constant and variable capital

Transcription

1 598 consan and variable capial consan and variable capial Definiion In Das Kapial Marx defined Consan Capial as ha par of capial advanced in he means of producion; he defined Variable Capial as he par of capial advanced in wages (Marx, 867, Vol. I, ch. 6). These definiions come from his concep of Value: he defined he value of commodiies as he amoun of labour direcly and indirecly necessary o produce commodiies (Vol. I, ch. ). In oher words, he value of commodiies is he sum of C and N, where C is he value of he means of producion necessary o produce hem and N is he amoun of labour used ha is direcly necessary o produce hem. The value of he capial advanced in he means of producion is equal o C. However, he value of he capial advanced in wages is obviously no equal o N, because i is he value of he commodiies which labourers can buy wih heir wages, and has no direc relaionship wih he amoun of labour which hey acually expend. Therefore, while he value of he par of capial ha is advanced in he means of producion is ransferred o he value of he producs wihou quaniaive change, he value of he capial advanced in wages undergoes quaniaive change in he process of ransfer o he value of he producs. This is he reason why Marx proposed he definiions of consan capial C and variable capial V. The definiion of consan capial and variable capial mus no be confused wih he definiion of fixed capial and liquid capial. Fixed capial is a par of consan capial which is oally used in producion process bu ransfers is value o producs only parially. Liquid capial is a par of consan capial which is oally used up and ransfers is whole value wihin one producion process. So consan capial is composed of boh fixed capial and liquid capial, and on he oher hand liquid capial belongs parly o consan capial and parly o variable capial. Marx inroduced he concep value-composiion of capial, μ, which is defined as he raio of consan capial C o variable capial V: C μ. (.) V Marx knew well ha he value composiion of capial reflecs no only maerial characerisics of he process of producion bu also he social relaionship beween capialiss and labourers. In fac definiion (.) can be rewrien as C N μ = (.) N V

2 599 consan and variable capial C/N reflecs he characer of he process of producion and N/V reflecs he class relaionship beween capialiss and labourers. C/N is he raio of he amoun of labour necessary o produce he means of producion o he amoun of labour direcly besowed, which is compleely deermined by he maerial condiion in he process of producion, while N/V is he raio of he amoun of labour which labourers acually expend o he amoun of labour ha is necessary in order o produce commodiies which labourers can purchase wih heir wages. If labourers are forced o work longer wih less wages, his raio mus rise. Marx proposed o call he value-composiion of capial, insofar as i is deermined by he maerial condiion of he process of producion, he organic composiion of capial. More explicily, The value-composiion of capial, inasmuch as i is deermined by, and reflecs, is echnical composiion, is called he organic composiion of capial (Capial, Vol. III, ch. 8). However, as shown above, he value composiion of capial is no deermined by he maerial condiion of he process of producion alone. So i is beer o inroduce he raio C/N in he place of he organic composiion of capial, which is deermined only by he maerial condiion in he process of producion. In order o avoid confusion, I call his raio he organic composiion of producion. This is he raio of dead labour o living labour, which Marx himself frequenly used in Das Kapial. Variable Capial and Source of Profi In conras o Smih, Ricardo and ohers, Marx aached grea imporance o analysis o find he source of profi. He found ha source in surplus labour, which is he excess of labour expended by labourers over he value of commodiies which labourers can obain wih heir wages (Capial, vol. I, ch. 5). Using he noaion inroduced above, N > V is he necessary condiion for profi o exis. In order o illuminae his fac, he called capial advanced in wages Variable Capial. So he validiy of his name depends on his analysis of he source of profi. How is i jusified? For simpliciy we se up he simples model which can reflec he fundamenal characerisics of a capialisic economy; hese characerisics are he prevalence of commodiy producion, and he exisence of class relaionships beween labourers and capialiss. There are only wo kinds of commodiies: he means of producion (commodiy ) and consumpion goods (commodiy ). In order o produce one uni of he ih commodiy an amoun of a i uni of means of producion and an amoun of labour τ i are necessary as inpu. Labourers are forced o work for T hours per day and earn he money wage rae w. In order for profi o exis in boh indusries he following inequaliies are necessary p > ap+ τ w (.) p > ap+ τ w (.)

3 600 consan and variable capial where p and p denoe he price of he means of producion and consumpion goods respecively. As labourers work for T hours a day a money wage w per hour, hey can purchase an amoun B of consumpion goods. wt B =, B T = R (.3) p where R is he real wage rae. In he firs volume of Das Kapial, Marx assumed ha all commodiies are exchanged a prices exacly proporionae o heir uni value (equivalen exchange). Uni values of commodiies are deermined by he following equaions = a + τ (.4) = a+ τ (.5) which assure unique and posiive values, provided a < (Dmiriev, 898; May, ; Okishio, 955a, 955b). Under he assumpion of equivalen exchange, we have p i = λ (.6) where λ is a consan which convers he dimension from hours o, say, dollars. Subsiuing (.3) and (.6) ino (.) and (.) we ge B > a + τ (.7) T By equaions (.4) and (.5) and he above inequaliies, we have Consequenly we arrive a he conclusion i B > a+ τ (.8) T B τ > 0 T B τ > 0 T (.9) (.0) T > B. (.) This inequaliy implies he exisence of surplus value, because surplus value is he excess of working hours T over he amoun of labour necessary o produce commodiies which labourers can receive wih wages B. If he number of workers employed is n, hen oal expended labour is

4 60 consan and variable capial nt and variable capial measured in erms of value is B n. So he inequaliy (.) can be rewrien as N > V (.) This is he reason Marx called capial advanced in wages variable capial. As shown above, Marx proved he heorem of he source of profi under he assumpion of equivalen exchange. Though his is a clear-cu way o show he resuls, i has induced various criiques. Many criics have said ha Marx s heorem would be righ if all exchanges were equivalen exchange, bu ha in realiy exchanges are seldom equivalen so his heorem canno be valid. In order o refue such a criicism we mus prove he heorem wihou he assumpion of equivalen exchange (see Okishio 955a, 955b, 963, 97, 978; Morishima, 973). Mahemaically, our ask is o find necessary and sufficien condiions for inequaliies (.), (.) and (.3) o have non-negaive soluions for p, p. From (.) we know easily ha he condiion a > 0 (.3) is necessary for p o be posiive. This condiion ensures ha he sociey will obain ne oupu. Nex, subsiuing (.3) ino (.), and from (.3) we have p τb > p T a ( ). (.4) On he oher hand, from (.) and (.3) we ge p T τ B >. (.5) p Ta We can easily ge from (.4) and (.5) Inequaliy (.6) is rewrien as By (.7), (.4) and (.5) he above becomes T aτ B ( a ) < T τ B. a τ > B + a τ. (.6) (.7) T > B. (.8) Thus we can arrive a Marx s resul. For laer convenience we show anoher expression for he exisence of surplus value. Dividing (.) and (.) by w, we ge

5 60 consan and variable capial p p a w w τ (.9) p p a w w τ (.0) By comparing (.9) and (.0), and (.4) and (.5), we ge pi i, ( i,) w > = (.) Equaion (.) implies ha if posiive profi exiss, hen he price wage raio (he amoun of commanded labour) is greaer han he amoun of value (necessary labour). In he famous conroversy wih Ricardo, Malhus poined ou his difference beween labour commanded and labour embodied. Though he wrongly hough ha his difference injured he validiy of he labour heory of value, he had come near o he Marxian heory of he source of profi (see Malhus, 80, pp. 6 3, 0). Condiion (.) is rewrien as i > w p i This condiion shows ha if posiive profi exiss, hen he produciviy of labour ( i ) greaer han he rae of real wages ( w p i ). 3 Organic Composiion and Producion Price mus be The concep of organic composiion of capial plays an imporan role in Marx s analysis of prices. The price of producion (Ricardo s naural price ) ha gives every indusry he equal rae of profi is deermined by he following equaions: ( )( τ ) ( )( τ ) p = + r a p + w (3.) p = + r a p + w (3.) where r is he general (equal) rae of profi. The firs problem is o examine he relaionship beween w= Rp (3.3) p ~. p

6 603 consan and variable capial If hey are equal hen we have equivalen exchange, if no we have non-equivalen exchange from he poin of view of he labour heory of value. The values of he commodiies are deermined by (.4) and (.5). The raio of he value of producion-goods o consumpion-goods is given as a τ + τ =. a τ + τ The relaive price of producion-goods o consumpion-goods deermined by (3.) and (3.) is given as Comparing (3.4) wih (3.5), we obain p p ap τ + w τ =. ap τ + w τ a ap w p τ + + τ τ =. p τ a ap + + w τ τ The expression in brackes on he RHS of (3.6) is given by a a = w p A, A> 0. τ τ [ ] ( ) If profi is posiive, from (.) w p is negaive. So we can conclude p a a. (3.8) p τ τ The RHS of he above means he comparison of he organic composiion of producion and also he organic composiion of capial, because as shown above he organic composiion of producion is a i τ i and he organic composiion of capial is a i τ i R. The second problem is o examine he influence of he change in real wage rae on he relaive prices deermined by (3.), (3.) and (3.3): (3.4) (3.5) (3.6) (3.7) p p d d R.

7 604 consan and variable capial Denoing he relaive price of producion-goods o consumpion-goods as p, from (3.), (3.) and (3.3) we obain ( ) ( τ ) Differeniaing (3.9) wih respec o R, we have dp τ τ p =. dr ap+ τ R a The denominaor above is posiive, because from (3.9) τ 0. f p a p + R a p R = (3.9) (3.0) denominaor p = a p + τ R> 0. We shall show ha he sign of he numeraor depends on he comparison beween he organic composiion of capial in boh secors. The funcion f(p) in (3.9) is drawn in Figure. The meaningful soluion of he equaion (3.9) is given a p*. Subsiuing τ τ ino f(p), we ge τ = τ τ τ ( ) f a a τ Therefore if a τ a τ 0 f τ τ > 0, so considering he graph of f(p) we know ha * τ τ > p. In he same way we can conclude ha if aτ aτ 0, hen τ / τ p. Consequenly, from (3.0) we can conclude > hen ( ). p a a d R p τ τ d 0. This proposiion is firs esablished in Ricardo s Principles (8, p. 43). 4 Organic Composiion and he Rae of Profi The concep of organic composiion of capial plays an imporan role in Marx s analysis of he movemen of he rae of profi.

8 605 consan and variable capial Figure Marx defined he rae of profi as By (.), equaion (4.) is rewrien as S r =. C+ V e r =, e= S V μ + where e is he rae of exploiaion. He assered ha if he organic composiion of capial μ increases sufficienly hen he rae of profi r mus ineviably decrease. This is he famous law of he endency for he rae of profi o fall (Capial, vol. III, ch. 3). Many people have criicized his heorem. They have said ha if he rae of exploiaion e increases sufficienly, r may increase in spie of he increase of μ. So r does no necessarily decrease, even if μ increases sufficienly (Robinson, 94; Sweezy, 94). Such a criique overlooks he logic of Marx s argumen. Marx saed: Since he mass of he employed living labour is coninually on he decline as compared o he mass of maerialized labour se in moion by i, i.e., o he producively consumed (4.) (4.)

9 606 consan and variable capial means of producion, i follows ha he porion of living labour, unpaid and congealed in surplus-value, mus also be coninually on he decrease compared o he amoun of value represened by he invesed oal capial. Since he raio of he mass of surplus-value o he value of he invesed oal capial forms he rae of profi, his rae mus consanly fall (Capial, vol. III, ch. 3, p. 3). Therefore Marx s rue inenion is o insis ha if he organic composiion of producion v = C/N (he raio of he mass of maerialized labour o he mass of living labour) increases sufficienly, he rae of profi mus fall. This can be proved as follows (Okishio, 97). From (4.) and (4.), and we have v = C N (4.3) S r r = r + + C+ + V+ e + = v+ ( + e+ ) + = r v e + + e ( ) where suffixes, + denoe periods. The RHS of (4.4) is an increasing funcion of e. If we ake he limiing value as e ends o infiniy, we have + v + r r r < r. (4.4) Therefore we conclude, if v+ > r, hen r+ r < 0. The above reasoning can be resaed. The reciprocal of he organic composiion of producion ses an upper limi o he rae of profi, because S S + V N r = < = (4.5) C+ V C C If his upper limi decreases sufficienly, he rae of profi mus evenually decrease, as shown in Figure.

10 607 consan and variable capial Figure In response o criicisms of his view we mus say ha as far as we accep Marx s assumpion ha he inverse of he organic composiion (N/C) ends oward zero, Marx s conclusion ineviably follows. So far we have defined he rae of profi as (4.) and C, V, S are all measured in erms of labour value. However, he general rae of profi r mus be deermined by (3.), (3.) and (3.3). Can we derive he same conclusions for such a redefined r? Eliminaing p, p, w from (3.), (3.) and (3.3) we have Differeniaing f(r, R) we have (, ) ( + ) ( τ τ) ( r)( a τ R) f r R r R a a = 0 (4.6)

11 608 consan and variable capial where Considering (4.6) From (3.), (3.), (3.3), we know From (4.8) f < 0. f is rewrien as r R r R f dr+ f dr= 0 (4.7) r R ( ) ( τ τ) ( τ ) ( ) ( τ τ ) ( ) τ f = + r R a a a + R f = + r a a + r ( r) f ( a τ R)( r) + = + + (4.8) r ( ) ( ) + r a > 0 + r τ R > 0 (4.9) { τ} ( ) ( ) τ ( ) fr = + r + r a + r a So by (4.9) f R < 0, from which dr dr< 0. As R goes o zero r ends o is upper limi, which is obained from (4.6) a rmax =. (4.0) a Since he value of he means of producion is deermined by (.4), we have a ( a) τ N = = = (4.) a a a C Thus he upper limi of he general rae of profi is given by he reciprocal of he organic composiion of producion in he means of producion secor. Therefore if he organic composiion in ha secor rises sufficienly, he general rae of profi mus fall. 5 Organic Composiion and Unemploymen The concep of organic composiion of capial plays an imporan role in Marx s analysis of he movemen of employmen (Capial, vol. I, ch. 3). Marx assumed a rise in labour produciviy o accompany he rise in he organic composiion of producion C/N. If C/N rises hen from he definiion of organic composiion he amoun of employmen mus decrease relaive o consan capial. However, how does he increase in he organic composiion influence he absolue level of employmen? Many people hough ha even if C/N rises sufficienly, sill if consan capial C also increases hen he absolue level of employmen can also increase, hough less han

12 609 consan and variable capial proporionaely o consan capial (Oppenheimer, 903). Bu by reasoning similar o ha used for he endency of he rae of profi o fall, we can prove ha if organic composiion rises sufficienly, hen he absolue level of employmen mus acually decrease. The organic composiion of producion in he h period v is defined as C v =. (5.) N The accumulaion of consan capial Δ C = C C is financed from surplus value S. + C C < + S. (5.) The surplus value S is a par of he amoun of living labour which labourers expend S < N. (5.3) By (5.), we obain, From (5.) and (5.3) we ge we can say, if ( ) N N = C C + + v+ v = ( C+ C) + C. v+ v+ v N N+ N < S + C < + C v+ v+ v v+ v+ v C = ( + v v+ ). v v + v v + < 0 hen N+ N < 0. Therefore, if he organic composiion of producion in he + h period, v +, increases sufficienly so as o exceed +v, hen he amoun of employed labourer, N + mus ineviably become less han N, however high he rae of accumulaion of capial may be (Okishio, 97). The rae of accumulaion of capial Δ CCiself is bounded by he reciprocal of he organic composiion. From (5.) and (5.3) Δ C N < = C C v +

13 60 consan and variable capial so ha, because i is reasonable o assume ha he growh rae of labour supply is non-negaive, we can say ha if he organic composiion rises sufficienly he rae of unemploymen ineviably rises. Though Marx did no sae his explicily, we hink ha his is wha he waned o say. In analysing Marx s heorem on he movemen of he rae of profi and employmen, we have acceped his cenral assumpion ha he organic composiion of producion rises sufficienly over ime. However, here arises he problem: under wha condiions do capialiss choose echniques ha have sufficienly high organic composiions of producion? Marx seemed o hink ha he rise in labour produciviy and he rise in he organic composiion are wo aspecs of he same hing. Bu hese wo do no always go ogeher. Marx himself knew ha if labour produciviy in he means of producion secor rises very high hen even if echnical composiion rises, sill he value composiion may remain consan or decrease. As o he capialiss inroducion of new echniques we have he following proposiions: () if he real wage rae remains consan and capialiss inroduce new echniques which raise he rae remains of profi (calculaed a he curren prevailing prices and wage) hen he new general rae of profi does no decrease, whaever he organic composiion may be. () if he real wage rae rises and capialiss adap o his siuaion wih he inroducion of new echniques, hen he new general rae of profi does is higher han he one which would be expeced if such a new echnique were no inroduced. For he proofs of hese proposiions, see CHOICE OF TECHNIQUE AND THE RATE OF PROFIT. N. Okishio See also Marxian value analysis; organic composiion of capial; surplus value. Bibliography Dmiriev, V.K The heory of value of David Ricardo. In V.K. Dmiriev, Economic Essays on Value, Compeiion and Uiliy, ed. D.M. Nui, Cambridge: Cambridge Universiy Press, 974. Malhus, R. 80. Principles of Poliical Economy considered wih a View o heir Pracical Applicaion. s edn, London. Marx, K Capial. Translaed from he hird German ediion by Samuel Moore and Edward Aveling, ed. Frederick Engels. New York: Inernaional Publishers, 967. May, K The srucure of classical heories. Review of Economic Sudies 7(), Morishima, M Marx s Economics: A Dual Theory of Value and Growh. Cambridge: Cambridge Universiy Press.

14 6 consan and variable capial Okishio, N. 955a. Kachi o Kakaku (Value and producion price). Keizaigaku Kenkyu Nempo (The Annals of Economic Sudies), Kobe Universiy, No. 9. Okishio, N. 955b. Monopoly and he raes of profi. Kobe Universiy Economic Review, Okishio, N A mahemaical noe on Marxian heorems. Welwirschafliches Archiv 9, p., Okishio, N. 97. A formal proof of Marx s wo heorems. Kobe Universiy Economic Review 8, 6. Okishio, N, e al Three opics on Marxian fundamenal heorems. Kobe Universiy Economic Review 4, 8. Oppenheimer, T Das Grundgesez der Marxschen Gesellschafslehre. Book II, ch. 5. Berlin: Reimer. Ricardo, D. 8. On he Principles of Poliical Economy and Taxaion. Vol. in Works and Correspondence of David Ricardo, ed. P. Sraffa, Cambridge: Cambridge Universiy Press, Robinson, J. 94. An Essay on Marxian Economics. London: Macmillan. Sweezy, P.M. 94. The Theory of Capialis Developmen: Principles of Marxian Poliical Economy. New York: Oxford Universiy Press.