Ο Henryk Grossmann και η Πτωτική Τάση του Ποσοστού Κέρδους: Μία...

7/29/2019 Henryk Grossmann :

1/25

Henryk Grossmann :

. .

. &

, Gutenberg

H.Grossmann

.

. , Grossmann

( P.Sweezy, Howard & King ..).

Grossmann,

.

1.

Henryk Grossmann1 ,

,

() (). ,

, 20

,

.

Grossmann 1881

.

Bohm-Bawerk Karl Grunberg.

,

, 1918,

.

.

, 1925, ,

Grunberg,

, 1930.

1933

. 1937 .

. , 1949,

.

19502.

1

Kuhn (2004) Grossmann

Grossman.

1


2/25

Grossmann

("Das Akkumulations-und Zusammenbruchsgesetz des

Kapitalistischen Systems") 1929

1992 (

). Sismonde

de Sismondi , 1924,

1924.

Marx ("Die Anderung des ursprngliche Aufbauplans des Marxschen

Kapital und ihre Ursachen") 1929

Marx* Roman

Rosdolsky.

Grossmann

.

Marx

.

Grossmann.

, .

Harrod (1939, 1948) Dommar (1946).

Grossmann. .

2.

,

. ,

( ),

.

. ,

,

. Marx

( ,

) ( ,

).

Marx, -

- (1) ,

(2)

3.

.

,

2 Kuhn (2004) , ,

Grossmann.3 ,

, & (1999, .5).

2


3/25

Marx

.

,

( ).

.

Marx,

,

(capacity utilization), .

(fixed capital)

.

, .

,

(, .)

. , ,

- ( )

( ).

( ). ,

, .

.

,

.

. ,

, .

.

.

( ) .

, . , ,

.

Marx

, ,

(..

), ,

.

Marx,

. , ,

.

,

.

3


4/25

,

, :

o (s)

(v):v

s=s .

, vc

sR+=

.

v

c= .

1

s

+

=R

.

0

R

s1

s2

.

.

Okishio (1961), , (

, .),

. ,

,

.

. ,

,

.

. Okishio. , Foley (1986)

4


5/25

,

. Fine (1989)

Okishio

(

) (

)4.

Okishio . , Shaikh

(1978a)

(,

)

(margin of profits ).

(

).

3. H.Grossmann Grossmann

20 .

, , Bernstein

.

(

Bernstein).

.Kautsky,

Bernstein. -

4 Fine (1989),

.

. Marx

(), () .

.

,

. ,

( )

.

.

.

.

. Marx

,

:

. ,

, .(Marx (1978), ., .612)

5


6/25

. Rosa

Luxemburg

. ,

Marx, ,

. Luxemburg

.

Sternberg,

Luxemburg -,

. , Sternberg,

, ,

.

Grossmann

.

, Grossmann

.

-

Luxemburg Sternberg.

Grossmann

(

, , .)

.

(

, .).

.

- .

Grossmann

,

.

.

.

- ,

( )

.

Bauer (1913).

, Luxemburg,

. Grossmann

4 Bauer 20

36 .

Bauer Grossmann

6


7/25

Grossmann

.

.

, . ,

, . ,

. ,

.

, ( 100%). ,

. , . ,

( ).

( [

] [ ]) Bauer

Marx.

,

. Grossmann,

Bauer, 10%

5%. , .

- Marx

Luxemburg5 ( )

(Grossmann (1992), .70).

, ,

:

/ / = / .

,

,

(

).

Grossmann ( ).

c: (c0: ,

ct: t

)

(1) t

trcc

0=

+=100

1 ca

r

v: (v0: ,

vt: t

)

(2) t

t wvv 0=

+= 1001v

a

w

k:

c:

v:

5 Luxemburg, ,

2 Marx

( )

( ).

Marx -

-

. Mavroudeas

(1992).

7


8/25

s: (100100

vcks vc ++= )

: (v

c= ), 0

s:

, (vc

sR+

= ):

vc

vck

Rvc

+

++= 100100

:

100100

vckvcAV

vc ++++=

s

k

( )

s

vcvc100100

+.

:

(3)

+

+=

100100v

t

c

t

av

acks

(4)

=100s

tvs

(3) (4) :

(5)

=

100100

)s( ct

vt

ac

avk

(1) (2) (5) :

( )

100100

s00 c

t

v

trcwv

k =

Bauer

. ( ). , . ,

. . . , .

8


9/25

( ) (

). ,

. , .

Grossmann ( k=0) :

( )( )

( ) ( )

00

000

00 sss100100

s

=

=

==

c

v

t

c

v

t

t

c

t

vc

t

v

t

w

r

c

v

w

rrcwv

rcwv

,

:

v

c

c

v

t

++

=

100

100log

slog

0

, s> v.

:() ( 0)() (c)() (v)

() (s)

, .

.

, ,

.

(

).

1920

(c) , ( ) .

Grossmann

- . Grossmann (1992, .69-70)

Bauer

200000 100000 .

120000 80000 ,

(50000) .

.

1. Grossmann.

9


10/25

c v k c v AV k/s /s R

1 200000 10000

0

75000 20000 5000 400000 75% 25% 33.3%

2 220000 10500

0

77750 22000 5250 430000 74.5% 25.95% 32.3%

3 242000 11025

0

80539 24200 5511 462500 73.04% 26.96% 31.2%

4 266000 11576

2

83374 26600 5788 497524 72.02% 27.98% 30.3%

5 292600 12150

0

86213 29260 6077 535700 70.9% 29.1% 29.3%

6 321860 12762

7

89060 32186 6381 577114 69.7% 30.3% 28.4%

7 354046 134008 91904 35404 6700 622062 68.6% 31.4% 27.4%

8 389450 14070

8

94728 38945 7035 670866 67.35% 32.7% 26.5%

9 428395 14774

3

97517 42839 7387 723881 66% 34% 25.6%

10 471234 15513

0

10025

1

47123 7756 781494 64.63% 35.37% 24.7%

15 758925 197988 112197 75892 9899 1154901 56.67% 43.23% 20.6%

20 122225

2

25296

1

11783

2

12222

5

1263

4

172763

4

46.6% 53.4% 16.4%

21 134447

7

26532

5

11761

2

13444

7

1326

6

187512

7

44.3% 55.7% 16.4%

25 196844

6

32250

3

10953

4

19684

4

1612

5

261345

2

33.9% 66.1% 14%

33 421953

6

47648

0

30703 42195

3

2328

4

517249

6

4.2% 95.8% 10.1%

34 464148

9

50030

4

11141 46414

8

2501

5

564209

7

0.45% 99.55% 9.7%

35 510563

7

52531

9

0 51056

3

1475

6

615627

5

0% 100% 9.3%

36 561620

0

55158

4

10


11/25

Grossmann

Bauer

4 Bauer-

35 (

). Bauer

(

(/s)

(k/s) .

, 20

( ) .

, Grossmann (1992, .71-2) -

, J.S.Mill

2. ,

. 21

.

Grossmann (1992, .77)

.

, . ,

.

Grossmann

.

,

. . ,

.

() , ()

.

Marx.

, 36

.

. , 35

14756 .

, 5%,

551584, 540075 ( 525319 35 14756 35 ),

11059 .

Bauer

Luxemburg. ,

. Grossmann

. ,

.

. ,

11


12/25

,

.

,

, .

Grossmann, 36

5616200 551584 .

540075.

( 5616200/551584=10.18),

540075 * 10.18=5499015.

117185 (5616200 - 5499015 =117185)

. Grossmann,

Marx

.

Bauer Grossmann

Orzech & Groll (1983)

Bauer Grossmann Harrod. Bronfenbrenner & Wolfson (1984) Samuelson & Wolfson (1986)),

Orzech & Groll. Bronfenbrenner &Wolfson (1984, .180-1),

1920 1930 (Luxemburg, Bauer, Grossmann .)

.

() ()

. ,

Harrod Domar. ,

, 1920 1930

:

() , ,

,() ,

.

,

,

.

, Bauer

Grossmann Orzech, Groll, Bronfenbrenner, Wolfson Samuelson

Harrod Domar.

. Grossmann, Bauer,

( ).

.

,

. . ,

(

) :

Vt = Vt Vt = (1+) Vt-1 (1)

, (v

s=s ) s=.

, () : = V. ,

:

12


13/25

t = Vt = (1+) Vt-1 (2)

(AC),

(AV)

(): = AC+ AV +

, . :

Ct = Ct Ct = (1+) Ct-1 (3)

, ,

, :

t = Vt + Mt

, (1) (2), :

t = (1+) Vt-1 + (1+) Vt-1 (4)

:

Vt = V1(1+)t-1 (1)

Ct = C1(1+)t-1 (2)

t = V1 (1+)t-1 (3)t = (1+) (1+)

t-1 V1 (4)

:

Ct = C1(1+)t-1 (5)

Vt = V1(1+)t-1 (6)

, , >.

, ,

. t (

) M t .

:

+

++

=+

+++=

+=

1

1

1

1

1

1

1

1

1 )1

1(

)1(V

)1()1( tt

tt

t

tt

t

t

V

CVaC

M

AVAC

M

A(7)

:+

+

1

1 a.

, , (>):

)1()(C

(t tt

tt

tt

t

tt

tt

t

ttt

tt

t

tt

tt

VC

CR

VC

C

VC

VC

V

VCC

VC

V

VC

MR

+=

+

++

=++

=+

=+

=

, (1) (2), :

))1()1(

)1(1(

1

1

1

1

1

1

++++

=tt

t

tVC

CR

(8)

,

. >,

Rt 0. :

(8) ,

- :

13


14/25

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

)1(

)1(lim1

1

)1(

)1(lim1

1

)1(

)1(lim

)1(

)1(lim

)1(

)1(lim

)1()1(

)1(lim

++

+=

++

+=

=

++

+++

++

=+++

+

t

t

t

t

t

t

t

t

t

t

tt

t

aC

V

aC

V

aC

V

aC

aC

aC

aC

VaC

aC

(8)

>, 11

1 (V+M) ( V

) ,

gG . ,

.

Bauer Grossmann

Harrod.

, Harrod

. :

GW = / = s

:

S:

s: ( )

:

:

:

S = sY

6 = :

)1(11

1

VCCRt +

= .

14


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= /

Harrod ( )

Bauer Grossmann:

St = Yt (Vt + AVt + Kt) = (Vt + Mt) (Vt + AVt + Kt) = (Vt + ACt + AVt + Kt) (Vt+ AVt + Kt) = ACt

, Harrod

.

Harrod

. Bauer Grossmann

:

st = St/Yt = It/Yt = ACt/(Vt + Mt) =1

1

1

1

)1)(1(

)1(

V

Ct

t

+++

(9)

O :

= / = /C = 11

1

1

)1(

)1()1(

+

++t

t

C

V

(10)

(9) (10) :

st =

Bauer Grossmann

Harrod. , Orzech & Groll,

. Harrod st . , Bauer

Grossmann st ( )

. ,

. (9) :

1

1

1

)1

1

()1(

+

+

+=t

t V

C

s

(11)

, (1+)/(1+)>1 , st .

, (6) :

1

1

1 )1

1(

)1(

+++

= tC

V

(12)

, (1+)/(1+)


16/25

.

. ,

. Harrod,

, . :

1

s

)1)(1(

)1(s)(ss

*

t

1

1

1

1*

t

*

tt +

=++

+==

V

V

Y

V t

t

t

(13)

,

( >0).

,

.

0


17/25

Samuelson & Wolfson

. , ,

. ,

. ,

Grossmann,

.

, Bauer

Grossmann,

( -) . Samuelson & Wolfson (1986)

, (

) *

.

. Bauer Grossmann

Harrod. .

Harrod (

).

Samuelson & Wolfson (1986)

.

,

.

, Luxemburg.

Bauer Grossmann,

-

. ,

Bauer Grossmann

.

.

, Bauer Grossmann

,

. .

,

Grossmann Bauer. ,

,

. ,

Bauer .

,

( )

Grossmann.

( )

. ,

.

, -

Bauer Grossmann

17


18/25

. ,

Grossmann.

4. Grossmann

Grossmann , ,

.

(.. Helene Bauer,

Otto

Bauer). , ,

.

.

Grossmann *

. . Grossmann,

Mattick, :

...

... , , ,

.

.

,

.

...

,

.

(Jacoby (1975), p.37)

(.. Bauer). ,

-

(.. Howard & King (1988) -

Grossmann

.

,

. , Grossmann,

,

,

.

Sweezy ((..), .236-9) Grossmann.

Grossmann

Sweezy . Sweezy

Grossmann .

(

). Grossmann

,

. Sweezy

. , Marx

( ). Grossmann

18


19/25

. , Sweezy

(

). ,

2 .

.

.

Grossmann

, . Grossmann

Luxemburg Bauer

. ,

() .

Howard & King (1988)

Grossmann. O Kuhn (1995)

. Howard & King

(1988) (.. Trigg (2004)) - .

To Grossmann Say

(

).

. ,

,

.

. Shoul (1957) Marx Say.

Say, Marx

(layered abstractions )

.

.

/

. ,

(

)

(

).

,

, (

) .

,

,

,

.

19


20/25

. , .

.

. Marx (1978), ., .268)

13 :

,

,

,

.

Marx

.

(

[profit squeeze]). Ricardo

, , .

Grossmann .

- - .

, Marx

.

:

,

, :

, .. 100,

. , ,

, ,

,

. :

,

, ,

.

, ,

, , .

(Marx (1978), ., .272-3)

Marx

(

) (

), :

, ...

,

,

.

(Marx (1978), ., .296)

20


21/25

, (Marx

(1978), ., .285).

, Marx (1978), ., .294),

Grossmann:

,

: ,

, , ,

, ,

,

.

, ,

, ,

, .

, (Marx (1978), ., .295)

, ,

. ,

( )

.

, Marx (1978), ., .296) - Grossmann

:

...

, . .

, , ,

, .

Grossmann, ,

.

7.

( Fine

Harris (1986)). ,

Marx

. Kuhn (1995) Grossmann

.

Marx Grossmann

.

, Bauer Grossmann,

( Grossmann).

7

, . , Grossmann

.

21


22/25

,

,

.

: R = s/(c+v).

.

,

(

). ,

. .

:

st = s1(1+)t-1 (15)

, :

t = stVt = s1(1+)t-1 V1(1+)

t-1 (16)

(9):

st = St/Yt = It/Yt = ACt/(Vt + Mt) = =

)])1(1[)1(

)1((

)1()1()1(

)1(1

1

1

1

1

1

1

1

1

1

1

1

1

1

++++

=++++

+tt

t

ttt

t

s

a

V

Ca

VsV

C

(17)

(17), ,

:

1

11

1

1

11

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

11

1

1

1

1

1

1

1

1

]1

1lim[])1(

)1)(1(lim[

)1(

)1()1(lim*0

)1(

)1()1(lim

)1(

)1(lim

)1(

)1(lim

)1()1()1(

)1(limlim

++++

=

+++

=

=

+++

+

=

+++

+++

++

=

=++++

+=

tt

t

tt

t

tt

t

t

t

t

ttt

t

t

Vs

C

Vs

C

VsV

C

VsV

C

VsV

Cs

1+ 1+++ ,

, ++. , :

1) ++> 1]

1

1[

+

+++ t

.

2) ++


23/25

st , 0

lim1

1

=

Vs

Cst

.

st ,

Vs

C

Vs

Cst

1

1

1

1

1

lim =

= .

.

.

.

. ,

.

,

.

,

8.

, . , ,

. , ,

. , ,

.

, ,

. ,

. ,

,

.

5.

Henryk Grossmann

.

, .

,

. ,

Hilferding

Luxemburg. Grossmann

Marx

Rosdolsky .

8 Bronfenbrenner & Wolfson (1984, .179) Samuelson & Wolfson (1986, part )

Bauer Grossmann .

:

1) = + , st

2) < + , st 0.

3) = + , st

., Samuelson & Wolfson (1986, .76) .

23


24/25

Grossmann

- . ,

. ,

Luxemburg

.

,

. ,

,

. Bauer

,

Grossmann

.

.

* Grossmann .

Marx

.

(.. Shaikh

(1978b), Trigg (2004)).

Grossmann

.

, ,

( )

1920 1930

.

Bauer, O. (1913), Die Akkumulation von Kapital, Die Neue Zeitno.31, pp.831-7, 862-74.

Translated in History of Political Economy, 1986, no.18, pp.87-11110.

Bronfenbrenner, M. & Wolfson, M. (1984), Marxian macrodynamics and the Harrod growth

model,History of Political Economy vol.16, no.2, pp.175-186.

Dommar, E. (1946), Capital expansion, rate of growth and employment, Econometrica

no.14, pp.137-47.

Fine, B. & Harris, L. (1986), , : Gutenberg.

Fine, B. (1989),Marxs Capital, London: Macmillan.

Foley, D. (1986), Understanding Capital, Cambridge MA: Harvard University Press.

Grossmann, H. (1929),Das Akkumulations und Zusammenbruchsgesetz des Kapitalistichen

Systems (Zugleich Eine Krisentheorie), Leipsig: Hirschfeld abridged translation (1992), TheLaw of Accumulation and Breakdown of the Capitalist System, London: Pluto Press.

24


25/25

Harrod, R. (1939), An essay in dynamic theory,Economic Journalno.49, pp.14-33.

Harrod, R. (1948), Towards a dynamic economics, London.

Howard, M.C. & King, J.E. (1988), Henryk Grossmann and the Breakdown of Capitalism,

Science & Society vol.52 no.3, pp.290-309.

Jacoby, R. (1975), The Politics of the Crisis Theory: Towards the Critique of Automatic

Marxism II, Telos no.23.

Kuhn, R. (1995), Capitalisms Collapse: Henryk Grossmanns Marxism, Science & Society

vol.59 no.2, pp.174-192.

Kuhn, R. (2004), Economic crisis and socialist revolution: Henryk Grossmans Law of

accumulation, its first critics and his responses, Research in Political Economy vol.21.,

http://eprints.anu.edu.au/archive/00002400/01/Economic_crisis_and_socialist_revolution_epr

int_secure.pdf.

, ., , . & , . (1999), ,

: .

Marx, K. (1978), , , , , : .

Mavroudeas, S. (1992), Relations between the Two Departments of Production and the

Problem of the So-called Motive Impulses, Spoudai vol.42 no.2, pp.116-129.

Okishio, N. (1961), Technical Change and the Rate of Profit, Kobe University Economic

Review n.7, pp.85-99.

Orzech, Z. & Groll, S. (1983), Otto Bauers scheme of expanded reproduction: an early

Harrodian growth model,History of Political Economy vol.15, no.4, pp.529-548.

Rosdolsky, R. (1977), The Making of Marx's Capital, London: Pluto Press.

Samuelson, L. & Wolfson, M. (1986), Expository Marxism and comparative economic

dynamics,History of Political Economy vol.18, no.1, pp.65-85.

Shaikh, A. (1978a), Political economy and capitalism: notes on Dobbs theory of crisis,

Cambridge Journal of Economics no.2.

Shaikh, A. (1978b), An Introduction to the History of Crisis Theories, in U.S. Capitalism inCrisis, New York: URPE, pp.219-241.

Shoul, B. (1957), Karl Marx and Says Law, Quarterly Journal of Economics vol.71, no.4,

pp.611-626.

Sweezy, P. (..), , : Gutenberg.

Trigg, . (2004), Kalecki and the Grossmann Model of Economic Breakdown, Science &

Society vol.68 no.2, pp.167-205.

Ο Henryk Grossmann και η Πτωτική Τάση του Ποσοστού Κέρδους: Μία...

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