The Labour Theory of Value develops through many thinkers. Marx provides a basic genaeology of it here:
<Petty reduces use-value to labour […] Hobbes […] asserts that the labour which determines exchange-value is the particular kind of concrete labour by which gold and silver is extracted […] Boisguillebert for his part, in fact, although he may not be aware of it, reduces the exchange-value of commodities to labour-time […] Benjamin Franklin […] regards labour-time from a restricted economic standpoint as the measure of value […] Sir James Steuart […] determines real value by labour-time […] Adam Smith declared that the sole source of material wealth or of use-values is labour in general […] David Ricardo […] neatly sets forth the determination of the value of commodities by labour-timehttps://www.marxists.org/archive/marx/works/1859/critique-pol-economy/ch01a.htmIt is only with Adam Smith (1776) that "labour" becomes "abstract" (e.g. generalised) rather than "concrete" (e.g. particular). Thus, all labours are essentially identical as units, so long as they are measured by production time. An example which Smith uses is barter. Person A makes (x) in 2 hours, and Person B makes (y) in 2 hours. They exchange because (x)=(y) in terms of labour time. Thus, exchange is presumed to occur where an equal quantity of labour time between goods is present. Marx takes an example from Aristotle, who uses the same basic logic, and so it can be expressed by a ratio of exchange [x:y].
To begin with Marx's own writing, we see that a product of labour becomes a "commodity" where it has a "use value" and an "exchange value". A use value is whatever makes a thing useful (e.g. quality), while exchange value is what a commodity will exchange for (e.g. quantity). Use values come from "concrete" labour (e.g. weaving, tailoring), and exchange values come from "abstract" labour (e.g. labour in general). Thus, weaving is different from tailoring, but both are still labour in general. Both concrete and abstract labour are expenditures of "labour power" (e.g. labour in potential), as Marx writes:
<all labour is, speaking physiologically, an expenditure of human labour power, and in its character of identical abstract human labour, it creates and forms the value of commodities. On the other hand, all labour is the expenditure of human labour power in a special form and with a definite aim, and in this, its character of concrete useful labour, it produces use values.https://www.marxists.org/archive/marx/works/1867-c1/ch01.htmSo then, we can simplify this as follows:
- Commodity = Use-Value + Exchange-Value
- Use-Value = Qualities of Concrete Labour
- Value = Quality of Abstract Labour
- Exchange-Value = Quantities of Abstract Labour
- Labour-Power = Concrete + Abstract Labour
So, use-value (e.g. utility) can exist without value, but value cannot exist without use-value. Value only has a form of appearance in commodity exchange, and this form is exchange-value. Exchange-value (e.g. magnitude of value) is measured according to "socially necessary labour time" (SNLT), which has its definition here;
<The labour time socially necessary is that required to produce an article under the normal conditions of production, and with the average degree of skill and intensity prevalent at the time. The introduction of power-looms into England probably reduced by one-half the labour required to weave a given quantity of yarn into cloth. The hand-loom weavers, as a matter of fact, continued to require the same time as before; but for all that, the product of one hour of their labour represented after the change only half an hour’s social labour, and consequently fell to one-half its former value. We see then that that which determines the magnitude of the value of any article is the amount of labour socially necessary, or the labour time socially necessary for its production.https://www.marxists.org/archive/marx/works/1867-c1/ch01.htmMarx does not disclose how this is actually calculated, but simply claims that it happens anyway, but Marx does offer some arithmetic in how a sum can be made:
<The value of a commodity, therefore, varies directly as the quantity, and inversely as the productiveness, of the labour incorporated in it. https://www.marxists.org/archive/marx/works/1867-c1/ch01.htmThis can be expressed as duration (d) and intensity (i). Thus, the longer one works, the greater the value of a commodity, but the more productive [intense] the labour, the less the value per commodity. So, it is a division:
- SNLT = Duration divided by Intensity [d/i]
So, to take Marx's example of the power-loom, the same duration is applied with the hand-loom (e.g. 10 hours), but a greater product is created with the power-loom, or what Marx describes as double the product, or half the value per commodity (e.g. 100 vs 200 products)::
- Hand-Loom: 10/100 = 0.1
- Power-Loom: 10/200 = 0.05
Thus, the less labour, the less value, the less price. SNLT then is what determines the exchange value of products to Marx. The less SNLT required per commodity, the less the exchange value will appear between commodities.
As I have said, value (e.g. abstract labour) only appears in the form of commodities, where it is represented as exchange-value (e.g. magnitude of value). Marx writes:
<They manifest themselves therefore as commodities, or have the form of commodities, only in so far as they have two forms, a physical or natural form, and a value form […] The value of commodities is the very opposite of the coarse materiality of their substance, not an atom of matter enters into its compositionhttps://www.marxists.org/archive/marx/works/1867-c1/ch01.htmWe see here that a commodity is distinguished in its "natural form" and "value form" similarly to use-value and exchange-value, or concrete and abstract labour. We also see that the value form is immaterial (abstract), while concreteness is natural. So, to simplify this:
- Commodities = Natural Form + Value Form
- Natural Form = Concrete Labour (Use-Value)
- Value Form = Abstract Labour (Value)
We see Marx describe the Value Form in four phases (A-D), which all develop from one another, so we will begin with the first, which is the "Elementary" Value Form (A).
The Elementary Value Form is expressed:
- x(A) = y(B)
- 20 Yards of (Linen) = 1 (Coat)
- 1 (Coat) = 20 Yards of (Linen)
So then, it is a basic sum, like Adam Smith's example. The arithmetic of the sum is developed by Marx, in that each pole of this "value relation" is either Relative, or Equivalent. To simplify, I will give the proper ordering:
- x(A) = y(B)
- Relative = Equivalent
- Natural Form = Value Form
So then, whatever x(A) is equating itself with is the form of equivalence, and whatever y(B) equates is relative. At the same time, x(A) serves as the Natural Form, while y(B) serves as the Value Form, as we read from Marx:
<the bodily form of commodity B becomes the value form of commodity A, or the body of commodity B acts as a mirror to the value of commodity A.https://www.marxists.org/archive/marx/works/1867-c1/ch01.htmSo then, when two commodities express themselves in this way, the form of value appears as exchange value:
<the value of a commodity obtains independent and definite expression, by taking the form of exchange value […] It never assumes this form when isolated, but only when placed in a value or exchange relation with another commodity of a different kind.https://www.marxists.org/archive/marx/works/1867-c1/ch01.htmHopefully this is not too complicated, but to put it most simply, value only appears in commodity exchange, and the form it takes is exchange-value, or the equivalent. Following from this, we move from the Elementary Form (A) to (B), the Expanded Form, which is expressed:
- z(A) = u(B), or = v(C), or = w(D), etc.
What this expresses is that the relative form: z(A), now has multiple equivalents. This is reversed in the General Form of Value (C), which is expressed contrarily:
- u(B), or v(C), or w(D), etc. = z(A)
Here, all commodities have a single equivalent form. This then features as the "universal equivalent", which in Form (D) becomes the Money-Form, expressed as:
- u(B), or v(C), or w(D), etc. = £(x)
Thus, a single commodity (e.g. gold) has been chosen to represent the values of all other commodities, and so we see how the Elementary moves toward Money as so:
- Elementary Form (A): x(A) = y(B)
- Expanded Form (B): z(A) = u(B), or = v(C), etc.
- General Form (C): u(B), or v(C), or w(D), etc. = z(A)
- Money Form (D): u(B), or v(C), or w(D), etc. = £(x)
A lot of this is mental masturbation. What Marx wants to show is that money as the "universal equivalent" form of value is what all commodities express their value in, and so "price" becomes an expression of value, but only the "natural price" (equilibrium of supply and demand):
<Price, taken by itself, is nothing but the monetary expression of value. […] It suffices to say the if supply and demand equilibrate each other, the market prices of commodities will correspond with their natural prices, that is to say with their values, as determined by the respective quantities of labour required for their production.https://www.marxists.org/archive/marx/works/1865/value-price-profit/ch02.htmSo then, the "natural price" of a commodity is equal to its value, given in SNLT, or the cost of its production.
Marx (following Ricardo) makes the inference that the labourer himself, when he is paid a wage, is also selling a commodity, but the commodity is not "labour", but "labour power", or his capacity to work. The wage pays for the cost of production (SNLT) for the labourer, and so like all other commodities, the labourer receives an equivalent value in exchange. There is no exploitation in circulation, but only in production. Production is split between two periods of the working day (e.g. 10 hours), between "necessary labour" (e.g. 5 hours) and "surplus labour" (e.g. 5 hours). Exploitation occurs where one works for longer than he has to, since his own SNLT has been fulfilled by the period. The reason why this is so obscured in exchange is by the wage form of payment:
<In the corvée, the labour of the worker for himself, and his compulsory labour for his lord, differ in space and time in the clearest possible way. In slave labour, even that part of the working-day in which the slave is only replacing the value of his own means of existence, in which, therefore, in fact, he works for himself alone, appears as labour for his master. All the slave’s labour appears as unpaid labour. [8] In wage labour, on the contrary, even surplus-labour, or unpaid labour, appears as paid. There the property-relation conceals the labour of the slave for himself; here the money-relation conceals the unrequited labour of the wage labourer.https://www.marxists.org/archive/marx/works/1867-c1/ch19.htmIn the labour process there are means of production, which are converted to "constant capital" (c) and labour power, which is converted to "variable capital" (v). There are two rates to consider here: the "rate of surplus value" (s/v) and the "rate of profit" (s/c+v). The rate of surplus value is then calculated by (surplus/necessary), which in our example, is a rate of 100% (5/5), while with profit, (c) is added, and so will always be lower than the rate of surplus value. As (c) becomes more expensive, the rate of surplus value will then increase, and the rate of profit will fall. To simplify: Surplus value is created by surplus labour above necessary labour, determined by the working day. The longer the working day, the longer the exploitation. The rate of surplus value generated is always higher than the rate of profit, and as means of production become more expensive, the rate of profit will fall, as the rate of exploitation increases.
In terms of "proof", there are no empirical examples, since Marx was not using an empirical framework, but a logical framework, and it holds basically sound, even to a method of pure deduction. If there was a world strike, where would profits come from? Who would run the machines etc? Regardless, Marx's "Critique of Political Economy" is largely a political polemic, not a textbook (e.g. the slave is compared to the wage slave, so the system of surplus extraction is predominant in all modes of production; it just becomes most "mystified" under capitalist relations). In case you want to know how Marx envisioned his communist society, I would suggest you read "Critique of the Gotha Programme" (1875), linked below. 🙂👍
https://www.marxists.org/archive/marx/works/1875/gotha/