Marx's schema of simple reproduction, set out in Capital II, Chapter 21 is:
Department I
c 4000 + v 1000 + s 1000 = 6000
Department II
c 2000 + v 500 + s 500 = 3000
So, Department I consumes means of production with a value of 4000. If it is considered as being just one huge producer, it does not sell the equivalent portion of its output to anyone, but simply takes it physically from its current output, and uses it to physically replace its own consumption. Its like a farmer who takes some of the wheat they have grown, and instead of selling all of it, uses a portion of the grain as seed to plant for the following year. The only part of Department I's output that is sold is that which is equivalent to the new value created by Department I labour, i.e. 2000. It is this same 2000 which forms the 2000 of constant capital consumed by Department II. In terms of modern GDP data, this 2000 is what is called intermediate production. Although it appears to constitute constant capital, because it is physically the means of production used by Department II, in value terms, it comprises not one penny of value of constant capital, but only the value of Department I (v + s), i.e. the new value created by Department I labour.
So, Department I directly reproduces its own means of production "on a like for like basis". The means of production for Department II are produced by Department I, and their value is equal to the new value created by Department I labour. Department II labour processes these means of production, and creates 1000 of new value, which is divided 500 for wages and 500 for profits. Now, Department I workers and capitalists can exchange 2000 of means of production for 2000 of consumer goods. Department II workers and capitalists consume the remaining 1000 of consumer goods. On this basis, provided the use values produced are in the right proportions, simple reproduction can continue.
But, as Marx and Lenin point out, capitalism (indeed every other mode of production) cannot proceed on the basis of simple reproduction. There must be expanded reproduction, because, at the very least, population expands, so more consumption goods are required, which in turn requires more means of production. Moreover, capitalism itself is a system based upon competition, and the production of profit. Each individual capital must be competitive to survive. To be competitive means to to produce on a larger scale, so that economies of scale, and falling marginal costs can be obtained. To produce on a larger scale means maximising profits so as to accumulate additional capital. So, capitalism must proceed on the basis of expanded reproduction, and that means that this equation between Department I (v + s) and Department II (c) cannot hold. For accumulation to occur, a portion of society's current production that would have gone to unproductive consumption must, instead, go to accumulation, to additional productive consumption.
Given that the reproduction of labour-power requires an objectively determined quantity of wage goods (use values) this additional productive-consumption can only arise from a portion of surplus value being diverted to that purpose. The consequence of this is that Department I must grow at a faster rate than Department II. Because Department I reproduces its own means of production, a growing proportion of output is this reproduction of means of production for the production of means of production. This tendency is increased precisely because, as output expands, it is more efficient; a larger mass of output is produced by a given mass of labour, and, as each capital attempts to be more competitive, by introducing labour-saving fixed capital, this tendency is increased even more. This is the basic underlying mechanism behind Marx's Law of the Tendency for the Rate of Profit to Fall, as rising social productivity leads to a growing proportion of c in the value of society's total output – c + v + s. (its not relevant here, but, as I have described elsewhere, this no longer applies, because increases in technology have massively depreciated the value of fixed capital, and other means of production, whilst the domination of production by services means that the quantity of materials now represents a continually falling proportion of total output value, as opposed to a rising proportion, as Marx had assumed.)
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