Marginal disutility in the labour theory of value

First insertion on Heterodoxe Gazet Sam de Wolff: 3 september 2012

E.A. Bakkum is a blogger for the Sociaal Consultatiekantoor. He loves to reflect on the labour movement.

Following H.H. Gossen and W.S. Jevons Sam de Wolff bases his theory of value on the disutility of labour. In this way he opposes the Austrian School, that denied the existence of a relation between the production costs and the value of the end products. In the Austrian view the value originates completely from the subjective preferences in the consumption. In the course of time this standpoint has become common in the economic science, albeit with some nuances. It is worth while to once more compare both standpoints, because in all his controversies De Wolff has always exhibited a sound intuitive sense.

The marginal disutility of labour

The idea, that besides pleasure (utility) also pain (disutility) determines the human preferences, has been formulated ages ago. Jeremy Bentham (who lived from 1748 until 1842, and incidentally was a rather unsociable scientist) developed a philosophy that is founded on the largest happiness principle. Pain is bad. In 1854 this idea was picked up by Hermann H. Gossen, who has expanded her into an economic theory of the marginal utility. Unfortunately the spirit of the time was not yet ripe for the proper appreciation of the work of Gossen. More than fifteen years later, in 1871, both William S. Jevons and Carl Manger rediscover independently of each other again this concept. Now it does catch on. Incidentally only Jevons introduces the concept of disutility in his argument, and not Menger.

Sam de Wolff calls himself a marxist, so that he ought to reject the neoclassical value theory, that is based on the human subjectivity. Value is produced during the production, as an objective asset. Yet he has to a large extend shared in the euphoria about the marginalist analysis, which in his era had come on firm ground. His marxist position becomes apparent mainly in his persistent resistance against the Austrian School, which then had important supporters like C. Menger, E. von Böhm-Bawerk, and F. von Hayek. In his main economic work Het Economisch Getij De Wolff invokes the publications of Gossen and Jevons for his counter-attack, and he seems to cite in particular the text of Gossen (without clear references)1.

Graph of utility and marginal disutility
Figure 1: Utility N and marginal
    disutility ∂L/∂t

De Wolff could not resist the temptation to invent new names for the analytic concepts in the theory. Where Gossen writes about pleasure in life (Lebensgenuss)2 and Jevons about utility3, there De Wolff chooses the name lust. And where Gossen and Jevons use the word inconvenience (Beschwerde respectively disutility), and others use the word Leid, there De Wolff prefers the name onlust. But for the rest De Wolff seems to apply simply the examples of Gossen. See an earlier column about this theme, as well as its elaboration. In imitation of Gossen he even models the marginal lust and onlust (called intensities by De Wolff) by means of linear functions4.

Both Gossen, Jevons, and later also Alfred Marshall start from the hypothesis, that under favourable conditions the work can be a pleasant and spiritually enriching activity. Labour becomes an onlust only, when the working-day is too long, or too intense, or when the conditions are otherwise inhumane. The figure 1 shows the utility of labour (casu quo disutility) N = −L and the marginal disutility ∂L/∂t as a function of time, like Gossen imagined5. In the picture below the marginal utility changes into a disutility, as soon as the horizontal axis is crossed. From that point onwards the labour obtains a special meaning, because the phenomenon of the disutility has the consequence, that the people put a clear limit on the number of hours, that the are prepared to work.

In the columns just mentioned a Robinsonade (originating from Gossen) is used to show, that the worker determines his working hours on the basis of the amount of goods, which he can produce during that time. Those goods yield a certain pleasure, and by doing so compensate for the onlust of the labour. The consequence of this model is, that the value of the goods is related to the expended number of working hourse. The production costs determine (partly) the value of a product unit.

This is worth a moment of reflection: a worker does not stop working, because he prefers to do a more pleasant activity. His motive is not the temptation of leisure time. No, it is the subjective aversion against additional working hours, which incites him to stop. The German sociologist Frank Deppe states:6 "In general workers experience their labour as a heavy load, which is insignificant in content, and which is seen and perceived as a means for survival (one does not live to work, but one works to live!). The work itself is without any interest, and causes merely resignation". Apparently the quality is miserable. Incidentally also the reader may recognize this feeling, and sociological studies are not needed to obtain this insight.

Thus the onlust intensity of labour seems to be an excellent concept for studying the wage and the supply of labour. Your columnist has searched the world wide web, but without results. In particular one wonders about the role of the labour productivity (ap) in this argument. The behaviour in the figure 1 is derived for a constant ap. However, if the worker is not free to stop working, then he will undoubtedly resort to decreasing his ap. The future onlust can be controlled. But admittedly your columnist does not know an economic theory, which models this phenomenon.

Leisure time according to the Austrian School

The representatives of the Austrian School have vehemently attacked the idea of the disutility. According to Spencer especially Von Böhm-Bawerk and Von Hayek wanted to discredit the labour theory of value of Karl Marx, and therefore they refused to attach meaning to the production costs7. In the Austrian paradigm all product value is caused by the subjective needs and preferences of the consumers. In their view the quality of labour is unimportant. This eliminates the debate about the exploitation and alienation of labour, which is leading in the political economy of Marx.

In the Austrian perspective the consumption determines all values, and that pertains even to labour. For the worker chooses the number of working-hours according to his need for leisure time. On the one hand his total wage rises, when he works longer. Then he can buy more consumer products, and these yield an additional utility. The opportunity costs, that he must pay for the extra work, consist of the renouncement of the leisure time. In this way he again gives up some utility. The worker himself chooses the length of his working-day, in accordance with his consumptive preferences.

The new paradigm, which later was named the neoclassical theory, is a rupture with the past, when the classical theory still dominated. In the classical theory the product value is derived from the production costs, including the expenses for wages. In the new paradigm the wage costs are completely absent, with regard to the price formation of the commodities. All prices are formed in the exchange process on the basis of subjective needs, and they are related to the scarcity of the products. Then the wage costs are merely relevant for the supply on the labour market. The labour is simply a means for the worker in order to obtain an income, which satisfies his need for consumer goods. The disutility of labour as a determining factor is eliminated. Time is a scarce commodity. That pertains both to the labour time and the leisure time. Leisure time is presented as a good, which is instrinsically pleasant8.

Now the reader will understand, that according to your columnist the Austrian paradigm is an impoverishment with respect to the paradigm of Gossen, Jevons, and De Wolff. The element of labour is missing, the disutility (inconvenience), which in practice is so obvious. Of course the Austrian position can be attacked with intellectual arguments. For instance Alfred Marshall stated, that many unemployed workers endure their leisure time as if it is an inconvenience instead of a pleasure (utility). That is true, just like labour can sometimes be a pleasure. The fundamental criticism is evidently, that the Austrian paradigm makes an unrealistic assumption in order to determine the size of the supply on the labour market.

The question naturally rises: why has the Austrian paradigm after all become the common opinion in the modern economy? In the end Spencer identifies two reasons9:

Spencer concludes that the neoclassical paradigm has left a theoretical void, which is filled by the American institutionalism10.

The neoclassical labour market

Your columnist does not warm to the Austrian and neoclassical model of the labour market. However, it is useful to describe it, because this is seldom done properly in the introductory text books. The present description originates from the excellent text book Volkswirtschaftslehre by M. Heine and H. Herr11. It is remarkable, that the disutility (in the interpretation of this model) is equated simply to the relinquished pleasure of leisure time.

Iso-utility diagram
Figure 2: Equal utility in the (tv, w) field

The model is founded on a number of assumptions. There is one type of labour, so that the diversity of professional qualifications is ignored. And the working-time can be divided at will, so that a labour contract can enforce any number of working-hours. The market is perfect. In other words, monopolies such as the organizations of employers and workers, are ignored. Another crucial assumption is that the system is a so-called one-good economy. The capital and the wage exist of a quantity of a single product, which is commonly chosen to be corn.

It has already been explained in the preceding paragraphs, that the households (the worker) has to solve an optimization problem in order to maximize his utility. This problem requires a simultaneous decision:

In the model the collection of consumer goods is limited to corn.

Thus the utility function of the households takes on the form

(1)     N = N(tv, w)

The utility function can be used to draw the indifference curves, which represent combinations (tv, w) with a constant utility value. The figure 2 displays four of those curves. The curves are valid for a limited time interval T, so that the range of tv values is bounded at the high end. The night's rest, meal-times, etcetera are excluded on the time scale, bacause these are not available as time. Then by definition the working-time is given by ta = T − tv. The coordinate axes of ta and tv have opposite directions. The slope of the indifference curves is given by

Iso-utility diagram with budget lines
Figure 3: Budgets in the utility field
(2)     dw/dtv = −(∂N/∂tv) / (∂N/∂w)

As is usual in this kind of analysis a budget restriction can be formulated:

(3)     w = ωu × (T − tv)

In the formula 3 ωu represents the hourly wage, the wage level, expressed in a quantity of corn. Of course the term T − tv is simply ta. It is immediately apparent that the maximal possible wage wmax equals w(tv=0). The slope of the budget line is given by the wage level ωu. In the figure 3 the budget line is drawn for four values of the wage level.

It is known from the theory of the marginal utility, that the optimum of the household can be found by searching for the iso-utility curve, which just touches the budget line. The figure 3 shows these optima for the four displayed budget lines. Obviously the slopes of the iso-utility curve and of the budget line in the optimum are exactly equal. Then the formulas 2 and 3 lead to the relation13

(4)     (∂N/∂tv) / ωu = ∂N/∂w

Finally the figure 3 allows to construct the supply curve A = A(ωu, N, T) of labour for the separate households. Then the optima of the households must be simply drawn in the cross of axes (ta, ωu). This is done in the figure 4. The social supply curve for labour from all households is obtained by adding for each value ωu the working-hours ta of all the separate households (workers). Then a curve is naturally found with a shape that is similar to the figure 4.

Your columnist has already complained about the absence of the disutility of labour in this argument. Moreover the explanation by Heine and Herr shows that the model is merely valid under certain limiting conditions. They draw attention to four points: Graph of supply of labour
Figure 4: Supply ta = A(ωu, N, T)

  1. In the neoclassical theory the demand curve is combined with the supply curve in order to determine the equilibrium on the labour market. However, in practice the stock of capital goods is given. Therefore the demand for labour can not rise indefinitely, contrary to the supposition of the neoclassical theory. Moreover the neoclassical theory assumes that the scale of the production does not influence the productivity. However, in reality it is common that the marginal productivity of labour rises when the scale is increased. A larger scale implies a higher wage level. In any case this phenomenon clearly shows, that the theory is sensitive to the development of the production technique.
  2. Evidently the assumption of a single-good economy implies that the model is far from reality. Unfortunately the assumption is indispensable, because else the wage level would influence in an unpredictable manner the prices of the consumer goods. This phenomenon has been discussed earlier on this web portal, in the column about the neoricardian theory of Sraffa. In a many-goods economy the wage level must be a money sum. For instance a rising wage level could force up the product prices to such an extent, that the households would be able to buy less products. That implies a loss of the utility of the wage, so that leisure time becomes more attractive. In that situation more wage means that the supply of labour would diminish14.
  3. Just now it has been stated, that in a many-goods economy the wage level must be a sum of money. This implies that the (nominal) wage level can rise, while a simultaneous inflation can prevent the rise of the purchasing power (real wage level). Then also the utility remains unchanged, and the workers will not supply more labour.
  4. The neoclassical model always supposes that the markets are completely cleared. A structural unemployment is impossible, because the wages can adapt in a downward direction. This ignores the possibility that the entrepreneurs simply lack the trust in the profitability of production expansions. In other words, the neoclassical theory ignores the Keynesian hierarchy of the markets. First investments are required, and then consumption is needed, before the employment can increase.

The reader sees how Heine and Herr have a crushing criticism with regard to the neoclassical model of the labour market. This criticism almost pales the phenomenon of the disutility, which in principe is reconcilable with the neoclassical paradigm. It is naturally important to include in the neoclassical theory also the real costs of the production. But if Sam de Wolff would have known all this, he would perhaps indeed have omitted several chapters in Het economisch getij.

The labour theory of Sam de Wolff revisited

In several columns it is explained how Sam de Wolff uses a so-called Robinsonade in order to relate the lust intensity LIn of a product n and the onlust intensity OI of the labour. For the sake of convenience he assumes here that the labour generates the same OI(t) in the production of all products. Thus De Wolff concludes, that in the optimum of the Robinson person one has LIn = LIm = OI, for two products n and m. In the nineth chapter of Het Economisch Getij De Wolff now crowns it all, by applying his findings for the Robinsonade to the society as a whole15. For he considers a society of individuals n (say with n=1, ..., N), who each make a product n. This is a division of labour, where each person specializes in a single product. Then the relation of intensities at the optimum topt just mentioned simplifies into:

(5)     LIn(n, topt) = OI(n, topt)

These intensities are not by definition equal to LIm(n), because n is not involved in the generation of the product m. It is obvious that each individual prefers to make the product, for which his labour productivity apn is the most competitive in comparison with the other individuals. However, De Wolff assumes that all individuals have the same apn. Then it is irrelevant who makes a certain product, and if desired two individuals are free to swap positions in the social production process16. Next all individuals start to exchange their products on the markets, hoping that the transaction enlarges their own lust (utility). It is generally known, that in such markets the second law of Gossen holds. For an individual k and two products n and m the law is17:

(6)     LIn(k) / LIm(k) = pn / pm

In the formula 6 the quantities pn and pm are intepreted as the prices of the products n and m. In other words, the exchange proportion equals the ratio of the lust intensities. De Wolff combines the formulas 5 and 6 into

(7)     OI(n) / LIm(n) = pn / pm

The formula 7 expresses that thanks to the option of exchange the optimal marginal disutility OI(n, topt) depends in part on the preferences for the other products m. The resemblance with the formula 4 is striking. Conversely the formula 7 has the peculiarity, that the price pn of the product n is related to the onlust intensity (the marginal onlust, or disutility) caused by its production. This reminds somewhat of the labour theory of value of Marx, where the price depends on the amount of expended labour time. The product price is determined by the workload, en not by the value of leisure time.

The formula 7 becomes even nicer, if the individual n is replaced by a representative (average) worker. For in that case all individuales have one single preference. This implies that one has LIm(n) = LIm(m). Besides the formula 5 states, that one has LIm(m) = OI(m). In combination these relations result in LIm(n) = OI(m). Substitution in the formula 7 results in18

(8)     OI(n) / OI(m) = pn / pm

This formula 8 truly conforms to the marxist tradition. For now the exchange proportions are determined completely by the ratio of the marginal disutilities of labour. The prices are no longer determined by the needs of the consumers, but by the onlust of the workers. De Wolff revives Marx in a mannier, which is unique in the economic science, as far as your columnist can see.

  1. See Het Economisch Getij, bijdrage tot de verklaring van het conjunctuurverschijnsel (1929, J. Emmering). The congeniality of Gossen and De Wolff becomes apparent especially in the arguments, that are advanced by De Wolff. On p.323 of Het Economisch Getij De Wolff states indeed, that he has studied the work of Gossen. (back)
  2. In this column most of the information about the work of Gossen is taken from the paper Gossens Theorie der Zeitallokation im Lichte neuerer Theorien (2000, Ludwig-Maximilians-Universität München) by Daniel Dohrn. (back)
  3. The information about the work of Jevons originates from the books The political economy of work (2009, Routledge series van Taylor & Francis Books) by D.A. Spencer and Theories of value and distribution since Adam Smith (1975, Cambridge University Press) by M. Dobb. Jevons was not a moral genius, and even developed a kind of race theory. Apparently he drowned at the age of 47 during a swim. Gossen also died relatively young. (back)
  4. It is interesting that all the mentioned economists assume that the utility can be measured in a quantitative way. In the following decades the economist V. Parteto promoted the view, that various types of utility can be ordered (ordinal utility), but they can not be made quantitative (cardinal utility). However during his whole life De Wolff had defended the existence of a cardinal utility. This aspect may not be essential for the concept of the disutility, but is does show the tenacity of De Wolff. It is remarable, that in 2004 the economist B.M.S. van Praag has made a speech precisely about this subject. On p.5 of the text he concludes: "The evaluation of any distribution and redistribution, such as for instance the evaluation of the social difference in incomes, requires indeed that she is based on the cardinal, interpersonally comparable utility function. For a meaningfull analysis of intertemporal behaviour, for instance the choice between consumption and saving, or decisions under uncertainty, a cardinal utility function is actually also indispensable. Thus we see that in many contemporary theoretical literature the cardinal utility functions are used without much discussion. The fact that the revealed preferences alone are insufficient for the identification of the cardinal utility functions, does not imply that the individuals do not employ a cardinal utility function at the emotional level. Neither does it imply, that those cardinal utility functions can not be measured, but only that the revealed preferences alone are insufficient in order to identify the cardinal utility functions". In this way De Wolff appears to be right after all. (back)
  5. Here the notation of De Wolff is abandoned, namely the symbols L for lust (utility) and O for onlust (disutility). His choice of notation has never found acceptance. (back)
  6. See p.98 in Das Bewusstsein der Arbeiter (1971, Pahl-Rugenstein Verlag). (back)
  7. See p.75 of The political economy of work. (back)
  8. The abstraction of the model is somewhat of a caricature. A brief space of time and a quantity of a physical product can not simply be exchanged. For the utility of time to live has obviously a different weight than a material pleasure, such as fly-paper. A human being disposes of a limited time of living, and she forms the essence of his existence. Moreover he does not know how much time will be given to him. This makes the utility of leisure elusive. Also Dohrn in Gossens Theorie der Zeitallokation im Lichte neuerer Theorien points out, that leisure time and goods are complementary. For instance, it takes time to install the fly-paper. Besides a time-related utility or disutility can be altered, because the future depends on individual actions. A consequence is that it is difficult to weigh the utility or disutility of a time-dependent activity, which has yet to occur. This type of aspects deserves reflection. (back)
  9. See p.88 and further in The political economy of work. (back)
  10. See p.93 in The political economy of work. He refers especially to Thorstein Veblen. Incidentally the institutionalism is indebted to the German Historical School, which in the second half of the nineteenth century was authoritative. (back)
  11. See p.120 and further in Volkswirtschaftslehre (2003, Oldenbourg Wissenschaftsverlag GmbH) by M. Heine and H. Herr. (back)
  12. On p.122 Heine and Herr note, that if desired a utility of labour can be included into the model without additional difficulties, for instance due to the self-realization. This does complicate the model. Heine and Herr do not seem toe realize, that this would introduce the quality of work as a substantial aspect of the theory. The production costs are brought into the model. Evidently this would not be in the spirit of the Austrian School. (back)
  13. De reader may prefer to include the price of a bale of corn pg: (∂N/∂tv) / (ωu × pg) = (∂N/∂w) / pg. Then the formula clearly has the form of the Second Law of Gossen. See for instance on p.43 in Volkswirtschaftslehre, or on p.164 in Micro-economie (1996, Stenfert Kroese) by F.J. Dietz, W.J.M. Heijman and E.P. Kroese. (back)
  14. On p.139 Heine and Herr use an argument, that mirrors this one. They criticize the growing demand on labour by the producers for the case that the wage level falls. For that does not need to be true. A falling wage level can make the relative prices of equipment fall to such an extent, that the entrepreneurs will substitute the factor labour by the factor capital. That is to say, they prefer a more capital-intensive production technique. Thus a falling wage level may lead to less employment. Your columnist prefers his own version of this argument, because this column centres on the supply of labour. (back)
  15. This paragraph has been added to the column only in august 2016. Your columnist must admit with some embarrassment that in 2012 he did not yet see the importance of the following text. That insight came several years later, thanks to the purchase and analysis of the thesis Over marxistische economie in Nederland (1993, Thesis Publishers) by Frank Kalshoven. Kalshoven gives an excellent explanation on p.178-186. Apparently it is indeed rewarding to study the texts of De Wolff in a thorough manner (more than your columnist did). (back)
  16. That is to say, your columnist interprets the text on p.343 in Het Economisch Getij in this way. Kalshoven chooses the same interpretation on p.185 of Over marxistische economie in Nederland, at least if your columnist understands him well. In this part of his book De Wolff is perhaps not mistaken, but his arguments are a bit sloppy and disorderly. Kalshoven shares this opinion. He formulates his critique in a pointed manner on p.360 in Die Rezeption der Marxschen Theorie in den Niederlanden (1992, Karl-Marx-Haus), edited by M. van der Linden. (back)
  17. To be precise, the Second Law of Gossen states that (∂u(xn, xm) / ∂xn
  18. ) / (∂u(xn, xm) / ∂xm) = πn / πm. Here u(xn, xm) is the utility function of an individual k for quantities xn and xm of the two products. And πn and πm are the respective market prices. Now De Wolff assumes a particular utility function, namely u(xn, xm) = un(xn) + um(xm). Then the law changes into (∂un / ∂xn) / (∂um / ∂xm) = πn / πm. It has been explained that De Wolff studies the marginal lust, expressed in labour time. This requires the transformation xn = t×apn, where t represents the expended working-hours, and apn is the corresponding labour productivity for the product n. In the main text it is assumed, that apn is not attached to a particular person. This transformation changes the law into (∂un / ∂t) / (∂um / ∂t) = (πn × apn) / (πm × apm). Note that the derivatives on the left-hand side of the equation are precisely the lust-intensities. That is to say, one has LIn / LIm = (πn × apn) / (πm × apm). If one now defines pn = πn×apn, then the formula 6 results. (back)
  19. It may be clarifying to remark, that in the following formula 8 the onlust intensities OI(n) and OI(m) refer to the products n and m. The workers n and m are both representative, so that their OI's have the same form. However, since they make different products, the workers n and m experience in their optimal situation still differing onlust intensities. Kalshoven justly states that sometimes De Wolff in Het Economisch Getij does not make a clear distinction between the individual and the product. Note also that the assumption of the representative worker implies, that a transition is made from a theory at the micro level to a theory at the macro level. Kalshoven argues in the paragraph 4.3 of Over marxistische economie in Nederland, and more succint on p.350-351 of Die Rezeption der Marxschen Theorie in den Niederlanden, that De Wolff in his argument about the micro-macro relation is influenced by his friend Jacob van der Wijk. (back)