Labor theory of value

The capitalist system renders things and actions (cars, apples, shining a shoe) into commodities, that is, objects and services exchanged for money. According to capitalist theory, the value of each thing is determined by market principles, a complex set of consumer choices about what is desirable and what is not: what consumers desire more, they will pay more for; what they do not desire, they will deem worthless, and will not buy. Thus things which consumers deem more desirable are more valuable.

Karl Marx argued against the market theory of value, which he believed was an obfuscation designed to hide the real source of value, which is none other than human labour. Marx believed that things only have value because of the human labour power that was expended on making them, and that the more labour power that was spent making things, the more valuable they are. (Marx was more focused on products than services in general.)

Well actually, Marx qualified the labour theory of value a bit. He said that it was the amount of socially necessary labour time embodied in a commodity which gave that commodity its value. Here he was acknowledging that the actual time it takes to make something may vary, depending, say, on the skill of the artisan or the technology utilized in the production process. If it takes me two hours to make a cake and sneff or any of his able colleagues one hour, then one hour is the socially necessary labour time involved, and will determine the value of the cake. I'm just slow and disorganized; it doesn't mean my cake's worth more. Another example: modern factories can produce chairs much more quickly than was the case fifty years ago, but that doesn't necessarily mean that older chairs are worth more (except to collectors); the amount of socially necessary labour time has simply changed as the means of production have evolved. Inefficiency, then, does not increase value.

In recognizing that value comes from labour, Marx was really only building on the theories of his predecessors and fellow political economists, primarily Adam Smith and David Ricardo. But Marx went further than they had, recognizing that what workers are selling under capitalism is not primarily the fruits of their labour, but rather their labour itself. Capitalists pay wages to workers which are not really equivalent to the total value of their labour - the value of the things they produce. Instead, workers are paid a subsistence wage which will allow them to survive. Over and above that amount is a surplus, the value of which, said Marx, is retained by the capitalist; this surplus value is what allows the capitalist to make a profit. For Marx, this was not a good thing: it was exploitation of workers by capitalists.

At root Marxism is a humanist theory. Marx believed that it was a fundamental condition of humanity to labour and produce useful things. Capitalism alienates workers from the fruits of their labour, which are not theirs to keep, use, or exchange; instead, these fruits are owned by capitalists. And of course workers are not able to realize the true value of these fruits - which, remember, only have value because they embody the workers' labour - instead realizing only a portion of that value, and in a condition of distance from those products. Think of a factory assembly line, for Marx in many ways the ultimate dehumanizing horror: no one has any connection with the production line's end product, instead knowing only their tiny own movement: the welding of a piece of metal, the folding of a piece of paper, the turning of a screw. Marx believed that only when people are freed from such horrifying violations of their humanity and reconnected to the products of their labour would they be fulfilled and free.

The Labor Theory of Value, or, Why Exploitation is Inevitable in a Capitalist System

Marx had an economic argument as to why exploitation and revolution were inevitable in a capitalistic market. It was based on what he called the Labor Theory of Value, which says this:

The value of any commodity, on the current market, is judged by how much a profit it can yield on the market. To fully evaluate the humanistic side of this, Marx said, you must also take into account the human cost of producing these commodities. The value, then, is based on the average amount of labor put into the product. The term value is not the same as price. Prices are based on the basis of demand and the fluctation of the market. Though products are sold on price, the value underlines the price. In capitalist society, a laborer sells his labor. Every commodity has a value, based on that labor. Ideas, as well, can be a commodity, such as the ideas a professor sells.

What is the value of labor as a commodity? Theoretically, the value of labor is determined by the cost of subsistence plus the cost of training. Under conditions of free trade, where capitalists want to suppress wages to increase profits, the value of labor is almost equal to the cost of subsistence.

The model of production cost is C+V+M, where C=Constant Capital (the money invested in machinery and further technological advancements), V=Variable Capital (the cost of worker's wages and training), and M=Mass of Surplus Value (the mass of goods produced that can be sold on the market above what is necessary to satisfy C and V and yield a profit).

Only labor is a source of value, says Marx. Machines themselves are products of former labor. Labor is the only thing valuable to a capitalist. Surplus value can only be created if the worker works more than is needed to reproduce the cost of his training and constant capital and his own physical reproduction. Surplus value, therefore, must be created by some quanitity of labor that is above the necessary working time (C+V) to prevent loss of capital: in the first three hours of the day, a worker must produce enough for a capitalist to invest in C, and in the next three hours enough for his own subsistence, and then above that to create a mass of surplus goods that will allow a capitalist to reap a profit.

Exploitation is inevitable in the capitalist economic system because a certain part of the day must be devoted solely to the capitalists. The rate of exploitation is defined as R=M/V. This is the relationship of profit to wages. Therefore, there is an objective situation for the exploitation of workers.

Every capitalist must maximize his or her own profit. How can he augment these profits? By either reducing wages or making the worker work longer hours. You can, therefore, increase the rate of exploitation. The upside is you get higher returns. The downside is that it provokes union action.

You can also increase profits by increasing efficiency. How does one do this? Various kinds of technology effiency measures, and investment in technological innovations. You can increase productivity by replacing human labor with machines. What will happen to competitors in an unrestrained system? They will also do the same, trying to increase productivity, to the points where they are more efficient and can push you out of the market, competing for the same clientele.

Where does this process of constant underpricing have to stop? When the price of the product falls so low the return is very small. This reduction of profit is called the tendency of the falling rate of profit. In addition to that, you will also have the problem of displacing mass numbers of workers because you are replacing them with machines. Capitalism therefore requires an unemployed pool of workers. The pool is called the reserve army of labor-- permanently available for hiring because of their desperation to get a job. If capitalists continue displacing and competing, in the end the unemployed will grow, and capitalists will face a social problem. Moreover, because of greater unemployment, these people will be willing to work for lower wages, and this will repress standards of living. Finally, the "big fish" will eat the "small fish," meaning small businesspersons and their employees will be the losers in the long run, and will lose their customers. The creation of this permanent army of surplus labor is built up by those that fall from the small business in competition.

Eventually there will be a conflict between the large number of those that fall out and the smaller business class, or the persons who own the means and relations of production. This itself is the mechanism of social revolution. Because of the cost of goods, the lack of money within the majority army of surplus labor, there will be a crisis of overproduction (overstock).

Economically, Marx says, capitalism is extremely rational. But, he says, the human cost is immense. Eventually it will be too great and revolution will occur.

 A     the matrix of inputs
 F     the wage goods linear form
 L     the labor price linear form
 M = A + FL the augmented input matrix
 μ    the rate of surplus value ( distinct from surplus labor )
 w     M1 value vector

An economy which can produce surplus products in all industries is called reproducible: and economy fulfilling the subsequent surplus condition(S.C.): for all x, x >= 0^m: x > Mx is said to be reproducible.

It is trivial that a reproducible ecoonomy is productive.

Next, consider the dual aspect of reproducibility. Given a valuation vector of products, and matrices pA and PFL of physical costs and unit wages rates st. pM expresses the societal unit cost of production across all industries. The residue of unit valuation subtracted by the total cost is called profit. Let

  p  := l x n  valuation vector,
  pi := l x n  profit vector,

  then 

  pi = p - pM

An economy which can produce profit in the industries for a given vector is called profitable: an economy fulfilling the following profitability condition(Pf.C.),

  for all p >= 0n : p > p M

is called profitable. From this follows:

Reproducibility is equivalent to profitablity: S.C <=> Pf.C.

Proof In fact it is easy to see that both are equivalent to

  (I-M)-1= 0

QED

That is, if surplus products are producibile in all the industries in a Leontief economy, profit is possible in the economy, and vice-versa. What is significant here is that profitability is derived from reproducibility independently of the concept of value. A very strong duality is thus observed in a Leontief economy.

As an immediated corollary of the above, one has the relationship between profitability and positivity of the rate of surplus value:

An economy is profitable if and only if the rate of surplus value is positive and there exists a positive value: Pf.C mu > 0 and for all w > 0_n>.
Proof

From Theorem I, Pf.C. implies (I-M)^-1 >= 0 and hence Pd.C. From PROPOSITION 2, one has w = L(I-A)^-1 > 0_n .

Now if wF >= 1 then one has

w = wA + L
which contradicts (I-M)^-1 >= 0.

Conversely, if mu > 0,

The Marxian interpretation of this theorem is that the source of profit is surplus value. Namely, surplus value created by the labour is expropriated by capital as profit. This explains the most significant qualitative feature of the capitalist economy: profit is the transformed form of surplus value.

A mathematical analysis of this transformation can also be presented.