Shocks in the rate of surplus value as a cause of crises

First insertion on Heterodoxe Gazet Sam de Wolff: 16 juli 2012

E.A. Bakkum is professionally active in the Sociaal Consultatiekantoor, where he holds the position of solicitor. He loves to reflect on the labour movement.

Sam de Wolff tries in his main work Het Economisch Getij1 to offer a better foundation for the marxist view on the economic conjuncture. Here he adopts the starting point that the fluctuations in the size of the total product are causes by the economic expansion process itself2. In an earlier column it is explained how De Wolff develops an advanced version of the growth model of Marx. He shows how the model can calculate the increase of the organic composition in the departments. Of course a rising organic composition requires also a different growth rate in the various departments. This part of the work of De Wolff is a bit unsound, but it is still interesting enough to merit a discussion. For it is a classic example of the then marxist way to analyze the economy.

In his growth model there are three departments, equiped for respectively (I) the production of the means of production c, (IIa) the production of the wage (consumption) goods in behalf of the workers, and (IIb) the production of the luxury goods m in behalf of the entrepreneurs. Since it is a marxist model, that is based on the labour theory of value, the symbols c, v and m represent the value in labour time. The value of the total product in each separate department, and thus also in the economy as a whole, has the form

(1)     c + v + m = C'

For a complete description of the model and of the meaning of the symbols the reader can consult the column just mentioned, if desired.

Thus De Wolff succeeds in calculating the development of the economic system in the successive production periods. His results are shown in the tables 1 and 3 of the mentioned column. For the sake of convenience the table 1 is repeated in the present column. It is immediately obvious, that the rate of surplus value m' equals 1, and that the organic composition o is largest in the department I, and smallest in the department IIb. The growth factor G of the department I is 1.1, and of the department IIa 1.05.

Table 1: example of expanded reproduction in period 1
Source: Het Economisch Getij p.387

De Wolff assumes in his calculations, that the rate of surplus value does not depend on the time t. However in the tenth chapter of Het Economisch Getij he acknowledges that his assumption is not realistic. For the purpose of the continuing capital accumulation is precisely the rise of the labour productivity (ap). An increasing ap implies a fall of the piece-value of the goods. When the piece-value of the wage goods for the consumption of the workers decreases, then also the value of the wage sum will fall. Namely, in the first instance the worker does not base his wage demands on the labour value, but on the real basket of wage goods, which he gets hold of. A falling wage sum reduces the costs of production for the entrepreneur, so that he can appropriate a larger surplus value. In other words, the theory of Marx (and De Wolff) expects, that the rate of surplus value will rise continuously.

In this column it will be explained how according to De Wolff the increase of the rate of surplus value must occur as shocks. De Wolff formulates his model in a very succint manner. There is more to it than a first (or second) reading reveals. It is rather troublesome that De Wolff bases his argument only on the system of labour values, and says litte about the material system. Therefore now the implied assumptions in the model of De Wolff will be discusses in some detail3.

The material system

The formula 1 is an equation for the various labour values in the production. Of course she is based on the material production process, At the start of the production, at the time t, each department i (i = I, IIa or IIb) disposes of a quantity Pmi(t) of means of production, and of a quantity li(t) of labour time. Suppose that the workers are rewarded for a unit of labour time with a quantity wR of wage goods. That is to say, wR is the real wage level. For the sake of convenience it is assumed that the wage level does not depend on the time t. Then at the start the producer in the department i must dispose of a stock of wage goodsλi(t), given by

(2)     λi(t) = wR × li(t)

The result of the production process in the department i is a quantity Qi(t) of product. Here and in the rest of the column the parameter t no longer refers to time itself, but to the concerning production period, also called revolution (in German language Umschlag). In the marxist schemes it is assumed that the total product Qi(t) is used completely, either as the consumption of the entrepreneurs (department IIb), or as investments for the production period t+1. The assumption leads to two equations:

(3a)     Pm(t+1) = QI(t)
(3b)     λ(t+1) = QIIa(t)

In the set of equations 3a-b one has Pm = PmI + PmIIa + PmIIb and λ = λI + λIIa + λIIb. The growth in the production scheme takes on the form ΔPm(t) = Pm(t+1) − Pm(t) and Δλ(t) = λ(t+1) − λ(t). The stocks of means of production and of wage goods increase during each revolution.

In the book Het Economisch Getij De Wolff refers only in passing to the material system. By that a guileless reader runs the risk to mix up the material and value quantities. That would be disastrous for the understanding of the model.

The system of labour values

The material system can be transformed into a system of labour values. Here use is made of the piece-values of the products. Each unit of the means of production (say, a machine) has a labour value of wI. Each unit of the wage goods (say, a bale of corn) has a labour value of wIIa. And each unit of the luxury goods (say, a tin of caviar) has a labour value of wIIb.

Thus one finds a set of 9 equations between the material and value quantities (i = I, IIa, IIb):

(4a)     ci(t) = wI(t) × Pmi(t)
(4b)     vi(t) = wIIa(t) × λi(t)
(4c)     C'i(t) = wi(t) × Qi(t)

The set can be completed with the formula

(4d)     mi = m'(t) × vi

In the formula 4d m' is the rate of surplus value, also called the degree of expoitation. She is the ratio between the unpaid and paid labour time. It is generally assumed, also by De Wolff, that for a given revolution t the rate of surplus value is identical in all departments.

In fact the formula 4c is the definition of the piece-value: wi(t) = C'i(t) / Qi(t). This quantity is the foundation of the model of De Wolff with regard to the intermittend growth of m', and therefore merits a digression. In the introduction of the column it has been stated, that the piece-value is influenced by the labour productivity api(t). There are various ways to measure the labour productivity. This column selects the definition ap = Q / l. In other words, she counts the total number of products, that is produced per worker. Thus the piece-value can be written as wi(t) = C'i(t) / (li × api(t)).

In the labour theory of value by Marx the labour time l is split up in a paid part v and an unpaid part m. That is to say, one has

(5)     li(t) = vi(t) + mi(t)

Therefore the formula 1 can also be expressed as c + l = C', both in the department i and for the aggregate values of the economic system. Thanks to this relation the piece-value can be rewritten as

(6)     wi(t) = (ci(t) / li(t) + 1) / api(t)

The formula 6 shapes the dependency between wi and api 4. When ci/li remains constant with time, then the piece-value will be inversely proportional to the labour productivity.

Now finally the role of the rate of surplus value m' becomes clear. The combination of the formulas 2, 4b, 4d and 5 yields a useful formula:

(7)     m'(t) = 1 / (wR × wIIa(t)) − 1

In the formula 7 the fall of the piece-value wIIa(t) is accompanied by a larger rate of surplus value. That is to say, the rate of surplus value rises according as the labour productivity increases. A higher ap leads to more "exploitation", at least as long as the real wage level wR remains unchanged. After the derivation of the important formula 7 (which is mentioned in Het Economisch Getij only in passing and in a narrative way) everything is ready for the presentation of the arguments of De Wolff.

The excess of value in the department IIa

In the preceding column about the production scheme of De Wolff the rate of surplus value has been constant with time, namely with a value m'=1. Because of the formula 7 De Wolff acknowledges that m'(t) will rise as a consequence of the technological progress. De Wolff analyzes this case, and for convenience's sake assumes that nothing else changes. For the second period the producers employ the same amount of labour time li(2), and they again invest the total value c(2)=5555 of means of production.

Consider first the means of production. The table 2 is a repetition of the table 3 in the preceding column, that has been calculated for m'=1. Now De Wolff introduces a rising m', but he leaves all ci(2) intact. That is to say: for convenience's sake he keeps the ratio ci/li in the formule 6 constant, when the exploitation increases. The formula 4a shows, that this is conceivable in two situations. In the first situation the increased exploitation does not change the quantity Pm of the means of production or their piece-value wI. In the second situation the piece-value wI changes (most likely is a fall), whereas then in compensation the quantity of the means of production Pm(2) has to change (rise) in an inverse proportion.

Table 2: example of expanded reproduction in period 2 (m'= 1)
Source: Het Economisch Getij p.395

Apparently De Wolff in Het Economisch Getij is thinking of the first situation5. Incidentally the second situation is more intriguing, and according to the formula 6 she can occur as the result of a rising labour productivity apI(2). Your columnist can not resist the temptation to ponder a moment on this situation. If the quantity Pm(2) of the means of production rises, while as supposed the increased exploitation does not influence li(2), then apparently less hours of labour are expended per means of production (machines and the like). Then the technological progress is labour saving. The so-called technical composition T, defined as Pm/l, increases.

Now De Wolff focuses on the wage sum of the workers. Here the formula 7 is interesting. The increasing exploitation in the second period of production is causes by the falling piece-value wIIa. De Wolff imagines the case, where thanks to the rising labour productivity apIIa the wage sum can fall from 2352 to 2340. He acknowledges the possibility, that at the same time the real wage level wR(2) may slightly improve. However, for convenience's sake here a constant wR is assumed for all production revolutions. Then according to the formula 4b the piece-value will fall with 0.5%. According to the formula 7 this coincides with a 1% rise of the rate of surplus value (from m'=1 to m'=1.01). In other words, in the second period only 2340 of the total added value l with a size of 4707 would be needed as the wage sum for the workers.

De Wolff troubles his head about this. The wage goods that are produced in the period 1 with a value of 2352 (see table 1) are advanced for the wage sum in the second period, but this leaves behind a rest of 12. Your columnist wishes that De Wolff would have elaborated in more detail on this point. The vagueness of De Wolff forces your columnist to invent several interpretations of the text. Does De Wolff mean that the piece-value falls during the production, or only when it is over? Formulated in the economic jargon: does he use a temporal approach or a simultaneous one?6

In no way can your columnist create an excess of 12 (or any other value) by means of the simultaneous approach7. The most promising speculation is that in stead of the simultaneous approach, which is common nowadays, De Wolff chooses for the temporal approach. At present the last mentioned approach is only found in the temporal single system interpretation (TSSI). In the temporal case the piece-value wIIa falls during the production process. At the end of the first production period the producers of the department IIa discover, that their physical product product QIIa is 0.5% larger than they had expected in advance. That is to say, at the beginning they have invested too much, because they did not take into account the rising labour productivity. As a consequence they choicely obtain the yield of 2352, as intended in advance, but the produced quantity is too large.

Indeed in this interpretation of the text of De Wolff the producers have left wage goods with a value of 12. So the interpretation looks defendable. It does seem strange, that the producers do not foresee their productivity in advance. For the rising productivity stems from their own innovations. It is a case of stupid and avoidable overproduction. Apparently in the vision of De Wolff the producers are not flexible enough to adapt their production to the technological progress8. His approach reminds of the growth models in the Keynesian paradigm. Also those assume that the entrepreneurs base their expectations and investments on the steady growth path. They believe that the system expands, but its structure does not change.

Contrary to the simultaneous vision, the temporal view ignores the fall of the piece-value between two revolutions. For she assumes, that the time interval between the revolutions is insignificant. The producers start the next production process immediately after the completion of the previous revolution.

Your columnist must admit, that he is not one hundred percent sure about the intention of De Wolff. Schemes of the value-system would have created clarity, but they are absent in this paragraph of Het Economisch Getij. If De Wolff indeed has the temporal explanation in mind, then that speaks well for his fine economic intuition. It means that he advocates a dynamic model, and that in a period, when most economists already had adopted the simultaneous vision of Bortkiewicz. The readers are invited to voice their opinion of the matter. After this heartfelt cry your columnist returns to the argument of De Wolff.

De Wolff asks the question what will happen with the value excess of 12. He considers three possible applications: (1) more consumption for the capitalists; (2) the start of a new department Ib; (3) the expansion of the department IIb. Now each of these applications is "disssected with the sharp dissecting-knife of the analyses" by De Wolff9.

More consumption for the capitalists

The capitalists can add the wage goods at a value of 12 to their surplus value. Then they must consume those goods by themselves, or they may give them away, for instance to the unemployed. De Wolff does not even want to consider the last option. But he also rejects the use for own consumption, because the model assumes explicitely, that the consumption of the capitalists is limited to the luxury goods from the department IIb, in casu tins of caviar. They do not like raw beans, in casu the corn.

The start of a new department Ib

So according to De Wolff there is a value excess of 12, consisting of wage goods, and for the moment your columnist accepts this fact. It is not much use for the capitalists themselves, and so they are forced to pay workers with it. The capitalists can start a new department Ib, where workers can be hired with the total value of 12. Those workers are always available, for in the capitalism according to Marx there is a structural reserve army of unemployed. Since De Wolff assumes that the relation c(2)=5555 remains valid, there is no excess of means of production (machines, equipment)10. Therefore the additional workers will have to operate (almost) without means of production. The organic composition in the new department would be extremely low.

De Wolff knows only one branche where this requirement is satisfied, namelijk the industry of extraction (mining). He cites from the first volume of Das Kapital by Karl Marx: In the extractive industry - the mines for instance - the raw materials are not parts of the advanced capital. Here the labour object is not a product of former labour, but it is granted for free by nature. Thus: iron ore, pit-coal, rocks etcetera. Here the constant capital consists almost exclusively of the tools, which can easily absorb an increased quantity of labour. (Day- and night-shifts of workers for instance). ... Due to the elasticity of the labour force, the possibility of accumulation is increased, while an increased advance of the constant capital remains unnecessary. ... Because the capital appropriates the archetypes of wealth, the labour force and the land, it obtains an elasticity, which allows it to expand the elements of its accumulation beyond the apparent limits, imposed by its own amount, limits that are imposed by the value and quantity of the already produces means of production11.

Therefore De Wolff proposes to use the value of 12 for hiring extra workers in the extractive industry. These workers cause the demand for the otherwise superfluous wage goods. Then at a rate of surplus value of 1.01 a line must be added the the table 2, namely the one in table 3.

Table 3: start of a new department Ib

Yet De Wolff can not accept this solution. For the extra raw materials at a value of 24.12, which are produced in the department Ib, will have to be processed in the third revolution, probably mainly by the department I (say, the heavy industry). De Wolff states on p. 402 of his book: [This would imply that] in all three departments the production must be continued on a still larger scale. For this would increase the disproportions and moreover as a consequence of overproduction would perpetuate the deviation of the surplus value from its optimum. That is to say, De Wolff fears that the fourth department will destabilize the system even further. The use of the extra means of production from Ib implies a technological progress, which again increases the productivity. The rate of surplus value would continue to rise. Moreover even more workers are hired, so that the unemployment falls, with the possible consequence that the wages will rise. Therefore De Wolff rejects also this use of the excess of wage goods, at least in case that the production of Ib is subsequently used in the departments I, Ib and/or IIa.

Expansion of the department IIb

If need be De Wolff is willing to use the production of Ib in behalf of the department IIb. For the department IIb makes luxury goods, that are meant only for the unproductive consumption of the capitalists. She does not interfere with the production in the departments I, Ib and IIa. In fact this is a displacement of the investments to the department IIb. For in the second revolution the workers of the department Ib will produce exclusively for the department IIb. And in the third revolution their production at a value of 24.12 will be added to the means of production of the department IIb. Etcetera.

Also this application is ultimately rejected by De Wolff. He writes on p.402 of his book: In the deregulated capitalism this relative expansion of the third department and relative contraction of the second department can be accomplished only by means of rising and falling prices. And thus the continuous increase of the rate of surplus value in the deregulated capitalism could only lead to new proportions, if it is accompanied by a continuous fall of the prices in the second department, and a continuous rise of the prices in the third department. De Wolff believes that the flux of capital to the department IIb has to be brought about by larger profits in this department, and lower profits in the department IIa 12. From this he concludes, again on p.402: Thus a continuous increase of the rate of surplus value would contradict the law of the equal average profit rate for all capitals, and consequently it is impossible.

Again the reader sees, that De Wolff deems the flexibiliy of the capitalists insufficient for restructuring the system. That can only be accomplished by a crisis. Your columnist adds to this, that other ways are conceivable for the expansion of the department IIb. For instance the idea of a new department Ib could be relinquished, and instead simply the equipment (machines) could be displaced from the departments I and IIa to the department IIb. That department is most labour intensive, and thus can employ most workers per machine. Thus the additional workers still have the disposal of the means of production13. However this apparent solution fails also due to the just advanced objection of De Wolff.

The discontinuous increase of the rate of surplus value

On the ground of the arguments presented just before, De Wolff concludes that the increase of the rate of surplus value should by necessity go on in a discontinuous manner. Now it is indeed known from experience that the reproduction and the expansion of the fixed capital (equipment) occurs in a discontinuous manner. They are not distributed evenly in time, but they are compressed in a couple of years. The reproduction of fixed capital displays a cyclical pattern, that is commonly called the conjuncture (business cycles). De Wolff claims to have explained this empirical find with his arguments, that expose the disproportions in the underlying value system. The rule of production that the increase of the rate of surplus value due to the introduction of better production methods must occur in a discontinuous manner, is in the end an expression of its desirability and possibility in capitalism. Jan Tinbergen calls this in his review of Het economisch getij the core of the conjuncture theory of De Wolff14.

Graph of conjuncture
Figure 1: m' and the conjuncture according to De Wolff

In his summary on p.437 of his book De Wolff repeats again his conclusion: We have explained that the increase of the rate of surplus value occurs in a discontinuous way and is concentrated in the start of the upswing. In the discussing of the schemes of the three departments it was stated that the increase of the rate of surplus value results in a plethora of consumption goods for the labour class. This last remark refers to the excess at a value of 12. Apparently De Wolff thinks that the rate of surplus value remains constant during the final phase of the economic prosperity, and during the crisis and the early recession or depression as well. Already in the upswing the fixed capital for the whole business cycle is reproduced in the required amount. Therefore De Wolff writes on p.411: During the prosperity the number of employed workers is larger than can be reconciled with the optimum of the surplus value, so there exists an "overproduction". In a compulsive way the stocks of capital goods and the production capacity are expanded. And: During times of depression, when the fixed capital is employed, that has been produced during the prosperity for the whole period of the cycle, less workers are employed, and thus there exists "underproduction" during this time interval. The figure 1 shows in a graphic way this behaviour of the conjuncture and of the rate of surplus value (not shown in the book of De Wolff).

It is an interesting thought. De Wolff calls again attention to the temporal approach in a period, when she was almost forgotten. That proves his excellent economic intuition. He expects that the technological progress will seduce the entrepreneurs to engage in overproduction in a structural and unintended manner. The excesses are consumed during the recession, which subsequently cnanges into a short period of innovation and improvements of the productivity. The innovations must occur as shocks, because they cause large capital fluxes between the departments, and these disturb the general profit rate. Afterwards everything is ready for the following phase of overproduction. But the objections of De Wolff with regard to a continuous growth of m' are rather cumbersome. It will not be easy to prove or refute them in a conclusive manner.

At the time the Dutch economist Jan Tinbergen has already criticized the objections of De Wolff to the redistribution of the excess of wage goods over all departments. The objection of De Wolff has just been explained in the preceding paragraph. In his review Tinbergen states that the conclusion of De Wolff is premature. He argues14: The law of the equal average rate of profit is a law that, if she is actually true, is only valid in states of equilibrium. Thus in my opinion the only conclusion can be, that the continuous growth of the rate of surplus value can not occur during a series of states of equilibrium. But nevertheless it is possible. For also states of non-equilibrium can pass in a completely continuous way. Here it seems worthwhile to elaborate on the model, especially by a consideration of the price system of the society in question. Indeed, in the end the observable business cycles and their consequences occur primarily in the price system, and not in the value system15.

  1. See Het Economisch Getij (1929, J. Emmering). (back)
  2. Jan Tinbergen states in a review in the annual volume XIV of De Socialistische Gids (October 1929), that the modern conjuncture research separates actually in a quite rigorous manner the size itself and the fluctuations in it. See p.855, or p.9 of the reprint (N.V. De Arbeiderspers). He writes: The first point in question is classified as a structural problem, that does not belong to the actual conjuncture research. This is partly so, because the size of the total product seems to depend on such a plethora of historical data, that it will require an enormous effort to complete a good quantitative survey. In the second place, it is best to separate the usual causes that lead to the fluctuations, from the other events, that explain only the general size of the product. The limitation to the fluctuations seems naturally justified, since is is easier to obtain statistical data about the changes of quantities than about the quantities themselves. Tinbergen may be right, but yet precisely the marxists like to study the growth and the conjuncture in their mutual interaction. A scientist can not object to that desire. (back)
  3. The explanation and the formulas are mainly taken from the book Die Marxsche Konjunkturtheorie (2009, PapyRossa Verlag) by Alfred Müller. In addition the interpretation uses the ideas in Reclaiming Marx' "Capital" (2007, Lexington Books) by Andrew Kliman. At the time not more than a handful of Dutchmen will really have understood the model of De Wolff. The review of Tinbergen does not really contribute to a better understanding. (back)
  4. Alfred Müller defines on p.112 of Die Marxsche Konjunkturtheorie the quantity ap* = ap / (c/l + 1), and calls her the productive force. She represents the combined productivity of labour and of the means of production. The piece-value is just the opposite of this quantity: w = C'/Q = 1/ap*. (back)
  5. For he writes on p.398 of Het Economisch Getij: "Then where do they get the means of production in order to work? The available 5555 units of means of production are completely taken up by the army of workers, that is paid with the 2340 value units". (back)
  6. With regard to temporal and simultaneous systems see for instance p.34 and further in Reclaiming Marx' "Capital". This books gives an excellent explanation of the Temporal Single System interpretation (TSSI). (back)
  7. Here are two unsuccessful attempt to explain the excess of De Wolff with a simultaneous interpretation. Since they are merely reflections of the columnist, and in vain on top, the reader can afford to skip this footnote. (back)
  8. Indeed De Wolff believes that the producers together are not able to coordinate the total production. Each producers keeps trying to produce more, without taking into account similar efforts by his competitors. For De Wolff writes on p.401 of Het Economisch Getij: "If the capitalist way of production were controlled in a purposive manner, then an increase in the rate of surplus value would not result in this plethora of variable capital, but the second department would have been reduced in advance in a purposive manner. What in a regulated capitalist manner of production would occur in advance and with prior knowledge, is accomplished a posteriori in the deregulated capitalist manner of production". (back)
  9. See p.398 of Het Economisch Getij. (back)
  10. That is to say, in the second revolution simply the same type of machines is used. See also the footnote 5. Due to the growth their number naturally does exceed the number of the first revolution. (back)
  11. See p.398 of Het Economisch Getij for the Dutch translation by De Wolff. Nearly the same text can be found on p.465 in Het Kapitaal (1984, De Haan/Unieboek), but then translated by I. Lipschits. Incidentally your columnist wonders whether in the extractive industry the absence of the means of production is still valid to-day, considering the increased automation in mining. (back)
  12. This argument is also used in the marxist transformation of labour values into prices. There it is as follows. The departments with the relatively low organic composition are most profitable, in principle. Therefore they offer an attractive investment for capitalists. Then the excess of investments causes an overproduction, which results in falling prices of the corresponding products. The falling prices reduce the profitability. The fall will end in a new equilibrium as soon as these departments have reached the same profit rate as the other ones. (back)
  13. Then the capitalists redistribute the wage goods at a value of 12 over the departments I, IIa and IIb. This is another way to employ more workers. As an illustration the table 5 shows the result for a rate of surplus value of 1.01, in for the rest identical circumstances (not analyzed in the book of De Wolff). In table 5 the organic compositions c/v of the departments are 0.5% larger than those in the table 2. For that compensates for the falling piece-value wIIa in such a way, that the technical compositions Pm/l can remain intact. The value GI=1.1 is maintained, so that cI also remains the same. One sees that means of production at a value of 25 have been transferred to the departments I and IIa. A capital flux is created towards the department IIb. The production of value in the department IIa slows down, because GIIa reduces to 1.03. That is pleasant, since in the first revolution especially that department has become more productive. On the other hand the production of value in the department IIb grows considerably.
    Table 5: v=2352 and m'=1.01

  14. See p.857 in Volume XIV of De Socialistische Gids (October 1929), or p.11 of the reprint (N.V. De Arbeiderspers). N.B. the text refers in two places to this footnote and page. (back)
  15. Here again the objection can be made, that according to several economists the general average rate of profit in the theory of Marx is not at all an equilibrium value. It is simply what its name says, namely the average, taken over the entire economy. (back)