Introduction
Social-reformist leftists and radical leftists often refer to capitalism. Radical leftists can often be criticized on that score because their references to capitalism are too vague. On the other hand, although social-reformist leftists also use the term “capitalism” in a vague sense, it is to their advantage since they sound radical without really being so.
In a number of other posts, I have tried to calculate the rate of exploitation or the rate of surplus value at the level of a particular capitalist company (see, for example, The Rate of Exploitation of General Motors Workers). I also tried to calculate, in a preliminary manner, the rate of exploitation of particular Canadian industries (see for example The Rate of Exploitation of Oil Sands Extraction (Oil And Gas) Workers: Preliminary Estimate).
How to Calculate a Surplus of Value (Profit)
The following data to calculate s come from Statistics Canada Table: 36-10-0103-01 (https://www150.statcan.gc.ca/t1/tbl1/en/tv.action?pid=3610010301) (GDP=gross domestic product; v=variable capital, or the total wage + benefits; CFC=consumption of fixed capital; NPISH=non-profit institutions serving households;
| All values in millions CAD | current prices |
| GDP is at market prices (Canada) | 2019 |
| Variable | Value |
| GDP | 2,313,563 |
| v (compensation of employees) | 1,174,784 |
| CFC corporations | 239,113 |
| CFC govt + NPISH | 77,075 |
| CFC unincorporated | 67,839 |
| Total CFC | 384,027 |
| An empirical approximation of surplus value: s=GDP – v – CFC | 754,752=2,313,563-1,174,784-384,027 |
I will describe how I obtained these numbers since these posts are meant for workers and not for academics. They may want to produce similar statistics or correct errors that I have made.
- GDP: the datum for this category is given in the Stats Can table, so there is no need to do any further calculation to determine it.
- v (compensation of employees) includes two categories from the table: a quarterly “wages and salaries”, on the one hand, and “employers’ social contributions” on the other. First, you add the two for each quarter, and then you add all quarters to obtain “compensation of employees” (you could, of course, add all quarterly “wages and salaries” and all quarterly “employers’ social contributions,” and then add the total “wages and salaries” to the total “employers’ social contributions”).Here is a table that illustrates the above:284,318+293,741+294,329+302,396=1,174,784
Date Wages and salaries Employers’ social contributions Quarterly and annual compensation of employees 2019-01 245,622 38,696 284,318 2019-04 253,821 39,920 293,741 2019-07 254,270 40,059 294,329 2019-10 261,046 41,350 302,396 Annual 1,014,759 160,025 1,174,784 Although Marx’s concept of variable capital refers to the value advanced for labour power, national accounts compensation of employees is used here as the closest empirical approximation because employer social contributions form part of the socially necessary cost of reproducing labour power.
- CFC corporations: Add the quarterly amounts together. Thus:
Date Consumption of fixed capital (CFC) 2019-01 59,149 2019-04 60,019 2019-07 59,488 2019-10 60,457 Annual 239,113 - CFC govt + NPISH: The same procedure as 3.:
Date Govt. And NPISH CFC 2019-01 18,988 2019-04 19,220 2019-07 19,371 2019-10 19,496 Annual 77,075
5. CFC unincorporated: The same procedure as 3. and 4.:
| Date | CFC Unincorporated |
| 2019-01 | 16,779 |
| 2019-04 | 16,932 |
| 2019-07 | 17,095 |
| 2019-10 | 17,033 |
| Annual | 67,839 |
6. Total CFC: Add annual CFC corporations +CFC govt + NPISH+CFC unincorporated: 239,113+77,075+67,839=384,027.
7. An empirical approximation of surplus value (s)=GDP-v-CFC=2,313,563-1,174,784-384,027=754,752. In effect, this empirical approximation of surplus value is a result of calculating the net domestic product (NDP) by subtracting CFC from GDP and then subtracting compensation of employees as an empirical approximation of v.
How to Calculate the Rate of Exploitation of Canadian Workers or the Rate of Surplus Value and its Meaning
Given that we now have both s and v, it is only necessary to divide s by v: s/v=754,752/1,174,784=64%.
The meaning of this rate can be understood when we look at the division of one hour that a worker works to produce her or his wage/salary and benefits and the surplus of value (profit) that s/he produces for the capitalist employer during the same hour. We can then consider working days with longer and longer working hours.
To calculate such a division, we have two variables, s and v, and the mathematical rule is that with two variables, if we are to find a solution, we must have two different equations.
We know that s/v=64%, so that is one equation. But if we also know that the working hour is 60 minutes and that in one hour total new value is added, which consists of s+v. So, we have a second equation: v+s=60.
Now, what we need to do is to express one of the variables–v or s–in terms of the other so that we in effect have only one variable with one equation.
Let us take the equation s/v=64% (or 0.64 since 64%=0.64). An arithmetic rule is that if you multiply both both sides of an equation by the same number or variable (except 0), then the equation does not change.
So, let us multiply s/v=0.64 by v in order to cancel out v on the left-hand side and express s in terms of v on the right-hand side. (sv/v)=0.64v.
We can now rewrite the left-hand side as s(v/v). This can be seen if we substitute arbitrary numbers; let s=5, v=10; (sv)/v=(5×10/10=5. But so too is 5(10/10)=5×1=5 (since any number divide by itself (except 0)=1, and any number times 1 (except 0)=the same number. v=5/10=0.5;
So, we have s=0.64v. But we have the second equation s+v=60. If we now subsitute for s 0.64v, we have in the second equation 0.64v+v=60; 1.64v=60. If we now divide both sides by 1.64, we have v=60/1.64, which equals approximately 37 minutes. Now that we know v=37, then in the equation s+37=60, s must=23.
Once we have gone through this process for a working hour of 60 minutes, we can then just substitute 240 for 60 in a working day of 4 hours (240 minutes), as v=240/1.64; or a working day of 5 hours (300 minutes), as 300/1.64, etc.
With a rate of exploitation of 64%, a worker works 37 minutes to producer her/his wage/salary and benefits and works for free 23 minutes to produce a surplus of value or profit for the capitalist employer.
A worker who works 4 hours a day (240 minutes) produces her/his wage/salary and benefits in 2 hours and 26 minutes (146 minutes) and produces a surplus of value or all the profit for the capitalist employer in 1 hour and 34 minutes (94 minutes).
A worker who works 5 hours (300 minutes) a day produces her/his wage/salary and benefits in 3 hours and 3 minutes (183 minutes) and produces a surplus of value or all the profit for the capitalist employer in 1 hour and 57 minutes (117 minutes).
A worker who works 6 hours (360 minutes) a day produces her/his wage/salary and benefits in 3 hours and 40 minutes (220 minutes) and produces a surplus of value or all the profit for the capitalist employer in 2 hours and 20 minutes (140 minutes).
A worker who works 7 hours (420 minutes) a day produces her/his wage/salary and benefits in 4 hours and 16 minutes (256 minutes) and produces a surplus of value or all the profit for the capitalist employer in 2 hours and 44 minutes (164 minutes).
A worker who works 8 hours (480 minutes) a day produces her/his wage/salary and benefits in 4 hours 53 minutes (293 minutes) and produces a surplus of value or all the profit for the capitalist employer in 3 hours 7 minutes (187 minutes).
A worker who works 9 hours (540 minutes) a day produces her/his wage/salary and benefits in 5 hours and 38 minutes (338 minutes) and produces a surplus of value or all the profit for the capitalist employer in 3 hours and 22 minutes (202 minutes).
A worker who works 10 hours (600 minutes) a day produces her/his wage/salary and benefits in 6 hours and 6 minutes (366 minutes) and produces a surplus of value or all the profit for the capitalist employer in 3 hours and 54 minutes (234 minutes).
A worker who works 11 hours (660 minutes) a day produces her/his wage/salary and benefits in 6 hours and 42 minutes (402 minutes) and produces a surplus of value or all the profit for the capitalist employer in 4 hours and 18 minutes (258 minutes).
A worker who works 12 hours (720 minutes) a day produces her/his wage/salary and benefits in 7 hours and 19 minutes (439 minutes) and produces a surplus of value or all the profit for the capitalist employer in 4 hours and 41 minutes (281 minutes).
The rate of exploitation measures the extent to which workers produce value in excess of the value paid to them in wages. It divides the working day into two parts: the portion that reproduces the value of wages and the portion that produces surplus value for the capitalist for free.
In empirical or factual terms, we measure:
- v: total compensation of employees (wages, salaries, benefits)
- s: surplus value, derived from national accounts
The rate of surplus value (or rate of exploitation) is defined as:.
s′=s/v
This is a definition, not a separate empirical measurement since its components consist of two interrelated but distinct aspects: s and v. It expresses surplus value relative to wages.
How to Calculate the Composition of Capital and its Importance for Calculating the Rate of Profit
As will be shown, the rate of profit, which is of major concern to employers, is a function of both the rate of exploitation and the composition of capital.
The Composition of Capital
There are different ways of measuring the composition of capital, such as c/v, but one problem with this measure is that v measures a flow (wages paid over time) whereas c measures a stock (fixed capital measured at a point in time).
Although this problem cannot be completely avoided, some researchers instead use the measure c/(c+v). This has the advantage of reducing sharp fluctuations caused by changes in wages and makes it easier to compare changes in the composition of capital over time (since it is a proportion that is between 0 (when c=0) and 1 (when v=0).
It has an additional advantage which we will discuss in the section on the rate of profit.
It should be pointed out that here c refers to fixed capital stock as an empirical or data proxy (substitute or approximation) for constant capital derived from publicly available data. Theoretically, constant capital is broader than fixed capital and also includes circulating constant capital, such as raw materials, energy, and other intermediate inputs that are used up during the production process. The measure used here therefore understates Marx’s full concept of constant capital but permits comparisons across years using consistent official statistics.
We can thus express the structure of production using:
This means: how much of total capital is machinery, buildings, and equipment (compared to wages)
So:
- higher value → more machinery relative to labour
- lower value → more labour relative to machinery
To obtain c, I used the StatsCan table 36-10-0098, “Flows and stocks of fixed non-residential capital for all industries, by type of asset, provinces and territories,” with the following categories: Prices=Current prices; Industry=Total all industries; Flows and stocks=Geometric end-year net stock; Assets=Total non-residential; in millions of dollars; and Value. For 2019, c=2,664,473, that is to say, since it is in millions of dollars, it is really 2 trillion 664 billion and 473 million.
Given the ratio c/(c+v) and the data about fixed capital (proxy for c) and v, we have:
2,664,473/(2,664,473 + 1,174,784=2,664,473/3,839,257=0.69=0.69×100=69%. This indicates that the value of the existing fixed capital stock is approximately 69% of the combined empirical measure of fixed capital stock plus annual compensation of employees, and it also indicates that the value of the annual compensation of employees is approximately 31% of the combined empirical measure of annual compensation of employees plus fixed capital stock.
Deriving surplus value from the rate of exploitation
The rate of profit is expressed as s/(c+v). Since the rate of exploitation is an expression of the extent or degree of exploitation, it would be useful to express the rate of profit in part as a function of the rate of exploitation. To do that, we must find a way of expressing s or the numerator (the top part of the fraction s/(c+v) in terms of the rate of exploitation.
Starting from the definition:
s′=s/v
Multiply both sides by v:
s′v=sv/v
The right-hand side simplifies because v cancels:
s’v=s
So we obtain:
s=s′v
This is not a new way of measuring surplus value. It is simply the definition of s′ rearranged so that surplus value can be expressed in terms of the rate of exploitation and the wage bill.
Rate of profit
The rate of profit is defined as:
p′=s/(c+v)
Substituting s=s′v:
We can separate this expression into two components:
So profit depends on:
(1) exploitation of labour
s′= how much surplus is taken from workers
(2) how big wages are compared to total capital
v/(c+v)
Since:
v/(c+v)=1−c/(c+v),
we can rewrite the rate of profit as:
p′=s′(1−(c/c+v)
This forms an additional reason for using c/(c+v) as an expression of the composition of capital rather than c/v–c/(c+v) can be related to the rate of profit by being related to the proportion of v to total capital advanced.
Given the equation p′=s′(1−(c/c+v), and the data about s’ and c/(c+v), we can approximate the rate of profit. It should be noted that using fixed capital stock as a proxy or substitute or representative for constant capital produces an approximate rate of profit. Because circulating constant capital (raw material, energy, accessory material and so forth) is excluded, this figure should be interpreted as an upper-bound estimate. That means that the maximum rate of profit would be this approximate rate of profit; if circulating constant capital were included, the rate of profit would decrease.
p’=0.64(1-0.69)=(0.64)(.31)=0.1984=19.84%=20% after rounding up.
Final Point
Putting it all together:
The rate of profit depends on two things:
- How much workers are exploited (s′)
- How production is structured between machinery and labour (c/(c+v)
Difference between the Rate of Exploitation or the Rate of Surplus Value and the Rate of Profit: Political Considerations
The rate of exploitation relates two variables that are internally related to each other since both are a function of the length of one working day. However, the capitalist employer must not only purchase the labour power or capacity to work of workers but also durable means of production (such as buildings, machinery and equipment and so forth) and raw material (such as soap for making the bottles in a brewery move with less friction along the line).
The capitalist–and economists–must thus be interested, not in the rate of exploitation but in the rate of profit–the extent to which money invested in labour power and means of production results in a surplus of value or profit.
This rate obscures the source of a surplus of value since the surplus is now related, not to its source, v, but to the total capital invested, c+v. This creates the illusion that a surplus of value arises from the joint use of c and v rather than just v. It also underestimates the extent of exploitation since s/(c+v) is always lower than s/v unless c=0, which is never the case.
It is in the interests of the working class to know that they are exploited to a much greater extent than what the rate of profit indicates.
On the other hand, and ironically, it is nowadays necessary to emphasize c as well as an essential aspect of forming a critique of capitalist society. Nowadays, among the left, we hear such preliminary statements as ‘we acknowledge that we are on stolen land of ….” and the name of indigenous peoples. That the left should recognize the oppression of indigenous peoples is not in dispute. However, by only referring to land and not the produced means of production owned and controlled by a minority called the class of employers, the nature of the problem we face–capitalism as such–is by a slight of hand ignored.
Indeed, social-reformist leftists have for a long time recognized the need to nationalize land–but not the means of production. From Meghnad Desai, Marxian Economic Theory, page 42:
To this day land nationalisation and appropriation of profits in real estate have been a part of the [British] Labour Party’s economic philosophy. Profits in industrial activities are regarded as legitimate.
Some Final Considerations
Another relevant point is that Marx referred to the law of the tendency of the rate of profit to fall, where s relative to c+v falls over time. I will not enter into that debate except to refer to the importance of not just the rate of profit for defining an economic crisis but also the rate of accumulation. The rate of accumulation is the extent to which s produced in one round of production is invested in the next round of production.
The rate of profit measures the amount of surplus value or profit produced per unit of c+v. Even if the rate of profit is falling, if the mass of surplus is growing (which is possible since the rate of profit is a ratio or relative proportion between s and c+v so that c+v may increase faster than s increases), the rate of accumulation can increase.
A proxy (due to limitations of data) for the rate of accumulation is the growth in capital stock. It is a proxy or substitute since in Marxian economics the rate of accumulation should also include the rate of accumulation of additional intermediate inputs, or inputs that form the object of labour. Furthermore, it should also include the use of money to hire additional workers (if that is indeed the case–the additional c may replace workers altogether).
Limitations of this Approach
I have already pointed out one limitation, namely the fixed capital stock serves as a proxy or substitute for c. Another limitation is that there is no distinction between productive labour and unproductive labour. Productive labour is labour that produces surplus value. Unproductive labour may be of various sorts: commercial activity (realizing C’-M’) and financial activity (M-C, and M-M), as well as governmental activity and various activities of non-governmental activities. A further limitation is that mixed capital stock (self-owners who both labour and use means of production and, on occasion, employ a few workers) is not taken into consideration.
Another limitation is that the categories of “gross mixed income” and “net mixed income” are excluded from the calculation.
The Abolitionary 