Chapter 9: The Rate of Surplus Value

Outline of Marx's Discussion
Section 1: The Degree of Exploitation of Labor Power

surplus value = excess of value of product over value of inputs = s
value of inputs = constant capital (c) + variable capital (v) = c + v
total value of product = C' = (c+v)+s
C' - C = s

constant capital = fixed capital (machinery, plant, etc) + raw materials (c2)
but fixed capital gives up only a part of its value (c1) in each period
so, constant capital (c) in a given period = c1 + c2

new value created = v + s
= reproduction of value of labor power + a surplus
= necessary labor time + surplus labor time
= necessary labor + surplus labor

measures of s:
s/v = rate of surplus value = rate of exploitation
s/(c+v) = rate of profit
Commentary

Partly these sections are just setting out some basic definitions that Marx will utilize in the rest of the text. Partly, he is explaining some of the implications of the last two chapters where he introduced surplus value, constant capital and variable capital.

The most interesting thing in this section concerns the difference between the two measures of the rate of extracting a surplus from the workers. The rate of surplus value compares surplus labor time with necessary labor time and measures the surplus in terms of the workers' labor as a whole; it gives an idea about what proportion of the workers' day is given up to the capitalist versus the amount spent on self-reproduction, i.e., reproducing the value of labor power. This is very much a worker's view of the issue because what is at issue is the worker's time and its allocation. Clearly, the higher the ratio s/v the higher percentage of the workers' day is being appropriated by the capitalist and the smaller the part the workers are working for themselves.

The rate of profit, on the other hand, which measures the surplus labor time against the capitalist's total investment, is a measure primarily of interest to the capitalists, in so far as it measures how much they earn in relation to how much they had to invest originally. This rate of profit, although expressed in value terms is a good first approximation for the actual calculations of rates of profit that occur in business and therefore expresses the capitalist point of view. (Of course, in actual calculations business would not only be measuring costs in money terms but would also take into account things like taxes on profits, from which Marx makes abstraction here.)

The rate of surplus value is never calculated by the capitalist, nor is it likely that any would ever attempt such a calculation, at least not publicly, for it would draw attention to the time the workers work for the capitalists. This of course is just Marx's purpose; he presents this moment of analysis to clarify what is going on from the workers' point of view, the view the capitalists would prefer to hide or cover up.

Another interesting point, not raised here by Marx, but worth contemplating, is the relations between necessary and surplus labor time understood dynamically. Isn't surplus labor today merely going to be invested tomorrow to raise the productivity of necessary labor and thus the standard of living? And if such investment is in fact necessary for such increases of productivity then does it make any sense today to speak of "surplus" labor? Shouldn't we rather speak of labor necessary today and labor necessary for the future? These questions throw us back to the issue of what is "necessary" about necessary labor, an issue first raised in chapter 6 and one that requires a more complex answer than Marx gave us there if we are to understand the dynamics of capitalist development and get beyond a static concept of exploitation. Marx addresses these questions in chapter 10.
Outline of Marx's Argument
Section 2: The Representation of Components of Value by Parts of the Product

Marx uses an example to show how the three components of value of the product: c, v, and s can be represented by proportional parts of the product itself. In his example the total product of 20 lbs of cotton yarn which is worth 30s (shillings) contains the following components of value:

c = 24s (shillings)
v = 3s
s = 3s
C' = 30s

These values of 24, 3 and 3 can be represented by 16, 2 and 2 lbs of yarn respectively. At the same time, following this logic, he also notes that newly created value of 12 hours work (and 6s value) can be represented by only 4 lbs of yarn. At 6s/12hrs, or .5s/hr, the 30s final product embodies 60 hrs labor, of which the other 48 derive from c.

Then, using the same example, Marx notes how the same components of value: c, v and s can be represented in terms of proportional parts of the total time employed in production, i.e., 12hrs. In this case the values of c = 24s, v = 3s and s = 3s, could be represented by 9hrs 38min, 1hr 12min, and 1hr 12min respectively.
Section 3: Senior's "Last Hour"
Marx here critiques Nassau Senior's argument, in defense of British manufacturers against the Factory Acts and against the workers efforts to reduce the working day to 10 hours, that the reduction of the working day by one hour would wipe out all manufacturing profits.

Senior's Argument (in Marx's jargon): the component parts of the total value of the final product can be represented by proportional parts of the time worked (as Marx described in section 2). In his case, the value of c + v is represented by 10.5 hours, the value of s by 1.0 hours. If, he therefore concludes, the working day is reduced by one hour, from 11.5 to 10.5, the surplus value s will be eliminated.

Marx's Critique: a) this is silly, why would a reduction of 1 hour drop s to zero? Why not drop c+v to 9.5 and use less constant capital and labor? b) more seriously he points out that in each hour of the working day, constant capital is being used up and its value transferred to the product through the exercise of labor, therefore a reduction of one hour would reduce not only total labor time but also the use of constant capital. Assuming the ratio of s/v equals unity, then 5.75 hours are producing v and 5.75 hours are producing s (where 5.75 + 5.75 = 11.5) A reduction of one hour, assuming wages constant would drop s from 5.75 to 4.75 and lower the rate of surplus value from 100% to 82.6%, hardly an elimination of profit! In a footnote, Marx notes that Senior "to his honor" later on came to support the factory legislation.

In another footnote, Marx notes with sarcasm Andrew Ure's argument that less work would also corrupt children's morals because "idleness is the parent of vice." This, of course, is an argument that has hardly disappeared and is often repeated to justify keeping children in school for long hours.
Commentary

These two sections go together because Marx is preparing in section 2 the critique of Senior that he wants to make in section 3. At first he sets out what appears to be a rather formalistic argument that the components of value can be "represented" by either parts of the product, or by parts of the time used to produce the product. Why anyone would want to do this is unclear and the example given is tedious. We discover the motivation in the next section, however, when we see how Senior has used this kind of an argument to defend profits.

Marx's critique is simple enough. He has only to show the fallacy of Senior's reasoning by recalling that each hour of production processes elements of constant capital and, by Senior's assumptions, one half the total time of labor creates surplus value, not just the last hour. Now, Marx concludes his argument in terms of the rate of surplus value, which he points out will only drop from 100% to 82.6%. Some may find this argument troubling, however, not because it is wrong, in Marx's terms, but because it is not framed in terms of profit (or net profit) as Senior would have it. It is, however, easy to frame the conclusion in terms of absolute levels of profit, the rate of profit or the rate of exploitation as Marx has done.

Restating Senior's example in Marx's terms, the initial case of an 11.5 hr day gives the following results:
C' = 115,000 (total value of product)
c = 95,000 (constant capital, adding depreciation to other c)
v = 10,000 (wages, assuming s/v = 1, or 100%)
net profit or s = 10,000 (absolute level of surplus value)
so, c + v = 105,000
therefore s/(c + v) = 9.5%

Senior's horror story of a one hour drop in the working day gives the following calculations for a 10.5 hour working day:

C' = 105,000 (assuming production falls proportionately, prices constant)
({115,000/11.5}10.5 = 105,000)
c = 86,739.1 (assuming costs fall proportionately)
({95,000/11.5}10.5 = 86,739.1)
v = 10,000 (assuming the wage bill remains the same)
so, c + v = 96,739.1
net profit s = 8,260.9 (105,000 - 96,739.1)
therefore, s/(c + v) = 8.5%
therefore, s/v = 82.6% (as in Marx's calculations)

So, we see in Senior's example that if the working day is reduced one hour the result would be a drop in absolute profits from 10,000 to 8,260.9 or a drop in the rate of profit from 9.5% to 8.5%, both of which confirm the argument Marx is making that Senior drastically overstates the potential impact of the 10 hours law on profits. We can also note, that in the more likely case that the wage rate rather than the the wage bill remained the same, the reduction of one hour would drop the wage bill (v) from 10,000 to 9,130.4, c would still be at 86,739.1 and profits (C' - {c + v}) would therefore only fall to 9,130.5 + with a resultant negligible change in s/v and s/(c + v)!

The history of Senior's hour, and of all other episodes like it --such as the one Marx cites in 1848-- bespeak much more than false logic. The desperate arguments put forward by capitalists and their apologists to resist any reduction of work time reflect more than fear of losing profits, their arguments which often foretell doom and societal collapse reflect a deeper intuition that all reductions in work threaten the social fabric of capitalism as a civilization built on the subordination of life to work. Down the path of less and less work lies another kind of world, one in which capitalists as a class are completely superfluous.

Partly this can be seen in Ure's argument that Marx cites in a footnote: the panic concern that a life not structured by work would be both idle and immoral. This has been typical of the capitalist work ethic whose ghost can still be found lurking in the darker spirits of society. The greatest fear of teacher's strikes is that of an uncontrolled mob of children being turned loose on society --this despite all evidence of how school discipline destroys creativity and imagination --qualities which only grow when given free time for free development.
Section 4: Surplus-Product

surplus product = the portion of the product that represents surplus value

rate of surplus product = surplus product/necessary product
Commentary
In this last, short section, Marx simply finishes his parallels between the distribution of value and the distribution of product. He emphasizes the ratio of surplus product to necessary product (i.e., the part that goes to working class consumption) for the same reason he emphasizes the ratio s/v: they both highlight distribution between the classes.

In the final footnote of this section (#13) Marx quotes T. Hopkins who writes:

"To an individual with a capital of £20,000, whose profits were £2,000 per annum, it would be a matter quite indifferent whether his capital would employ a hundred or a thousand men [ . . . ]"

Such indifference is an attribute of what I would call a narrow-minded, fetishistic capitalist who can not see beyond the bottom line --one who thinks that the point of business is merely profit making and self enrichment. Such capitalists rarely rise to the level of policy making because they cannot see that it often does matter whether a hundred or a thousand people are employed. Being organized around the endless and universal imposition of work, capitalists collectively must worry about whether they are providing enough employment to absorb the existing labor force. If they do not, and unemployment grows, and if it grows too large, their ability to control society is threatened. It has been the recognition of this that has driven policy makers in high unemployment areas to be concerned with the issue of "appropriate technology," i.e., whether a given technology will contribute to solving the "problem" of unemployment. [NB: a certain amount of unemployment is necessary in capitalism to keep pressure on workers to accept alienated low paying jobs; but too much unemployment creates a terrain of unrest.] It was also this recognition during the last twenty years of the 20th Century that led the International Labor Organization to warn of the need for the creation of a billion jobs by century's end to absorb the growth in the world's labor force --or risk widespread unrest.
Concepts For Review
necessary labor time
surplus labor time
rate of profit
exploitation
rate of exploitation
Senior's last hour
surplus produce
Questions For Review
(An * means that one possible answer can be found at the end of the study guide.)

*1. Explain the difference between the rate of exploitation and the rate of profit. Why is the former a reasonable measure for workers and the latter a reasonable measure for capitalists?

*2. Discuss the concept of necessary labor. What is included; what is excluded? What would be the results of redefining the concept in dynamic terms, e.g. over time, rather than statically as Marx defines it?

3. Keeping in mind that one pound = 20 shillings, that a quarter = 8 bushels, examine Marx's example taken from Jacob. What would the total value of the produce have to be for his example to be consistent? What would this imply for his measures of price and productivity?

4. Why do you think Marx goes through the analysis of Section 2 looking at c, v and s in terms of proportional parts of the product?

*5. Explain Senior's argument as to why the extension of the working day by one hour would wipe out capitalist profits and bring wreck and ruin to the economy. Then explain the fallacy in his reasoning. Would his analysis be relevant today? Why or why not?