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(1)OLIVE 香川大学学術情報リポジトリ. Fa l 1i n gR a t eo fP r o f i ti nt h eG r u n d r i s s e TakaoFujimoto 1 . T h i se s s a yisωreconsiderone o ft h e1 a w so ft h et r a n s f o r m a t i o no f. s u r p 1 u sv a 1 u ei n t op r o f i t，t h a ti s，t h et e n d e n c yo ft h er a t eo fp r o f i tt o d e c l i n e( ( 3，p .7 6 3 ) ) . Wes h o u 1 dn o tremaint obe a g r u n t e ra b o u tt h e r x ' sd i s c u s s i o n sont h i sp r o b 1 e m，b u ts h o u 1 da n a 1 y s et h i s a m b i g u i t i e so fMa c h a l l e n g i n gp r o p o s i t i o n by modern t o o 1 so rm o d e 1 s . Here i nt h i sp a p e r M a r x ' sf a l l i n gp r o f i tr a t et h e o r y wi l 1b ed i s c u s s e dd e p e n d i n g on h i s. Grundr ' i s s e，p a r t l yb e c a u s et h o s en o t e b o o k sp r e s e n tt h ed i a 1 e c t i c a 1n a t u r e o fc a t i t a 1 i s td e v e 1 0 p m e n tv i v i d 1 y，t h o u g hi nan i l 1 e g i b l es c r i p t .L e b o w i t z a sa 1 r e a d yg i v e nani n t e r e s t i n gviewb u tt h i s view seems t o have (2Jh beenh e l dbyn o tafewMarxiansa san a t u r a 1i n t e r p r e t a t i o no ft h el a w . 2 . Thes t o r yg o e sl i k et h i s .P r o f i t shave many b a r r i e r s and l i m i t s .F o r example，t h ea b s o 1 u t el i m i to fs u r p l u sv a l u eo rt h ei n c r e a s ei nt i m eo f c i r c u 1 a t i o n . These l i m i t s must be s u r p a s s e dt b r o u g ha c c u m u 1 a t i o n and g r o w t h . Thena n o t h e rs e to fb a r r i e r swi l 1t u r no u ti nt h ec o u r s eo fd e ‑ r o w t h ‑ B a r r i e r ‑ G r o w t hc y c l e . Butt h ef i n a 1 1 i m i ti st h e v e l o p m e n t . Thus，G p r o l e t a r i a twhobecomesc o n s c i o u so ft h en a t u r eo fc a p i t a l and r e c o g n i z e s t h a tt h eg r e a t e s ts o u r s eo fc o n t r a d i c t i o ni s c a p i t a li t s e l f . 3 . L e b o w i t z (2Jd o e sn o t， however， g i v ead i a l e c t i c a lt r e a t m e n tt oM a r x ' s. G r u n d r i s s emodelont h ef a l l i n gr a t eo fp r o f i t( L e b o w i t z ' smodeli si nf a c t o r ‑ o n l yf o rNotebookI I IandI V ) . He c o n c l u d e dt h a ti nM a r x ' smodel，c h et e n d e n c yi sf o rt h ep r o f i tr a t et or i s e !L e tu sr e p r o r e c t 1 yexamined，t 酬.

(2) OLIVE 香川大学学術情報リポジトリ ‑110‑. 第5 3 巻第 1号. 1 1 0. duce L e b o w i t z ' smodel 'a sf o l l o w s :. s= 1‑n， wheresand na r e，r e s p e c t i v e l y，s u r p l u sl a b o U1 p e rworkerandn e c e 鈴a r y l a b o u rp e rw o r k e r . Noteh e r et h el e n g t ho ft h eworkdayi sn o r m a l i z e dt o b eu n i t γ ;. n=W/l， where Wand1a r e，r e s p e c t i v e l y， u s e ‑ v a l u e se n t e r i n gi n t oaw o r k e r ' sc o n ‑ s u m p t i o n， andt h ep r o d u c t i v i t yo fl a b o u r ; t : 三 K/N ，. wheretd e n o t e st h et e c h n i c a lc o m p o s i t i o no fc a p i t a l，K meanso fp r o d u c 幽. t i o n，andN t h enumbero fw o r k e r s ; 1=αt ，. whereαisane f f i c i e n c yc o e f f i c i e n to fme C l n so fp r o d u c t i o n . Nowl e tC，V andn cd e n o t ec o n s t a n t回 . p i t a l，v a r i a b l ec a p i t a l andt h e a v e r a g ev a l u eo fmeanso fp r o d u c t i o n，r e s p e c t i v e l y . Then， C‑=nc.K and V=n.N. c /n and assume βconstant， i m p l y i n g no b i a si nt e c h n i c a l D e f i n e β芸 n c h a n g e .V V ehave 三 ( n c. K)/( n. N)=t β. C/V. Thust h ev a l u ep r o f i tr a t e r'==sN/(C+V)ココ (1‑n)/( tβ ‑ 1 ‑l )n =(α t/W‑1) / ( tβ +1).. d r ' / d t =( α 十 βW)/ W(tβ十 1)2> 0 a s s u m i n g α， βand W a r ec o n s t a n t .T h i sl a s ti n e q u a l i t y shows t h a tt h e. v a l u er a t eo fp r o f i tw i l lr i s ea st i m eg o e s on，g i v e nt h ea s s u m p t i o n s m e n t i o n e da b o v e . 4 . Thev a l u er a t eo fp r o f i t，r '，i se q u a lt ot h emoneyr a t ewhen，e .g .，.

(3) OLIVE 香川大学学術情報リポジトリ 1 1 1. e s s i r d n u r eG h nt ti i f o r fP eo t a gR n 1i l a F. ‑111‑. e h d when t e i f s i t a ss .i I l o i t i d n o sc i h . T . s e c i r op lt a n o i t r o p o r ep r sa e u l a v t l u s e sr ' z t i w o b e .L s r o t c e ss u o i r a e、sameamong v h st ni o i t i s o p m o cc i n a g r o e(5)) e S o( i h s i k aandN. O t a b i h dbyK. S e n i a t b ewas，however，o v o b a e h st e s i a lchanger a c i n : h c e gt n i c u d e r ‑ t s o s，c sway"Thati u o r o g i namorer i . ) ) 6 4， 1， o( s l ea e S t( n a t s n o nc i a m e or st lwagei a e er h ft ti i f o r fp eo t a r ‑ l o ef h e modelfromt v o b ea h tt u so e s i v e thed a h st y a z(2j s t i w o b e . L 5 . e s s i ' r d n u r eG h nt si t n e m e l le a c i t i r rc u o gf n i w o l ‑ l a u aq. t e es m i rt u o b a sl u l p r u hs t i nw i a sg u l p r u fs yo t i t n e d (1) Thei. … ， eworkingday， h l，namely，t a t i p a fc no o i t a l u m u c c ea h tont i m i el v i t a t i . ) ) 5 7 .3 3，p ( ( e u l a sv u l p r u ' s )，OI t n i o p d n a t ss ' r e k r o ew h mt o r f r( u o b a sl u l p r (2) もu n o i t r o p o r lp a c i r e m u esamen h nt tgrowi o sn e o )d t n i o p d n a t 'ss al t i p a mc o r f ( . ) ) 5 3 .3 3，p ( '( . e c r o nf o i t c u d o r ep h st a ‑ e ed h ot nt o i t a l e rr e l l a m nan even s s，buti e s i er u l a sv u l p ' I (3) SU . ) ) 0 4 .3 3，p ( '( . e c r o nf o i t c u d o r ep h ft to n e m p o l e v it a tp n a t s n o ec h tt a h emeanst c r o ef v i t c u d o r ep h nt ei s a e r c n (4) ani . ) ) 9 8 .3 3，p ( 町 ( e， l b a i r a ev h ot et v i t a l e sr w o r lg a t i p a fc o s 、. ' z t i w o b e sformL t n e m e l ee s e h ehowt e os t γ s a obee rt a e p p ta o sn e o td 6. 1 . r e t t a em l p m i gs n i w o l l o ef h . (2)and(3)meant t h g i lr l sa . (1) i l e d o m n si rworkera e rp u o b a sl u l p r u rands u o b a yl r a s s e c e en t o n e Letnandsd l a c i n h c e r some t e t f ta n e i c i f f e o yc t i v i t c u d o r ep h st e t o n e . Pd n3 o i t c e s s̲ u l p r u ρands / ecomesn 'b I u o b a yl r a s s e c e e，n g n a h sc i h rt e t f .Thena e g n a h c slabourδis u l p r u ns ei s a e r c n fi /ρ. Therateo rbecomes 1‑n u o b a l. ， ) す円台 (1ー. g 泡 Fi 閃e向 Se 加 (伽. tρif n e i c i f f e o nc o i 討 t c u d o r ep h nt a h rt e l l a m ss i srateoぬ i h T ). ρ / 1 ' ' ' : ' ' /(1十 ρ ρ nく:.

(4) OLIVE 香川大学学術情報リポジトリ ‑112 ー. 第5 3巻. 1 1 2. 第 1号. FromF i g .2，i ti sc l e a rt h a tt h ea b o v ei n e q u a l i t yi sa l w a y ss a t i s f i e . dwhen ρisn e a ru n it y，( n o t enく 1).T h i sseemswhat (2) a b o v es a y s . Ont h e o t h e r hand，(3) means t h a t 0becomes s m a l l e r，t h es m a l l e rng e t sa s t e c h n i c a lp r o g r e s sgo 色so n( N o t et h a tg i v e nt， 0d e c r e a s e sa snd e c r e a s e s ) . L a s t l y (4)祖 γ sn o t h i n gb u tt h ep r e v a l e n c eo fc a p i t a l ‑ u s i n g ‑ l a b o u rs a v i n g . . t e c h n i c a lc h a n g e s. s=l~-n_. ' /̲̲̲̲n‑ ー¥ 、. 「. y. i‑‑. ーす ). 内 / [1斗 ρ. η. y. ムこ込i n 一一. ‑. ーす ). n( 1. F i g .1. O. F i g 2. 7 . . Nowwep r e s e n tas i m p l em o d e l whichg e t sa l o n gw e l lw i t hv a r i o u s a s s u m p t i o n sandp r o p o s i t i o n si nt h eG r u n d r i s s e .S u p p o s eo n e ‑ s e c t o rm o d e l. ム噌S. /s. ¥3 ノ. ︑ ︑. h ep r i c ee q u a t i o ni sw r i t t e na s andi nt h eo r i g i n a ls i t u a t i o n，t O 1=roK。十 wOL ，. whererO，wO，KOandL0 a r et h er a t eo fp r o f i t，t h er e a lwager a t e，t h e amounto fc a p i t a lp e ru n i to fn e to u t p u t and t h e amount o fl a b o u rp e r fs i m p l i c i t yt h es a k eo h a t n e to u t p u t，r e s p e c t i v e l y .I ti s assumed f o rt wagesa r ep a i da f t e rp r o d u c t i o n .S u p p o s enowt h a tc a p i t a l ‑ u s i n g‑ l a b o u r ‑ 右 a ndt h e ya r ec o s t ‑ r e d u c i n g， s a v i n g (CU‑LS) t e c h n i c a lc h a n g e st a k ep l a c. t h a ti s，t h ep r i c e e q u a t i o nbecomes.

(5) OLIVE 香川大学学術情報リポジトリ F a l l i n gR a t eo fP r o f i ti nt h eG r u n d r i s s e. 1 3. ‑113ー. 1>roK*十 wOL ぺ. (2). wheret h enewc o e f f i c i e n t sK*andL*s a t i s f yt h ei n e q u a I : i t i e s O K*>KO>O，and 0く L*く L . Ap a i ro fnewe q u i l i b r i u mr a t e s( 1 ' * ， ω *) musts a t i s f y 1=r*K 中十ω !*L*.. (3) o I fω。r e m a i n sunchangeda f t e rt e c h n i c a lp r o g r e s s，t h e n1'~ >r ( H e r er~. s t a n d sf o rt h enewe q u i l i b r i u mp r o f i tr a t ew i t hω。k e p tc o n s t a n t .I nt h e s e q u e l，t h es u p e r s c r i p t s0 and*show t h eo r i g i n a land new e q u i l i b r i u m m a g n i t u d e sandt h es u b s c r i p tl e t t e ri n d i c a t e s wh ic hr a t ei st ob ef i x e d . Thus，e.g..，. ω~. i st h enewwager a t ewhenrO i sk e p tc o n s t a n t ) .. Whatw i l lhappent ot h er a t eo fe x p l o i t a t i o n ?The l a b o u rv a l u eo ft h e commodityi sL0 b e f o r et e c h n i c a lp r o g r e s sandL*a f t e r .Weassumework‑ e r sdon o ts a v eande a r nnop r o f i t sona s s e t s . 80， t h er a t eo fe x p l o i t a t i o n b e f o r eanda f t e ri n n o v a t i o na r er e s p e c t i v e l y 三 ( eO l'̲wO LO )jwO LO，and計三 ( 1 ‑ ω*L*)jw*L*. Thus，ifωor e m a i n sc o n s t a n t，e~>eo ， i .e .，t h er a t eo fe x p l o i t a t i o ni n ‑ c r e a s e s . Theo r g a n i cc o m p o s i t i o no fc a p i t a li sgivena s CjV=.KLjwL 2=KjwL=(1十 e)K.. T h i sa l s oi n c r e a s e sw'henω。i sk e p tc o n s t a n t . 8 . Nowt a k eupt h emovement o ft h er a t eo fp r o f i t when t h er a t eo f e x p l o i t a t i o ni st obef i x e d . Thec o n s t a n c yo fei m p l i e st h a t ω。 LO=ω:L*. Then，りく ' 10 b e c a u s eo fe q . s(1) a r i d (3). On t h eo t h e r hand，ωt > ωoandCjVa l s oincrea~es. I nsummary，i fc o s t ‑ r e d u c i n gC U‑L8t e c h n i c a l p r o g r e s si sa d o p t e dandt h er a t eo fe x p l o i t a t i o ni sk e p tc o n s t a n t，t h e nt h e r a t eo fp r o f i tf a l l sw h i l et h e wager a t eand t h eo r g a n i cc o m p o s i t i o no f c a p i t a lr i s e ..

(6) OLIVE 香川大学学術情報リポジトリ第5 3 巻第 1号. ‑114‑. 1 1 4. Onemaγobjectt ot h ec o n s t a n c yo ft h er a t eo fe x p l o i t a t i o ns i n c e no oneknowst h i sr a t ee x a c t l yandw i s h e st of i xi te i t h e r .Butonr e f l e c t i o n， t h esameo b j e c t i o nw i l la l s oa p p l yt ot h ec o n s t a n c yo ft h er e a lwager a t e ( R e c e n t l γ t h e r ea p p e a r e dsomet r a d eu n i o n sw hi ch i n s i s t on t h ec o n s t a n t r e a lwagea st h eminimumwagel e v e lo fa g r e e m e n t ) . Thec o n t r a p o s i t i o no ft h ef o r e g o i n gr e s u l ti ss i g n i f i c a n t . Thati s，i ft h e e c h ‑ r a t eo fp r o f i ti st h esamea f t e rt h ea b o p t i o no fc o s t ‑ r e d u c i n gCU‑LSt n i c a lc h a n g e s，t h er a t eo fe x p l o i t a t i o nmustb ei n c r e a s e d . 9 . . Thea b o v ep r o p o s i t i o n sc a nbeo b t a i n e di n an e a s i e rwaybyu s i n ga d i a g r a m . Thee q u i l i b r i u mr e l a t i o nbetweenrandωis1=rK十 ωL，which i sc a l l e dt h ew a g e ‑ p r o f it 'c u r v e( H e r ea s t r a i g h tl i n e ) . Thee x p l o i t a t i n r a t e. e=~1 = ‑ : ‑ L . ‑l 一wL 一一一一一 . L ‑ l ‑ ‑ r ' k Theseg r a p h sa r ed e p i c t e di nF i g .3 .I ti sc l e a rfromt h i sf i g u r et h a t. 一一一一一一一一 before'technicalprogress 一一尚一一町一一 ̲after technical progress. e. と ?. 、、 ¥. 、、句、. ¥. ¥. 一一一一一ー一一一入ご. 一一わー. ¥ l ¥. 九. ¥ ¥ ¥ ￨ ¥ U. ¥¥」. L I L : 〉三人. l ¥ ¥ l ¥ i ¥. i\\ト_J~____一一一一 --:tーとへ ¥ 、. ¥. 1九. v 民、. 、¥!¥レト¥￨¥¥. ペポ t ' e‑‑‑ 一一一ーー「一て十一一一寸¥. e. l. e*. e*. e. 0 J 0. Fig 3. ¥ ¥ J. Q. w. •. . 1. I '. " 1 キ. C. L *.

(7) OLIVE 香川大学学術情報リポジトリ F a l l i n gR a t eo fP r o f i ti nt h eG r u n d r i s s e. 1 1 5. *、。 ¥ ψ. ‑115ー. ，. r “ ~">'r，v ， > 1 ' 7 ;. ω~>ω~>ω 。，. * . ‑ ‑ ‑ ‑ . . . . * ¥. e~>eγ ;:>e-. ，. ( C /V);>(C/V)~>(C/ V)~で吋 The reader should note thep e c u l i a rp o s i t i o no fr O • References C1 ) F u j i m o t o，T .，' N o t eon T e c h n i c a lChangesandt h eWage.ProfitCurve， 'E c o ‑. 1( 1 9 8 0 ) . nomicReview (Iwanami)，3. r 2). L e b o w i t z，M. A "M a r x ' sF a l l i n gR a t eo fP r o f i t :A D i a l e c t i c a lView， 'C anad. J .E c o n .，9 ( 1 9 7 6 ) . (31 Marx，K，G r u n d r i s s e，( t l a n s L byM. N i c o l a u s )，Penguin，1 9 7 3 . (4) N a k a t a n i，T .， ' P r o f i t，WageandT e c h n i c a lChange， '( i nJ a p a n e s e )，E conomic 9( 1 9 7 8 )。 Review (Iwanami)，2 (5) O k i s h i o， N .， TheFundamentalT h e o r yo faC a t i t a l i s tEconomy，( i p .J a p a n e s e )， Sobunsha，1 9 6 5 . C6) R oemer，九 T e c h n i c a lChangeandt h e Tendency o ft h e Rateo fP r o f i tt o. ヘ. .Econ. Theory，主6(1977). F a l l ，I.

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