Theprofit，suchasitisrepresentedhere，isthusthesameassurplus-value，onlyinamystifiedformthatisnonethelessanecessaryoutgrowthofthecapitalistmodeofproduction。Thegenesisofthemutationofvaluesthatoccursinthecourseoftheproductionprocess，mustbetransferredfromthevariableportionofthecapitaltothetotalcapital，becausethereisnoapparentdistinctionbetweenconstantandvariablecapitalintheassumedformationofthecost-price。Becauseatonepolethepriceoflabour-powerassumesthetransmutedformofwages，surplus-valueappearsattheoppositepoleinthetransmutedformofprofit。
Wehaveseenthatthecost-priceofacommodityissmallerthanitsvalue。SinceC=k+s，itfollowsthatk=C-s。TheformulaC=k+sreducesitselftoC=k，orcommodity-value=commoditycost-priceonlyifs=0，acasewhichneveroccursonthebasisofcapitalistproduction，althoughpeculiarmarketconditionsmayreducethesellingpriceofcommoditiestothelevelof，orevenbelow，theircost-price。
Hence，ifacommodityissoldatitsvalue，aprofitisrealisedwhichisequaltotheexcessofitsvalueoveritscost-price，andthereforeequaltotheentiresurplus-valueincorporatedinthevalueofthecommodity。
Butthecapitalistmaysellacommodityataprofitevenwhenhesellsitbelowitsvalue。Solongasitssellingpriceishigherthanitscost-price，thoughitmaybelowerthanitsvalue，aportionofthesurplus-valueincorporatedinitisalwaysrealised，thusalwaysyieldingaprofit。Inourillustrationthevalueofthecommodityis£；600，andthecost-price£；500。
Ifthecommodityissoldat£；510，520，530，560or590，itissoldrespectively£；90，80，70，40，or10belowitsvalue。Yetaprofitof£；10，20，30。60，or90respectivelyisrealisedinitssale。Thereisobviouslyanindefinitenumberofsellingpricespossiblebetweenthevalueofacommodityanditscost-price。Thegreaterthesurplus-valueelementofthevalueofacommodity，thegreaterthepracticalrangeoftheseintermediateprices。
Thisexplainsmorethanjusttheeverydayphenomenaofcompetition，suchascertaincasesofunderselling，abnormallylowcommodity-pricesincertainlinesofindustry[5]，etc。Thefundamentallawofcapitalistcompetition，whichpoliticaleconomyhadnothithertograsped，thelawwhichregulatesthegeneralrateofprofitandtheso-calledpricesofproductiondeterminedbyit，rests，asweshalllatersee，onthisdifferencebetweenthevalueandthecost-priceofcommodities，andontheresultingpossibilityofsellingacommodityataprofitunderitsvalue。
Theminimallimitofthesellingpriceofacommodityisitscost-price。
Ifitissoldunderitscost-price，theexpendedconstituentelementsofproductivecapitalcannotbefullyreplacedoutofthesellingprice。Ifthisprocesscontinues，thevalueoftheadvancedcapitaldisappears。Fromthispointofviewalone，thecapitalistisinclinedtoregardthecost-priceasthetrueinnervalueofthecommodity，becauseitisthepricerequiredforthebareconservationofhiscapital。Butthereisalsothis，thatthecost-priceofacommodityisthepurchasepricepaidbythecapitalisthimselfforitsproduction，thereforethepurchasepricedeterminedbytheproductionprocessitself。Forthisreason，theexcessvalue，orthesurplus-value，realisedinthesaleofacommodityappearstothecapitalistasanexcessofitssellingpriceoveritsvalue，insteadofanexcessofitsvalueoveritscost-price，sothataccordinglythesurplus-valueincorporatedinacommodityisnotrealisedthroughitssale，butspringsoutofthesaleitself。WehavegiventhisillusioncloserconsiderationinBookI(Kap。IV，2)[Englishedition:Ch。V，2——Ed。](”ContradictionsintheGeneralFormulaofCapital”)，butreverthereforamomenttotheforminwhichitwasreaffirmedbyTorrens，amongothers，asanadvanceofpoliticaleconomybeyondRicardo。”Thenaturalprice，consistingofthecostofproduction，or，inotherwords，ofthecapitalexpendedinraisingorfabricatingcommodities，cannotincludetheprofit……Thefarmer，wewillsuppose，expendsonehundredquartersofcornincultivatinghisfields，andobtainsinreturnonehundredandtwentyquarters。Inthiscase，twentyquarters，beingtheexcessofproduceaboveexpenditure，constitutethefarmer’sprofit；butitwouldbeabsurdtocallthisexcess，orprofit，apartoftheexpenditures……
Themastermanufacturerexpendsacertainquantityofrawmaterial，oftoolsandimplementsoftrade，andofsubsistenceforlabour，andobtainsinreturnaquantityoffinishedwork。Thisfinishedworkmustpossessahigherexchangeablevaluethanthematerials，tools，andsubsistence，bytheadvanceofwhichitwasobtained。”Torrensconcludestherefromthattheexcessofthesellingpriceoverthecost-price，orprofit，isderivedfromthefactthattheconsumers，”eitherbyimmediateorcircuitousbartergivesomegreaterportionofalltheingredientsofcapitalthantheirproductioncosts”。[6]
Indeed，theexcessoveragivenmagnitudecannotformapartofthismagnitude，andthereforetheprofit，theexcessvalueofacommodityoverthecapitalist’sexpenditures，cannotformapartoftheseexpenditures。
Hence，ifnootherelementthanthevalueadvanceofthecapitalistentersintotheformationofthevalueofacommodity，itisinexplicablehowmorevalueshouldcomeoutofproductionthanwentintoit，forsomethingcannotcomeoutofnothing。ButTorrensonlyevadesthiscreationoutofnothingbytransferringitfromthesphereofcommodity-productiontothatofcommodity-circulation。Profitcannotcomeoutofproduction，saysTorrens，forotherwiseitwouldalreadybecontainedinthecostofproduction，andtherewouldnotbeasurplusoverthiscost。Profitcannotcomeoutoftheexchangeofcommodities，repliesRamsay，unlessitalreadyexistedbeforethisexchange。Thesumofthevalueoftheexchangedproductsisevidentlynotalteredintheexchangeoftheseproducts，whosesumofvalueitis。Itisthesamebeforeandaftertheexchange。ItshouldbenotedherethatMalthusrefersexpresslytotheauthorityofTorrens[7]althoughhehimselfhasadifferentexplanationforthesaleofcommoditiesabovetheirvalue，orratherhasnoexplanationatall，sinceallargumentsofthissortnever，ineffect，failtobereducedtothesamethingastheonce-famednegativeweightofphlogiston。
Inasocialorderdominatedbycapitalistproductioneventhenon-capitalistproducerisgrippedbycapitalistconceptions。Balzac，whoisgenerallyremarkableforhisprofoundgraspofreality，aptlydescribesinhislastnovel，LesPaysans，howapettypeasantperformsmanysmalltasksgratuitouslyforhisusurer，whosegoodwillheiseagertoretain，andhowhefanciesthathedoesnotgivethelattersomethingfornothingbecausehisownlabourdoesnotcosthimanycashoutlay。Asfortheusurer，hethusfellstwodogswithonestone。Hesavesthecashoutlayforwagesandenmeshesthepeasant，whoisgraduallyruinedbydeprivinghisownfieldoflabour，deeperanddeeperinthespider-webofusury。
Thethoughtlessconceptionthatthecost-priceofacommodityconstitutesitsactualvalue，andthatsurplus-valuespringsfromsellingtheproductaboveitsvalue，sothatcommoditieswouldbesoldattheirvalueiftheirsellingpriceweretoequaltheircost-price，i。e。，ifitweretoequalthepriceoftheconsumedmeansofproductionpluswages，hasbeenheraldedtotheworldasanewlydiscoveredsecretofsocialismbyProudhonwithhiscustomaryquasi-scientificchicanery。Indeed，thisreductionofthevalueofcommoditiestotheircost-priceisthebasisofhisPeople’sBank。
Itwasearliershownthatthevariousconstituentelementsofthevalueofaproductmayberepresentedinproportionalpartsoftheproductitself。
Forinstance(BuchI，Kap。VI1，2，S。211/203)[Englishedition:Ch。IX，2，pp。220-21——Ed。]ifthevalueof20lbs。ofyarnis30shillings——namely24shillingsofmeansofproduction，3shillingsoflabour-power，and3shillingsofsurplus-value——thenthissurplus-valuemayberepresentedas1/10oftheproduct=2lbs。ofyarn。Shouldthese20lbs。ofyarnnowbesoldattheircost-price，at27shillings，thenthepurchaserreceives2lbs。ofyarnfornothing，orthearticleissold1/10belowitsvalue。
Butthelabourerhas，asbefore，performedhissurplus-labour，onlythistimeforthepurchaseroftheyarninsteadofthecapitalistyarnproducer。
Itwouldbealtogetherwrongtoassumethatifallcommoditiesweresoldattheircost-price，theresultwouldreallybethesameasiftheyhadallbeensoldabovetheircost-price，butattheirvalue。Forevenifthevalueofthelabour-power，thelengthoftheworking-day，andthedegreeofexploitationoflabourwerethesameeverywhere，thequantitiesofsurplus-valuecontainedinthevaluesofthevariouskindsofcommoditieswouldbeunequal，dependingonthedifferentorganiccompositionofthecapitalsadvancedfortheirproduction。[8]
FOOTNOTES[1]InBookI(Kap。VII，3，S。216/206ff。)[Englishedition:Ch。IX，3，225
ff——Ed。]wehavegiventheexampleofN。W。Seniortoshowwhatconfusionthismaycreateinthemindoftheeconomist。
[2]”Fromwhathasgonebefore，weknowthatsurplus-valueispurelytheresultofavariationinthevalueofv，ofthatportionofthecapitalwhichistransformedintolabour-power；consequently，v+s=v+Dv(orvplusanincrementofv)。Butthefactthatitisvalonethatvaries，andtheconditionsofthatvariation，areobscuredbythecircumstancethatinconsequenceoftheincreaseinthevariablecomponentofthecapital，thereisalsoanincreaseinthesumtotaloftheadvancedcapital。Itwasoriginally£；500，andbecomes£；590。”(BuchI，Kap。VII，1，S。203/195。)[Englishedition:Ch。IX，1，p。214——Ed。]
[3]Malthus，PrinciplesofPoliticalEconomy，2nded。，London，1836，p。268。
[4]”Capitalisthatwhichisexpendedwithaviewtoprofit。”Malthus，DefinitionsinPoliticalEconomy，London，1827，p。86。
[5]Cf。BuchI。Kap。XVIII，1，S。571/561ff。[Englishedition:Ch。XX，1，p。549ff——Ed。]
[6]R。Torrens，AnEssayontheProductionofWealth，London，1821，pp。51-53，and349。
[7]Malthus，DefinitionsinPoliticalEconomy，London，1853，pp。70，71。
[8]”Themassesofvalueandofsurplus-valueproducedbydifferentcapitals——thevalueoflabour-powerbeinggivenanditsdegreeofexploitationbeingequal——varydirectlyastheamountsofthevariableconstituentsofthesecapitals，i。e。，astheirconstituentstransformedintolivinglabour-power。”(Buch1，Kap。IX。S。312/303。)[Englishedition:Ch。XI，pp。306/307——Ed。]
Capital，Vol。3，Chapter2KarlMarxCAPITALVol。III
THEPROCESSOF
CAPITALISTPRODUCTIONASAWHOLEPartI
THECONVERSIONOFSURPLUS-VALUEINTOPROFITANDOFTHERATEOFSURPLUS-VALUE
INTOTHERATEOFPROFITCHAPTER2
TheRateofProfitThegeneralformulaofcapitalisM——C——M’。Inotherwords，asumofvalueisthrownintocirculationtoextractalargersumoutofit。
Theprocesswhichproducesthislargersumiscapitalistproduction。Theprocessthatrealisesitiscirculationofcapital。Thecapitalistdoesnotproduceacommodityforitsownsake，norforthesakeofitsuse-value，orhispersonalconsumption。Theproductinwhichthecapitalistisreallyinterestedisnotthepalpableproductitself，buttheexcessvalueoftheproductoverthevalueofthecapitalconsumedbyit。Thecapitalistadvancesthetotalcapitalwithoutregardtothedifferentrolesplayedbyitscomponentsintheproductionofsurplus-value。Headvancesallthesecomponentsuniformly，notjusttoreproducetheadvancedcapital，butrathertoproducevalueinexcessofit。Theonlywayinwhichhecanconvertthevalueofhisadvancedvariablecapitalintoagreatervalueisbyexchangingitforlivinglabourandexploitinglivinglabour。Buthecannotexploitthislabourunlesshemakesasimultaneousadvanceoftheconditionsforperformingthislabour，namelymeansoflabourandsubjectsoflabour，machineryandrawmaterials，i。e。，unlessheconvertsacertainamountofvalueinhispossessionintotheformofconditionsofproduction；forheisacapitalistandcanundertaketheprocessofexploitinglabouronlybecause，beingtheowneroftheconditionsoflabour，heconfrontsthelabourerastheownerofonlylabour-power。Asalreadyshowninthefirstbook[Englishedition:Vol。1，pp。168-69。714-16——Ed。]，itispreciselythefactthatnon-workersownthemeansofproductionwhichturnslabourersintowage-workersandnon-workersintocapitalists。
Thecapitalistdoesnotcarewhetheritisconsideredthatheadvancesconstantcapitaltomakeaprofitoutofhisvariablecapital，orthatheadvancesvariablecapitaltoenhancethevalueoftheconstantcapital；
thatheinvestsmoneyinwagestoraisethevalueofhismachineryandrawmaterials，orthatheinvestsmoneyinmachineryandrawmaterialstobeabletoexploitlabour。Althoughitisonlythevariableportionofcapitalwhichcreatessurplus-value，itdoessoonlyiftheotherportions，theconditionsofproduction，arelikewiseadvanced。Seeingthatthecapitalistcanexploitlabouronlybyadvancingconstantcapitalandthathecanturnhisconstantcapitaltogoodaccountonlybyadvancingvariablecapital，helumpsthemalltogetherinhisimagination，andmuchmoresosincetheactualrateofhisgainisnotdeterminedbyitsproportiontothevariable，buttothetotalcapital，notbytherateofsurplus-value，butbytherateofprofit。Andthelatter，asweshallsee，mayremainthesameandyetexpressdifferentratesofsurplus-value。
Thecostsoftheproductincludealltheelementsofitsvaluepaidbythecapitalistorforwhichhehasthrownanequivalentintoproduction。
Thesecostsmustbemadegoodtopreservethecapitalortoreproduceitinitsoriginalmagnitude。
Thevaluecontainedinacommodityisequaltothelabour-timeexpendedinitsproduction，andthesumofthislabourconsistsofpaidandunpaidportions。Butforthecapitalistthecostsofthecommodityconsistonlyofthatportionofthelabourmaterialisedinitforwhichhehaspaid。
Thesurplus-labourcontainedinthecommoditycoststhecapitalistnothing，although，likethepaidportion，itcoststhelabourerhislabour，andalthoughitcreatesvalueandentersintothecommodityasavalue-creatingelementquitelikepaidlabour。Thecapitalist’sprofitisderivedfromthefactthathehassomethingtosellforwhichhehaspaidnothing。Thesurplus-value，orprofit，consistspreciselyintheexcessvalueofacommodityoveritscost-price，i。e。，theexcessofthetotallabourembodiedinthecommodityoverthepaidlabourembodiedinit。Thesurplus-value，whateveritsorigin，isthusasurplusovertheadvancedtotalcapital。Theproportionofthissurplustothetotal，capitalisthereforeexpressedbythefractions/C，inwhichCstandsfortotalcapital。Wethusobtaintherateofprofits/C=s/(c+v)，asdistinctfromtherateofsurplus-values/v。
Therateofsurplus-valuemeasuredagainstthevariablecapitaliscalledrateofsurplus-value。Therateofsurplus-valuemeasuredagainstthetotalcapitaliscalledrateofprofit。Thesearetwodifferentmeasurementsofthesameentity，andowingtothedifferenceofthetwostandardsofmeasurementtheyexpressdifferentproportionsorrelationsofthisentity。
Thetransformationofsurplus-valueintoprofitmustbededucedfromthetransformationoftherateofsurplus-valueintotherateofprofit，notviceversa。Andinfactitwasrateofprofitwhichwasthehistoricalpointofdeparture。Surplus-valueandrateofsurplus-valueare，relatively，theinvisibleandunknownessencethatwantsinvestigating，whilerateofprofitandthereforetheappearanceofsurplus-valueintheformofprofitarerevealedonthesurfaceofthephenomenon。
Sofarastheindividualcapitalistisconcerned，itisevidentthatheisonlyinterestedintherelationofthesurplus-value，ortheexcessvalueatwhichhesellshiscommodities，tothetotalcapitaladvancedfortheproductionofthecommodities，whilethespecificrelationshipandinnerconnectionofthissurpluswiththevariouscomponentsofcapitalfailtointeresthim，anditis，moreover，ratherinhisintereststodrawtheveiloverthisspecificrelationshipandthisintrinsicconnection。
Althoughtheexcessvalueofacommodityoveritscost-priceisshapedintheimmediateprocessofproduction，itisrealisedonlyintheprocessofcirculation，andappearsallthemorereadilytohavearisenfromtheprocessofcirculation，sinceinreality，undercompetition，intheactualmarket，itdependsonmarketconditionswhetherornotandtowhatextentthissurplusisrealised。Thereisnoneedtowastewordsatthispointaboutthefactthatifacommodityissoldaboveorbelowitsvalue，thereismerelyanotherkindofdivisionofsurplus-value，andthatthisdifferentdivision，thischangedproportioninwhichvariouspersonsshareinthesurplus-value，doesnotinanywayaltereitherthemagnitudeorthenatureofthatsurplus-value。ItisnotalonethemetamorphosesdiscussedbyusinBookIIthattakeplaceintheprocessofcirculation；theyfallinwithactualcompetition，thesaleandpurchaseofcommoditiesaboveorbelowtheirvalue，sothatthesurplus-valuerealisedbytheindividualcapitalistdependsasmuchonthesharpnessofhisbusinesswitsasonthedirectexploitationoflabour。
Intheprocessofcirculationthetimeofcirculationcomestoexertitsinfluencealongsidetheworking-time，therebylimitingtheamountofsurplus-valuerealisablewithinagiventimespan。Stillotherelementsderivedfromcirculationintrudedecisivelyintotheactualproductionprocess。Theactualprocessofproductionandtheprocessofcirculationintertwineandinterminglecontinually，andtherebyinvariablyadulteratetheirtypicaldistinctivefeatures。Theproductionofsurplus-value，andofvalueingeneral，receivesnewdefinitionintheprocessofcirculation，aspreviouslyshown。Capitalpassesthroughthecircuitofitsmetamorphoses。
Finally，steppingbeyonditsinnerorganiclife，sotosay，itentersintorelationswithouterlife，intorelationsinwhichitisnotcapitalandlabourwhichconfrontoneanother，butcapitalandcapitalinonecase，andindividuals，againsimplyasbuyersandsellers，intheother。Thetimeofcirculationandworking-timecrosspathsandthusbothseemtodeterminethesurplus-value。Theoriginalforminwhichcapitalandwage-labourconfrontoneanotherisdisguisedthroughtheinterventionofrelationshipsseeminglyindependentofit。Surplus-valueitselfdoesnotappearastheproductoftheappropriationoflabour-time，butasanexcessofthesellingpriceofcommoditiesovertheircost-price，thelatterthusbeingeasilyrepresentedastheiractualvalue(valeurintrinsË；que)，whileprofitappearsasanexcessofthesellingpriceofcommoditiesovertheirimmanentvalue。
True，thenatureofsurplus-valueimpressesitselfconstantlyupontheconsciousnessofthecapitalistduringtheprocessofproduction，ashisgreedforthelabour-timeofothers，etc。，hasrevealedinouranalysisofsurplus-value。But:1)Theactualprocessofproductionisonlyafleetingstagewhichcontinuallymergeswiththeprocessofcirculation，justasthelattermergeswiththeformer，sothatintheprocessofproduction，themoreorlessclearlydawningnotionofthesourceofthegainmadeinit，i。e。，theinklingofthenatureofsurplus-value，standsatbestasafactorequallyvalidastheideathattherealisedsurplusoriginatesinamovementthatisindependentoftheproductionprocess，thatitarisesincirculation，andthatitbelongstocapitalirrespectiveofthelatter’srelationtolabour。EvensuchmoderneconomistsasRamsay，Malthus，Senior，Torrens，etc。，identifythesephenomenaofcirculationdirectlyasproofsthatcapitalinitsbarematerialexistence，independentofitssocialrelationtolabourwhichmakescapitalofit，is，asitwere，anindependentsourceofsurplus-valuealongsidelabourandindependentoflabour。2)
Undertheitemofexpenses，whichembracewagesaswellasthepriceofrawmaterials，wearandtearofmachinery，etc。，theextortionofunpaidlabourfiguresonlyasasavinginpayingforanarticlewhichisincludedinexpenses，onlyasasmallerpaymentforacertainquantityoflabour，similartothesavingwhenrawmaterialsareboughtmorecheaply，orthedepreciationofmachinerydecreases。Inthiswaytheextortionofsurplus-labourlosesitsspecificcharacter。Itsspecificrelationshiptosurplus-valueisobscured。Thisisgreatlyfurtheredandfacilitated，asshowninBookI(Abschn。VI)[Englishedition:PartVI，pp。535-43——Ed。]，byrepresentingthevalueoflabour-powerintheformofwages。
Therelationshipsofcapitalareobscuredbythefactthatallpartsofcapitalappearequallyasthesourceofexcessvalue(profit)。
Thewayinwhichsurplus-valueistransformedintotheformofprofitbywayoftherateofprofitis，however，afurtherdevelopmentoftheinversionofsubjectandobjectthattakesplacealreadyintheprocessofproduction。Inthelatter，wehaveseen，thesubjectiveproductiveforcesoflabourappearasproductiveforcesofcapital。[Englishedition:Vol。
1，pp。332-33——Ed。]Ontheonehand，thevalue，orthepastlabour，whichdominateslivinglabour，isincarnatedinthecapitalist。Ontheotherhand，thelabourerappearsasbaremateriallabour-power，asacommodity。
Eveninthesimplerelationsofproductionthisinvertedrelationshipnecessarilyproducescertaincorrespondinglyinvertedconceptions，atransposedconsciousnesswhichisfurtherdevelopedbythemetamorphosesandmodificationsoftheactualcirculationprocess。
Itisaltogethererroneous，asastudyoftheRicardianschoolshows，totrytoidentifythelawsoftherateofprofitwiththelawsoftherateofsurplus-value，orviceversa。Thecapitalistnaturallydoesnotseethedifferencebetweenthem。Intheformulas/Cthesurplus-valueismeasuredbythevalueofthetotalcapitaladvancedforitsproduction，ofwhichapartwastotallyconsumedinthisproductionandapartwasmerelyemployedinit。Infact，theformulas/Cexpressesthedegreeofself-expansionofthetotalcapitaladvanced，or，takeninconformitywithinnerconceptualconnectionsandthenatureofsurplus-value，itindicatestheratiooftheamountofvariationofvariablecapitaltothemagnitudeoftheadvancedtotalcapital。
Initself，themagnitudeofvalueoftotalcapitalhasnoinnerrelationshiptothemagnitudeofsurplus-value，atleastnotdirectly。Sofarasitsmaterialelementsareconcerned，thetotalcapitalminusthevariablecapital，thatis，theconstantcapital，consistsofthematerialrequisites-themeansoflabourandmaterialsoflabour-neededtomaterialiselabour。
Itisnecessarytohaveacertainquantityofmeansandmaterialsoflabourforaspecificquantityoflabourtomaterialiseincommoditiesandtherebytoproducevalue。Adefinitetechnicalrelationdependingonthespecialnatureofthelabourappliedisestablishedbetweenthequantityoflabourandthequantityofmeansofproductiontowhichthislabouristobeapplied。
Hencethereisalsotothatextentadefiniterelationbetweenthequantityofsurplus-value，orsurplus-labour，andthequantityofmeansofproduction。
Forinstance，ifthelabournecessaryfortheproductionofthewageamountstoadailysixhours，thelabourermustwork12hourstodosixhoursofsurplus-labour，orproduceasurplus-valueof100%。Heusesuptwiceasmuchofthemeansofproductionin12hoursashedoesinsix。Yetthisisnoreasonforthesurplus-valueproducedbyhiminsixhourstobedirectlyrelatedtothevalueofthemeansofproductionusedupinthosesix，orin12hours。Thisvalueisherealtogetherimmaterial；itisonlyamatterofthetechnicallyrequiredquantity。Itdoesnotmatterwhethertherawmaterialsormeansoflabourarecheapordear，aslongastheyhavetherequireduse-valueandareavailableintechnicallyprescribedproportiontothelabourtobeapplied。IfIknowthatxlbs。ofcottonareconsumedinanhourofspinningandthattheycostashillings，then，ofcourse，Ialsoknowthat12hours’spinningconsumes12xlbs。ofcotton=12ashillings，andcanthencalculatetheproportionofthesurplus-valuetothevalueofthe12aswellastothatofthesix。Buttherelationoflivinglabourtothevalueofmeansofproductionobtainshereonlytotheextentthatashillingsserveasanameforxlbs。ofcotton；becauseadefinitequantityofcottonhasadefiniteprice，andtherefore，conversely，adefinitepricemayalsoserveasanindexforadefinitequantityofcotton，solongasthepriceofcottondoesnotchange。IfIknowthatthelabourermustwork12hoursformetoappropriatesixhoursofsurplus-labour，thatthereforeImusthavea12-hoursupplyofcottonreadyforuse，andifIknowthepriceofthisquantityofcottonneededfor12hours，thenIhaveanindirectrelationbetweenthepriceofcotton(asanindexoftherequiredquantity)andthesurplus-value。But，conversely，Icanneverconcludethequantityoftherawmaterialthatmaybeconsumedin，say，onehour，andnotsix，ofspinningfromthepriceoftherawmaterial。
Thereis，then，nonecessaryinnerrelationbetweenthevalueoftheconstantcapital，nor，therefore，betweenthevalueofthetotalcapital(=c+v)
andthesurplus-value。
Iftherateofsurplus-valueisknownanditsmagnitudegiven，therateofprofitexpressesnothingbutwhatitactuallyis，namelyadifferentwayofmeasuringsurplus-value，itsmeasurementaccordingtothevalueofthetotalcapitalinsteadofthevalueoftheportionofcapitalfromwhichsurplus-valuedirectlyoriginatesbywayofitsexchangeforlabour。
Butinreality(i。e。，intheworldofphenomena)thematterisreversed。
Surplus-valueisgiven，butgivenasanexcessofthesellingpriceofthecommodityoveritscost-price；anditremainsamysterywherethissurplusoriginated-fromtheexploitationoflabourintheprocessofproduction，orfromoutwittingthepurchaserintheprocessofcirculation，orfromboth。Whatisalsogivenistheproportionofthissurplustothevalueofthetotalcapital，ortherateofprofit。Thecalculationofthisexcessofthesellingpriceoverthecost-priceinrelationtothevalueoftheadvancedtotalcapitalisveryimportantandnatural，becauseineffectityieldstheratioinwhichtotalcapitalhasbeenexpanded，i。e。，thedegreeofitsself-expansion。Ifweproceedfromthisrateofprofit，wecannotthereforeconcludethespecificrelationsbetweenthesurplusandtheportionofcapitalinvestedinwages。Weshallseeinasubsequentchapter[K。Marx，TheorienberdenMehrwert。K。Marx/F。Engels，Werke，Band26，Teil3，S。25-28——Ed。]whatamusingsomersaultsMalthusmakeswhenhetriesinthiswaytogetatthesecretofthesurplus-valueandofitsspecificrelationtothevariablepartofthecapital。Whattherateofprofitactuallyshowsisratherauniformrelationofthesurplustoequalportionsofthetotalcapital，which，fromthispointofview，doesnotshowanyinnerdifferenceatall，unlessitbebetweenthefixedandcirculatingcapital。Anditshowsthisdifference，too，onlybecausethesurplusiscalculatedintwoways；namely，first，asasimplemagnitude-asexcessoverthecost-price。Inthis，itsinitial，form，theentirecirculatingcapitalgoesintothecost-price，whileofthefixedcapitalonlythewearandteargoesintoit。Second，therelationofthisexcessinvaluetothetotalvalueoftheadvancedcapital。Inthiscase，thevalueofthetotalfixedcapitalentersintothecalculation，quitethesameasthecirculatingcapital。Therefore，thecirculatingcapitalgoesinbothtimesinthesameway，whilethefixedcapitalgoesindifferentlythefirsttime，andinthesamewayascirculatingcapitalthesecondtime。
Underthecircumstancesthedifferencebetweenfixedandcirculatingcapitalistheonlyonewhichobtrudesitself。
If，asHegelwouldputit，thesurplusthereforere-reflectsitselfinitselfoutoftherateofprofit，or，putdifferently，thesurplusismorecloselycharacterisedbytherateofprofit，itappearsasasurplusproducedbycapitalaboveitsownvalueoverayear，orinagivenperiodofcirculation。
Althoughtherateofprofitthusdiffersnumericallyfromtherateofsurplus-value，whilesurplus-valueandprofitareactuallythesamethingandnumericallyequal，profitisneverthelessaconvertedformofsurplus-value，aforminwhichitsoriginandthesecretofitsexistenceareobscuredandextinguished。Ineffect，profitistheforminwhichsurplus-valuepresentsitselftotheview，andmustinitiallybestrippedbyanalysistodisclosethelatter。Insurplus-value，therelationbetweencapitalandlabourislaidbare；intherelationofcapitaltoprofit，i。e。，ofcapitaltosurplus-valuethatappearsontheonehandasanexcessoverthecost-priceofcommoditiesrealisedintheprocessofcirculationand，ontheother，asasurplusmorecloselydeterminedbyitsrelationtothetotalcapital，thecapitalappearsasarelationtoitself，arelationinwhichit，astheoriginalsumofvalue，isdistinguishedfromanewvaluewhichitgenerated。Oneisconsciousthatcapitalgeneratesthisnewvaluebyitsmovementintheprocessesofproductionandcirculation。
Butthewayinwhichthisoccursiscloakedinmysteryandappearstooriginatefromhiddenqualitiesinherentincapitalitself。
Thefurtherwefollowtheprocessoftheself-expansionofcapital，themoremysterioustherelationsofcapitalwillbecome，andthelessthesecretofitsinternalorganismwillberevealed。
Inthispart，therateofprofitisnumericallydifferentfromtherateofsurplus-value；whileprofitandsurplus-valuearetreatedashavingthesamenumericalmagnitudebutonlyadifferentform。Inthenextpartweshallseehowthealienationgoesfurther，andhowprofitrepresentsamagnitudedifferingalsonumericallyfromsurplus-value。
Capital，Vol。3，Chapter3KarlMarxCAPITALVol。III
THEPROCESSOF
CAPITALISTPRODUCTIONASAWHOLEPartI
THECONVERSIONOFSURPLUS-VALUEINTOPROFITANDOFTHERATEOFSURPLUS-VALUE
INTOTHERATEOFPROFITCHAPTER3
TheRelationoftheRateofProfittotheRateofSurplus-ValueHere，asatthecloseoftheprecedingchapter，andgenerallyinthisentirefirstpart，wepresumetheamountofprofitfallingtoagivencapitaltobeequaltothetotalamountofsurplus-valueproducedbymeansofthiscapitalduringacertainperiodofcirculation。Wethusleaveasideforthepresentthefactthat，ontheonehand，thissurplus-valuemaybebrokenupintovarioussub-forms，suchasinterestoncapital，ground-rent，taxes，etc。，andthat，ontheother，itisnot，asarule，identicalwithprofitasappropriatedbyvirtueofageneralrateofprofit，whichwillbediscussedinthesecondpart。
Sofarasthequantityofprofitisassumedtobeequaltothatofsurplus-value，itsmagnitude，andthatoftherateofprofit，isdeterminedbyratiosofsimplefiguresgivenorascertainableineveryindividualcase。Theanalysis，therefore，firstiscarriedonpurelyinthemathematicalfield。
WeretainthedesignationsusedinBooksIandII。TotalcapitalCconsistsofconstantcapitalcandvariablecapitalv，andproducesasurplus-values。Theratioofthissurplus-valuetotheadvancedvariablecapital，ors/v，iscalledtherateofsurplus-valueanddesignateds’。Therefores/v=s’，andconsequentlys=s’v。Ifthissurplus-valueisrelatedtothetotalcapitalinsteadofthevariablecapital，itiscalledprofit，p，andtheratioofthesurplus-valuestothetotalcapitalC，ors/C，iscalledtherateofprofit，p’。Accordingly，p’=s——
C=s——
c+vNow，substitutingforsitsequivalents’v，wefindp’=s’v——
C=s’v——
c+vwhichequationmayalsobeexpressedbytheproportionp’:s’=v:C；
therateofprofitisrelatedtotherateofsurplus-valueasthevariablecapitalistothetotalcapital。
Itfollowsfromthisproportionthattherateofprofit，p’，isalwayssmallerthans’，therateofsurplus-value，becausev，thevariablecapital，isalwayssmallerthanC，thesumofv+c，orthevariableplustheconstantcapital；theonly，practicallyimpossiblecaseexcepted，inwhichv=C，thatis，noconstantcapitalatall，nomeansofproduction，butonlywagesareadvancedbythecapitalist。
However，ouranalysisalsoconsidersanumberofotherfactorswhichhaveadetermininginfluenceonthemagnitudeofc，v，ands，andmustthereforebebrieflyexamined。
First，thevalueofmoney。Wemayassumethistobeconstantthroughout。
Second，theturnover。Weshallleavethisfactorentirelyoutofconsiderationforthepresent，sinceitsinfluenceontherateofprofitwillbetreatedspeciallyinalaterchapter。[Hereweanticipatejustonepoint，thattheformulap’=s’v/Cisstrictlycorrectonlyforoneperiodofturnoverofthevariablecapital。Butwemaycorrectitforanannualturnoverbysubstitutingforthesimplerateofsurplus-value，s’，theannualrateofsurplus-value，s’n。Inthis，nisthenumberofturnoversofthevariablecapitalwithinoneyear。(Cf。BookII，ChapterXVI，1)-
F。E。]
Third，dueconsiderationmustbegiventoproductivityoflabour，whoseinfluenceontherateofsurplus-valuehasbeenthoroughlydiscussedinBookI(AbschnittIV)。[Englishedition:PartIV-Ed。]Productivityoflabourmayalsoexertadirectinfluenceontherateofprofit，atleastofanindividualcapital，if，ashasbeendemonstratedinBookI(Kap。
X，S。323/324[=MEW23，S。335/336])[Englishedition:Ch。XII，pp。316-17-
Ed。]thisindividualcapitaloperateswithahigherthantheaveragesocialproductivityandproducescommoditiesatalowervaluethantheiraveragesocialvalue，therebyrealisinganextraprofit。However，thiscasewillnotbeconsideredforthepresent，sinceinthispartoftheworkwealsoproceedfromthepremisethatcommoditiesareproducedundernormalsocialconditionsandaresoldattheirvalues。Hence，weassumeineachcasethattheproductivityoflabourremainsconstant。Ineffect，thevalue-compositionofacapitalinvestedinabranchofindustry，thatis，acertainproportionbetweenthevariableandconstantcapital，alwaysexpressesadefinitedegreeoflabourproductivity。Assoon，therefore，asthisproportionisalteredbymeansotherthanamerechangeinthevalueofthematerialelementsoftheconstantcapital，orachangeinwages，theproductivityoflabourmustlikewiseundergoacorrespondingchange，andweshalloftenenoughsee，forthisreason，thatchangesinthefactorsc，v，andsalsoimplychangesintheproductivityoflabour。
Thesameappliestothethreeremainingfactorsthelengthoftheworking-day，intensityoflabour，andwages。Theirinfluenceonthequantityandrateofsurplus-valuehasbeenexhaustivelydiscussedinBookI[Englishedition:Vol。1，pp。519-30-Ed。]Itwillbeunderstood，therefore，thatnotwithstandingtheassumption，whichwemakeforthesakeofsimplicity，thatthesethreefactorsremainconstant，thechangesthatoccurinvandsmayneverthelessimplychangesinthemagnitudeofthese，theirdeterminingelements。Inthisrespectwemustbrieflyrecallthatthewageinfluencesthequantityofsurplus-valueandtherateofsurplus-valueininverseproportiontothelengthoftheworking-dayandtheintensityoflabour；thatanincreaseinwagesreducesthesurplus-value，whilealengtheningoftheworking-dayandanincreaseintheintensityoflabouraddtoit。
Supposeacapitalof100producesasurplus-valueof20employing20
labourersworkinga10-hourdayforatotalweeklywageof20。Thenwehave:80c+20v+20s；s’=100%，p’=20%。
Nowtheworking-dayislengthenedto15hourswithoutraisingthewages。
Thetotalvalueproducedbythe20labourerswilltherebyincreasefrom40to60(10:15=40:60)。Sincev，thewagespaidtothelabourers，remainsthesame，thesurplus-valuerisesfrom20to40，andwehave:80c+20v+40s；s’=200%，p’=40%。
If，conversely，theten-hourworking-dayremainsunchanged，whilewagesfallfrom20to12，thetotalvalue-productamountsto40asbefore，butisdifferentlydistributed；vfallsto12，leavingaremainderof28fors。Thenwehave:80c+20v+28s；s’=2331/3%，p’=28:92=3010/23%。
Hence，weseethataprolongedworking-day(oracorrespondingincreaseintheintensityoflabour)andafallinwagesbothincreasetheamount，andthustherate，ofsurplus-value。Conversely，ariseinwages，otherthingsbeingequal，wouldlowertherateofsurplus-value。Hence，ifvrisesthroughariseinwages，itdoesnotexpressagreater，butonlyadearerquantityoflabour，inwhichcases’andp’donotrise，butfall。
Thisindicatesthatchangesintheworking-day，intensityoflabourandwagescannottakeplacewithoutasimultaneouschangeinvandsandtheirratio，andthereforealsop’，whichistheratioofstothetotalcapitalc+v。Anditisalsoevidentthatchangesintheratioofstovalsoimplycorrespondingchangesiiiatleastoneofthethreeabove-mentionedlabourconditions。
Preciselythisrevealsthespecificorganicrelationshipofvariablecapitaltothemovementofthetotalcapitalandtoitsself-expansion，andalsoitsdifferencefromconstantcapital。Sofarasgenerationofvalueisconcerned，theconstantcapitalisimportantonlyforthevalueithas。Anditisimmaterialtothegenerationofvaluewhetheraconstantcapitalof&；pound；1，500represents1，500tonsofironat，say，&；pound；1，or500tonsofironat&；pound；3。Thequantityofactualmaterial，inwhichthevalueoftheconstantcapitalisincorporated，isaltogetherirrelevanttotheformationofvalueandtherateofprofit，whichvariesinverselytothisvaluenomatterwhattheratiooftheincreaseordecreaseofthevalueofconstantcapitaltothemassofmaterialuse-valuewhichitrepresents。
Itisdifferentwithvariablecapital。Itisnotthevalueithas，notthelabourincorporatedinit，thatmatteratthispoint，butthisvalueasamereindexofthetotallabourthatitsetsinmotionandwhichisnotexpressedinit-thetotallabour，whosedifferencefromthelabourexpressedinthatvalue，hencethepaidlabour，i。e。，thatportionofthetotallabourwhichproducessurplus-value，isallthegreater，thelesslabouriscontainedinthatvalueitself。Suppose，aten-hourworking-dayisequaltotenshillings=tenmarks。Ifthelabournecessarytoreplacethewages，andthusthevariablecapital=5hours=5shillings，thenthesurplus-labour=5hoursandthesurplus-value=5shillings。Shouldthenecessarylabour=4hours=4shillings，thenthesurplus-labour=6hoursandthesurplus-value=6
shillings。
Hence，assoonasthevalueofthevariablecapitalceasestobeanindexofthequantityoflaboursetinmotionbyit，and，moreover，themeasureofthisindexisaltered，therateofsurplus-valuewillchangeintheoppositedirectionandinversely。
Letusnowgoontoapplytheabove-mentionedequationoftherateofprofit，p’=s’v/C，tothevariouspossiblecases。Weshallsuccessivelychangethevalueoftheindividualfactorsofs’v/Canddeterminetheeffectofthesechangesontherateofprofit。Inthiswayweshallobtaindifferentseriesofcases，whichwemayregardeitherassuccessivealteredconditionsofoperationforoneandthesamecapital，orasdifferentcapitalsexistingsidebysideandintroducedforthesakeofcomparison，taken，asitwere，fromdifferentbranchesofindustryordifferentcountries。
Incases，therefore，wheretheconceptionofsomeofourexamplesassuccessiveconditionsforoneandthesamecapitalappearstobeforcedorimpracticable，thisobjectionfallsawaythemomenttheyareregardedascomparisonsofindependentcapitals。
Hence，wenowseparatetheproducts’v/Cintoitstwofactorss’andv/C。Atfirstweshalltreats’asconstantandanalysetheeffectofthepossiblevariationsofv/C。Afterthatweshalltreatthefractionv/C
asconstantandlets’passthroughitspossiblevariations。Finallyweshalltreatallfactorsasvariablemagnitudesandtherebyexhaustallthecasesfromwhichlawsconcerningtherateofprofitmaybederived。I。c’constant，v/CvariableThiscase，whichembracesanumberofsubordinatecases，maybecoveredbyageneralformula。Taketwocapitals，CandC1，withtheirrespectivevariablecomponents，vandv1，withacommonrateofsurplus-value，s’，andratesofprofitp’andp1’。
Then:
p’=s’v——
Cp1’=s’v1——
C1NowletusmakeaproportionofCandC1，andofvandv1。Forinstance，letthevalueofthefractionC1/C=E，andthatofv1/v=e。ThenC1=EC，andv1=ev。Substitutingintheaboveequationthesevaluesforp1，C1andv1，weobtainp1’=s’ev——
ECAgain，wemayderiveasecondformulafromtheabovetwoequationsbytransformingthemintotheproportion:
v——
C:s’v1——
C1=v——
C:v1——
C1Sincethevalueofafractionisnotchangedifwemultiplyordivideitsnumeratoranddenominatorbythesamenumber，wemayreducev/Candv1/C1topercentages，thatis，wemaymakeCandC1both=100。Thenwehavev/C=v/100andv1/C1=v1/100，andmaythendropthedenominatorsintheaboveproportion，obtaining:p’:p1’=v:v1’，or:
Takinganytwocapitalsoperatingwiththesamerateofsurplus-value，theratesofprofitaretoeachotherasthevariableportionsofthecapitalscalculatedaspercentagesoftheirrespectivetotalcapitals。
Thesetwoformulasembraceallthepossiblevariationsofv/C。
Onemoreremarkbeforeweanalysethesevariouscasessingly。SinceCisthesumofcandv，oftheconstantandvariablecapitals，andsincetheratesofsurplus-value，asofprofit，areusuallyexpressedinpercentages，itisconvenienttoassumethatthesumofc+visalsoequalto100，i。e。，toexpresscandvinpercentages。Forthedeterminationoftherateofprofit，ifnotoftheamount，itisimmaterialwhetherwesaythatacapitalof15，000，ofwhich12，000isconstantand3，000isvariable，producesasurplus-valueof3，000，orwhetherwereducethiscapitaltopercentages:15，000C=12，000c+3，000v(+3，000s)100C=80c+20v(+20s)。
Ineithercasetherateofsurplus-values’=100%，andtherateofprofit=20%。
Thesameistruewhenwecomparetwocapitals，say，theforegoingcapitalwithanother，suchas12，000C=10，800c+1，200v(+1，200s)100C=90c+10v(+10s)。
inbothofwhichs’=100%，p’=10%，andinwhichthecomparisonwiththeforegoingcapitalisclearerinpercentageform。
Ontheotherhand，ifitisamatterofchangestakingplaceinoneandthesamecapital，theformofpercentagesisrarelytobeused，becauseitalmostalwaysobscuresthesechanges。Ifacapitalexpressedintheformofpercentages:80c+20v+20sassumestheformofpercentages:90c+10v+10s，wecannottellwhetherthechangedcompositioninpercentages，90v+10c，isduetoanabsolutedecreaseofvoranabsoluteincreaseofc，ortoboth。Wewouldneedtheabsolutemagnitudesinfigurestoascertainthis。
Intheanalysisofthefollowingindividualcasesofvariation，however，everythingdependsonhowthesechangeshavecomeabout；whether80v+20cchangedinto90c+10vthroughanincreaseoftheconstantcapitalwithoutanychangeinthevariablecapital，forinstancethrough12，000c+3，000vchanginginto27，000c+3，000v(correspondingtoapercentageof90c+10v)；
orwhethertheytookthisformthroughareductionofthevariablecapital，withtheconstantcapitalremainingunchanged，thatis，throughachangeinto12，000c+1，3331/3v(alsocorrespondingtoapercentageof90c+10v)；or，lastly，whetherbothofthetermschangedinto13，500c+1，500v(correspondingoncemoretoapercentageof90c+10v)。Butitispreciselythesecaseswhichweshallhavetosuccessivelyanalyse，andinsodoingdispensewiththeconvenientformofpercentages，oratleastemploytheseonlyasasecondaryalternative。1)s’andCconstant，vvariable。
Ifvchangesinmagnitude，Ccanremainunalteredonlyifc，theothercomponentofC，thatis，theconstantcapital，changesbythesameamountasv，butintheoppositedirection。
IfCoriginally=80c+20v=100，andifvisthenreducedto10，thenC
can=100onlyifcisincreasedto90；90c+10v=100。Generallyspeaking，ifvistransformedintov&；plusmn；d，intovincreasedordecreasedbyd，thencmustbetransformedintoc+&；macr；d，intocvaryingbythesameamount，butintheoppositedirection，sothattheconditionsofthepresentcasearesatisfied。
Similarly，iftherateofsurplus-values’remainsthesame，whilethevariablecapitalvchanges，theamountofsurplus-valuesmustchange，sinces=s’v，andsinceoneofthefactorsofs’v，namelyv，isgivenanothervalue。
Theassumptionsofthepresentcaseproduce，alongsidetheoriginalequation，p’=s’v——
C，stillanotherequationthroughthevariationofv:
p’=s’v1——
C，inwhichvhasbecomev1andp1’，theresultantchangedrateofprofit，istobefound。
Itisdeterminedbythefollowingproportion:
p’:p1’=s’v——
C:s’v1——
C=v:v1Or:withtherateofsurplus-valueandtotalcapitalremainingthesame，theoriginalrateofprofitistothenewrateofprofitproducedbyachangeinthevariablecapitalastheoriginalvariablecapitalistothechangedvariablecapital。
Iftheoriginalcapitalwas，asabove:
I。15，000C=12，000c+3，000v(+3，000s)，andifitisnow:
II。15，000C=13，000c+2，000v(+2，000s)，thenC=15，000ands’=100%ineithercase，andtherateofprofitofI，20%，istothatofII，131/3%，asthevariablecapitalofI，3，000，istothatofII，2，000，i。e。，20
%:131/3%=3，000:2，000。
Now，thevariablecapitalmayeitherriseorfall。Letusfirsttakeanexampleinwhichitrises。Letacertaincapitalbeoriginallyconstitutedandemployedasfollows:I。100c+20v+10s；C=120，s’=50%，p’=81/3%。
Nowletthevariablecapitalriseto30。Inthatcase，accordingtoourassumption，theconstantcapitalmustfallfrom100to90sothattotalcapitalremainsunchangedat120。Therateofsurplus-valueremainingconstantat50%，thesurplus-valueproducedwillthenrisefrom10to15。Weshallthenhave:II。90c+30v+15s；C=120，s’=50%，p’=121/2%。
Letusfirstproceedfromtheassumptionthatwagesremainunchanged。
Thentheotherfactorsoftherateofsurplus-value，i。e。，theworking-dayandtheintensityoflabour，mustalsoremainunchanged。Inthateventtheriseofv(from20to30)cansignifyonlythatanotherhalfasmanylabourersareemployed。Thenthetotalvalueproducedalsorisesone-half，from30to45，andisdistributed，justasbefore，2/3forwagesand1/3forsurplus-value。Butatthesametime，withtheincreaseinthenumberoflabourers，theconstantcapital，thevalueofthemeansofproduction，hasfallenfrom100to90。Wehave，then，acaseofdecreasingproductivityoflabourcombinedwithasimultaneousshrinkageofconstantcapital。Issuchacaseeconomicallypossible？
Inagricultureandtheextractiveindustries，inwhichadecreaseinlabourproductivityand，therefore，anincreaseinthenumberofemployedlabourersisquitecomprehensible，thisprocessisonthebasisandwithinthescopeofcapitalistproductionattendedbyanincrease，insteadofadecrease，ofconstantcapital。Eveniftheabovefallofcwereduemerelytoafallinprices，anindividualcapitalwouldbeabletoaccomplishthetransitionfromItoIIonlyunderveryexceptionalcircumstances。
Butinthecaseoftwoindependentcapitalsinvestedindifferentcountries，orindifferentbranchesofagricultureorextractiveindustry，itwouldbenothingoutoftheordinaryifinoneofthecasesmorelabourers(andthereforemorevariablecapital)wereemployedandworkedwithlessvaluableorscantiermeansofproductionthanintheothercase。
Butletusdroptheassumptionthatthewageremainsthesame，andletusexplaintheriseofthevariablecapitalfrom20to30throughariseofwagesbyone-half。Thenweshallhaveanentirelydifferentcase。Thesamenumberoflabourers-say，twenty-continuetoworkwiththesameoronlyslightlyreducedmeansofproduction。Iftheworking-dayremainsunchanged-say，10hours-thenthetotalvalueproducedalsoremainsunchanged。Itwasandremains=30。Butallofthis30isnowrequiredtomakegoodtheadvancedvariablecapitalof30；thesurplus-valuewoulddisappear。Wehaveassumed，however，thattherateofsurplus-valueshouldremainconstant，thatis，thesameasinI，at50%。Thisispossibleonlyiftheworking-dayisprolongedbyone-halfto15hours。Thenthe20labourerswouldproduceatotalvalueof45in15hours，andallconditionswouldbesatisfied:II。90c+30v+15s；C=120，s’=50%，p’=121/2%。
Inthiscase，the20labourersdonotrequireanymoremeansoflabour，tools，machines，etc。，thanincaseI。Onlytherawmaterialsorauxiliarymaterialswouldhavetobeincreasedbyone-half。Intheeventofafallinthepricesofthesematerials，thetransitionfromItoIImightbemorepossibleeconomically，evenforanindividualcapitalinkeepingwithourassumption。Andthecapitalistwouldbesomewhatcompensatedbyincreasedprofitsforanylossincurredthroughthedepreciationofhisconstantcapital。
Nowletusassumethatthevariablecapitalfalls，insteadofrising。
Thenwehavebuttoreverseourexample，takingIIastheoriginalcapital，andpassingfromIItoI。
II。90c+30v+15s，thenchangesintoI。100c+20v+10s，anditisevidentthatthistranspositiondoesnotintheleastalteranyoftheconditionsregulatingtherespectiveratesofprofitandtheirmutualrelation。
Ifvfallsfrom30to20because1/3fewerlabourersareemployedwiththegrowingconstantcapital，thenwehavebeforeusthenormalcaseofmodernindustry，namely，anincreasingproductivityoflabour，andtheoperationofalargerquantityofmeansofproductionbyfewerlabourers。Thatthismovementisnecessarilyconnectedwithasimultaneousdropintherateofprofitwillbedevelopedinthethirdpartofthisbook。
If，ontheotherhand，vfallsfrom30to20，becausethesamenumberoflabourersisemployedatlowerwages，thetotalvalueproducedwould，withtheworking-dayunchanged，asbefore=30v+15s=45。Sincevfellto20，thesurplus-valuewouldriseto25，therateofsurplus-valuefrom50%
to125%，whichwouldbecontrarytoourassumption。Tocomplywiththeconditionsofourcase，thesurplus-value，withitsrateat50%，mustratherfallto10，andthetotalvalueproducedmust，therefore，fallfrom45
to30，andthisispossibleonlyiftheworking-dayisreducedbyone-third。
Then，asbefore，wehave:100c+20v+10s；s’=50%，p’=81/3%。
Itneedhardlybesaidthatthisreductionoftheworking-time，inthecaseofafallinwages，wouldnotoccurinpractice。Butthatisimmaterial。
Therateofprofitisafunctionofseveralvariablemagnitudes，andifwewishtoknowhowthesevariablesinfluencetherateofprofit，wemustanalysetheindividualeffectofeachinturn，regardlessofwhethersuchanisolatedeffectiseconomicallypracticablewithoneandthesamecapital。2)s’constant，vvariable，Cchangesthroughthevariationofv。
Thiscasediffersfromtheprecedingoneonlyindegree。Insteadofdecreasingorincreasingbyasmuchasvincreasesordecreases，c，remainsconstant。Underpresent-dayconditionsinthemajorindustriesandagriculturethevariablecapitalisonlyarelativelysmallpartofthetotalcapital。
Forthisreason，itsincreaseordecrease，sofaraseitherisduetochangesinthevariablecapital，arelikewiserelativelysmall。
Letusagainproceedwithacapital:I。100c+20v+10s；C=120，s’=50%，p’=81/3%。
whichwouldthenchange，say，into:II。100c+30v+15s；C=130，s’=50%，p’=117/13%。
Theoppositecase，inwhichthevariablecapitaldecreases，wouldagainbeillustratedbythereversetransitionfromIItoI。
Theeconomicconditionswouldbeessentiallythesameasintheprecedingcase，andthereforetheyneednotbediscussedagain。ThetransitionfromItoIIimpliesadecreaseintheproductivityoflabourbyone-half；forIItheutilisationof100，requiresanincreaseoflabourbyone-halfoverthatofI。Thiscasemayoccurinagriculture。[9]
Butwhilethetotalcapitalremainsconstantintheprecedingcase，owingtotheconversionofconstantintovariablecapital，orviceversa，thereisinthiscaseatie-upofadditionalcapitalifthevariablecapitalincreases，andareleaseofpreviouslyemployedcapitalifthevariablecapitaldecreases。3)s’andvconstant，candthereforeCvariable。
Inthiscasetheequationchangesfrom:
p’=s’v——
Cintop’=s’v1——
C1，andafterreducingthesamefactorsonbothsides，wehave:p1’:p’=C:C1；
withthesamerateofsurplus-valueandequalvariablecapitals，theratesofprofitareinverselyproportionaltothetotalcapitals。
Shouldwe，forexample，havethreecapitals，orthreedifferentconditionsofthesamecapital:I。80c+20v+20s；C=100，s’=100%，p’=20%；II。100c+20v+20s；C=120，s’=100%，p’=162/3%；III。60c+20v+20s；C=80，s’=100%，p’=25%。
Thenweobtaintheproportions:20%:162/3%=120:100and20%:25%=80:100。
Thepreviouslygivengeneralformulaforvariationsofv/Cwithaconstants’was:
P1’=s’ev——
EC；nowitbecomes:P1’=s’v——
EC，sincevdoesnotchange，thefactore=v1/v，becomes=1。
Sinces’v=s，thequantityofsurplus-value，andsinceboths’andvremainconstant，itfollowsthats，too，isnotaffectedbyanyvariationofC。Theamountofsurplus-valueisthesameafterthechangeasitwasbeforeit。
Ifcweretofalltozero，p’would=s’，i。e。，therateofprofitwouldequaltherateofsurplus-value。
Thealterationofcmaybedueeithertoamerechangeinthevalueofthematerialelementsofconstantcapital，ortoachangeinthetechnicalcompositionofthetotalcapital，thatis，achangeintheproductivityoflabourinthegivenbranchofindustry。Inthelattercase，theproductivityofsociallabourmountingduetothedevelopmentofmodernindustryandlarge-scaleagriculturewouldbringaboutatransition(intheaboveillustration)
inthesequencefromIIItoIandfromItoII。Aquantityoflabourwhichispaidwith20andproducesavalueof40wouldfirstutilisemeansoflabourtoavalueof60；ifproductivitymountedandthevalueremainedthesame，theusedupmeansoflabourwouldrisefirstto80，andthento100。Aninversionofthissequencewouldimplyadecreaseinproductivity。
Thesamequantityoflabourwouldputasmallerquantityofmeansofproductionintomotionandtheoperationwouldbecurtailed，asmayoccurinagriculture，mining，etc。
Asavinginconstantcapitalincreasestherateofprofitontheonehand，and，ontheother，setsfreecapital，forwhichreasonitisofimportancetothecapitalist。Weshallmakeacloserstudyofthis，andlikewiseoftheinfluenceofachangeinthepricesoftheelementsofconstantcapital，particularlyofrawmaterials，atalaterpoint。[Presentedition:Ch。
V，VI-Ed。]
Itisagainevidentherethatavariationoftheconstantcapitalequallyaffectstherateofprofit，regardlessofwhetherthisvariationisduetoanincreaseordecreaseofthematerialelementsofc，ormerelytoachangeintheirvalue。4)s’constant，v，candCallvariable。
Inthiscase，thegeneralformulaforthechangedrateofprofit，givenattheoutset，remainsinforce:
P1’=s’v——
EC。Itfollowsfromthisthatwiththerateofsurplus-valueremainingthesame:
a)TherateofprofitfallsifEisgreaterthane，thatis，iftheconstantcapitalisaugmentedtosuchanextentthatthetotalcapitalgrowsatafasterratethanthevariablecapital。Ifacapitalof80c+20v+20schangesinto170c+30v+30s，thens’remains=100%，butv/Cfallsfrom20/100
to30/100，inspiteofthefactthatbothvandChavegrown，andtherateofprofitfallscorrespondinglyfrom20%to15%。
b)Therateofprofitremainsunchangedonlyife=E，thatis，ifthefractionv/Cretainsthesamevalueinspiteofaseemingchange，i。e。，ifitsnumeratoranddenominatoraremultipliedordividedbythesamefactor。Thecapitals80c+20v+20sand160c+40v+40sobviouslyhavethesamerateofprofitof20%，becauses’remains=100%andv/C=20/100=40/200representsthesamevalueinbothexamples。
c)TherateofprofitriseswheneisgreaterthanE，thatis，whenthevariablecapitalgrowsatafasterratethanthetotalcapital。If80c+20v+20sturnsinto120c+40v+40s，therateofprofitrisesfrom20%
to25%，becausewithanunchangeds’v/C=20/100risesto40/160，orfrom1/5to1/4。
IfthechangesofvandCareinthesamedirection，wemayviewthischangeofmagnitudeasthough，toacertainextent，bothofthemvariedinthesameproportion，sothatv/Cremainedunchangeduptothatpoint。
Beyondthispoint，onlyoneofthemwouldvary，andweshallhavetherebyreducedthiscomplicatedcasetooneoftheprecedingsimplerones。
Should，forinstance，80c+20v+20sbecome100c+30v+30s，thentheproportionofvtoc，andalsotoC，remainsthesameinthisvariationupto:100c+25v+25s。
Uptothatpoint，therefore，therateofprofitlikewiseremainsunchanged。
Wemaythentake100c+25v+25sasourpointofdeparture；wefindthatvincreasedby5tobecome30v，sothatCrosefrom125to130，thusgivingusthesecondcase，thatofthesimplevariationofvandtheconsequentvariationofC。Therateofprofit，whichwasoriginally20%，risesthroughthisadditionof5vto231/13%，providedtherateofsurplus-valueremainsthesame。
ThesamereductiontoasimplercasecanalsotakeplaceifvandC
changetheirmagnitudesinoppositedirections。Forinstance，letusagainstartwith80c+20v+20s，andletthisbecome:110c+10v+10s。Inthatcase，withthechangegoingasfaras40c+10v+10s，therateofprofitwouldremainthesame20%。Byadding70ctothisintermediateform，itwilldropto81/3%。Thus，wehaveagainreducedthecasetoaninstanceofchangeofonevariable，namelyofc。
Simultaneousvariationofv，c，andC，doesnot，therefore，offeranynewaspectsandinthefinalanalysisleadsbacktoacaseinwhichonlyonefactorisavariable。
Eventhesoleremainingcasehasactuallybeenexhausted，namelythatinwhichvandCremainnumericallythesame，whiletheirmaterialelementsundergoachangeofvalue，sothatvstandsforachangedquantityoflabourputinmotionandcforachangedquantityofmeansofproductionputinmotion。
In80c+20v+20s，let20voriginallyrepresentthewagesof20labourersworking10hoursdaily。Thenletthewagesofeachrisefrom1to11/4。
Inthatcasethe20vwillpayonly16labourersinsteadof20。Butif20
labourersproduceavalueof40in200working-hours，16labourersworking10hoursdailywillin160working-hoursproduceavalueofonly32。Afterdeducting20，forwages，only12ofthe32wouldthenremainforsurplus-value。
Therateofsurplus-valuewouldhavefallenfrom100%to60%。Butsincewehaveassumedtherateofsurplus-valuetobeconstant，theworking-daywouldhavetobeprolongedbyone-quarter，from10to121/2hours。If20labourersworking10hoursdaily=200working-hoursproduceavalueof40，then16labourersworking121/2hoursdaily=200hourswillproducethesamevalue，andthecapitalof80c+20vwouldasbeforeyieldthesamesurplus-valueof20。
Conversely，ifwagesweretofalltosuchanextentthat20vwouldrepresentthewagesof30labourers，thenswouldremainconstantonlyiftheworking-daywerereducedfrom10to62/3hours。For20x10=30
&；times；62/3=200working-hours。
Wehavealreadyinthemaindiscussedtowhatextentcmayinthesedivergentexamplesremainunchangedintermsofvalueexpressedinmoneyandyetrepresentdifferentquantitiesofmeansofproductionchangedinaccordancewithchangingconditions。Initspureformthiscasewouldbepossibleonlybywayofanexception。
Asforachangeinthevalueoftheelementsofcwhichincreasesordecreasestheirmassbutleavesthesumofthevalueofcunchanged，itdoesnotaffecteithertherateofprofitortherateofsurplus-value，solongasitdoesnotleadtoachangeinthemagnitudeofv。
Wehaveherewithexhaustedallthepossiblecasesofvariationofv，c，andCinourequation。Wehaveseenthattherateofprofitmayfall，remainunchanged，orrise，whiletherateofsurplus-valueremainsthesame，withtheleastchangeintheproportionofvtocortoC，beingsufficienttochangetherateofprofitaswell。
Wehaveseen，furthermore，thatinvariationsofvthereisacertainlimiteverywherebeyondwhichitiseconomicallyimpossiblefors’toremainconstant。Sinceeveryone-sidedvariationofcmustalsoreachacertainlimitwherevcannolongerremainunchanged，wefindthattherearelimitsforeverypossiblevariationofv/C，beyondwhichs’mustlikewisebecomevariable。Inthevariationsofs’whichweshallnowdiscuss，thisinteractionofthedifferentvariablesofourequationwillstandoutstillclearer。II。s’variableWeobtainageneralformulafortheratesofprofitwithdifferentratesofsurplus-value，nomatterwhetherv/Cremainsconstantornot，byconvertingtheequation:
p’=s’v——
Cintop1’=s1’v1——
C1，inwhichp1’，s1’，v1andC1denotethechangedvaluesofp’，s’，vandC。Thenwehave:
p’:p1’=s’v——
C:s1’v1——
C1，andhence:
p1’=s1’——
s1xv1——
vxC——
C1xp’。1)s’variable，v/Cconstant。
Inthiscasewehavetheequations:
p’=s’v——
C；p1’=s’v——
C，inbothofwhichv/Cisequal。Therefore:p’:p1’=s’:s1’
Theratesofprofitoftwocapitalsofthesamecompositionaretoeachotherasthetwocorrespondingratesofsurplus-value。Sinceinthefractionv/CitisnotaquestionoftheabsolutemagnitudesofvandC，butonlyoftheirratio，thisappliestoallcapitalsofequalcompositionwhatevertheirabsolutemagnitude。80c+20v+20s；C=100，s’=100%，p’=20%160c+40v+20s；C=200，s’=50%，p’=10%100%:50%=20%:10%。
IftheabsolutemagnitudesofvandCarethesameinbothcases，theratesofprofitaremoreoveralsorelatedtooneanotherastheamountsofsurplus-value:p’:p1’=s’v:s1’v=s:s1。
Forinstance:80c+20v+20s；s’=100%，p’=20%80c+20v+10s；s’=50%，p’=10%20%:10%=100&；times；20:50&；times；20=20s:10s。
Itisnowclearthatwithcapitalsofequalabsoluteorpercentagecompositiontherateofsurplus-valuecandifferonlyifeitherthewages，orthelengthoftheworking-day，ortheintensityoflabour，differ。Inthefollowingthreecases:I。80c+20v+10s；s’=50%，p’=10%II。80c+20v+20s；s’=100%，p’=20%III。80c+20v+40s；s’=200%，p’=40%
thetotalvalueproducedinIis30(20v+10s)；inIIitis40；inIII
itis60。Thismaycomeaboutinthreedifferentways。
First，ifthewagesaredifferent，and20vstandsforadifferentnumberoflabourersineveryindividualcase。SupposecapitalIemploys15labourers10hoursdailyatawageof&；pound；11/3，whoproduceavalueof&；pound；30，ofwhich&；pound；20replacethewagesand&；pound；10aresurplus-value。Ifwagesfallto&；pound；1，then20labourersmaybeemployedfor10hours；theywillproduceavalueof&；pound；40，ofwhich&；pound；20willreplacethewagesand&；pound；20
willbesurplus-value。Shouldwagesfallstillmore，to&；pound；2/3，thirtylabourersmaybeemployedfor10hours。Theywillproduceavalueof&；pound；60，ofwhich&；pound；20willbedeductedforwagesand&；pound；40willrepresentsurplus-value。
Thiscase-aconstantcompositionofcapitalinpercent，aconstantworking-dayandconstantintensityoflabour，andtherateofsurplus-valuevaryingbecauseofvariationinwages-istheonlyoneinwhichRicardo’sassumptioniscorrect:”Profitwouldbehighorlow，exactlyinproportionaswageswereloworhigh。”(Principles，Ch。I，Sect。III，p。18
oftheWorksofD。Ricardo，ed。byMacCulloch，1852。)
Orsecond，iftheintensityoflabourvaries。Inthatcase，say，20labourersworking10hoursdailywiththesamemeansofproductionproduce30piecesofacertaincommodityinI，40inII，and60inIII，ofwhicheverypiece，asidefromthevalueofthemeansofproductionincorporatedinit，representsanewvalueof&；pound；1。Sinceevery20pieces=&；pound；20
makegoodthewages，thereremain10pieces=&；pound；10forsurplus-valueinI，20pieces=&；pound；20inII，and40pieces=&；pound；40inIII。
Orthird，theworking-daydiffersinlength。If20labourersworkwiththesameintensityfor9hoursinI，12hoursinII，and18hoursinIII，theirtotalproducts，30:40:60varyas9:12:18。Andsincewages=20ineverycase，10，20，and40respectivelyagainremainassurplus-value。
Ariseorfallinwages，therefore，influencestherateofsurplus-valueinversely，andariseorfallintheintensityoflabour，andalengtheningorshorteningoftheworking-day，actthesamewayontherateofsurplus-valueandthereby，withv/Cconstant，ontherateofprofit。2)s’andvvariable，Cconstant。
Thefollowingproportionappliesinthiscase:
p’:p1’=s’v——
C:s’v1——
C=s’v:s1’v1=s:s1。Theratesofprofitarerelatedtooneanotherastherespectiveamountsofsurplus-value。
Changesintherateofsurplus-valuewiththevariablecapitalremainingconstantmeantachangeinthemagnitudeanddistributionoftheproducedvalue。Asimultaneousvariationofvands’alsoalwaysimpliesadifferentdistribution，butnotalwaysachangeinthemagnitudeoftheproducedvalue。Threecasesarepossible:
a)Variationofvands’takesplaceinoppositedirections，butbythesameamount；forinstance:80c+20v+10s；s’=50%，p’=10%90c+10v+20s；s’=200%，p’=20%
Theproducedvalueisequalinbothcases，hencealsothequantityoflabourperformed；20v+10s=10v+20s=30。Theonlydifferenceisthatinthefirstcase20ispaidoutforwagesand10remainsassurplus-value，whileinthesecondcasewagesareonly10andsurplus-valueistherefore20。Thisistheonlycaseinwhichthenumberoflabourers，theintensityoflabour，andthelengthoftheworking-dayremainunchanged，whilevands’varysimultaneously。
b)Variationofs’andvalsotakesplaceinoppositedirections，butnotbythesameamount。Inthatcasethevariationofeithervors’outweighstheother。I。80c+20v+20s；s’=100%，p’=20%II。72c+28v+20s；s’=713/7%，p’=20%III。84c+16v+20s；s’=125%，p’=20%。
CapitalIpaysforproducedvalueamountingto40with20v，IIavalueof48with28v，andIIIavalueof36with16v。Boththeproducedvalueandthewageshavechanged。Butachangeintheproducedvaluemeansachangeintheamountoflabourperformed，henceachangeeitherinthenumberoflabourers，thehoursoflabour，theintensityoflabour，orinmorethanoneofthese。
c)Variationofs’andvtakesplaceinthesamedirection。Inthatcasetheoneintensifiestheeffectoftheother。90c+10v+10s；s’=100%，p’=10%80c+20v+30s；s’=150%，p’=30%92c+8v+6s；s’=75%，p’=6%。
Heretoothethreevaluesproducedaredifferent，namely20，50，and14。Andthisdifferenceinthemagnitudeoftherespectivequantitiesoflabourreducesitselfoncemoretoadifferenceinthenumberoflabourers，thehoursoflabour，andtheintensityoflabour，orseveralorallofthesefactors。3)s’，vandCvariable。
ThiscaseoffersnonewaspectsandissolvedbythegeneralformulagivenunderII，inwhichs’isvariable。
Theeffectofachangeinthemagnitude，oftherateofsurplus-valueontherateofprofithenceyieldsthefollowingcases:
1)p’increasesordecreasesinthesameproportionass’ifv/Cremainsconstant。80c+20v+20s；s’=100%，p’=20%80c+20v+10s；s’=50%，p’=10%100%:50%=20%:10%。
2)p’risesorfallsatafasterratethans’ifv/Cmovesinthesamedirectionass’，thatis，ifitincreasesordecreaseswhens’increasesordecreases。80c+20v+10s；s’=50%，p’=10%70c+30v+20s；s’=662/3%，p’=10%50%:662/3%<10%:20%。
3)p’risesorfallsataslowerratethans’ifv/Cchangesinverselytos’，butataslowerrate。80c+20v+10s；s’=50%，p’=10%90c+10v+15s；s’=150%，p’=15%50%:150%>10%:15%。
4)p’riseswhiles’falls，orfallswhiles’risesifv/Cchangesinverselyto，andat，afasterratethan，s’。80c+20v+20s；s’=100%，p’=20%90c+10v+15s；s’=150%，p’=15%。
s’hasrisenfrom100%to150%，p’hasfallenfrom20%to15%。
5)Finally，p’remainsconstantwhereass’risesorfalls，whilev/C
changesinverselyto，butinexactlythesameproportionas，s’。
Itisonlythislastcasewhichstillrequiressomeexplanation。Wehaveobservedearlierinthevariationsofv/Cthatoneandthesamerateofsurplus-valuemaybeexpressedinverymuchdifferentratesofprofit。
Nowweseethatoneandthesamerateofprofitmaybebasedonverymuchdifferentratesofsurplus-value。ButwhileanychangeintheproportionofvtoCissufficienttoproduceadifferenceintherateofprofitsolongassisconstant，achangeinthemagnitudeofsmustleadtoacorrespondinginversechangeofv/Cinorderthattherateofprofitremainthesame。
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