David Yaffe - The Marxian Theory of Crisis, Capital and the State
(a) The rising organic composition of capital
Capitalist production has as its aim and driving force the production of surplus-value as additional exchange-value, Surplus-value is the difference between exchange-value of labour-power (representing that part of the working day in which the worker produces the equivalent of his own means of subsistence, necessary labour-time) and its productive capacity (representing the total working day). So that an increase in the productivity of labour, viewed capitalistically, makes no sense unless it increases surplus-value, i.e. decreases the value of labour-power or the time necessary to sustain and reproduce the workers. In other words, the productivity of labour is constrained by the need to produce value and surplus-value, is bound to the reproduction and self-expansion of capital.
The class struggle cannot prevent the fall in the value of labour-power (as productivity increases) but it can prevent, however, the occurrence that the value falls in the same relation as the productivity increase. That is, ensure a rise in real wages takes place with increases in productivity at the same time as an increase in surplus-value .
While, in exceptional cases, extended reproduction on the same technological scale is possible, in general, accumulation 'revolutionises out and out the technical processes of labour' . Since continuous accumulation under capitalist production conditions soon comes across the limits of the existing working population, that is since the normal working day has its physical and social limits , a transition from the production of absolute surplus-value (extension of the working day) to that of relative surplus-value (decreasing the necessary part of the working-day by an increase in the social productivity of labour) takes place. Together with this change, occurs, generally, an increase in the intensity of labour as capitalism tries to obtain more value per unit of time (increased expenditure of labour in a given time  from the same worker. Both increased productivity and greater intensity of labour augment the mass of articles produced in a given time and therefore shorten the part of the working day necessary to produce the wages of the workers. In so far as increasing intensity of labour requires, as compensation, an equivalent increasing real wage, it has no effect on the rate of exploitation. Otherwise, it will increase it. The increase of the intensity of labour has also physical and social limits so that the main method open for increasing surplus-value under developed capitalist conditions of production is to increase the productivity of labour, i.e. through technical change.
Increases in the productivity of labour from the standpoint of material production involve a change in what Marx calls the technical composition of capital.
'This latter composition is determined by the relation between the mass of the means of production employed, on the one hand, and the mass of labour necessary for their employment on the other' .
Increases in productivity involving increases in the technical composition of capital are represented under capitalist production by changes in the value composition of capital, i.e. the ratio of constant capital, or value of means of production, and variable capital or value of labour power. Between the technical and value composition there is a 'strict correlation'. Marx expresses this relation by saying that:
'The value composition, in so far as it is determined by its technical composition and mirrors the changes of the latter (is called) the organic composition of capital' .
The importance of grasping the process of accumulation from both its material and value side is crucial for understanding Marx's general theory.
The increase in the mass of means of production per worker (rise in the technical composition) is not merely a technical premise which enters into Marx's argument at a particular stage. It is the expression in general terms of the only way that the productivity of labour can rise under capitalist production, that is, by the extension of the social division of labour. This latter process, accompanied by an increase of the mass and volume of means of production, is also the basis of Marx's argument that the organic composition of capital, insofar as it is determined by the technical composition, will rise, although not as fast as the technical composition, due to the increasing productivity of labour.
'with the growth in the proportion of constant to variable capital, grows also the productivity of labour, the productive forces brought into being, with which social labour operates. As a result of this increasing productivity of labour, however, a part of the existing constant capital is continuously depreciated in value, for its value depends not on the labour time that it costs originally but on the labour time with which it can be reproduced and this is continuously diminishing as the productivity of labour grows. Although, therefore, the value of the constant capital does not increase in proportion to its amount, it increases nevertheless because its amount increases even more rapidly than its value falls'. 
Marx regarded it as an incontrovertible fact , as a self- evident or a tautological proposition  that the organic composition of capital should rise. To show that this was not a mere assertion but follows logically from the concept of capital itself will be the concern of the rest of this section.
The compulsion to employ machinery under capitalist production and to increase by these means the productivity of labour is expressed in reality by competition and the consequent need to reduce the costs of production. But this is not its explanation which must be deduced, in terms of Marx's method, from the concept of capital itself . The concept of capital is a contradictory one. On the one side we have capital as 'value in process' as value attempting to expand itself without limit and on the other side we have the working population, the limited basis of that expansion. Capital, therefore, must, on the one hand, try and make itself as independent as possible of that basis in its process of self-expansion; it attempts to reduce the necessary labour time to a minimum by increasing the productivity of labour. On the other hand it needs to increase the basis of its expansion, that is the labour-power available for exploitation; that means to increase simultaneously the working population. This can be expressed in another way. Given the working-population (in labour-time units, i.e. number of working days multiplied by the time per working day) available to society, then surplus-value can only be increased by increasing the productivity of labour, that is, by a reduction of. the (relative) working population. Similarly, assume a given development of the productive forces then surplus-value can only be increased by increasing the available working population, i.e. by an increase in the (relative) working population. Marx then argues that
'the unity of this contradictory tendency therefore, of the living contradiction, (comes) first with machinery' .
The dialectical solution to this contradiction (its removal to a higher level) is to increase the scale of production through the replacing of living labour by objectified (dead) labour in the form of machinery. In this sense machinery in so far as it comprises fixed capital is capital in its most adequate form.
'Thus machinery appears therefore as the most adequate form of fixed capital and fixed capital in so far as capital can be considered as being related to itself, as the most adequate form of capital generally' 
Marx clarifies this important point in the following passages taken from the Grundrisse:
'In machinery, objectified (dead) labour appears in the labour process itself as the dominating force opposed to living labour, a force represented by capital in so far as it appropriates living labour. . . .
The development of the means of labour into machinery is not fortuitous for capital ; it is the historical transformation of the traditional means of labour into means adequate to capitalism. . . .
Thus the full development of capital does not take place-in other words, capital has not set up the means of production corresponding to itself-until the means of labour is not only formally determined as fixed capital but has been transcended in its direct form, and fixed capital in the shape of a machine is opposed to labour within the production process. . . .
The quantitative volume, and the efficiency (intensity) with which capital develops as fixed capital, thus shows in general the degree to which capital has developed as capital, as domination over living labour and the degree to which it dominates the production process in general. It also expresses the accumulation of objectified productive forces and likewise of objectified labour. . . . ' .
What we have tried to show from an examination of the concept of capital is the necessity of increasing the social division of labour, through the application of machinery and therefore, of replacing on an increasing scale living labour by objectified (dead) labour. It follows from this that both the technical composition of capital and the organic composition of capital must increase in the process of capitalist production although the latter will not increase as quickly as the former due to increases in the productivity of labour.'
This is clearly expressed by Marx when he says :
'However much the use of machinery may increase the surplus-labour at the expense of necessary labour by heightening the productiveness of labour, it is clear that it attains this result, only by diminishing the number of workmen employed by a given amount of capital. It converts what was formerly variable capital, invested in labour power, into machinery which, being constant capital does not produce surplus-value. . . . '.
The necessity to continually extend and substitute objectified labour for living labour is clearly expressed in the condition for the introduction of machinery for the purpose of cheapening a product. That is, that less labour must be expended in the production of the machine than the (paid) labour (value of labour power) that is displaced by the employment of the machinery. The limit to the use of the machinery is given by the difference between the value of the machine and the value of the labour power replaced by it . This latter point can be expressed algebraically as follows:
ct + 1 - ct < vt - vt + 1 (usual notation)
Clearly if all labour available for exploitation is to be employed in the interest of capital this requires a further extension of the division of labour (material side) and C must increase at a faster rate than V for total social capital (value-side). Likewise if we consider total social capital in periods 't' and 't+1' and let w be the total value produced in one period of production, then with the usual notation:
Ct + Vt + St = wt
Ct + 1 + Vt + 1 + St + 1 = wt + 1
If the total working-time available to capital for its employment remains constant (v + s = const) then for accumulation to take place:
wt + 1 > wt
so that with or without an increase in the rate of exploitation, if all labour is to be employed:
Ct + 1 > Ct
Vt + 1 Vt
If the working population increases then accumulation would have to be that much faster (greater than the increase in the working population) to satisfy the condition for the introduction of machinery and the expansion requirements of capital.
Before finally concluding this section we must say something about capital saving innovation. This term can only have real significance if the innovation is brought about by 'gratis' increases in the productivity of labour. In general 'the increase in the productive power itself must be paid for from capital, it is not free (gratis)' . In such a case all the above arguments hold. What of the case where the cheapening of the elements of constant capital comes about 'gratis'? Marx compares this to the increased exploitation of natural wealth by the mere increase in the tension of labour power. 'Science and technology give capital a power of expansion, independent of the given magnitude of the capital functioning' .
A number of points can be made here:
(1) Capital saving innovation is a confusing ideological term. From the standpoint of total social capital such innovation is laboursaving; less labour time is necessary to reproduce constant capital. Such innovation would therefore allow accumulation to take place at a much faster rate without the increase in the organic composition that would have occurred without the innovation. So that accumulation and expansion will be given an impetus. Unless such inventions are continually re-occurring the general tendency of the organic composition to rise would reappear. Logically such 'gratis' inventions have to be treated separately from the accumulation process. They modify it but do not belong to its internal logic. To give any more significance to such inventions it has to be shown that, necessarily, they must continually re-occur.
(2) The introduction of such inventions pre-supposes that a developed capital structure already exists. That is, the development of capitalist production has taken place along the lines indicated above; accumulation and the consequent rising organic composition of capital. So that new 'waves' of such inventions have as a presupposition for their introduction into the production process a further normal development of capitalist production.
(3) The effect of such inventions will be less the higher the organic composition of capital already achieved i.e. more developed and widespread is capitalist production.
(4) There is no reason to assume that such 'gratis' inventions will not affect labour equally. After all a great deal of so-called `scientific management' is concerned with just such an application of 'science' to the labour process. If this is the case, the effect of such 'gratis' increases in productivity will be even more limited for the organic composition.
(b) The tendency of the rate of profit to fall and the crisis theory
That it is inherent in capitalist production for capital in the process of its self-expansion, to create an ever increasing basis for that expansion, that is, the proletariat , and at the same time seek to increase the productiveness of social labour, that is set into motion a constantly increasing quantity of means of production with less expenditure of labour power, leads to the formation of the industrial reserve army.
'The same causes which develop the expansive power of capital, develop also the labour-power at its disposal. The relative mass of the industrial reserve army increases therefore with the potential energy of wealth' 
Marx calls this the absolute general law of capitalist accumulation which like all other laws, he says, is modified in its working by many circumstances.
This law is the general expression of the contradictory nature of capitalist production, of the increase in the social productivity of labour under the 'domination of capital'. The size of the reserve army is relative to the rate of capital accumulation. During periods of stagnation and average prosperity it weighs down on the working population and during periods of rapid expansion, being a reservoir of labour power, holds back the 'pretensions' of the labour force .
The process of capitalist production, of accumulation and the increase of the social productivity of labour has so far been examined through an analysis of its 'invisible and unknown essence'. The appearance of surplus-value and rate of surplus-value 'on the surface of the phenomenon' in the form of profit and the rate of profit is the next step in the analysis.
'Although the rate of profit thus differs numerically from the rate of surplus-value, while surplus-value and profit are actually the same thing and numerically equal, profit is nevertheless a converted form of surplus value, a form in which its origin and the secret of its existence are obscured and extinguished. In effect, profit is the form in which surplus-value presents itself to view, and must be initially stripped by analysis to disclose the latter' .
The general law of capitalist accumulation from the standpoint of capital (and the capitalist) represents itself 'on the surface of the phenomenon' as a tendency of the rate of profit to fall. This is not a mechanical or algebraic relation but the expression of the contradictory nature of the accumulation process from the standpoint of capital.
The development of the social productivity of labour under capitalism, leads to a decrease of exchange-value of commodities relative to their use-value, (they are produced with less expenditure of labour-time) together with an increase of the mass of use-values. The accompanying rise in the organic composition of capital means that the mass of the means of production grows faster than the mass of labour employed the from material side, and from the value side, constant capital grows faster than variable capital. However, due to the increasing productivity of labour the value-composition rises slower than the technical-composition. If the rate of exploitation, the proportion between surplus and necessary labour-time remained the same, the rise in the organic composition of capital would lead to a falling rate of profit since it is only the -variable part of capital that yields surplus-value, while the rate of profit is measured on total investments, i.e. constant and variable capital. This inherent tendency for the rate of profit to fall is called by Marx
'the most important law of modern political economy and the most essential one for understanding the most complicated relationships. It is the most important law from an historical standpoint' .
Since the increase in the organic composition of capital represents an increase in productivity, the rate of surplus-value will not remain constant but will be increased because the value of the mass of products constituting the equivalent for the necessary labour-time is cheapened. This is the result of an increase in relative surplus-value.
'The tendency of the rate of profit to fall is bound up with a tendency of the rate of surplus-value to rise, hence with a tendency for the rate of labour exploitation to rise. . . . Both the rise in the rate of surplus-value and the fall in the rate of profit are but specific forms through which growing productivity of labour is expressed under capitalism' .
Does this mean that the fall in the rate of profit can be completely compensated by an increase of surplus-value? Or as Sweezy puts it
'it is not possible to demonstrate a falling rate of profit by beginning the analysis with the rising organic composition of capital' .
Marx was quite aware of this objection when he said that
'the compensation of the reduction in the number of labourers by means of an increase of exploitation has certain insurmountable limits. It may, for this reason, check the fall in the rate of profit, but cannot prevent it entirely' .
Sweezy could find no real answer to this problem because he fails to see the capitalist process of production from both its value and material side. His own discussion rests on purely value considerations whereas Marx sees the process in its entirety. Surplus-value is produced by living labour and the physical and social limitations and possibilities involving this labour affect the production of surplus-value.
'Inasmuch as the development of the productive forces reduces the paid portion of employed labour, it raises the surplus value, because it raises its rate; but in as much as it reduces the total mass of labour employed by a given capital, it reduces the factor of the number by which the rate of surplus-value is multiplied to obtain its mass. Two labourers, each working 12 hours daily, cannot produce the same mass of surplus-value as 24 who work only 2 hours, even if they could live on air and hence did not have to work for themselves at all' .
Although the argument is unclear as to what is the surplus labour-time of the twenty-four labourers, the point is clear. While the means of production per man employed have no 'finite' limit theoretically the mass of surplus-value produced by a worker has an impassable limit, namely the duration of the working day. Further as capitalism develops it becomes increasingly more difficult to shorten the necessary labour-time by an increase in productivity.
'The greater the surplus-value appropriated by capital because of the augmented productivity . . . or the smaller the already established fraction of the working-day which provides an equivalent for the workers so much the smaller is the increase in surplus-value which capital can obtain from an increase in productivity. Surplus-value increases, but in ever diminishing proportion to productivity. To the extent that capital is already developed . . . so much the more frightfully must it increase productivity even to expand (i.e. to increase surplus-value) by a lessened proportion-because its barrier always remains the proportion between the fraction of the day which expresses necessary labour and the entire working-day. Only within these boundaries can it move,'  .
Marx gives numerous arithmetical examples in the Grundrisse of the decreasing effect an increase of productivity of labour will have, the smaller is the already established part of the working day which provides an equivalent for the workers. We shall just give one of his extreme examples which makes the point very clear. Suppose the necessary labour is already reduced to 1/1,000 of the working day. The total surplus-value would be 999/1,000. Increase the productivity of labour by a thousand so that the necessary part of the working day is 1/1,000,000 and the total surplus value 999,999/1,000,000. Now the increase in surplus-value due to a thousand-fold increase in productivity will be
999,999 - 999 = 999
1,000,000 1,000 1,000,000
So that a thousand-fold increase in the productivity of labour increases surplus-value by less than 1/1001 (or 0.1 %). While this rather unrealistic example only brings the point home, the point can be made more generally.
If n is the labour-time available to society (assumed constant). Then with the usual notation
v + s = n (1)
If e is the rate of exploitation (= s/v) , then
s + s = n (2)
So that: s (1/e + 1) = n (3)
Differentiating (3) with respect to time, we obtain
ds ( 1 + 1 ) - s de = 0 (4)
dt e e2 dt
1 . ds = 1 . 1 . de (5)
s dt (1 + e) e dt
So that a unit increase in s will require a larger increase in e, the larger e is already. So that the higher the rate of exploitation (the less-time it requires to reproduce the value of labour-power) the greater must be the increase in the rate of exploitation in order to increase the mass of profits sufficiently to compensate for the falling rate of profit.
The tendency of the rate of profit to fall is an expression of the increasing difficulty in raising the rate of exploitation sufficiently to satisfy the self-expansion requirements of capital as capitalism progresses.
The accumulation process involves a rise in the organic composition of capital a rise in the productivity of labour and a relative decrease (absolute increase) in the labour employed. These express themselves in a tendency of the rate of profit to fall, although the mass of profits or surplus-value absolutely increases and the rate of exploitation increases. This means,
The progress of the process of production and accumulation must therefore, be accompanied by a growth of the mass of available and appropriated surplus labour and consequently by a growth of the absolute mass of profit appropriated by the social capital. . . . The same laws, then, produce for the social capital an increase in the absolute mass of profit and a falling rate of profit.' 
So long as accumulation increases the mass of profits sufficiently to compensate for the falling rate of profit, all is well. This is the case if capital grows at a faster rate than the rate of profit falls. This only expresses the fact that capital of a higher organic composition of capital must grow at a faster rate than that of a lower composition to employ the same, let alone an increased amount of labour-power.
Besides the immanent tendency, within the accumulation process, to check the tendency of the rate of profit to fall by an increase in the mass of profits there are other counteracting tendencies that can apply temporarily. These are the increase in the rate of surplus-value by lengthening the working-day or intensification of labour, the pushing down of wages below their value, the cheapening of the elements of constant capital, and foreign trade. The fall, in the rate of profit is, therefore, not linear but in some periods is only latent coming to the fore more or less strongly in other periods and appearing in the form of a crisis cycle.
On this theory capitalism is always driven to a higher and higher productivity of social labour in order to produce sufficient surplus-value for the continuous reproduction and expansion of the growing capital. But this process is a contradictory one.
'The contradiction . . . consists in this that the capitalist mode of production has a tendency to develop the productive forces absolutely, regardless of value and of the surplus-value contained in it and regardless of the social conditions under which capitalist production takes place; while it has on the other hand for its aim the preservation of the value of the existing capital and its self expansion to the highest limit (that is an ever accelerated growth of this value)' 
When the expansion of production outruns its profitability, when existing conditions of exploitation preclude a further profitable capital-expansion or what amounts to the same thing, an increase of accumulation does not increase the mass of surplus-value or profits, an absolute over-accumulation has occurred and the accumulation process comes to a halt. This interruption of the accumulation or its stagnation constitutes the capitalist crisis. It represents an overproduction of capital with respect to the degree of exploitation. From the point of view of profitability at this stage, existing capital is at the same time too small and too large. It is too large in relation to the existing surplus-value and it is not large enough to overcome the lack of surplus-value. Capital has only been over-produced in relation to profitability. This is not a material overproduction for the world in this respect is undercapitalised . This stresses once again the central contradiction between the commodity as a use-value and as an exchange-value, between production for use and that for profit.
There exists besides the Marxian theory of value and accumulation (of which the second is only a more concrete development of the first) no separate theory of crisis. As Mattick has put it:
'Marx's value theory of capital development is at once a general theory of accumulation and a special crisis theory; that is to say neither one nor the other can be dealt with separately'. 
Although the actual crisis has to be explained out of the real movement of capitalist production, credit and competition , it is the general tendencies of the accumulation process itself and the long-run tendency of the rate of profit to fall that constitutes the basis of that explanation. These tendencies have been analysed through an understanding of the 'inner nature of capital'. The overproduction of capital arises out of the conflict between the increase and development of the productivity of labour from a material standpoint and the narrow basis and aim of that development under capitalist conditions of production, i.e. the self-expansion of capital.
'The real barrier of capitalist production is capital itself. It is the fact that capital and its self-expansion appear as the starting and closing point, as the motive and aim of production; that production is merely production for capital, and not vice versa, the means of production mere means for an ever expanding system of the life process for the benefit of the society of producers. The means-unconditional development of the productive forces of society-comes continually into conflict with the limited end, the self-expansion of the existing capital' 
We have shown the tendency that capitalism has towards overproduction and crisis without considering competition. In the discussion so far it has also been assumed that all goods are actually sold at their value and there are no realisation difficulties; that is the tendency towards crisis and overproduction of capital can be deduced independent of such considerations. In order to indicate why the crisis takes the form of 'periodically reoccurring cycles' with each cycle tending to be more severe than the next, we need to discuss the role of the crisis in restoring the conditions for a new profitable expansion. It is here that competition becomes a decisive factor in the whole discussion.
With a relatively decreasing mass of surplus-value in relation to the growing mass of constant capital, competition for this declining mass becomes a vital element in the accumulation process. Competition is the result of the struggle for profits and extra-profits accompanying the rise in the productivity of labour. For those first introducing new methods of production can sell their cheaper produced commodities above their price of production, and under their social value, (above their individual value). Competition is the force that equilibrates different production prices to a new social average value.
'a fall in the rate of profit connected with accumulation necessarily calls forth a competitive struggle. Compensation of a fall in the rate of profit by a rise in the mass of profit applies only to the total social capital and to the big, firmly placed capitalists. The new additional capital operating independently does not enjoy any such compensating conditions. It must still win them and so, it is that a fall in the rate of profit calls forth a competitive struggle amongst capitalists, not vice versa' 
Competition comes into its own in the crisis situation. The crisis, while representing an end to the accumulation process, is nevertheless the precondition for its continuation on a higher level. In the crisis profitability of capitalist production is restored, in principle, in a number of ways. Assuming no physical destruction of capital takes place (either through lack of use or abandonment or destruction through war), the same quantity of use-value, of means of production, before the crisis represents a smaller exchange-value of means of production after the crisis through _devaluation of constant capital. However, neither the rate of surplus-value nor the mass of surplus-value are affected as they relate to the unaltered use-value of capital and hence to its unaltered productive capacity. Hence the rate of profit will increase because the same amount of surplus-value relates to a lower total capital. Clearly, this only holds once the expansionary process has begun again and represents a redistribution of profits (or potential profits) in favour of those capitalists who have managed to buy up capital 'cheaply'.
Secondly, with the centralisation and restructuring of capital that takes place in the crisis through competition, only the more productive capitals survive and allow for a higher social productivity of labour with increased markets. It is this mechanism which decreases the value of labour-power and thereby increases the rate of exploitation and mass of surplus-value. The larger markets allow for increasing 'economies of scale'.
Thirdly, this restructuring usually includes the abandoning of part of the least profitable and often obsolete constant capital and as such frees the surviving capital (in money or commodity form) for new, more productive investment.
Fourthly, due to the relative surplus-population (increase in unemployment) wages, which had a tendency to go above their value in the period of prosperity previous to the crisis are now temporarily pushed below their value. Simultaneously, the working-day can also be lengthened and the intensification of labour can be increased resulting in an addition of surplus-value. Further through 'rationalisations' in the labour-force new methods and techniques of work, new methods of production can be introduced without the 'frictions' that would have taken place before the 'disciplining' effect of the crisis on the labour-force.
All these factors together play a role in the restoration of profitability of capital and this allows the accumulation process to continue on a new higher level. The crisis therefore, removes the temporary barrier to further accumulation but only to set new limits on a higher level still.
We have explained why competition has only been introduced at this stage. In effect competition takes place throughout the production process reflecting the striving after surplus-value and tending to equalise profit rates, establishing prices of production and driving the less efficient capitals out of business. But it is only in the crisis that competition really becomes `a life and death struggle'.
'Under all circumstances, a portion of the old capital would be compelled to lie fallow, to give up its capacity of capital and stop acting and producing value as such. The competitive struggle would decide what part would have to go into this fallow state. So long as everything goes well, competition effects a practical brotherhood of the capitalist class as we have seen in the case of the average rate of profit, so that each shares in the common loot in proportion to the magnitude of his share of investment. But as soon as it is no longer a question of sharing profits, but of sharing losses, everyone tries to reduce his own share to a minimum and load as much as possible upon the shoulders of some other competitor ... competition then transforms itself into a fight of hostile brothers. The antagonism of the interests of the individual capitalists and those of the capitalist class as a whole then makes itself felt as previously the identity of these interests impressed itself practically as competition' 
The overproduction of capital, and therefore the crisis, was due to the fact that accumulation and the expansion of production had outrun profitability. Given the degree of exploitation any further capital invested would not yield sufficient profits. The crisis mechanism restructures capital and increases the rate of exploitation so that a new expansion becomes possible. In this sense the capitalist crisis can be regarded as the strongest counteracting tendency to the long-run tendency of the rate of profit to fall . The tendency towards 'breakdown' and stagnation therefore takes the form of cycles due to the effects of the countertendencies of which the actual crisis is an extreme case.
'Otherwise, it would not be the fall of the general rate of profit, but rather its relative slowness, that would be incomprehensible. Thus, the law acts as a tendency. And it is only under certain circumstances, and only after long periods that its effects become strikingly pronounced' .
The actual periodicity of crises simply stems' from the ability of capitalism to overcome the overproduction of capital, through changes in the conditions of production which increase the mass of surplus-,value and restore an adequate rate of exploitation relative to existing capital.
Whether the crisis will be successful in restructuring capital to a greater profitability clearly is not merely a narrow 'economic' question. Nothing is more clear in the crisis than the wasteful and destructive side of capitalism. Its 'civilising' tendencies are seen to be bought at an enormous expense. The struggle between capital and labour, the class-struggle in the widest sense, becomes a struggle about the system itself. The outcome of the struggle cannot be predicted, and in this sense `no crisis is the final crisis' for capitalism. The 'crisis' is the most poignant expression of the 'disease' of the contradictions of capitalist production but it is also the `cure' `the forcibly established unity of elements that have become independent' 
 This important point, overlooked by those who use a Ricardian type model, i.e. see wages inversely proportional to profits, is merely another way of stressing that
'the rate of accumulation is the independent not the dependent variable; the rate of wages the dependent, not the independent variable' (Capital Volume I, p. 620).
Marx again makes this point in relation to the rise and fall of the rate of profit in Theories of Surplus-Value Part III p.312.
'The rise and fall in the rate of profit insofar as it is determined by the rise or fall of wages resulting from the conditions of demand and supply (in the labour market) . . . has as little to do with the general law of the rise or fall in the profit rate as the rise or fall in the market prices of commodities has to do with the determination of value in general'
This point could be particularly directed against many of the arguments in the Glyn & Sutcliffe book mentioned earlier.
 Theories of Surplus-Value Part III p.312 and p.300.
 Capital Volume I p.510.
 Theories of Surplus-Value Part III p300.
 Capital Volume I p.524.
 The relevance of the class-struggle is important here. One aspect of productivity deal bargaining quite clearly involves the question of compensation for increases in the intensity of work.
 Capital Volume I p.612.
 Theories of Surplus-Value Part II p415-6.
 Theories of Surplus-Value Part III p.364.
 Ibid p.366.
 Grundrisse p.662.
 Ibid p.660-1.
 Ibid p.586. See David McLellan Marx's Grundrisse. McMillan & Co. 1971 p134 for English translation. Marx continues: 'On the other hand, in so far as fixed capital is firmly tied to its existence as a particular use-value, it no longer corresponds to the concept of capital which, as a value, can take up or throw off any particular form of use value, and incarnate itself in any of them indifferently. Seen from this aspect of the external relationships of capital, circulating capital appears as the most adequate form of capital as opposed to fixed capital.'
 Ibid p.585-7 and McLellan p.133-5.
 For a discussion of the relation between the technical composition, the organic composition of capital and the scale of production, see Theories of Surplus-Value Part III, p. 382.
 Capital Volume I p.407
 Ibid p.392
 Grundrisse p662.
 Capital Volume I p605
 'Accumulation of capital is therefore increase of the proletariat' Capital Volume I p.614.
 Ibid p.644.
 Ibid p.639.
 Capital Volume III p.47.
 Grundrisse p.634.
 Capital Volume III p.234. It is quite amazing that critics of Marx such as Joan Robinson can say that Marx's theory rests on the assumption of a constant rate of exploitation. Our analysis of the general law of capital accumulation shows nothing could be further from the truth. And Marx makes the point many times in Volume III of Capital. See Joan Robinson An Essay on Marxian Economics London MacMillan 1963,p38.
 P. Sweezy Theory of Capitalist Development 1962, p.103. M. Dobb in his Political Economy and Capitalism (1940) 1968, p.109 expresses a similar view which is repeated by M. Blaug in Economic Theory in Retrospect p.249-51. Heinemann London, 2nd Edition. 1968.
 Capital Volume III p.242. (slightly corrected translation).
 Grundrisse p.246.
 Ibid p.244 See also p.239-47
 We can assume a uniformly increasing population i.e. dn/dt = k (const).
Instead of (5) we would obtain:
1 . ds = k . e + 1 . 1 . de
s dt (1 + e)s (1 + e) e dt
As s increases k . e → 0 and our result is not significantly altered.
(1 + e)s
 Capital Volume III p.214 (The translation is taken from the C.H. Kerr ed. Chicago 1909. Volume III p.256).
 Theories of Surplus-Value Part II p.542.
 Although we cannot discuss the theory of imperialism here it can only be developed in relation to theory of crisis. For a discussion of the relation of accumulation and imperialism see my review article, 'Imperialism and the Accumulation of Capital', Bulletin of the Conference of Socialist Economists 2, 2 August 1972 p. 70 ff. See also Capital Volume III p.232-3.
 Capital Volume III p.244 (Translation Kerr ed. P.292. taken from)
 P. Mattick Marx and Keynes op. cit. p.68.
 See Rudi Schmiede op. cit., p. 165 for a discussion on this point.
 P. Mattick op.cit. p.98.
 Theories of Surplus-Value Part II p.512.
 Capital Volume III p.245 (Kerr ed. P.293)
 This is not quite the same as accepting Says Law for the purpose of developing the long-term trend. Says Law is concerned with the equality of an ex-post magnitude 'proceeds' to an ex-ante schedule 'aggregate supply price'. Marx assumes the identity of 'proceeds' and aggregate value and both of these are ex-post magnitudes. See S.H. Mage The Law of the Tendency of the Rate of Profit to Fall Columbia University Ph.D thesis 1963. University Microfilms Ann Arbor Michigan p129ff. For an interesting discussion on Karl Marx and Says Law see Bernice Shoul in J.J. Spengler and W.R Allen (eds) Essays in Economic Thought (Rand McNally, Chicago, 1960) pp. 454-469.
 Capital Volume III p.251.
 Capital Volume III p248 (Translation Kerr ed. Volume III p.297)
 Rudi Schmiede op. cit. p197.
 Capital Volume III p233.
 Mattick, op cit, p73.The definite crisis-cycle of the last century, as Mattick says, is not directly related to the Marxian theory.
of Surplus-Value, Part II p.513. In this sense
says 'Permanent crises do not exist' ibid, p. 497.
That Marx clearly held to such a position can be seen from this passage in the Grundrisse, a great deal of it written by Marx in English.
Hence the highest development of
productive power with the
expansion of existing wealth will coincide with depreciation of
capital, degradation of the labourer, and a most straightened
exhaustion of his vital powers. These contradictions lead to
explosions, cataclysms, crises in which by momentaneous
suspension of labour and
of a great portion of capital, the latter is violently reduced to the
point, where it can go on . . . whereby it is enabled (to) fully
(employ) its productive powers without committing suicide. Yet, these
regularly recurring catastrophes lead to their repetition on a higher
scale, and finally to its (capitals) violent overthrow'.
Grundrisse, p. 636.