火曜日, 12月 13, 2016

Michal Kalecki The Marxian equations of reproduction and moderneconomics

NAMs出版プロジェクト: カレツキ(Kalecki):「投資と資本家消費が利潤と国民所得を決定する」という 命題

     栗田康之 :カレツキの資本主義経済論―マルクスおよび宇野理論との関連で―(PDF形式:563KB)


Michal Kalecki
The Marxian equations of reproduction and modern economics
Version of Record - Dec 1, 1968

  That Marx was deeply conscious of the impact of effective demand
upon the dynamics of the capitalist system follows clearly from this passage
of the third volume of the Capital : "The conditions of direct exploitation
and those of the realisation of surplus-value are not identical. They
are separated not only by time and space but logically as well. The former
are limited merely by the productive capacity of the society, the latter by
the proportions of various branches of production and by consumer power
of the society ".

カレツキ(Kalecki):「投資と資本家消費が利潤と国民所得を決定する」という 命題
( 経済学リンク::::::::::

カレツキ「国民所得の経済表」(tableau economique of the national income)
("The Marxian equations of reproduction and modern economics"「マルクスの再生産の方程式と近代経済学」1968,1991未邦訳より)

| 1  2  3|  |
|P1 P2 P3| P|
|W1 W2 W3| W|
|I  Ck Cw| Y|


NAMs出版プロジェクト: ケインジアンの交差図
ケインズ=カレツキ往復書簡 Keynes ,Kalecki Correspondence 1937


The Marxian equations of reproduction and modern economics *



Before we start dealing with the proper subject of this paper we shall
modify somewhat the Marxian division of economy into departments in
order to simplify our argument and in order to focus on the basic problem
of the reproduction schemes.
  First, instead of including producer goods in Department 1, we will ,
assume that it covers the total value of gross investment inclusive of
the respective raw materials. Thus this department represents the integrated
production of all final non-consumer products. (We disregard
in our argument as does Marx ー when he deals with reproduction schemes
ー both foreign trade and government revenue and expenditure.)
  Second, we treat likewise the consumer goods, i.e., we include in the
department which covers their output the production of respective raw
materials from top to bottom. Moreover, fully in the Marxian spirit,
we distinguish the following two departments : Department 2 producing
consumer goods for capitalists and Department 3 producing wage goods.
  We obtain thus the following " tableau économique" of the national ‘
income where Pi, P2, P3 are gross profits (before deduction of depreciation)
in the respective departments, WI, W2, W3 ー the respective wages; P and
W aggregate profits and wages, and finally I ー gross investment, C k ー capi-
talists’ consumption, Cw ー workers’ consumption and Y ー gross national
income (before deduction of depreciation).

* This article was presented as a background paper for the Symposium on the
 influence of Karl Marx on contemporary scientific thought, Paris, May 8-10, 1968,
 organized under the auspices of Unesco by the International Social Science Council
 and the International Council for Philosophy and Humanistic Studies.

  It will be assumed, as Marx does, that the workers do not save. Moreover,
we shall disregard the problem of possible piling up of stocks of
unsold goods as only a passing phenomenon. It is then easy to arrive
at the fundamental Marxian " equation of exchange " between Departments
1 and 2 on the one hand and Department 3 on the other.
Profits in the latter, P3, are materialised in the wage goods which are
left to the capitalists of that department after payment of wages W3 which
absorb an equal amount of wage goods. Thus the wage-goods of the
value P3 are sold to the workers of Departments 1 and 2, that is :

(1)   P3=W1+W2

  Marx considers this equation in the context of expanded reproduction
proceeding at a given constant rate r. It is easy to see, however, that the
equation holds good under all circumstances as long as there is no piling
up of stocks of unsold goods, as mentioned above.
  Considered in this general context equation (1) leads to a proposition
that - given the distribution of income between profits and wages in the
three departments - investment I and consumption of capitalists Ck determine
profits and the national income. Indeed, let us add PI + P2 to both
sides of equation ( 1 ). We obtain :
Hence :

(2) P=I+Ck

Moreover, if we denote Wl/Ⅰ , W2/Ck, W3/Cw by w1, w2, w3 respectively, we obtain
from equation ( 1 ) :(1-w3)Cw=w1Ⅰ+w2Ck

Consequently, we have for the consumption of wage goods :

(3) Cw=(w1Ⅰ+w2Ck)/(1-w3)

and for the national income :

(4) Y=Ⅰ+Ck+Cw=Ⅰ+Ck+(w1Ⅰ+w2Ck)/(1-w3)

  Thus the national income (or product) Y which can be sold and the
profits P which can be realised are determined in all circumstances (and
not only in a state of uniformly expanding reproduction) by the level of
investment I and consumption of capitalists Ck (given the distribution
of income between wages and profits). A question may be raised as to
why equations (2) and (4) must be interpreted in this way and not the
other way around, i.e., that investment and consumption of capitalists
are determined by profits and national income. The answer to this rather
crucial query is as follows.
  Investment and capitalists’ consumption in the short period considered
are the outcome of decisions taken in the past and thus should be
considered as given. With regard to investment, this follows directly
from the time-lag dependent on the period of construction. But changes
in capitalists’ consumption also follow those in profits with some delay.
Now, sales and profits in a given period cannot be a direct outcome of past
decisions : the capitalists can decide how much they will invest and consume
next year but they cannot decide how much they shall sell and profit. The
independent variables in a given period are investment and capitalists’
consumption. It is these magnitudes that through the equations (2) and
(4) determine the levels of national income and profits which can be realised.

  The decisions of capitalists with regard to their investment and consum-
ption are made in " real " rather than in money terms, that is I and Ck should
be calculated in stable prices. If wl, w2, w3 are constant and money wage
rates in all three departments change in the same proportion, the same
is true in this case of prices of the produce of these departments. Moreover,
as is easy to see, equations (2) and (3) will hold also in "real" terms.
Any increase in "real" investment or capitalists’ consumption results
under these circumstances, in an increase in output of Department 3, Cw
to provide for a surplus of this department P3 sufficient to meet the demand
generated by the higher wage bills in Departments I and 2, i.e., W2 + W3.
However, such repercussions of an increase in I or Ck are obviously
possible only if there exist unused capacities in Department 3. Imagine
that such is not the case. Then Cw is fixed in real terms, i.e., is equal to a
constant B. In this case the increase in money value of W1 + W2 will
cause a rise in prices rather than in production of wage goods. The result
will be that the " value of W1, W2 and W3 will be reduced as compared
with the levels which would be achieved if unused capacities existed in

Department 3. Consequently w1= W1/I , w2 = W2/Ck, w3=W3/Cw=W3/B, where
all magnitudes involved are to be now interpreted in " real " terms, will
decline in the proportion reciprocal to the increase in the prices of wage
goods. Equation (3) can now be written in the form :

When I and/or Ck decrease, w1, w2 and w3 decline in such a proportion
as to render the left hand side of the equation equal to B 1.
  Sections II and III represent in fact the gist of the modern theory of
effective demand. As will be seen, this theory may be derived in full
from the Marxian equation (1) representing the exchange between Departments
1 and 2 on the one hand and Department 3 on the other, if this
equation is considered in the general context rather than in that of uniformly
expanding reproduction.


Let us now turn to the significance of the equations (2) and (4) just
in the latter context, i.e., in the process of a uniform accumulation of capital.
Let us denote the " real " stock of capital by K, the rate of net accumulation
by r and the rate of depreciation by δ. In this case we may write
the " equation of accumulation ", recalling that I is investment gross of
depreciation, in the form :

(5)    I =(r+δ)K

Since we are considering the long-run process of growth, let us postulate
that capitalists’ consumption Ck is proportional to profits P. Since
according to formula (2) the latter are equal to I + Ck it follows that Ck
bears a constant relationship to I. We thus have :


In consequence we may write equation (4) in the form :

(6)   Y=(1+m)I+{I(w1+mw2)/(1−w3)}=I{1+m+(w1+mw2)/(1−w3)}

and substituting in it for I its value from equation (5) we obtain :

(7)     Y=K(r+δ){1+m+(w1+mw2)/(1−w3)}

In a socialist economy prices of consumer goods are always fixed relative to wages
in such a way as to secure a full utilisation of the productive capacity B, i.e., the equation
(w1I)/(1−w3) = B is permanently fulfilled (Ck obviously equals 0 in this case).

  The national income Y thus bears a constant relationship to the stock
of capital K (provided that w1, w2, w3 do not change (*2)). With a given
relationship of productive capacity to the stock of capital the degree of
utilisation of equipment is constant. Thus if capital equipment is
satisfactorily utilised in the initial position, this state of affairs is maintained
in the course of expanded reproduction and the problem of
effective demand does not arise.
  It is this approach that is inherent in many contemporary theories
of economic growth. In particular if we differentiate the equation (7)
we obtain :


Now, with a constant satisfactory utilisation of equipment, d Y is the
so-called capital-output ratio which we denote by R. Moreover, r K is
the net investment and thus rK/Y is the relative share of accumulation in
the national income which we shall denote by a. We thus have :

or   r=a/R

which is the basic formula of the Harrod-Domar theory (in which, however,
the coefficient a represents the " propensity to save of the population "
rather than the ratio of net accumulation out of profits to the national income
which depends on its distribution between capitalists and workers).
   In fact many of the contemporary theories of growth are simply
variations on the theme of Marxian schemes of expanded reproduction
which are represented in this paper by equations :

(1)  W1+W2=P3


(5)  I=(r+σ)K

  The repercussions of changes in investment and capitalists’ consumption
described in section II do not raise, I believe, any major misgivings.
In contrast to this, the moving equilibrium described in section III depends
on the very far-reaching assumption that capitalists are willing to engage

   *2. If the productive capacities of all three departments expand at the same rater
   the shortage of wage-goods discussed in the preceding section will not come into the picture.

in investment which increases their capital at a constant rate r per annum.
What happens, however, if having become more cautious (perhaps under
the influence of a change in the social structure of their class) they decide
to reduce investment from (r + δ) K to (r' + δ) K where r’< r?
  It follows directly from formula (7) that Y/K and thus the degree of utilisa-
tion of equipment declines in the proportion (r'+δ)/(r+δ) as a result of the decline
of effective demand. It is clear that in this situation the " cautious " capitalists
will not be any more agreeable to a lower rate of accumulation r’
but will reduce it further to r " < r’, and this will in turn affect correspondingly
the degree of utilisation of equipment.
  Some economists tend to consider this phenomenon as a down-swing
phase of the business cycle which takes place around the initial path of
growth. However, such a proposition is not well founded : there is no
reason why having left the initial unstable path, investment must fluctuate
around it rather than around the depreciation level δK. Or to put it in
Marxian terms : why cannot a capitalist system, once it has deviated downwards
from the path of expanded reproduction, find itself in a position of
a long-run simple reproduction ?
  In fact we are absolutely in the dark concerning what will actually
happen in such a situation as long as we have not solved the problem of
determinants of investment decisions. Marx did not develop such a theory
but nor has this been accomplished in modern economics. Some attempts
have been made in the development of the theory of cyclical fluctuations.
However, the problems of the determination of investment decisions involving
the elements associated with the long-run trend are much more difhcult
than in the case of the "pure business cycle " (i.e., in a system which
in the long run is subject to simple reproduction). I myself tried to do
something along these lines but I consider my work in this field to be definitely
of a pioneer nature (*3). One thing, however, is clear to me : the longrun
growth of the national income involving satisfactory utilisation of
equipment in a capitalist economy is far from obvious.

  That Marx was deeply conscious of the impact of effective demand
upon the dynamics of the capitalist system follows clearly from this passage
of the third volume of the Capital : "The conditions of direct exploitation
and those of the realisation of surplus-value are not identical. They
are separated not only by time and space but logically as well. The former

  *3. A new paper of mine on the subject appeared in the June issue of the Economic

are limited merely by the productive capacity of the society, the latter by
the proportions of various branches of production and by consumer power
of the society ".
  However, he did not systematically scrutinise the process described
by his reproduction schemes from the point of view of the contradictions
inherent in capitalism as a result of the problem of effective demand.
  It is one of his most prominent followers, Rosa Luxemburg, who expressed
very definite and even extreme views on the subject : she rejected altogether
the possibility of long-run expanded reproduction if no " external
markets " are in existence. By ”external markets ” she understood
those outside the world capitalist system consisting not only of underdeveloped
countries but also of the non-capitalist sectors of developed capitalist
economies, for instance, peasant agriculture as well as government purchases.
  Her argument suffers from the fact that she considers investment
decisions as being made by the capitalist class as a whole and this class is
frustrated by the knowledge that finally there is no market for the economic
surplus. However, her scepticism as to the possibility of long-run expanded
reproduction is valuable because the self-propelled growth of capitalist
economy cannot, indeed, be taken for granted. If this economy expands
at all without the assistance of "external markets" , this, to my mind, is
due to certain aspects of technical progress which, however, do not necessarily
assure a satisfactory long-run utilisation of equipment.
  Nor should the significance of ”external markets ”in the development
of capitalism be disregarded. In particular, in present-day capitalism
the " external markets " in the form of government expenditure,
especially on armaments, play an important role in the functioning of capitalist
economies. This expenditure to the extent that it is financed by
loans, or even by taxation of capitalists, contributes to the solution of the
problem of effective demand because its effect is not offset by the decline
in investment and consumption. (The latter would be the case if this
expenditure were financed by indirect or direct taxation of workers.) Thus
today the ”external markets ” in this particular form are even of greater
significance for expanded reproduction than at the time when Rosa Luxemburg
propounded her theory.
  The high degree of utilisation of resources resulting in fact from these
government-made”external markets ”has a paradoxical impact upon Western
economic theory. It creates an atmosphere favourable to the construction
of models for the growth of ” laissez faire ” capitalist economies
unperturbed by the long-run problem of effective demand.


Michal Kalecki is Professor of Economics at the Central School of Planning and Statistics
in Warsaw, and a member of the Polish Academy of Science. Among his major
works a:re Essay on the theory of the business cycle (1933)( in Polish); Theory of
economic dynamics (1954); Outline of the theory of growth in a socialist economy
(1963) (in Polish); " Trend and business cycles reconsidered ", Economic journal,
June 1968.

Michal Kalecki
The Marxian equations of reproduction and modern economics

Social Science Information
The online version of this article can be found at:
DOI: 10.1177/053901846800700609
Social Science Information 1968 7: 73
Michal Kalecki
The Marxian equations of reproduction and modern economics
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