The Laws of Movement of Capitalism
The link between the division of labour and social structure underlies the major attempts to single out the basic trends in human society, or in other words to understand ‘where we are going’. The most celebrated of such attempts is that of Marx. In his opinion, capitalism is not the final stage in the history of human societies, but only an intermediate stage: it was preceded by other forms of organisation of society (serfdom, feudalism) and will give way to new forms of social organisation (socialism first, then communism). By studying the laws of motion underlying capitalism, we understand how it came into being, how it has changed in the course of its evolution and the reasons why it will have to give way to a new form of social organisation, namely socialism.
In this respect Marx noted the tendency of capitalistic societies towards increasing economic and social polarisation: on the one hand we have the growing misery of an increasing proportion of population, in other words proletarisation, i.e. the formation of ever vaster masses of common workers; on the other hand we have the tendency to increasing concentration of manufacturing production in a few big firms, entailing ever greater economic and political power concentrating in a few hands, while small entrepreneurs and independent artisans end up joining the ranks of dependent workers. Hence the thesis of inevitable collapse facing the capitalistic mode of production, when the proletariat - by then the overwhelming majority of the population - expropriate the capitalist class, economically dominant but numerically weak. The way is thus opened to socialism.
Another thesis developed by Marx, the law of the falling rate of profits illustrated in Book 3 of Capital, takes much the same course. The process of increasing mechanisation entails progressive increase in the organic composition of capital, or in other words of the ratio between constant capital c (the value of means of production utilised in the productive process other than labour power) and variable capital v (the value of labour power employed in production), both expressed in terms of labour contained. Therefore, if the organic composition of capital increases and the rate of exploitation does not increase pari passu, the rate of profits necessarily decreases. 
The reasoning is flawed, though, by confusion between variables expressed in terms of labour values and underlying quantities of the various commodities. In fact, mechanisation does not necessarily imply an increase in the organic composition of capital. This is not the case, for instance, if a growing number of machines, thanks to technical progress, require the same or a smaller quantity of labour for their production, so that the organic composition of capital remains constant or decreases. Furthermore, technical progress itself, by reducing the quantity of labour required for the production ofsubsistence goods, causes an increase in the rate of exploitation for a constant real wage.
-  Marx 1867-94, vol. 3, pp. 317-75.
-  The rate of profit s/c + v may be expressed (dividing numerator and denominator by v) as(s/v)/(c/v + 1), with the numerator being the rate of exploitation and the denominator theorganic composition of capital plus 1. If the denominator grows while the numeratorremains unchanged, the ratio, i.e. the rate of profits, must decrease.
-  Section 2 of Book 3 of Capital is devoted to the subject: Marx (1867-94, vol. 3,pp. 245-316). Book 3 was published posthumously, edited by Engels on the basis ofnotes left by Marx; thus we have no certainty about just how convinced Marx himself wasof the solution he worked out.