN AGGREGATE SUPPLY CURVE WITH A POSITIVE SLOPE. Based on EXPECTATIONS: Lecture. t t t t THE SHORT-RUN AGGREGATE SUL CURVE WITH A OSITIVE SLOE. Basd on EXECTATIONS: Lcur., 0. In Mankiw:, 0 Ths quaions sa ha oupu dvias from is naural ra whn h pric lvl dvias from h xpcd pric lvl. Th paramr a

More information

Institute of Actuaries of India

Institute of Actuaries of India Insiu of Acuaris of India ubjc CT3 Probabiliy and Mahmaical aisics Novmbr Examinaions INDICATIVE OLUTION Pag of IAI CT3 Novmbr ol. a sampl man = 35 sampl sandard dviaion = 36.6 b for = uppr bound = 35+*36.6

More information

4.1 The Uniform Distribution Def n: A c.r.v. X has a continuous uniform distribution on [a, b] when its pdf is = 1 a x b

4.1 The Uniform Distribution Def n: A c.r.v. X has a continuous uniform distribution on [a, b] when its pdf is = 1 a x b 4. Th Uniform Disribuion Df n: A c.r.v. has a coninuous uniform disribuion on [a, b] whn is pdf is f x a x b b a Also, b + a b a µ E and V Ex4. Suppos, h lvl of unblivabiliy a any poin in a Transformrs

More information

Assessing Reliable Software using SPRT based on LPETM

Assessing Reliable Software using SPRT based on LPETM Iraioal Joural of Compur Applicaios (75 888) Volum 47 No., Ju Assssig Rliabl Sofwar usig SRT basd o LETM R. Saya rasad hd, Associa rofssor Dp. of CS &Egg. AcharyaNagarjua Uivrsiy D. Hariha Assisa rofssor

More information

Ideal Amplifier/Attenuator. Memoryless. where k is some real constant. Integrator. System with memory

Ideal Amplifier/Attenuator. Memoryless. where k is some real constant. Integrator. System with memory Liear Time-Ivaria Sysems (LTI Sysems) Oulie Basic Sysem Properies Memoryless ad sysems wih memory (saic or dyamic) Causal ad o-causal sysems (Causaliy) Liear ad o-liear sysems (Lieariy) Sable ad o-sable

More information

Linear Systems Analysis in the Time Domain

Linear Systems Analysis in the Time Domain Liar Sysms Aalysis i h Tim Domai Firs Ordr Sysms di vl = L, vr = Ri, d di L + Ri = () d R x= i, x& = x+ ( ) L L X() s I() s = = = U() s E() s Ls+ R R L s + R u () = () =, i() = L i () = R R Firs Ordr Sysms

More information

Chapter 2 Infinite Series Page 1 of 11. Chapter 2 : Infinite Series

Chapter 2 Infinite Series Page 1 of 11. Chapter 2 : Infinite Series Chatr Ifiit Sris Pag of Sctio F Itgral Tst Chatr : Ifiit Sris By th d of this sctio you will b abl to valuat imror itgrals tst a sris for covrgc by alyig th itgral tst aly th itgral tst to rov th -sris

More information

Ring of Large Number Mutually Coupled Oscillators Periodic Solutions

Ring of Large Number Mutually Coupled Oscillators Periodic Solutions Iraioal Joural of horical ad Mahmaical Physics 4, 4(6: 5-9 DOI: 59/jijmp446 Rig of arg Numbr Muually Coupld Oscillaors Priodic Soluios Vasil G Aglov,*, Dafika z Aglova Dparm Nam of Mahmaics, Uivrsiy of

More information

The transition:transversion rate ratio vs. the T-ratio.

The transition:transversion rate ratio vs. the T-ratio. PhyloMah Lcur 8 by Dan Vandrpool March, 00 opics of Discussion ransiion:ransvrsion ra raio Kappa vs. ransiion:ransvrsion raio raio alculaing h xpcd numbr of subsiuions using marix algbra Why h nral im

More information

NON-LINEAR PARAMETER ESTIMATION USING VOLTERRA SERIES WITH MULTI-TONE EXCITATION

NON-LINEAR PARAMETER ESTIMATION USING VOLTERRA SERIES WITH MULTI-TONE EXCITATION NON-LINER PRMETER ESTIMTION USING VOLTERR SERIES WIT MULTI-TONE ECITTION imsh Char Dparm of Mchaical Egirig Visvsvaraya Rgioal Collg of Egirig Nagpur INDI-00 Naliash Vyas Dparm of Mchaical Egirig Iia Isiu

More information

Spring 2006 Process Dynamics, Operations, and Control Lesson 2: Mathematics Review

Spring 2006 Process Dynamics, Operations, and Control Lesson 2: Mathematics Review Spring 6 Procss Dynamics, Opraions, and Conrol.45 Lsson : Mahmaics Rviw. conx and dircion Imagin a sysm ha varis in im; w migh plo is oupu vs. im. A plo migh imply an quaion, and h quaion is usually an

More information

Quality Monitoring Calibration Assuring Standardization Among Monitors

Quality Monitoring Calibration Assuring Standardization Among Monitors Qualiy Moioig alibaio Assuig Sadadizaio Amog Moios MOR Rspod oopaio Wokshop Spmb 2006 Ral Soluios fo Tlpho Suvy Mhodology alibaio - accodig o Wbs To sadadiz by dmiig h dviaio fom a sadad as o ascai h pop

More information

APPENDIX: STATISTICAL TOOLS

APPENDIX: STATISTICAL TOOLS I. Nots o radom samplig Why do you d to sampl radomly? APPENDI: STATISTICAL TOOLS I ordr to masur som valu o a populatio of orgaisms, you usually caot masur all orgaisms, so you sampl a subst of th populatio.

More information

AR(1) Process. The first-order autoregressive process, AR(1) is. where e t is WN(0, σ 2 )

AR(1) Process. The first-order autoregressive process, AR(1) is. where e t is WN(0, σ 2 ) AR() Procss Th firs-ordr auorgrssiv procss, AR() is whr is WN(0, σ ) Condiional Man and Varianc of AR() Condiional man: Condiional varianc: ) ( ) ( Ω Ω E E ) var( ) ) ( var( ) var( σ Ω Ω Ω Ω E Auocovarianc

More information

EEE 303: Signals and Linear Systems

EEE 303: Signals and Linear Systems 33: Sigls d Lir Sysms Orhogoliy bw wo sigls L us pproim fucio f () by fucio () ovr irvl : f ( ) = c( ); h rror i pproimio is, () = f() c () h rgy of rror sigl ovr h irvl [, ] is, { }{ } = f () c () d =

More information

22/ Breakdown of the Born-Oppenheimer approximation. Selection rules for rotational-vibrational transitions. P, R branches.

22/ Breakdown of the Born-Oppenheimer approximation. Selection rules for rotational-vibrational transitions. P, R branches. Subjct Chmistry Papr No and Titl Modul No and Titl Modul Tag 8/ Physical Spctroscopy / Brakdown of th Born-Oppnhimr approximation. Slction ruls for rotational-vibrational transitions. P, R branchs. CHE_P8_M

More information

(A) 1 (B) 1 + (sin 1) (C) 1 (sin 1) (D) (sin 1) 1 (C) and g be the inverse of f. Then the value of g'(0) is. (C) a. dx (a > 0) is

(A) 1 (B) 1 + (sin 1) (C) 1 (sin 1) (D) (sin 1) 1 (C) and g be the inverse of f. Then the value of g'(0) is. (C) a. dx (a > 0) is [STRAIGHT OBJECTIVE TYPE] l Q. Th vlu of h dfii igrl, cos d is + (si ) (si ) (si ) Q. Th vlu of h dfii igrl si d whr [, ] cos cos Q. Vlu of h dfii igrl ( si Q. L f () = d ( ) cos 7 ( ) )d d g b h ivrs

More information

5.1 The Nuclear Atom

5.1 The Nuclear Atom Sav My Exams! Th Hom of Rvisio For mor awsom GSE ad lvl rsourcs, visit us at www.savmyxams.co.uk/ 5.1 Th Nuclar tom Qustio Papr Lvl IGSE Subjct Physics (0625) Exam oard Topic Sub Topic ooklt ambridg Itratioal

More information

A Simple Proof that e is Irrational

A Simple Proof that e is Irrational Two of th most bautiful ad sigificat umbrs i mathmatics ar π ad. π (approximatly qual to 3.459) rprsts th ratio of th circumfrc of a circl to its diamtr. (approximatly qual to.788) is th bas of th atural

More information

CPSC 211 Data Structures & Implementations (c) Texas A&M University [ 259] B-Trees

CPSC 211 Data Structures & Implementations (c) Texas A&M University [ 259] B-Trees CPSC 211 Daa Srucurs & Implmnaions (c) Txas A&M Univrsiy [ 259] B-Trs Th AVL r and rd-black r allowd som variaion in h lnghs of h diffrn roo-o-laf pahs. An alrnaiv ida is o mak sur ha all roo-o-laf pahs

More information

Bipolar Junction Transistors

Bipolar Junction Transistors ipolar Juctio Trasistors ipolar juctio trasistors (JT) ar activ 3-trmial dvics with aras of applicatios: amplifirs, switch tc. high-powr circuits high-spd logic circuits for high-spd computrs. JT structur:

More information

1 João Garcia is a Senior Quantitative Analyst at Artesia BC, Helmut Van Ginderen is the head of the Risk

1 João Garcia is a Senior Quantitative Analyst at Artesia BC, Helmut Van Ginderen is the head of the Risk O h Pricig of Crdi Sprad Opios: a wo Facor HW-BK Algorihm João Garcia Hlmu Va Gidr ad Rialdo Garcia 1 his Vrsio: Dc 2 d 2001 4 h Vrsio Summar I his aricl w dscrib wha a crdi sprad opio CSO is ad show a

More information

Chapter (8) Estimation and Confedence Intervals Examples

Chapter (8) Estimation and Confedence Intervals Examples Chaptr (8) Estimatio ad Cofdc Itrvals Exampls Typs of stimatio: i. Poit stimatio: Exampl (1): Cosidr th sampl obsrvatios, 17,3,5,1,18,6,16,10 8 X i i1 17 3 5 118 6 16 10 116 X 14.5 8 8 8 14.5 is a poit

More information

Decline Curves. Exponential decline (constant fractional decline) Harmonic decline, and Hyperbolic decline.

Decline Curves. Exponential decline (constant fractional decline) Harmonic decline, and Hyperbolic decline. Dlin Curvs Dlin Curvs ha lo flow ra vs. im ar h mos ommon ools for forasing roduion and monioring wll rforman in h fild. Ths urvs uikly show by grahi mans whih wlls or filds ar roduing as xd or undr roduing.

More information

A Generalized Cost Malmquist Index to the Productivities of Units with Negative Data in DEA

A Generalized Cost Malmquist Index to the Productivities of Units with Negative Data in DEA Proceedigs of he 202 Ieraioal Coferece o Idusrial Egieerig ad Operaios Maageme Isabul, urey, July 3 6, 202 A eeralized Cos Malmquis Ide o he Produciviies of Uis wih Negaive Daa i DEA Shabam Razavya Deparme

More information

LINEAR 2 nd ORDER DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS

LINEAR 2 nd ORDER DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS Diol Bgyoko (0) I.INTRODUCTION LINEAR d ORDER DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS I. Dfiiio All suh diffril quios s i h sdrd or oil form: y + y + y Q( x) dy d y wih y d y d dx dx whr,, d

More information

Dr. Junchao Xia Center of Biophysics and Computational Biology. Fall /21/2016 1/23

Dr. Junchao Xia Center of Biophysics and Computational Biology. Fall /21/2016 1/23 BIO53 Bosascs Lcur 04: Cral Lm Thorm ad Thr Dsrbuos Drvd from h Normal Dsrbuo Dr. Juchao a Cr of Bophyscs ad Compuaoal Bology Fall 06 906 3 Iroduco I hs lcur w wll alk abou ma cocps as lsd blow, pcd valu

More information

Learning objectives. Three models of aggregate supply. 1. The sticky-wage model 2. The imperfect-information model 3. The sticky-price model

Learning objectives. Three models of aggregate supply. 1. The sticky-wage model 2. The imperfect-information model 3. The sticky-price model Larig objctivs thr modls of aggrgat supply i which output dpds positivly o th pric lvl i th short ru th short-ru tradoff btw iflatio ad umploymt kow as th Phillips curv Aggrgat Supply slid 1 Thr modls

More information

Chapter 9 Review Questions

Chapter 9 Review Questions Chapr 9 Rviw Qusions. Using h - modl, show ha if marks clar and agns hav raional xpcaions hn mporary shocks canno hav prsisn ffcs on oupu. If marks clar and agns hav raional xpcaions hn mporary produciviy

More information

H2 Mathematics Arithmetic & Geometric Series ( )

H2 Mathematics Arithmetic & Geometric Series ( ) H Mathmatics Arithmtic & Gomtric Sris (08 09) Basic Mastry Qustios Arithmtic Progrssio ad Sris. Th rth trm of a squc is 4r 7. (i) Stat th first four trms ad th 0th trm. (ii) Show that th squc is a arithmtic

More information

Adomian Decomposition Method for Dispersion. Phenomena Arising in Longitudinal Dispersion of. Miscible Fluid Flow through Porous Media

Adomian Decomposition Method for Dispersion. Phenomena Arising in Longitudinal Dispersion of. Miscible Fluid Flow through Porous Media dv. Thor. ppl. Mch. Vol. 3 o. 5 - domia Dcomposiio Mhod for Disprsio Phoma risig i ogiudial Disprsio of Miscibl Fluid Flow hrough Porous Mdia Ramakaa Mhr ad M.N. Mha Dparm of Mahmaics S.V. Naioal Isiu

More information

Acquisition of Context-based Active Word Recognition by Q-Learning Using a Recurrent Neural Network

Acquisition of Context-based Active Word Recognition by Q-Learning Using a Recurrent Neural Network Acquisiio of Cox-basd Aciv Word Rcogiio by Q-Larig Usig a Rcurr Nural Nwork Ah Afif Mohd Faudzi 1 ad Kasuari Shibaa 3 1 Kyushu Uivrsiy, Fukuoka, Japa, Uivrsii Malaysia Pahag, Malaysia, afif@cig.s.kyushu-u.ac.jp

More information

Nonlinear PID-based analog neural network control for a two link rigid robot manipulator and determining the maximum load carrying capacity

Nonlinear PID-based analog neural network control for a two link rigid robot manipulator and determining the maximum load carrying capacity Noliar PID-basd aalog ural work corol for a wo lik rigid robo maipulaor ad drmiig h maximum load carryig capaciy Hadi Razmi Aabak Mashhadi Kashiba Absrac A adapiv corollr of oliar PID-basd aalog ural works

More information

Lecture 12: Introduction to nonlinear optics II.

Lecture 12: Introduction to nonlinear optics II. Lcur : Iroduco o olar opcs II r Kužl ropagao of srog opc sgals propr olar ffcs Scod ordr ffcs! Thr-wav mxg has machg codo! Scod harmoc grao! Sum frqucy grao! aramrc grao Thrd ordr ffcs! Four-wav mxg! Opcal

More information

THE EFFECT OF SHEAR RATE ON APPARENT VISCOSITY FOR DIFFERENT PULP SUSPENSIONS

THE EFFECT OF SHEAR RATE ON APPARENT VISCOSITY FOR DIFFERENT PULP SUSPENSIONS 5h Iraioal Cofrc o Mchaics ad Marials i Dsig THE EFFECT OF SHEAR RATE ON APPARENT VISCOSITY FOR DIFFERENT PULP SUSPENSIONS SYNOPSIS A. Vaz, C. Gil, R. Simõs, J. Silvy Dparamo d Ciêcia Tcologia do Pl da

More information

Triple Play: From De Morgan to Stirling To Euler to Maclaurin to Stirling

Triple Play: From De Morgan to Stirling To Euler to Maclaurin to Stirling Tripl Play: From D Morga to Stirlig To Eulr to Maclauri to Stirlig Augustus D Morga (186-1871) was a sigificat Victoria Mathmaticia who mad cotributios to Mathmatics History, Mathmatical Rcratios, Mathmatical

More information

Fourier Techniques Chapters 2 & 3, Part I

Fourier Techniques Chapters 2 & 3, Part I Fourir chiqus Chaprs & 3, Par I Dr. Yu Q. Shi Dp o Elcrical & Compur Egirig Nw Jrsy Isiu o chology Email: shi@i.du usd or h cours: , 4 h Ediio, Lahi ad Dog, Oord

More information

Research Article Modelling of Rehydration of Freeze-dried Dumpling Wrapper

Research Article Modelling of Rehydration of Freeze-dried Dumpling Wrapper Rsarch Joural of Applid Scics, Egirig ad Tchology 1(5): 556-561, 16 DOI:1.196/rjas.1. 683 ISSN: 4-7459; -ISSN: 4-7467 16 axwll Sciific Publicaio Corp. Submid: Spmbr 1, 15 Accpd: Ocobr 3, 15 Publishd: arch

More information

Pricing and Hedging of Long-term Futures and Forward Contracts by a Three-Factor Model

Pricing and Hedging of Long-term Futures and Forward Contracts by a Three-Factor Model CIRJE-F-68 Pricig ad Hdgig of Log-rm Fuurs ad Forward Coracs by a hr-facor Modl Kichiro Shiraya Mizuho-DL Fiacial chology Co. Ld. Akihiko akahashi Uivrsiy of okyo April 009 CIRJE Discussio Paprs ca b dowloadd

More information

Chap 2: Reliability and Availability Models

Chap 2: Reliability and Availability Models Chap : lably ad valably Modls lably = prob{s s fully fucog [,]} Suppos from [,] m prod, w masur ou of N compos, of whch N : # of compos oprag corrcly a m N f : # of compos whch hav fald a m rlably of h

More information

P a g e 5 1 of R e p o r t P B 4 / 0 9

P a g e 5 1 of R e p o r t P B 4 / 0 9 P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e

More information

An Indian Journal FULL PAPER. Trade Science Inc. A stage-structured model of a single-species with density-dependent and birth pulses ABSTRACT

An Indian Journal FULL PAPER. Trade Science Inc. A stage-structured model of a single-species with density-dependent and birth pulses ABSTRACT [Typ x] [Typ x] [Typ x] ISSN : 974-7435 Volum 1 Issu 24 BioTchnology 214 An Indian Journal FULL PAPE BTAIJ, 1(24), 214 [15197-1521] A sag-srucurd modl of a singl-spcis wih dnsiy-dpndn and birh pulss LI

More information

4.3 Design of Sections for Flexure (Part II)

4.3 Design of Sections for Flexure (Part II) Prsrssd Concr Srucurs Dr. Amlan K Sngupa and Prof. Dvdas Mnon 4. Dsign of Scions for Flxur (Par II) This scion covrs h following opics Final Dsign for Typ Mmrs Th sps for Typ 1 mmrs ar xplaind in Scion

More information

Lecture 1: Photoconductors and p-i-n Photodiodes

Lecture 1: Photoconductors and p-i-n Photodiodes Lcur 1: Poocoucors a p-i- Pooios Isrucor: Mig C. Wu Uivrsiy of Califoria, Brkly Elcrical Egirig a Compur Scics Dp. 1 Prof. Mig Wu Poocors Covrs lig o lcric sigals Mai yps of poocors Poocoucors P-i- pooios

More information

Statistics 3858 : Likelihood Ratio for Exponential Distribution

Statistics 3858 : Likelihood Ratio for Exponential Distribution Statistics 3858 : Liklihood Ratio for Expotial Distributio I ths two xampl th rjctio rjctio rgio is of th form {x : 2 log (Λ(x)) > c} for a appropriat costat c. For a siz α tst, usig Thorm 9.5A w obtai

More information

Option 3. b) xe dx = and therefore the series is convergent. 12 a) Divergent b) Convergent Proof 15 For. p = 1 1so the series diverges.

Option 3. b) xe dx = and therefore the series is convergent. 12 a) Divergent b) Convergent Proof 15 For. p = 1 1so the series diverges. Optio Chaptr Ercis. Covrgs to Covrgs to Covrgs to Divrgs Covrgs to Covrgs to Divrgs 8 Divrgs Covrgs to Covrgs to Divrgs Covrgs to Covrgs to Covrgs to Covrgs to 8 Proof Covrgs to π l 8 l a b Divrgt π Divrgt

More information

Control Systems (Lecture note #6)

Control Systems (Lecture note #6) 6.5 Corol Sysms (Lcur o #6 Las Tm: Lar algbra rw Lar algbrac quaos soluos Paramrzao of all soluos Smlary rasformao: compao form Egalus ad gcors dagoal form bg pcur: o brach of h cours Vcor spacs marcs

More information