Intensification of Labor and the Rate and Form of Exploitation

Abstract

Does the intensification of labor increase the rate of exploitation? Does it produce absolute surplus value or relative surplus value? This article develops a framework to answer these questions by incorporating intensity of labor in the widely used linear model of production, both in its one- and two-department forms. We show that (a) an intensification of labor always leads to an increase in the rate of exploitation, and (b) the increase in the rate of exploitation takes the form of the production of absolute surplus value in all realistic situations. We also highlight, in the case of any model with more than one industry or sector, an interesting difference in short- and long-run changes in the rate and form of surplus value.

JEL Classification: B51, C02

1. Introduction

In Marxist economics, the rate of exploitation occupies a central place. It is a quantitative expression of the exploitation of labor by capital. The rate of exploitation is defined as the ratio of surplus labor and necessary labor, or equivalently as the ratio of surplus labor-time and necessary labor-time. Converted to value-theoretic terms, the rate of exploitation is equal to the ratio of surplus value generated in production per day (or hour) and the variable capital advanced per day (or hour) of work to purchase labor power. Surplus value, in turn, is the difference between the value added per hour by the use of labor power and the value of labor power.

The value of labor power is the value of the means of subsistence necessary for the maintenance of the worker, where necessity is determined not biologically but historically, morally and politically (Marx 1992: ch. 6). In the normal functioning of capitalism, the worker is able to earn a nominal wage income that allows her, on average, to purchase the means of subsistence necessary for her maintenance. Thus, the value of labor power per hour of work, for instance, is equal to the value of the real wage bundle that the worker earns, on average, per hour of work (Morishima 1973: 50). Once the necessary means of subsistence and the daily real wage bundle is fixed, the rate of exploitation depends on the interaction of three variables: the length of the working day, the productivity of labor, and the intensity of labor.

In volume 1 of Capital, Marx discussed two different methods available to capitalism to increase the rate of exploitation: (a) the production of “absolute surplus value” and (b) the production of “relative surplus value”:

I call the surplus-value which is produced by the lengthening of the working day, absolute surplus-value. In contrast to this, I call that surplus-value which arises from the curtailment of the necessary labor-time, and from the corresponding alteration in the respective lengths of the two components of the working day, relative surplus-value. (Marx 1992: 432)

In this article, we call these two methods of increasing the rate of exploitation as forms of surplus value.

Among the three variables that interact to determine the rate of exploitation, the impact of changes in the length of the working day and the productivity of labor are easy to see. If there is an increase in the length of the working day, holding the daily real wage bundle, the productivity of labor and the intensity of labor fixed, that is by definition the production of absolute surplus value—because it is the “lengthening of the working day.” On the other hand, if the productivity of labor increases because of technical change, holding the length of the working day, the daily real wage bundle, and the intensity of labor fixed, then this leads to a production of relative surplus value. This can be seen easily by considering the case of a pure labor-saving technical change, which increases labor productivity. The increase in the productivity of labor reduces the unit value of commodities, which, in turn, reduces the value of labor power per day (or hour) of work as the daily real wage bundle is held constant at the level of the necessary means of subsistence. Since the length of the working day is held constant, this is clearly an instance of the production of relative surplus value—because this is the “curtailment of the necessary labor-time,” as the labor-time required to produce the necessary means of subsistence falls.

In contrast to this, the effect of changes in the intensity of labor on the production of absolute or relative surplus value is less obvious. This is because an increase in the intensity of labor has two distinct effects. On the one hand, it increases labor’s capacity to process inputs into output (CPIO) per unit of time, which is akin to an increase in the productivity of labor due to technical change. On the other hand, an intensification of labor also implies a larger expenditure of labor power per unit of time, which is like an increase in the length of the working day, albeit in an intensive sense (Marx 1992: 534), and hence increases labor’s capacity to create value (CCV) per unit of time. The overall impact of the intensification of labor, being the result of these two effects, is not immediately obvious. The CPIO effect tends to indicate toward the production of relative surplus value; the CCV effect points in the direction of the production of absolute surplus value. This might be the reason behind the disagreement in the extant Marxist literature about the effect of the intensification of labor. While some scholars argue that an increase in the intensity of labor produces absolute surplus value (Foley 1986; Catephores 1989; Sekine 1997; Joosung 1999; Hudson 2001; Heinrich 2012), others claim that an intensification of labor leads to a production of relative surplus value (Philp, Slater, and Harvie 2005; Mavroudeas and Ioannides 2011).

Our aim in this article is to provide a theoretical framework to think about the value dimensions of the intensification of labor. This framework allows us to clearly address the question of the form of surplus value, that is, whether intensification leads to the production of absolute or relative surplus value. In concrete terms, our article makes two important contributions. First, we offer a simple way of incorporating the intensity of labor in the linear model of production that is widely used in classical and Marxian economics. Our proposed method rests on clearly and quantitatively separating out labor’s CPIO and CCV, so far as they are related to the intensity of labor. While most scholars have associated with intensification of labor what we have called labor’s CCV, there is far less attention devoted to labor’s CPIO. Second, using our model, we draw out the implications of an intensification of labor on the rate and form of surplus value in a variety of linear production models of the capitalist economy.

With regard to the rate of surplus value, we demonstrate the intuitive result that an intensification of labor always leads to an increase in the rate of surplus value. Hence, it is always in the interest of the capitalist class and always against the interest of the working class to increase the intensity of labor. ¹ We can therefore expect a pronounced class struggle over the intensity of labor in capitalist economies, much like the struggle in mid-nineteenth-century England over the length of the working day.

Our results about the form of surplus value are more complex because they depend on the relative magnitudes of labor’s CPIO and CCV. We show that (a) if labor’s CPIO and CCV are impacted equally by the intensification of labor, then there is production of only absolute surplus value; (b) if, with the intensification of labor, labor’s CPIO rises less than its CCV, even then there is production of only absolute surplus value; and (c) if the intensification of labor is associated with labor’s CPIO rising more than its CCV, then the rise in the rate of surplus value can be decomposed into the sum of two components, one associated with the production of absolute surplus value and the other associated with the production of relative surplus value.

The first case, where labor’s CPIO and CCV are impacted equally by the intensification of labor, seems most common and would arise when intensification of labor does not exceed the normal limits of work and effort. The second case, where labor’s CPIO rises less than its CCV by the intensification of labor, would occur when intensification of labor breaches normal working conditions and leads to exhaustion of workers. The third case, where labor’s CPIO rises more than its CCV by the intensification of labor, seems unlikely to occur in any realistic scenario. Hence, we conclude that an intensification of labor leads to the production of only absolute surplus value in all realistic scenarios.

Our analysis has important political implications. It has been common in the Marxist tradition to associate the production of absolute surplus value primarily with the early stages of capitalism. In early capitalism, capitalist relations of production are imposed with little technical change, resulting in a longer working day and an intensification of labor. Marx refers to this as the formal subsumption of labor (Marx 1992: 1020). Once the length of the working day has been more or less determined by the struggle of the working class, the main method of raising the rate of surplus value is through the production of relative surplus value—this is what Marx calls the real subsumption of labor, where the capitalist mode of production entrenches itself through the division of labor and the use of machinery (Marx 1992: 1024). Our analysis highlights that the production of absolute surplus value remains important in later stages of capitalism, much as Marx had pointed out in his analysis of the formal and real subsumption of labor by capital.

The final point that we would like to highlight in this introductory section relates to empirical evidence about the rising intensity of labor. There is a large literature in sociology and labor studies that has documented the rising intensity of work in advanced capitalist countries since the early 1980s. A conference on this issue was held in Paris, France, in November 2002. The papers presented in this conference have been published in the Eastern Economic Journal, volume 30, number 4 (Fall 2004). These papers present various types of empirical evidence on work intensification since the early 1980s. Social scientists in the United Kingdom have been studying this issue for many years. Using data from the British Skills and Employment Survey for the years 2001–2007, a group of scholars have presented evidence about work intensification in the United Kingdom (Green et al. 2021). The evidence presented in these studies clearly establish the rising intensity of work over the past few decades in advanced capitalist countries. This empirical evidence increases the relevance of the theoretical analysis developed in this article.

The rest of the article is organized as follows. In section 2, we use a one-commodity model of production with linear technology, that is, a corn model, to study the impact of an intensification of labor on the rate and form of exploitation. In section 3, we analyze the same set of issues in the simplest two-department model, where department I produces the single means of consumption and department II produces the single means of production. The final section concludes the discussion with some thoughts about the broader implications of our research. The main points of our analysis can be fully conveyed with the one-commodity model and the simple two-department model, but for completeness, we also present all the results in general linear settings in the appendix: appendix A ( $n$ -sector model), and appendix B ( $m$ -sector model with two departments).

2. One-Commodity Linear Model

2.1. Technology and value

Consider a capitalist economy that produces one commodity, called “corn,” and assume that it can be both consumed and invested. Production of corn requires both a nonlabor input, corn itself, and labor. Consider a benchmark case where it takes $a$ units of corn and $l$ hours of labor to produce $1$ unit of corn. In such a case, we represent the technology of production with the pair of real numbers, $\left(a,l\right)$ . ²

Given this technological relationship, we can determine the value of a unit of corn. If we denote by $\mathrm{\lambda }$ the value of a unit of corn, we have:

$$\mathrm{\lambda }=\mathrm{\lambda }a+l$$

where $\mathrm{\lambda }a$ is the value transferred by the nonlabor input and $l$ is the value added by direct labor. Hence:

$$\mathrm{\lambda }=\frac{l}{1-a}$$

(1)

For the technology represented by $\left(a,l\right)$ to be feasible we need $0<a<1$ , that is, the amount of corn that is needed as input to produce $1$ unit of corn is a positive fraction. The lower bound comes from the requirement that some corn be always used as input, and the upper bound comes from the requirement that strictly less corn be used as input than what is produced as output. We also assume that labor is essential to production, so that $l>0$ . These two assumptions applied to (1) ensure that the value of corn is positive.

2.2. Intensity of labor

We would now like to define two important aspects of labor that allow us to make precise the notion of the intensification of labor. By labor’s capacity to process inputs into output (CPIO), we refer to the physical amount of inputs converted into output per unit of time. By labor’s capacity to create value (CCV), we refer to the magnitude of expenditure of labor power per unit of time. With these two notions in place, we can now define the intensity of labor by following Steedman (1977: ch. 6).

• Definition 1. Given the technology of production $(a,l)$ , we will say that there has been an intensification of labor if there are two real numbers µ₁ > 1 and µ₂ > 1, such that

• 1. $l$ units of labor can convert µ₁a units of corn as input into µ₁ units of corn as output; and

• 2. each hour of labor creates µ₂ units of value.

In this definition, µ₁ captures labor’s CPIO and µ₂ captures labor’s CCV. The fact that µ₁ > 1 implies that compared to the situation before intensification, each hour of labor now converts a larger physical magnitude of inputs into output. In a similar way, the assumption that µ₂ > 1 captures the fact that when workers work with higher intensity, there is larger expenditure of labor power per unit of time, compared to the situation before intensification. Since expenditure of labor power creates value, intensification of labor increases labor’s CCV, and this is captured by µ₂ > 1. ³

To analyze the impact of intensification of labor on the value of corn, let ${\mathrm{\lambda }}^{\prime }$ denote the value of $1$ unit of corn after the increase in intensity of labor. ⁴ After intensification of labor, $l$ units of intensified labor works with µ₁a units of corn to produce µ₁ units of corn. Since each unit of intensified labor creates µ₂ units of value (whereas before intensification, each unit of labor created 1 unit of value), we have:

$${\mathrm{\lambda }}^{\prime }{\mathrm{\mu }}_1={\mathrm{\lambda }}^{\prime }{\mathrm{\mu }}_{1}a+{\mathrm{\mu }}_{2}l$$

where, like before, the first term on the right-hand side (RHS), ${\mathrm{\lambda }}^{\prime }{\mathrm{\mu }}_{1}a$ , denotes value transferred by the corn input and the second term, µ₂l, captures value added by direct (intensified) labor. Hence:

$${\mathrm{\lambda }}^{\prime }=\frac{{\mathrm{\mu }}_{2}l}{{\mathrm{\mu }}_1\left(1-a\right)}$$

Using (1), we get:

$$\frac{{\mathrm{\lambda }}^{\prime }}{\mathrm{\lambda }}=\frac{{\mathrm{\mu }}_2}{{\mathrm{\mu }}_1}$$

(2)

Here we see an interesting result. When there is an increase in the intensity of labor, the change in the unit value of corn depends on the relative magnitude of µ₁ and µ₂. If ${\mathrm{\mu }}_1={\mathrm{\mu }}_2$ , then the value of corn remains unchanged; if µ₁ < µ₂,then the value of corn rises; if µ₁ > µ₂, then the value of corn falls. The intuition for this result is straightforward. If, for instance, intensification of labor increases labor’s CPIO, captured by µ₁, by more than its CCV, captured by µ₂, then each hour of labor creates a larger magnitude of use-values than the increment in the addition of value. Hence, the unit value of the commodity falls. The other two cases can be understood in a similar manner.

Note that the notion of intensification of labor can only be defined in relative terms, that is, in comparison to a situation before intensification occurred. The magnitude of labor value of a commodity is the amount of socially necessary labor time necessary to produce a commodity “under the conditions of production normal for a given society and with the average degree of skill and intensity of labor prevalent in that society” (Marx 1992: 129). After intensification has occurred and has become the new norm, one can recalibrate value definitions using the new level of labor intensity as defining the “normal conditions of production.” It is equally meaningful to keep the previous intensity of labor as the definition of “normal conditions of production.” We choose to adopt the second strategy. That is why we include µ₂ > 1 in our definition of intensification (definition 1). If, instead, one chooses to adopt the first strategy, then one would specify ${\mathrm{\mu }}_2=1$ .

2.3. Rate of exploitation

In the benchmark situation, let the working day be $T$ hours long and let the real wage bundle for a day’s work be given by $B$ units of corn, that is, workers get a nominal wage for $T$ hours of work that enables them to purchase $B$ units of corn. Let us denote by $b$ the real wage bundle per hour of work, that is, $b=B/T$ . Note that $B$ units of corn are the necessary means of subsistence per day and, hence, the value of labor-power per day is the value of $B$ units of corn. In a similar manner, the value of labor-power per hour of work is the value of $b$ units of corn.

In the benchmark situation, workers earn a real wage bundle $b$ for every hour of work; that is, the hourly real wage rate is equal to the value of labor-power per hour of work. In the benchmark situation, each hour of labor creates one unit of value. The value of the hourly real wage bundle (which is equal to the value of labor power per hour of work) is given by $\mathrm{\lambda }b$ . Hence, surplus value produced per hour of work is given by $1-\mathrm{\lambda }b$ . Thus, the rate of exploitation is given by:

$$e=\frac{1-\mathrm{\lambda }b}{\mathrm{\lambda }b}$$

so that:

$$1+e=\frac{1}{\mathrm{\lambda }b}$$

(3)

Now suppose there is an intensification of labor, where the latter is captured by the two real numbers µ₁ and µ₂, as specified in definition 1. In this case, if ${\mathrm{\lambda }}^{\prime }$ denotes the value of a unit of corn, then surplus value created per hour of work is given by ${\mathrm{\mu }}_2-{\mathrm{\lambda }}^{\prime }b$ . This is because each hour of work creates µ₂ units of value and the value of the hourly real wage bundle, in this new situation, is given by ${\mathrm{\lambda }}^{\prime }b$ (which is the value of $b$ units of corn, the necessary means of subsistence per hour). Hence, the rate of exploitation, after intensification of labor, is given by:

$$e^{\prime }=\frac{{\mathrm{\mu }}_2-{\mathrm{\lambda }}^{\prime }b}{{\mathrm{\lambda }}^{\prime }b}$$

so that:

$$1+e^{\prime }=\frac{{\mathrm{\mu }}_2}{{\mathrm{\lambda }}^{\prime }b}$$

(4)

We can now combine (3) and (4) to get:

$$\frac{1+e^{\prime }}{1+e}=\frac{{\mathrm{\mu }}_2\mathrm{\lambda }b}{{\mathrm{\lambda }}^{\prime }b}$$

Using (2), we get:

$$\frac{1+e^{\prime }}{1+e}={\mathrm{\mu }}_1$$

(5)

Our first result can be stated as:

• Claim 1. If the intensity of labor rises, holding the real wage bundle per hour fixed, then the rate of exploitation rises.

Proof. This can be seen immediately from (5) by noting that µ₁ > 1 whenever there is an intensification of labor (definition 1).

The intuition for this result is straightforward. Since the intensity of labor rises, each hour of labor produces a larger magnitude of corn, captured by the real number µ₁ > 1. But the magnitude of corn that the worker gets back in her real wage bundle remains unchanged at $b$ (because the hourly real wage bundle has not changed). This means that the ratio of what the worker produces to what she gets back in her real wage bundle increases. Hence the rate of exploitation increases. ⁵

2.4. Form of exploitation

In volume 1 of Capital, Marx discusses two methods to increase the rate of exploitation: the production of absolute surplus value and the production of relative surplus value. We refer to these as forms of exploitation (or forms of surplus value). The key difference between these two forms of exploitation is whether they involve what Marx calls the “curtailment of the necessary labor-time,” that is, whether there is a decline in the value of labor power per hour or per day of work. Following Marx (1992: 432), we use the following rule: If the value of labor power does not decline, that is, it either stays constant or rises, then any increase in the rate of exploitation necessarily takes the form of the production of absolute surplus value (ASV); on the other hand, if there is a decline in the value of labor power per hour or per day of work, then an increase in the rate of exploitation can take the form of the production of relative surplus value (RSV). We have noted earlier that the form of exploitation is determined by the interaction of three factors: length of the working day, productivity of labor, and intensity of labor. While the main purpose of this article is to study changes in the intensity of labor, we would like to first comment briefly on the other two factors.

2.4.1. Length of working day

Suppose the length of the working day increases, holding everything else, including the daily real wage bundle, $B$ , fixed. This leads to a rise in the rate of exploitation in the form of the production of ASV. To see this, let us recall that in the benchmark situation before the increase in the length of the working day, the rate of exploitation was given by $e=(T-\mathrm{\lambda }B)/\mathrm{\lambda }B$ , where $T$ is the length of the working day, $\mathrm{\lambda }$ is the unit value of corn, $B$ is daily real wage bundle (measured in units of corn). When the length of the working day rises from $T$ to $T^{\prime }$ , holding $B$ fixed, the rate of exploitation is now given by $e^{\prime }=(T^{\prime }-\mathrm{\lambda }B)/\mathrm{\lambda }B$ (note that the unit value of corn does not change because technology and intensity of labor is held constant). Since $T^{\prime }>T$ , the rate of exploitation has increased. Moreover, the increase has come about because the value created by the worker in a day of work has increased from $T$ to $T^{\prime }$ units, while the value of the daily real wage bundle—which is equal to the value of labor power per day—has remained fixed at $\mathrm{\lambda }B$ . Hence, surplus value produced in a day has increased from $T-\mathrm{\lambda }B$ to $T^{\prime }-\mathrm{\lambda }B$ . Thus, this is production of ASV, a conclusion that is widely accepted in the existing literature.

Would we arrive at a different conclusion if we took an hourly, rather than a daily, perspective? When the length of the working day rises from $T$ to $T^{\prime }$ hours, holding the daily real wage bundle fixed at $B$ units of corn, the hourly real wage bundle earned by the worker falls from $b=B/T$ to $b^{\prime }=B/T^{\prime }$ . Thus, in each hour of work, the worker now produces $1-\mathrm{\lambda }{b}^{\prime }$ , instead of $1-\mathrm{\lambda }b$ , units of surplus value. There is an increase in the production of surplus value for each hour of work, which, in turn, leads to an increase in the rate of exploitation from $e=(1-\mathrm{\lambda }b)/\mathrm{\lambda }b$ to $e^{\prime }=(1-\mathrm{\lambda }{b}^{\prime })/\mathrm{\lambda }{b}^{\prime }$ , which are the same expressions we arrived at using a daily perspective.

To see why this is production of ASV, recall that the necessary means of subsistence per hour of work is $b$ units of corn. This does not change when the length of the working day rises. Thus, when the length of the working day increases, holding the daily real wage bundle fixed, the hourly real wage earned by the worker falls below the necessary means of subsistence per hour of work. Hence, the value of the hourly real wage bundle earned by the worker, $\mathrm{\lambda }{b}^{\prime }$ , falls below the value of labor power per hour of work, $\mathrm{\lambda }b$ . Thus, more surplus value is produced per hour of work, with the value of labor power remaining unchanged. Hence, this is production of ASV. Thus, whether we take a daily or an hourly perspective, we reach the same conclusion: an increase in the length of the working day holding the daily real wage bundle fixed at the necessary means of subsistence per day leads to an increase in the rate of exploitation in the form of the production of ASV.

2.4.2. Productivity of labor due to technical change

We can capture the increase in labor productivity due to technical change by positing a new technique of production, $(a^{\prime },l^{\prime })$ , where $a^{\prime }=a$ and $l^{\prime }<l$ . Note that the new technique represents a pure labor-saving technical change because the amount of labor needed to produce each unit of corn falls, but the amount of corn needed to produce each unit of corn remains unchanged. Letting ${\mathrm{\lambda }}^{\prime }$ denote the unit value of corn after the new technique is adopted, we have:

$${\mathrm{\lambda }}^{\prime }=\frac{l^{\prime }}{1-a}$$

Since the daily (and hourly) real wage bundle remains fixed at the necessary means of subsistence, that is, $b$ units of corn per hour, the value of labor-power per hour of work falls from $\mathrm{\lambda }b$ to ${\mathrm{\lambda }}^{\prime }b$ . ⁶ Hence, the rate of exploitation rises because:

$$e^{\prime }=\left[\frac{1}{{\mathrm{\lambda }}^{\prime }b}-1\right]>\left[\frac{1}{\mathrm{\lambda }b}-1\right]=e$$

and this is production of RSV (because the value of labor-power per hour of work has declined with the rise in the productivity of labor), but the total value produced per hour of work has not changed.

2.4.3 Intensity of labor

If the intensity of labor rises, as specified in definition 1, holding the hourly real wage bundle fixed at $b$ units of corn (which is the necessary means of subsistence per hour), then the analysis of the form of exploitation (or form of surplus value) is complicated because of the dependence of the result on the relative magnitudes of µ₁ (which captures labor’s CPIO) and µ₂ (which captures labor’s CCV). We need to consider three cases.

• Case 1: ${\mathrm{\mu }}_1={\mathrm{\mu }}_2$ . Consider the case in which ${\mathrm{\mu }}_1={\mathrm{\mu }}_2$ . This condition means that an increase in the intensity of labor leads to an equal increase in its CCV, captured by µ₂, as in its CPIO, captured by µ₁. From (2), we see that if ${\mathrm{\mu }}_1={\mathrm{\mu }}_2$ , then ${\mathrm{\lambda }}^{\prime }=\mathrm{\lambda }$ . Thus, the value of each unit of corn remains unchanged. Since the hourly real wage bundle is fixed at $b$ units of corn (the necessary means of subsistence per hour), the value of labor-power per hour of work does not change. Moreover, value added in an hour’s work has increased to µ₂ from $1$ , where µ₂ > 1. Hence, this is clearly a case of the production of absolute surplus value.

• Case 2: µ₁ < µ₂. Consider the case when µ₁ < µ2. This condition means that an increase in the intensity of labor leads to a lower increase in its CPIO, captured by µ₁, than in its CCV, captured by µ₂. From (2), we see if µ₁ < µ₂, then ${\mathrm{\lambda }}^{\prime }>\mathrm{\lambda }$ . Thus, the value of each unit of corn rises. Since the hourly real wage bundle is fixed at $b$ units of corn (the necessary means of subsistence per hour), this leads to an increase in the value of labor-power per hour of work. What happens to value added? Since value added in an hour’s work is µ₂, where µ₂ > 1, the value added increases in comparison to the original situation when it was $1$ . From claim 1, we know that $e^{\prime }>e$ . Is this production of absolute surplus value or relative surplus value? Recall that in this case, the value of labor-power per hour of work has increased. That rules out the production of relative surplus value. We are left with the conclusion that here too we have a case of the production of absolute surplus value.

• Case 3:µ₁ > µ₂. Consider the case when µ₁ > µ₂.This condition means that an increase in the intensity of labor leads to a higher increase in its CPIO, captured by µ₁, than in its CCV, captured by µ₂. From (2), we see that if µ₁ > µ₂, then ${\mathrm{\lambda }}^{\prime }<\mathrm{\lambda }$ . Hence the value of corn falls. Since the hourly real wage bundle is fixed at $b$ units of corn (the necessary means of subsistence per hour), this leads to a fall in the value of labor-power per hour of work. What happens to value added? Since value added by an hour’s work is µ₂, where µ₂ > 1, the value added per hour increases from its original magnitude of $1$ . Hence, surplus value increases. Is this production of absolute or relative surplus value?

Using (3) and (4), we see that:

$$e^{\prime }-e=\frac{{\mathrm{\mu }}_2}{{\mathrm{\lambda }}^{\prime }b}-\frac{1}{\mathrm{\lambda }b}=\frac{{\mathrm{\mu }}_2-1}{{\mathrm{\lambda }}^{\prime }b}+\left(\frac{1}{{\mathrm{\lambda }}^{\prime }b}-\frac{1}{\mathrm{\lambda }b}\right)$$

This shows that the change in the rate of surplus value comes from a combination of both absolute surplus value (the first term on the RHS) and relative surplus value (the second term on the RHS). The first term represents absolute surplus value because it captures an increase in labor’s CCV, that is, µ₂ > 1, which increases the value added in an hour’s work from $1$ to µ₂. It is as if workers work µ₂ hours in place of every $1$ hour keeping intensity fixed. That is why the first term can be associated with the production of absolute surplus value. The second term represents relative surplus value because it comes from a fall in the value of a unit of corn, that is, ${\mathrm{\lambda }}^{\prime }<\mathrm{\lambda }$ . With a fall in the value of corn and the hourly real wage bundle fixed at $b$ units of corn, there is a fall in the value of labor-power per hour of work, that is, ${\mathrm{\lambda }}^{\prime }b<\mathrm{\lambda }b$ . Hence, the second term indicates the production of relative surplus value.

2.5. Which case is relevant?

At some places in volume 1 of Capital, Marx argued that an intensification of labor would keep the unit value of commodities unchanged:

Increased intensity of labor means increased expenditure of labor in a given time. Hence a working day of more intense labor is embodied in more products than is one of less intense labor, the length of each working day being the same. Admittedly, an increase in the productivity of labor will also supply more products in a given working day. But in that case the value of each single product falls, for it costs less labor than before, whereas in the case mentioned here that value remains unchanged, because each article costs the same amount of labor as before. (Marx 1992: 660–61, emphasis added)

This understanding of the effect of an intensification of labor can be captured by case 1. This is because, only in this case, that is, when ${\mathrm{\mu }}_1={\mathrm{\mu }}_2$ , does the value of corn remain unchanged after an intensification of labor. To our mind, this is the most common case, and the intuition for this case is straightforward. In ordinary circumstances, an intensification of labor is likely to increase its CPIO and CCV in equal magnitudes. That is, when the intensity of work increases, workers convert more inputs into output; they also add more value per unit of time because of a higher rate of use of their labor power. In ordinary circumstances, these two effects are quantitatively equal.

We might also entertain another possibility, that is, when intensification of labor leads to a relatively lower increase in its CPIO than in its CCV. This can happen, for instance, when the intensification of labor leads to exhaustion of the workers beyond normal levels. In such a situation, their ability to handle inputs and convert them into output might be impaired. Thus, for every hour of time, workers might be expending a larger magnitude of labor power—reflecting an intensification of labor—but because of sheer exhaustion, their ability to convert input into output might have declined. Marx indirectly discusses this in volume 1 of Capital:

Up to a certain point, the increased deterioration of labour-power is inseparable from a lengthening of the working day and may be compensated for by making amends in the form of higher wages. But beyond this point deterioration increases in geometrical progression, and all the requirements for the normal reproduction and functioning of labour-power cease to be fulfilled. The price of labour-power and the degree of its exploitation cease to be commensurable quantities. (Marx 1992: 664)

In this quote, Marx speaks of how increasing the payment for workers’ labor may in fact not compensate for the rapid deterioration of the value of labor power. This is only possible when the value of labor power increases by more than the increase of their payment. Since, in this example, the value of labor power increases, this is clearly case 2. To see this, note that, since the real wage bundle is fixed at $b$ units of corn, the value of labor power, $\mathrm{\lambda }b$ , can increase if and only if $\mathrm{\lambda }$ , the unit value of corn, rises. From (2), we see that, in the context of the intensification of labor, $\mathrm{\lambda }$ can only rise if µ₂ > µ₁. That is why this is case 2. Other Marxist scholars have also highlighted this aspect prominently, for instance, Joosung (1999: 186) and Mavroudeas and Ioannides (2011: 431).

The third case, that is, where µ₁ > µ₂, seems to us to be unrealistic and unlikely. We cannot conceive of any situation in which an intensification of labor leads to a larger increase in its CPIO than in its CCV. Intuitively, when the intensity of work rises, workers are able to increase the rate at which inputs are converted into output. This also implies an increase in the rate at which labor power is used. We do not see how the first effect can be quantitatively larger than the second. Hence, we think, while case 3 is a logical possibility, it is unlikely to be of any interest when we are studying a real capitalist economy. It is difficult to conceive of situations when an intensification of labor leads to a relatively larger increase in labor’s CPIO than in its CCV. This means that an intensification of labor, in all realistic scenarios, leads only to the production of absolute surplus value.

3. Simple Two-Department Model

So far, the analysis has been conducted in the context of a one-commodity model. This is decidedly simple and unrealistic. Hence, we would now like to extend the analysis to more realistic and also more complicated setups. The first step in this direction is to consider an economy with two commodities, one a capital good and the other a wage good. We can think of this as a simplified version of Morishima’s representation of the Marxian two department model (Morishima 1973). The simplification we introduce at this point is that each department produces only one commodity. ⁷

Let us denote commodity $1$ to be the capital good (produced in department I) and commodity $2$ as the wage good (produced in department II). We are interested in understanding the impact of an intensification of labor in one of the departments on the rate and form of exploitation in both the departments. We first analyze the case when the intensification of labor occurs in department I and then investigate the case when the intensification of labor occurs in department II. We find that the results are essentially symmetric, but with some differences.

3.1. Baseline scenario

In the baseline scenario, technology of production in the two departments are specified by $(a_1,l_1)$ and $(a_2,l_2)$ , where $a_1$ units of commodity $1$ and $l_1$ hours of labor are required to produce $1$ unit of commodity $1$ ; and $a_2$ units of commodity $1$ and $l_2$ hours of labor are needed to produce $1$ unit of commodity $2$ . Suppose the hourly real wage bundle is the same in both departments and is given by $b$ units of the consumption good (which is the necessary means of subsistence per hour). ⁸ Let ${\mathrm{\lambda }}_1$ and ${\mathrm{\lambda }}_2$ denote the unit values of the capital and wage good. Then, the value determination equation in department I can be written as ${\mathrm{\lambda }}_1={\mathrm{\lambda }}_1{a}_1+l_1$ , so that:

$${\mathrm{\lambda }}_1=\frac{l_1}{1-a_1}$$

(6)

and the value determination equation in department II can be written as ${\mathrm{\lambda }}_2=a_2{\mathrm{\lambda }}_1+l_2$ , so that, using (6), we have:

$${\mathrm{\lambda }}_2=\frac{l_1{a}_2}{1-a_1}+l_2$$

(7)

Let $e_1$ and $e_2$ denote the rate of exploitation in department I and department II before the intensification of labor. Since the hourly real wage bundle is given by $b$ units of the consumption good, the rate of exploitation is the same in the two departments and is given by:

$$e_1=e_2=e=\frac{1-b{\mathrm{\lambda }}_2}{b{\mathrm{\lambda }}_2}$$

3.2. Intensification of labor in department I

Suppose there is an intensification of labor in department I that is captured by two constants µ₁ > 1 and µ₂ > 1, as specified in definition 1. Here µ₁ captures labor’s CPIO and µ₂ captures labor’s CCV.

3.2.1. Rate of exploitation

Let us denote by ${{\mathrm{\lambda }}^{\prime }}_1$ and ${{\mathrm{\lambda }}^{\prime }}_2$ the unit value of the capital and wage good, respectively, after the intensification of labor in the capital good sector. Value determination in department I is given by ${{\mathrm{\lambda }}^{\prime }}_1{\mathrm{\mu }}_1={{\mathrm{\lambda }}^{\prime }}_1{\mathrm{\mu }}_1{a}_1+{\mathrm{\mu }}_2{l}_1$ , so that:

$${{\mathrm{\lambda }}^{\prime }}_1=\frac{{\mathrm{\mu }}_2}{{\mathrm{\mu }}_1}\left(\frac{l_1}{1-a_1}\right)$$

(8)

Value determination in department II is given by ${{\mathrm{\lambda }}^{\prime }}_2={{\mathrm{\lambda }}^{\prime }}_1{a}_2+l_2$ , so that, using (8), we have:

$${{\mathrm{\lambda }}^{\prime }}_2=\frac{{\mathrm{\mu }}_2}{{\mathrm{\mu }}_1}\left(\frac{l_1{a}_2}{1-a_1}\right)+l_2$$

(9)

Let ${e^{\prime }}_1$ and ${e^{\prime }}_2$ denote the rate of exploitation in department I and department II after intensification of labor. Since there is intensification of labor in department I, the rate of exploitation in this department is impacted both by a higher CCV, captured by µ₂, and by a change in the unit value of the consumption good, given by ${{\mathrm{\lambda }}^{\prime }}_2$ . To be more precise, we have:

$${e^{\prime }}_1=\frac{{\mathrm{\mu }}_2-b{{\mathrm{\lambda }}^{\prime }}_2}{b{\mathrm{\lambda }}_{2^{\prime }}}$$

The intensity of labor does not change in department II. Hence, the change in the rate of exploitation in department II is driven only by the change in the unit value of the consumption good. In fact, we have:

$${e^{\prime }}_2=\frac{1-b{{\mathrm{\lambda }}^{\prime }}_2}{b{\mathrm{\lambda }}_{2^{\prime }}}$$

Hence, using the expressions for the rate of exploitation in both departments, before and after intensification of labor in department I, we have:

$$\frac{1+{e^{\prime }}_1}{1+e_1}=\frac{{\mathrm{\mu }}_2{\mathrm{\lambda }}_2}{{{\mathrm{\lambda }}^{\prime }}_2}$$

and:

$$\frac{1+{e^{\prime }}_2}{1+e_2}=\frac{{\mathrm{\lambda }}_2}{{{\mathrm{\lambda }}^{\prime }}_2}$$

• Claim 2. If there is an intensification of labor in department I, then:

• (a) the rate of exploitation in department I rises unambiguously, that is, ${e^{\prime }}_1>e_1$ ; and

• (b) the change in the rate of exploitation in department II depends on the relative magnitudes of µ₁ and µ₂, that is:

$${e^{\prime }}_2\stackrel{>}{\underset{<}{=}}{e}_{2}if{\mathrm{\mu }}_2\stackrel{<}{\underset{>}{=}}{\mathrm{\mu }}_1$$

Proof. For the first part, that is, change in the rate of exploitation in department I, we have to consider three cases. Case 1: If µ₁ > µ₂, then a comparison of (7) and (9) shows that ${{\mathrm{\lambda }}^{\prime }}_2<{\mathrm{\lambda }}_2$ ; hence, the rate of exploitation has increased. Case 2: If ${\mathrm{\mu }}_1={\mathrm{\mu }}_2$ , then a comparison of (6) and (9) shows that ${{\mathrm{\lambda }}^{\prime }}_1={\mathrm{\lambda }}_1$ and ${{\mathrm{\lambda }}^{\prime }}_2={\mathrm{\lambda }}_2$ . Thus, $(1+{e^{\prime }}_1)/(1+e_1)={\mathrm{\mu }}_2>1$ ; hence, ${e^{\prime }}_1>e_1$ . Case 3: If µ₂ > µ₁, then (7) and (9) shows that ${{\mathrm{\lambda }}^{\prime }}_2>{\mathrm{\lambda }}_2$ . But a little algebra also shows that:

$${{\mathrm{\lambda }}^{\prime }}_2={\mathrm{\mu }}_2\left[\frac{1}{l_1}\frac{l_1{a}_2}{1-a_1}+\frac{l_2}{{\mathrm{\mu }}_2}\right]<{\mathrm{\mu }}_2\left[\frac{l_1{a}_2}{1-a_1}+l_2\right]={\mathrm{\mu }}_2{\mathrm{\lambda }}_2$$

where the inequality follows because µ₁, µ₂ > 1. Hence, $1+{e^{\prime }}_1>1+e_1$ , so that ${e^{\prime }}_1>e_1$ .

For the second part, that is, change in the rate of exploitation in department II, note that:

$$\frac{1+{e^{\prime }}_2}{1+e_2}=\frac{{\mathrm{\lambda }}_2}{{{\mathrm{\lambda }}^{\prime }}_2}$$

and recall that:

$${\mathrm{\lambda }}_2=\frac{l_1{a}_2}{1-a_1}+l_2$$

and:

$${\mathrm{\lambda }}_{2^{\prime }}=\frac{{\mathrm{\mu }}_2}{{\mathrm{\mu }}_1}\left(\frac{l_1{a}_2}{1-a_1}\right)+l_2$$

If ${\mathrm{\mu }}_2={\mathrm{\mu }}_1$ , then ${{\mathrm{\lambda }}^{\prime }}_2={\mathrm{\lambda }}_2$ , so that ${e^{\prime }}_2=e_2$ ; if µ₂ > µ₁, ${{\mathrm{\lambda }}^{\prime }}_2>{\mathrm{\lambda }}_2$ , and so, ${e^{\prime }}_2<e_2$ ; if µ₂ < µ₁, and thus, ${e^{\prime }}_2>e_2$ .

• Claim 3. If there is an intensification of labor in department I, the increase in the rate of exploitation is higher in department I than in department II.

Proof. Note that:

$${e^{\prime }}_1-{e^{\prime }}_2=\frac{{\mathrm{\mu }}_2-{{\mathrm{\lambda }}^{\prime }}_{2}b}{{{\mathrm{\lambda }}^{\prime }}_{2}b}-\frac{1-{{\mathrm{\lambda }}^{\prime }}_{2}b}{{{\mathrm{\lambda }}^{\prime }}_{2}b}>0$$

because µ₂ > 1. Since the rate of exploitation in both departments were the same before the increase in the intensity of labor in department I, that is, $e_1=e_2$ , we see immediately that the increase in the rate of exploitation in department I is larger than the change in the rate of exploitation in department II.

3.2.2. Forms of exploitation

Let us start by investigating the question of the form of exploitation, that is, relative and absolute surplus value, in department I. We have the same three cases to consider that we had encountered in the one-commodity model. If ${\mathrm{\mu }}_1={\mathrm{\mu }}_2$ , then (7) and (9) shows that the value of labor power per hour (which is value of the hourly real wage bundle) stays unchanged. Since the rate of exploitation has increased, this is a form of absolute surplus value production in department I. If µ₁ < µ₂, then (7) and (9) shows that the value of labor power per hour of work has increased. This rules out the production of relative surplus value. Since the rate of surplus value has increased, as demonstrated in claim 2, this must be a case of the production of absolute surplus value in department I. If µ₁ > µ₂, then (7) and (9) shows that the value of labor power per hour of work has declined. To pin down the form of surplus value, note that:

$${e^{\prime }}_1-e_1=\left(1+{e^{\prime }}_1\right)-\left(1+e_1\right)=\frac{{\mathrm{\mu }}_2}{{{\mathrm{\lambda }}^{\prime }}_{2}b}-\frac{1}{{\mathrm{\lambda }}_{2}b}=\frac{{\mathrm{\mu }}_2-1}{{{\mathrm{\lambda }}^{\prime }}_{2}b}+\left(\frac{1}{{{\mathrm{\lambda }}^{\prime }}_{2}b}-\frac{1}{{\mathrm{\lambda }}_{2}b}\right)$$

Thus, in this case, we see a combination of the production of absolute surplus value (first term on the RHS) and the production of relative surplus value (second term on the RHS) in department I.

What about the form of exploitation in department II? Note that:

$${e^{\prime }}_2-e_2=\left(1+{e^{\prime }}_2\right)-\left(1+e_2\right)=\frac{1}{b{{\mathrm{\lambda }}^{\prime }}_2}-\frac{1}{b{\mathrm{\lambda }}_2}$$

If ${\mathrm{\mu }}_1={\mathrm{\mu }}_2$ , then (7) and (9) shows that ${\mathrm{\lambda }}_2={{\mathrm{\lambda }}^{\prime }}_2$ . Hence, there is no change in the rate of exploitation. If µ₁ < µ₂, then ${\mathrm{\lambda }}_2<{{\mathrm{\lambda }}^{\prime }}_2$ ; hence, the rate of exploitation falls in department II. If µ₁ > µ₂, then ${\mathrm{\lambda }}_2>{{\mathrm{\lambda }}^{\prime }}_2$ ; hence, the rate of exploitation rises in department II. Since there is no change in the intensity of labor in department II, the fall in the unit value of the consumption good means that the rise in the rate of exploitation in department II is an instance of the production of RSV. We summarize our findings about the rate and forms of exploitation in table 1.

Table 1.

Rate and Form of Exploitation in the Two Departments after an Increase in the Intensity of Labor in Department I.

	Department I		Department II
	Rate of Exploitation	Form of Exploitation	Rate of Exploitation	Form of Exploitation
${\mathrm{\mu }}_1={\mathrm{\mu }}_2$	Increase	ASV	No change	NA
µ2 < µ1	Increase	ASV	Decrease	NA
µ2 > µ1	Increase	ASV + RSV	Increase	RSV

Note: ASV = absolute surplus value; RSV = relative surplus value.

3.2.3. Short run versus long run

As soon as we introduce more than one sectors (or industries) in the analysis, we face the following question: how does the intensity of labor compare across sectors? In any model with more than one sector, including the simple two-department model being discussed in this section, we cannot have different intensities of labor across departments if, at the same time, we have the same real wage bundle and the same rate of exploitation across sectors. If intensities differ across sectors, then the rate of exploitation will also differ. For instance, we know from claim 3 that the rate of exploitation in department I will be higher than the rate of exploitation in department II, after department I witnesses an intensification of labor. This means that the analysis we have presented so far should be understood as a short run exercise. While we might have different intensities of labor across departments in the short run, class struggle, and/or mobility of labor, ensures that every sector has the same intensity of labor in the long run, given that the hourly real wage bundle and the rate of exploitation are same across sectors. ⁹ There are many long run configurations that can emerge. To consider all the possibilities, let us consider two extreme cases.

The first extreme scenario occurs if the relative class power of labor is higher. In this scenario, labor forces the intensity to go down in department I. Thus, in the long run both departments will have the original intensity. The (common) rate of exploitation will fall back to the original level, $e$ , after a temporary increase in department I. The second extreme scenario occurs if the relative class power of capital is higher. In this case, capital forces an increase in intensity in department II. If this happens, then both departments will have the new intensity captured by (µ₁, µ₂). The rate of exploitation will increase in department II to become ${e^{\prime }}_2={e^{\prime }}_1$ . The configuration that actually occurs might fall between these extreme cases; that is, the outcome of class struggle leads to a new intensity of labor captured by $({{\mathrm{\mu }}^{\prime }}_1,{{\mathrm{\mu }}^{\prime }}_2)$ , which is common to both departments and where $1<{{\mathrm{\mu }}^{\prime }}_1<{\mathrm{\mu }}_1$ and $1<{{\mathrm{\mu }}^{\prime }}_2<{\mathrm{\mu }}_2$ .

3.3. Intensification of labor in department II

Suppose there is an intensification of labor in department II that is captured by two constants µ₁ > 1 and µ₂ > 1, as specified in definition 1. Just like before, µ₁ captures labor’s CPIO and µ₂ captures labor’s CCV. The analysis of this case is symmetric to the analysis of an increase in the intensity of labor in department I that we have presented above.

Value determination in department I, before and after intensification of labor in department II, are captured by:

$${\mathrm{\lambda }}_1={\mathrm{\lambda }}_1{a}_1+l_1$$

and:

$${{\mathrm{\lambda }}^{\prime }}_1={{\mathrm{\lambda }}^{\prime }}_1{a}_1+l_1$$

which shows that ${{\mathrm{\lambda }}^{\prime }}_1={\mathrm{\lambda }}_1$ . The rate of exploitation in department I, before and after intensification of labor in department II, are related to each other as:

$$\frac{1+{e^{\prime }}_1}{1+e_1}=\frac{{\mathrm{\lambda }}_2}{{{\mathrm{\lambda }}^{\prime }}_2}$$

Determination of unit value in department II, before and after intensification of labor in this department are given by:

$${\mathrm{\lambda }}_2={\mathrm{\lambda }}_1{a}_2+l_2$$

and:

$${{\mathrm{\lambda }}^{\prime }}_2{\mathrm{\mu }}_1={\mathrm{\lambda }}_1{a}_2{\mathrm{\mu }}_1+{\mathrm{\mu }}_2{l}_2$$

The rate of exploitation in department II, before and after intensification of labor in department II, are related to each other as:

$$\frac{1+{e^{\prime }}_2}{1+e_2}=\frac{{\mathrm{\mu }}_2{\mathrm{\lambda }}_2}{{{\mathrm{\lambda }}^{\prime }}_2}$$

It is straightforward to then derive the analogues of claim 2 and claim 3. The analysis of the short deviations in the rates of exploitation in the two-department and the long run adjustment to equality is also similar to the case when the intensification of labor occurs in department I.

4. Conclusion

As a system of social production built on exploitation, capitalism is driven by the need to continuously generate, realize, and accumulate surplus value, the ultimate source of which is the unpaid labor of the working class. Competitive pressures in capitalism enforce the systemic need to keep increasing the rate of exploitation. Capitalism has two broad methods to increase the rate of exploitation: the production of absolute surplus value, and the production of relative surplus value.

The production of absolute surplus value can happen when the length of the working day increases, holding the productivity and intensity of labor fixed. By most historical accounts, the production of absolute surplus value was the main way of increasing the rate of exploitation during the early phases of capitalism. What happens when the struggle of the working class manages to force the State to regulate the length of the working day? Does capitalism then abandon the production of surplus value and focus solely on the production of relative surplus value?

When class struggle by the workers has forced the State to put a limit on the length of the working day, the capitalist system does not lose its ability to produce absolute surplus value. While production of relative surplus value, and therefore growth of labor productivity, becomes the most important way of increasing the rate of surplus value, simultaneously the system uses intensification of labor—which is a reliable way to produce absolute surplus value.

In this article, we have developed a simple framework to incorporate intensification of labor into the widely used linear model of production. Using this model, we have demonstrated that an intensification of labor always increases the rate of exploitation. Hence, it is in the interest of the capitalist class, and against the interest of the working class, to increase the intensity of labor. We have also demonstrated, in various versions of the linear model of production, that an intensification of labor can, in most realistic situations, only increase the rate of exploitation in the form of the production of absolute surplus value.