Marxian exploitation

Introduction

My understanding of Marx’s theory of exploitation is that it starts by observing that there is class resentment of the capitalists by the proletariat, it proceeds by judging that this is an undesirable state of affairs, continues by assuming that the resentment is justified by the exploitation of the proletariat by the capitalists, and concludes by locating the exploitation in the appropriation by the capitalists of the economic surplus produced by the labour of the proletariat.

The observation is true: there is such resentment; the judgement is subjective, or at least its moral valence can’t be assessed without additional analysis; the assumption is of no value without evidence; the location of exploitation in the appropriation of economic surplus is false, or at least need not be true, and that’s what I demonstrate in this article.

Workers producing artifacts

Suppose a worker can work to produce a particular artefact. Producing the artefact requires working in 12 particular stages, one after the other, each stage taking 1 month.1 At the end of 12 months the worker can sell the artefact on the open market for $61,000. There is no exploitation here: the worker keeps all the money paid in exchange for the result of his labour.

Now suppose a capitalist employs 12 workers who work on an assembly line, such that worker 1 always works on stage 1 of artefact production, worker 2 always works on stage 2, and so on up to worker 12 who always works on stage 12. One artefact is completed per month, which the capitalist can sell on the open market for $61,000. Suppose further he uses that revenue to pay each of the 12 workers a monthly wage of $5,000 and keeps $1,000 for himself. Here is the capitalist’s cash flow report:

wages $60,000
profit $1,000
sales $61,000

Marx locates the exploitation in the capitalist system here: the capitalist has arranged for the workers to produce artefacts (true), and that he sells the product of the workers’ labour for its market value (true), retains some of the proceeds (true) and pays the workers less than the value that they created (false).

Exploitation or not?

How can it be false that the workers are paid less than the value that they created? After all, 12 workers received $5,000 each, i.e. $60,000 in total, for producing one artefact, whereas one worker working alone receives $61,000 for producing the same artefact. Why the difference? The difference lies in when the workers are paid. When working alone, payment is only received at the end of a year; working for the capitalist, payment is received at the end of every month. If a worker were to invest his monthly wage at the prevailing interest rate he would end up with more than $60,000 from his labour at the end of 12 months. Assuming that the prevailing interest rate is 3.66% per year (equivalent to 0.3% per month, compounded),2 the worker who invests their entire monthly wage for 12 months will have $61,000 at the end of the year,3 exactly the same amount as the worker who worked alone!

Work in progress

So, workers who work for the capitalist are not receiving less than if they worked alone, but that in itself does not prove that the capitalist is not exploiting them. After all the capitalist takes $1,000 of the revenue for doing seemingly nothing. How can that be justified? One could attempt to say that the capitalist is being paid for “organising the workers”, “having the idea to set up the business” or “taking the risk that the product won’t sell”, each of which may be a valid justification in some scenarios, but none of which is needed to justify the profit in the scenario we are considering. In our scenario the justification is much easier: the capitalist is receiving interest on the work in progress.

What is “work in progress”? Consider what happens during each month: worker 12, working on stage 12 of the production line, receives from worker 11 a partial artefact that is 11/12ths complete and turns it into a complete artefact for the capitalist to sell; but also worker 11, working on stage 11, receives from worker 10 a 10/12ths complete artefact and turns it into a 11/12ths complete artefact for worker 12 to work on next month; worker 10 receives a 9/12th complete artefact and turns it into a 10/12ths complete artefact, all the way back to worker 1 who creates a 1/12th artefact from raw materials.

In summary, the work of each month starts from work in progress from the previous month. The work in progress at the start, and at the end, of any month is, in aggregate, the result of 664 person-months of work. Each month of work costs $5,000, so its total value is close to $330,000.5 The capitalist’s income, $1,000 per month, is exactly the interest due on an investment of this size. In order to start up the production line the capitalist needed to produce or purchase 66 person-months of partial artefacts and his $1,000 monthly “profit” is simply the interest on that investment.


  1. For simplicity let’s assume that producing the artefact requires no specific tools, and the effort gathering the raw materials needed to produce the artefact is incorporated into this 12 months of labour, and that the materials otherwise have no cost – perhaps wood is gathered from a nearby ample forest.↩︎

  2. \(1.003^{12} = 1.0366\)↩︎

  3. \(5000 * (1.003^{12} - 1) / 0.003 = 61000\)↩︎

  4. \((11 * 12) / 2 = 66\)↩︎

  5. Due to compounding, the true value is closer to $333,333.↩︎