EC120 Lecture Notes PDF

Title EC120 Lecture Notes
Course Introduction to Microeconomics
Institution Wilfrid Laurier University
Pages 72
File Size 242.9 KB
File Type PDF
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Summary

EC 120 Structure of Assessments - DSM - on MyEconLab - before class - iClicker - in-class - Homework assignments - on MyEconLab - after class - Review Quizzes - before tests/exams What is the Value of Human Life? - based on the spending in Canada via cost-benefit analysis, approximate val of a human...


Description

EC120 St r uc t ur eofAs s es s ment s

-DSM -onMyEconLab-bef or ecl as s -i Cl i c k er-i nc l as s -Homewor kas s i gnment s-onMy Ec onLab-af t erc l as s -Revi ewQui z z es-bef or et est s / ex ams

Whati st heVal ueofHumanLi f e ?

-basedont hes pendi ngi nCanadav i acos t benefitanal y s i s,appr ox i mat ev alofahumanl i f ei nCanadai s$5m ( $2m -$10m)

-der i v edf r om peopl e’ sdec i s i ons -howmuchmor edoy ouneedt oear nt ot ak eamor edanger ousj ob? -howmucht i mear epeopl ewi l l i ngt ot ak et omak es ur et hei rk i dsar es af e ? -et c

KeyConcept s

-oppor t uni t yc os t :whati st het r adeoffi nv ol v edi nadec i s i on? -mar gi nalcos t :whati st heappr opr i at edi mens i onf oradec i s i on? -posi t i v ev snor mat i v equest i ons :whatques t i onsdoeconomi s t sf ocuson? -posi t i v e:t her ei sa“ cor r ec t ”ans wer -nor mat i ve:ans werbas edonv al ues,manydi ffer entans wer swi t hs amei nf o -economi s t sl i k et of oc usonpos i t i v eques t i ons ,butwei ghi nonnor mat i v eques t i ons

1

Ec onomi s t sandGener alKnowl edge

-l i mi t edbyt het ool st heyc anus e,nott heques t i onst he yans wer -Economi c s:t hes t udyofhows oci et ymanagess c ar c er es our ces -Scar ci t y :t hel i mi t ednat ur eofs oc i et y’ sr es our ces -Al lr es our cesar es c ar c e,andt her ef or e,al lus eofr es our cesi nv ol v esanoppor t uni t y cos twher er es our c esc oul dhav ebeenusedi not herpl ac es

-Ther ef or e,c hoi c esonhowr es our c esar eus edmus tbemade -whomakest hes ec hoi c es ? -howmuchi nf odot heyhav et omak et hesechoi c es ? -whatf ac t or saffec tt hei rdec i s i onmak i ng? -mar k etv scommandv smi x ed? -mar k et :f r eemar k etdi c t at esr es our ces -command:gover nmentdi ct at esr es our c es -mi x ed:bot h -Mi c r oi st hes t udyoft hedec i s i onsofi ndi vi dual s,hous ehol ds ,andfi r ms ,andhowt hey i nt er ac ti nt heec onomy

-Macr oi st hes t udyoft heaggr egat edec onomi csout comess uc hasi nfl at i on,unempl oyment ,oreconomi cgr owt h

-Economi c sus esmat hors t at s -demonst r at eswher ei nt ui t i onbr eak sdown -assessesf eedbackeffec t s -gr aphsal l owust ovi s ual i z ec ompl i cat edpr obl emsi nt os i mpl eans wer s -Cor r el at i onv sCaus at i on

2

-I nt er pr etv er yc ar ef ul l y -doesAcauseB -doesBcauseA -ext er nalf ac t or s ? -r andom c hanc e ? -Rat i onal i t yandChoi c e -economi s t sgener al l yas sumepeopl ear er at i onal ,andt heyar enot -doesnoti mpl yt hatpeopl ear eal way sr i ght ,orc er t ai naboutout c omes -r at i onal i t yi mpl i est hatpeopl emak ec hoi cesbas edonr eas ons -economi csi sbasedonmodel l i ngt hepr oc essofmak i ngadec i s i on

Oppor t uni t yCos t

-i fr es our c esar es c ar c e,al lc hoi cesi mpl yt her ei sanal t er nat i v eus eofs ai dr esour ce -t heal t er nat i v esar edes c r i besbyv al ueas“ oppor t uni t ycos t ” -dependsonyourbestal t er nat i v eopt i on-ex :goi ngt ouni v er s i t yv swor k i ngf ul lt i me -sunkcost s :c os t st hatwi l l notber ecoupedaf t eradec i s i onhasbeenmade,s unk cos t smak eoppor t uni t yc os tl ower

-CostBenefitAnal y s i s -benefitvscost -whati st hebenefitofac upofc offee ? -whati st hec os tofac upofcoffee ? -Exampl e:Oppor t uni t yCos tofac upofc offee -$2,ort hev al ueofwhatc anbepur c has edof$2 3

-Exampl e:oppor t uni t yc os tofr unni ngabus i nes s -$50, 000r ev enue,nocos t s -useper s onalc omp,wor kf r om home -Account i ngpr ofit :t ax ,wr i t eoffper s onali t ems ,r es ti spr ofi t -howmuchmoneyi smade ? -Economi cpr ofit :oppor t uni t ycostofus edt i me( ot herj ob,et c ) ,oppor t uni t yc ost sofusi ngper s onali t ems( v er yl owt onone,y ouwoul downt hem any way s )

-doIoper at et hebus i nessornot ?

“ HowManyPeopl ear ePoori nCanada?”

-commoni t emsi nt henews ,s omet i mesf ocus edonc hi l dr en -nor mat i v e-whatdoesi tmeant obepoor ? -posi t i v e-gi v enadefi nedbenc hmar k ,howmanypeopl ehav ei ncomebel owt hat ? -St at sCandefi nesaLowI nc omec ut offl i ne -expl i c i t l y“ not ”apov er t yl i ne -i npr act i ce-i sus edasonei nCanada -i n2012,9. 7% off ami l i eshav eani nc omebel owt hel owi nc omec ut off

Pos i t i vev sNor mat i v eQues t i ons

-i sec onomi csas c i ence ?doesi tmat t er ? -posi t i v eques t i on-aques t i ont hatpot ent i al l yhasar i ghtanswer -nor mat i v equest i on-aques t i ont hatc oul dnothav ear i ghtans wer

4

Model l i ngEc onomi cAc t i v i t y

-model sar es i mpl i fi c at i ons-onl ys howi mpor t anti nf or mat i on -economi cmodel sar eus ual l yt abl esorgr aphs -model sus e“ unr eal i st i c”as s umpt i ons -usedt ohi ghl i ghtpar t i cul ari s s uesandas pec t s ,nott hei s s ueasawhol e -assumpt i onss i mpl i f ypr obl ems -mar k et sar eas s umedt obeper f ec t l yc ompet i t i v e -PPF-economysi mpl i fi edt o2goods -pr oduct i onpos s i bi l i t i esc ur v e -St ubber t :gunsandbut t er -“ c et er i sper abi s ”=al lt hi ngsr emai ni ngequal

Pr oduct i onPos si bi l i t i esFr ont i er( Cur v e)

-agr aphs howi ngt hepos s i bl ec ombi nat i onsofout put -si mpl i fi edt ot woout put swi t honei nput -hi ghl i ght sc onc ept s -t r adeoff:oppor t uni t yc os t ,t hec onc eptofs car c i t y -effici enc y :us i ngt her es our c eswehav et odos omet hi ng

Cons t r uc t i ngaPPF( PPC)

-consi der :100, 000hr sofl abour ,1000hr st obui l dahous e,100hr st obui l dac ar -gr aphal loft hepos s i bl ec ombi nat i onsoft het wo 5

-oneaxi s :c ar s ,ot herax i s :hous es -anyt hi ngi nsi deoft hel i neoroni t :f eas i bl e -anyt hi ngal ongt hel i ne:effici ent-us i ngt hel abourt oi t smax i mum pot ent i al -anyt hi ngout s i det hel i ne:unf easi bl e-needmor er es our c esi nor dert oi ncr eas e pr oduc t i on

-Oppor t uni t yc ostandPPF -movi ngal ongt hePPFs howsoppor t uni t yc os t-mor eofonet hi ngbei ngpr oduc ed meansl es soft heot herc anbepr oduc ed

-Oppor t uni t yc os tofXi st he( negat i v e)s l ope -i nt heex ampl eabov e:oppor t uni t yc os tofahousei s10c ar s -Oppor t uni t yc os tofYi st he( negat i v e)r ec i pr oc als l ope -i nt heex ampl eabov e:t heoppor t uni t yc os tofacari s1/ 10hous e -Shapesoft hePPF -Li near -const antoppor t uni t yc os t( s l ope)meanst het r adeoffbet weent het wonev er c hanges

-basi cf or m oft hePPFmodel -Sl oped( awayf r om or i gi n) -t heoppor t uni t yc os tc hangesov ert hec our s eoft hecur ve -i fr es our c esar ebet t erus edf oroneoft hepos si bi l i t i est hant heot her( ex :mec hani cst obui l dc ar s ,c ar pent er st obui l dhous es )t hent hec ur v ewi l l2nds l ope outf r om t heor i gi n

-Sl oped( t owar dor i gi n) -ver yr ar e,notusedi nt hec our s e

6

-onl ypos s i bl ei nv er ys pec i fi cci r c ums t ances( ex :l i mi t edbyt i me) -I fr es our c esi ncr ease,t hePPFs hi f t sout war d( par al l elt r ans l at i on) -oppor t uni t ycos tdoesnotc hange,butt ot alpr oduc t i oni nc r eas es -i feffic i enc yi nc r eas es ,t hes l opeoft hec ur v ewi l lc hange -ex:popul at i onbecomesbet t eratbui l di nghous es ,c hangest hes l opeoft hePPF c ur v e

-oppor t uni t ycos tdec r easesasawhol e

Whati saMar k et ?

-gr oupofbuy er sands el l er sofagoodors er v i c e -canbeor gani z edordi s or gani z ed -si z eofamar k etdependsont henat ur eoft hegood( ex :s t oc kmar k et s ) -keyi s s uef orgover nmentpol i c y-Canadi anCompet i t i onBur eau -CCBensur est hatCanadi anbus i nes s esandcons umer spr os peri nac ompet i t i ve andi nnov at i v emar ket pl ace

Whati sCompet i t i on?

-compet i t i v emar k et sr equi r et hatt her ear emanybuyer swi t hf r eec hoi c e -homogeneouspr oduct s-nobr anddi ffer ent i at i on -numer ousbuy er sands el l er s -i ft her ei sonl yones el l er-monopol y -i ft her ear eaf ews el l er s-ol i gopol y -per f ec tcompet i t i oni sv er yr ar e,butagoods t ar t i ngpoi nt

7

T er mi nol ogyar oundDemand

-Quant i t yDemanded( QD) -gi v enanamountofagoodbuy sar ewi l l i ngandabl et opur c has eatagi v enpr i c e -whenapr i ceofagoodc hanges ,QDc hanges -LawofDemand -aspr i c er i s es ,quant i t ydemandedf al l s -DemandSchedul e -t abl es howi ngt her el at i onshi pbet weenpr i ceandquant i t ydemanded -DemandCur v e -gr aphoft hedemandsc hedul e -Mar ketDemandv sI ndi v i dualDemand -mar k etdemandaddsupi ndi v i dualdemand -summi ngi ndi v i dualdemandc ur v eshor i z ont al l y

Shi f t i ngt heDemandCur ve

-I nc ome -r i s i ngi nc omei nc r eas esdemand:nor malgood -r i s i ngi nc omer educ esdemand:i nf er i orgood -Pr i cesofRel at edGoods -i nc r eas epr i ceXi nc r eas esdemandf orY:s ubs t i t ut egood -i nc r eas epr i ceXr educesdemandf orY:compl ement ar ygood -Tast es :di ffic ul tt opr edi ct ,butmaybemeas ur ed

8

-Expect at i ons :f ut ur epr i c esofadur abl egood( l ongt er m good) -pr i c eex pect edt ogodown:demandl oweri ns hor tt er m -pr i c eex pect edt or i s e:demandhi gheri ns hor tt er m -NumberofBuyer s :affec t smar k etdemand( demandasawhol e) -mor epeopl ei nt hemar ket=buymor es t uff

Defini ngSuppl y

-Quant i t ySuppl i ed( QS) -amountofagoodt hatsel l er sar ewi l l i ngandabl et os el l -LawofSuppl y -aspr i c er i s es ,quant i t ys uppl i edal s or i s es -Suppl ySc hedul e -t abl es howi ngt her el at i onshi pbet weenpr i ceandquant i t ys uppl i ed -Suppl yCur v e -gr aphoft hes uppl ys c hedul e -Mar ketSuppl yv sI ndi v i dualSuppl y -t hes uppl yofamar k etasawhol ev st hes uppl yofones el l erofagood

Shi f t i ngt heSuppl yCur v e

-i nputpr i c e:wages ,s uppl i es ,c api t alc os t -t ec hnol ogy :abi l i t yt opr oduc ewi t hf eweri nput s -expect at i ons :f ut ur epr i c eofadur abl egood -numberofsel l er s :affec t smar k ets uppl y 9

I nt er s ec t i onofSuppl yandDemand

-equi l i br i um:i nt er s ec t i onofs uppl yanddemand -equi l i br i um pr i c e:t hepr i c eatt hei nt er s ec t i onofs uppl yanddemand -equi l i br i um quant i t y :t hepr i c eat… “ ” -excesssuppl y :QS>QD -excessdemand( s hor t age) :QD>QS -gr aphs :Quant i t yont heXax i s ,Pr i c eont heYax i s -downwar ds l opi ngDcur ve,upwar ds l opi ngSc ur v e

Changesi nEqui l i br i um

-whi c hcur veshi f t s-s uppl y ,demand,orbot h? -whi c hdi r ect i ondot heys hi f t ? -dr awt hegr aph,andnot et hec hangei nQ andP -onexams-t ak et het i meanddr awt hegr aph

WhendoesEl as t i c i t yMat t er ?

-busi nes ss t r at egy -opt i malpr i c i ngs t r at egi esf orc ompani es -t axpol i c y -whathappensi fwer ai s et ax esont her i c hes t1%? -envi r opol i c y -whatwoul dbet heeffectofagas ol i neorc ar bont ax ? 10

-i nt er nat i onali s s ues -whyar ef oodpr i c eshi ghl yv ol at i l e ? -answer st hes eques t i onsdependi npar tonpr i c eel as t i c i t yofdemandorsuppl y

Bey onds uppl yanddemand

-whatar et hec ons equencesofadr oughtonf oodpr i ces ?( i mpl i edr educ eds uppl y )

El as t i ci t y

-pr opor t i onat el y ,howmuc hdoesonef ac t orc hangeaswev ar yanot her -t hepr i ceel as t i c i t yofdemand -E=Per cent agec hangei nQD /Per c ent agechangei nPr i ce -t hepr i ceel as t i c i t yofs uppl y -E=Per cent agec hangei nQS/Per cent agec hangei nPr i ce -t her ef or e,E=%changei nQS/%c hangei nP -E=%QX/%P

El as t i ci t yofDemand-t y pi c al l ynegat i v e

-i nel ast i cdemand:0negat i v es l ope( l awofDR) -shor tr un— s omef ac t or sar efix ed,s omec ost sar es unk -t ot alc ost=t ot al fix edc ost s+t ot alv ar i abl ec os t s -t ot alfi x edcos t s :t hi ngsy oucannotc hoos et oc hange -costoffixedf ac t or ss uc hascapi t al( bui l di ngs ,equi pment ,et c ) -doesnotchangewi t ht hel ev el ofout put 25

-t ot alv ar i abl ec os t s :t hi ngsy oucanc hooset ochange -costofvar i abl ei nput s,s uc hasl abour -i nc r eas eswi t hhel ev elofout put -aver agec os tmeas ur es -aver aget ot alc os t :ATC=TC/Q -ATC=AFC+AVC;ATCgr aphwi l lal way sbe“ above”ot hert wogr aphs -aver agefix edcos t :AFC=TFC/Q -t hi si ss pr eadi ngov er headov ermor euni t s :get ssmal l erasy ougetbi gger -al way sdec r eas i ngasquant i t yi nc r eases -aver agev ar i abl ec ost :AVC=TVC/Q -mar gi nalcos tmeasur es -i nc r eas ei nv ar i abl ec os t sf oranaddi t i onaluni tofout put -changei nVC/c hangei nQ -mar gi nalc os tgr aphi nt er s ec t sav er agev ar i abl ecostati t smi ni mum -fixedcost sdonotaffec tt hi s -maydecr eas eori nc r eas e -di mi ni s hi ngmar gi nal pr oductr el at edt oi nc r eas i ngmar gi nal cos t

Capac i t yandEffici entScal e— t r yt ouseeffic i entsc al emor eof t en?

-effici ents cal e:t hel owes tl ev el ofout putwi t hmi ni mum av er aget ot alcos t s -capaci t y:t hel ar ges tl ev elofout putwi t hmi ni mum av er aget ot alc os t s

Pr oduct i onFunc t i onandTot alCostCur v e 26

-assumi ngi nc r eas i ngandt hendi mi ni s hi ngmar gi nalpr oduc t -pr oduc t i onf unc t i on:i nc r eas i ngs l opeunt i ldi mi ni shi ngr et ur ns ,whent hes l opegoest o dec r eas i ng

-fir s tf ew wor k er sar enotv er ypr oduc t i v e,enoughwor k er sbec omespr oduc t i v e,t oo manywor k er sdi mi ni s hespr oduc t i v i t y

-t ot alc ostc ur v e:s t ar t sf r om y i nt( fix edc os t s ) ,dec r eas i ngs l opeunt i ldi mi ni s hi ngr et ur ns ,whens l opegoest oi ncr eas i ng

-fir s tf ew wor k er sar enotpr oduc t i ve,andt her ef or ei nc r eas i ng,enoughwor k er si nc r eas espr oduc t i vi t y ,andev ensoutcos tt odec r easi ng,t oomanywor k er sdi mi ni s hespr oduc t i v i t y ,andt her ef or ei nc r eas i ngc os tagai n

-poi ntonei t herc ur v edependsonwher ei nt hel i f ecy c l eac ompanyi s -canbeusedt oder i v es uppl yanddemandc ur v es

Shor tRunCos tCur v es

-aver aget ot alcos t( ATC) ,av er agefi x edcost( AFC) ,av er agev ar i abl ec os t( AVC) ,mar gi nalcos t( MC)

-Xaxi s :out put ,Yax i s :c ost -AFC:downwar ds l opi ngcur ve( fi x edcos t/i nc r eas i ngout put ) -AVC:st ar t smedi um,bot t omsoutt oami ni mum >i ncr eas i ng,( i ncr eas i ngc os twi t hi ncr eas i ngout put ,di mi ni shi ngr et ur nsonout putc r eat esi nc r eas i ngc os tathi gherout put s )

-ATC:st ar t shi gh,dec r easest oami ni mum,>i nc r easi ng,( fi x edc os t scr eat ehi gh st ar t i ngpoi nt ,i nc r eas i ngeffic i enc yl ower st ot alc os t swi t hi nc r eas edout put ,r eac hesa mi ni mum atpoi ntofdi mi ni s hi ngr et ur ns )

-MC:samest ar t i ngpoi ntasAVC,cur v ei nc r eas essot hati tgoest hr ought het womi ni mum poi nt sofAVCandATC

27

TheLongRun— nofix edf act or s

-fir mschoos ehowmuchc api t alandl abourt ous ei npr oduct i on -pr ofitmax i mi z at i oni mpl i esc os tmi ni mi z at i on -costmi ni mi z at i on— c hoos i ngt hel eas tc os t l ywayt opr oduc eagi v enquant i t yof out put

-l ongr unc os tmi ni mi z at i on— equat emar gi nalpr oduc t i v i t yperdol l arspent ac r os sc at egor i es

-MP( c api t al )/P( capi t al )=MP( l abour )/P( l abour ) -i ft hi swasnott r ue— adj us tus eofcapi t alandl abourt or educec ost -pr ofi tmax i mi zat i on— r equi r esel ec t i ngt hec or r ec tamountofout putt opr oduc e

Pr i nci pl eofSubst i t ut i on

-i fi nputpr i c esc hanges ,fir mswi l ladj ustpr oduc t i ont ous emor eoft her el at i v el y cheaperi nput , andl essoft her el at i v el ymor ee xpens i v ef act or

-ver ys i mi l art os ubs t i t ut i oneffec t si nchapt er6( 1s tmi dt er m) -l ot sofe x ampl es : -banksl eani ngt owar dsaut omat i on— TDCas e -GoodLi f eFi t nes sr epl ac i ngt onsofj obswi t haut omat i oni nt henearf ut ur e -pr oduc t i oni nc ount r i eswi t hl owwagesus esmor el abour ,l es sc api t al -cl i mat ec hangepol i c y :i ft hepr i c eofener gygoesup,compani eswi l ls hi f taway f r om us i ngener gyandt owar dst hi ngst hatus el es sener gy— butbyhowmuc h?

I s oquant sanI s oc os t— ani nt r oduc t i on( Kc api t al ,Ll abour ,Q out put )

-Xaxi s :l abour ;Yax i s :capi t al

28

-I s ocos tl i ne:st r ai ghtl i nec onnec t i ngXandYax i s -anypoi ntal ongt hel i nei st hes amec ost ,wi t hdi ffer entcombi nat i onsofKandL -I s oquant :c ur v et ouc hi ngas i ngul arpoi ntont hei soc ostl i ner epr es ent i ngout put -anypoi ntal ongt hei s oquantc ur v er epr es entpos s i bl ec ombi nat i onsofKandLt hat pr oduc easi ngl equant i t yofout put( Q)

-t hepoi ntt ouc hi ngt hei s oc ostc ur v ei st hel owes tcos topt i onf orafi r mt opr oduc ea gi v enQ ofagoodwi t haquant i t yof( L,K)atpoi nt( X,Y)

-i nt hel ongr un,i soc os tc ur v esc anc hange,asfir msc hangeamountofLandK -i nt hev er yl ongr un,i s oquantc ur v escanc hange,ast ec hnol ogyc anal l owf ormor e effic i entus esofLandK

LongRunAv er ageTot alCos tCur ves( ATC)

-shor t r unATCc ur v esar egener al l yUs haped -fir msc anonl yadj us tl abour -l ongr un— fi r msc anadj us tc api t alandl abour -fir msc anshi f tt hei rav er aget ot al c ostc ur v ebyc hangi ngc api t al( bui l di nganot her f act or yt omi t i gat edi mi ni s hi ngr et ur ns ,et c )

-i nt hel ongr un,fir msar edec i di ngwhi c hoft hei rs hor t t er m opt i onst he ywantt o pr oduc ei nt hef ut ur e

-t hel ongr unATCc ur v ei st he“ mi ni mum”ofal loft heopt i onsf ort hel ongr un -al way sflat t ert hant heATCc ur v esi nt heshor tr un,asi ti st hemi ni mum ofal lof t heopt i onsf ors hor tr unATCi nt hef ut ur e

TheVer yLongRun— Changesi nTec hnol ogy

-shor tr un— fi r msv ar yl abouri nput s 29

-chooseonespotonashor t r unATCc ur v e -l ongr un— fi r msc hoos ehow muchcapi t alandl abourt ous ei npr oduc t i on -chooseonespotonal ongr unATCcur v e -ver yl ongr un— fi r msc anc hanget ec hnol ogy -changet hel ongr unATCc ur v e -wi der angeofopt i onsf orfir ms :l owercos t s ,i nc r eas ecapaci t y ,newpr oduc t s ,et c

T echnol ogi c alChangesandLongRunGr owt h

-t ec hnol ogi c alc hangei sc ons i der edt hecor edr i v erofl ongr uneconomi cgr owt h -over al lmeas ur esoft ec hnol ogygr owt har edi ffic ul t— f oc usonpr oduc t i v i t y( out put perempl oy edwor k er ;Q/L)

-r at eofgr owt hofpr oduc t i vi t yi nCanadal owert hani nt heUSAorUK -t ec hnol ogyc hangescanbedemanddr i v en -newpr oduc t sormodi fi cat i onst oex i s t i ngpr oduc t s :whatdopeopl ewant ? -t ec hnol ogyc hangec anbedr i v enbys uppl yf ac t or s -changi ngpr oduct i ont ec hni quest ous ef ewerorc heaperi nput s -i mpr ovi ngt hequal i t yofi nput s ,mayowner scos t s ,oral t erpr oduc t s -gover nmentpol i c ycanaffectt ec hnol ogyc hange -Pat entLaw— cr eat i ngnewpr oduc t st hatar epat ent edbyafir m? -subsi di z edpr i v at eorpubl i cr es ear c h( t axi ncent i ves ,uni v er s i t i es ,et c )

LongRunv sVer yLongRun

-howdofir msr es pondst oc hangest hepr i ceofi nput s ,s uc haswages ?( mi nwage) 30

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