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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
7/29/2019 Henryk Grossmann :
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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
7/29/2019 Henryk Grossmann :
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Marx
.
,
( ).
.
Marx,
,
(capacity utilization), .
(fixed capital)
.
, .
,
(, .)
. , ,
- ( )
( ).
( ). ,
, .
.
,
.
. ,
, .
.
.
( ) .
, . , ,
.
Marx
, ,
(..
), ,
.
Marx,
. , ,
.
,
.
3
7/29/2019 Henryk Grossmann :
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,
, :
o (s)
(v):v
s=s .
, vc
sR+=
.
v
c= .
1
s
+
=R
.
0
R
s1
s2
.
.
Okishio (1961), , (
, .),
. ,
,
.
. ,
,
.
. Okishio. , Foley (1986)
4
7/29/2019 Henryk Grossmann :
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,
. 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
7/29/2019 Henryk Grossmann :
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. Rosa
Luxemburg
. ,
Marx, ,
. Luxemburg
.
Sternberg,
Luxemburg -,
. , Sternberg,
, ,
.
Grossmann
.
, Grossmann
.
-
Luxemburg Sternberg.
Grossmann
(
, , .)
.
(
, .).
.
- .
Grossmann
,
.
.
.
- ,
( )
.
Bauer (1913).
, Luxemburg,
. Grossmann
4 Bauer 20
36 .
Bauer Grossmann
6
7/29/2019 Henryk Grossmann :
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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
7/29/2019 Henryk Grossmann :
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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
7/29/2019 Henryk Grossmann :
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( ) (
). ,
. , .
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
7/29/2019 Henryk Grossmann :
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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
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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
7/29/2019 Henryk Grossmann :
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,
.
,
, .
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
7/29/2019 Henryk Grossmann :
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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
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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
7/29/2019 Henryk Grossmann :
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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+)
7/29/2019 Henryk Grossmann :
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.
. ,
. 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
7/29/2019 Henryk Grossmann :
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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
7/29/2019 Henryk Grossmann :
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. ,
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
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. , 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
7/29/2019 Henryk Grossmann :
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. , .
.
. Marx (1978), ., .268)
13 :
,
,
,
.
Marx
.
(
[profit squeeze]). Ricardo
, , .
Grossmann .
- - .
, Marx
.
:
,
, :
, .. 100,
. , ,
, ,
,
. :
,
, ,
.
, ,
, , .
(Marx (1978), ., .272-3)
Marx
(
) (
), :
, ...
,
,
.
(Marx (1978), ., .296)
20
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, (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
7/29/2019 Henryk Grossmann :
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,
,
.
: 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) ++
7/29/2019 Henryk Grossmann :
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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
7/29/2019 Henryk Grossmann :
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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
7/29/2019 Henryk Grossmann :
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.