Understanding Capital Volume II, John Fox, 1985

### Chapter 20: Simple Reproduction

 "On the assumption of simple reproduction the total value of the annually produced articles of consumption is therefore equal to the annual value-product, i.e., equal to the total value produced during the year by social labor, and this must be so, because in simple reproduction this entire value is consumed." (p. 429 [501])

Marx begins his treatment of the reproduction of the aggregate social capital with simple reproduction, the subject of the present chapter. The analysis of simple reproduction provides the point of departure for Marx's consideration of extended reproduction in the concluding chapter of Volume II. An examination of social reproduction must include not only an accounting of values, but also
an analysis of how material reproduction takes place, that is, an accounting of use-values. For this reason, as mentioned at earlier points in the text, Marx employs the circuit of commodity capital for his treatment of reproduction, because this form of the circuit begins and ends with capital in the shape of particular use-values. Moreover, in treating reproduction it is necessary to show the relationship between capitalist production and the personal consumption of workers and capitalists, for part of the annual product of society is consumed.

Marx divides the annual social product into two parts: the part of the product that furnishes new means of production; and the part that serves as articles of consumption. Those spheres of production that produce new means of production are aggregated into a "department" of social production, labeled Department I. Articles of consumption are produced in Department II.
For simplicity, Marx assumes that all production takes place on a capitalist basis. Under this assumption, the value of the product in each department is the sum of the values of constant and variable capital employed in that department, together with the surplus-value produced there. Note that this analysis parallels the decomposition of the value of the product of an individual capital. Writing an equation for each deparment, we have the following relations:

 Department I Means of Production C'1 = c1 + v1 + s1 Department II Articles of Consumption C'2 = c2 + v2 + s2

The notation used here requires some explanation, for it differs somewhat from that employed by Marx. C' represents the value of the annual commodity product; c is the constant capital, employed in a year, and therefore includes constant circulating capital together with the portion of fixed capital that wears away during the year; v is variable capital advanced for wages; and s is surplus-value produced. The subscript (1 or 2) attached to each symbol represents the department. This notation is more modern and less unwieldy than Marx's, which uses a Roman numeral for the department, sub-scripted by a value component. For example, Marx symbolizes the constant capital in Department II by IIc, while we employ c2 for the same quantity.

Marx uses the following example throughout the chapter:

 Department I: C'1   =    c1    +    vl    +    sl 6000 = 4000 + 1000 + 1000 Department II: C'2   =    c2    +    v2    +    s2 3000 = 2000 + 500 + 500

Thus, in this example, two-thirds (6000/9000) of society's annual product is absorbed in producing new means of production, and one-third (3000/9000) in producing articles of consumption. The value composition of capital (c/v) is the same in both departments: 4/1 = 4000/1000 = 2000/500. The rate of surplus-value (s/v) is also the same in both departments, and is 100 per cent. None of these properties of the example is fundamental, but they make for a clear and simple illustration.

Under the system of simple reproduction, the scale of production is unchanged from year to year. Thus, all of surplus-value is spent by capitalists far articles of consumption. The demand for new means of production, then, is equal to the constant capital used in both departments, while the demand for articles of consumption is equal to the variable capital and surplus-value in both departments, representing the revenue of workers and capitalists, respectively. We have the supply and demand value relations shown in Table 2.

Table 2. Supply and Demand in the Two-Department Model

 Supply Demand Department I Means of Production C'1= c1 + v1 + s1 c1 + c2 Department II Articles of Consumption C'2= c2 + v2 + s2 v1 + v2 + s1 + s2

If the system is in equilibrium, supply and demand must balance. Table 3 verifies that this is the case for Marx's example.

Table 3. Balancing of Supply and Demand in Marx's Example

 Supply Demand Department I C'1 = c1 + c2 6000 4000 + 2000 Department II C'2 = v1 + v2 + s1 + s2 3000 1000 + 500 + 1000 + 500

More generally, by equating supply to demand in either department, we may derive the fundamental equilibrium condition for simple reproduction: c2 = v1 + s1. In Department I, we have c1 + v1 + s1 = c1 + c2, which yields the equilibrium condition by canceling c1 from the two sides of the equation; likewise, in Department II, we get the equilibrium condition by canceling v2 + s2 from both sides of c2 + v2 + s2 = v1 + v2 + s1 + s2. For Marx's example, we have c2 = 2000 = v1 + s1 = 1000 + 1000. In words: the expenditures of Department II for means of production (c2) must equal the expenditures of Department I workers (v1) and capitalists (s1) for articles of consumption. Although we have derived this equilibrium condition formally by equating supply to demand, we shall see presently that the condition makes intuitive sense when we consider the meaning of simple reproduction.

Social reproduction entails a sequence of exchanges between workers and capitalists, among capitalists in their capacities as producers and consumers, between and within the two departments of social production. These exchanges of commodities and money are the subject of much of Marx's exposition of the process of simple reproduction. We shall deal with them more briefly here.
Commodity flows in the two-department model are shown in Figure 7.

Figure 7. Commodity Flows in the Two-Department Model of Simple Reproduction

The actors in the diagram the collective capitalists and workers in the departments. Each arrow represents a commodity exchange (more properly, a class of exchanges) and is labeled with the value of commodities exchanged. The direction of the arrow represents the direction of the exchange: from seller to buyer. Money (of equal value) flows in the opposite direction. Thus, for example, the arrow from workers in Department I to capitalists in the same department represents the sale of these workers' labor-power to their employers. As a consequence of this transaction, capitalists in Department I acquire labor-power of value v1, and workers in Department I receive value v1 in the form of money, that is, wages. With their wages, workers in Department I purchase consumption goods of value v1 from capitalists in Department II; this exchange is shown as the arrow from capitalists II to workers I. Capitalists and workers in both departments purchase their consumption goods from the capitalists of Department II. Capitalists in both departments buy their means of production from the capitalists of Department I. Workers in each department sell their labor-power to the capitalists of the same department.

A word should be said about the arrow from capitalists in Department I to themselves: at first glance this relation seems paradoxical, until we recall that capitalists producing new means of production themselves employ means of production, which must be bought from other capitalists in their department. (In certain special circumstances capitalists may in fact employ part of their own product to furnish new means of production -e.g., seed in agriculture -- but these are exceptional cases.) A similar comment applies to the self-directed arrow for capitalists in Department II: they purchase articles of consumption from each other.

Recall the equilibrium condition for simple reproduction: c2 = v1 + s1. In terms of commodity flows, this condition implies a balanced exchange between departments. v1 + s1 is the value of Department II sales of consumption goods to Department I; c2 is the value of Department I sales of means of production to Department II. If the exchange between departments were unbalanced, there would be a drain of value from one department to the other, making the system of reproduction unstable.

A point that is made with great clarity in Marx's two department model of reproduction is that part of society's annual product is not consumed, but rather furnishes next year's means of production. Indeed, in Marx's example, two-thirds of society's annual output consists of new means of production. (Recall that this is precisely the point that Smith failed to grasp clearly.) Under simple reproduction, however, all newly created value must be consumed. Row, then, is it possible for a portion of society's labor to be directed not towards the production of articles of consumption, but rather to the production of new means of production?

To solve this apparent problem, Marx appeals to the (previously introduced) distinction between the annual value product and the value of the annual product. The annual value product consists of newly created value in both departments: v1 + v2 + s1 + s2. The value of the annual product, C'1 + C'2, contains as well the constant capital employed in both departments, that is, c1 + c2. Thus, part of the value of the annual product is contributed by means of production that themselves are not produced in the current year, but were part of the previous year's product. In the same way, part of the current year's product is incorporated in means of production to be used next year. For simple reproduction to take place, the value of new means of production, produced during and left at the end of the year, must be the same as the value of old means of production available at the beginning of the year and used during the year. Only value equal to newly created value in both departments can (and must) be consumed. Thus, the total of newly created value from both departments (i.e., v1 + s1+ v2 + s2) must be equal to the value of consumption goods, the production of Department II (C'2 = c2 + v2 + s2). Equating these two quantities gives the now familiar equilibrium condition. It is the pre-existing value embodied in means of production available at the beginning of the year, then, that makes it possible for a portion of society's product (2/3, in the example) to be incorporated in new means of production, at the same time that all newly created value is consumed.

Marx traces in detail how money mediates the exchanges by which the aggregate social capital circulates. This analysis does not alter the conclusions presented thus far. All of the money required to circulate the annual social product is advanced, in one form or another, by the capitalist class: to purchase means of production (constant capital), labor-power (variable capital), and capitalists' consumption goods. This money returns to the capitalist class when the commodity product is sold, for this product includes the value of constant and variable capital together with the surplus-value which finances the capitalists' personal consumption.

The routes by which money returns to the capitalists who advanced it are often indirect, even at the aggregate level of the two departments. For example, capitalists in Department I advance money in the form of wages to workers in the same department; these workers purchase articles of consumption from the capitalists of Department II who, in turn, buy means of production from the capitalists of Department I. As was pointed out above, money flows maybe discerned by reading the commodity-flow diagram backwards.

The actual quantity of money required to circulate the annual product depends not only upon the size of this product, but also upon the rapidity of circulation: after all, the aggregate annual product does not circulate wholly at the end of the year. To the extent that money wears away in the sphere of circulation, it is replaced by new production of the money commodity (as explained, for example, in Chapter 1).

For part of his analysis of simple reproduction, Marx divides Department II (the production of articles of consumption) into two sub-departments: Department IIa, which produces necessities consumed by both workers and capitalists; and Department lib, which produces luxury goods consumed only by capitalists. For simplicity, Marx assumes that capitalists in all departments divide their consumption into necessities and luxuries in the same proportions: suppose that k represents the proportion of capitalists' revenue spent for necessities and the remainder, 1- k, the proportion spent fo luxuries. (Marx does not employ this notation, but k is implicitly 3/5 in his example.)

The "three department" model is represented by the supply and demand equations shown in Table 4:

Table 4. Supply and Demand in the Three-Department Model

 Department Supply Demand I: Means of Production C'1= c1 + v1 + s1 = c1 + c2a+ c2b IIa: Necessities C'2a= c2a + v2a + s2a = v1 + v2a+ v2b + k(s1 + s2a+ s2b) IIb: Luxuries C'2b= c2b + v2b + s2b = (1 - k)(s1 + s2a+ s2b)

The supply and demand relations for Marx's illustration appear in Table 5.

Table 5. Balancing of Supply and Demand in Marx's Example

 Department Supply Demand I C'1  =   c1   +   v1   +   s1 = c1   +   c2a  +   c2b 6000   4000  4000  1000 4000  1600   400 IIa C'2a =  c2a  +  v2a  +  s2a = v1  +  v2a  +  v2b  +  k( s1   +   s2a  +   s2b) 2400   1600    400    400 1000   400   100   0.6 1000   400    100 IIb C'2b =  c2b  +  v2b  +  s2b = (1 - k)( s1   +   s2a  +   s2b) 600     400    100     100 0.4    1000   400    100

Note that for equilibrium to obtain, not only must there be balanced exchange between Departments I and II (c2 = c2a + c2b = v1 + s1), but as well, there must be a division of production of articles of consumption into necessities and luxuries that reflects capitalists' expenditures for these goods. The more complex commodity flows for the three department model are shown in Figure 8. As before, money and commodities flow in opposite directions.

Figure 8. Commodity Flows in the Three-Department Model of Simple Reproduction

Marx takes pains to point out that the reproduction of the aggregate social capital includes the reproduction of the class relation between workers and capitalists. Workers exchange their labor-power for wages, with which they purchase articles of consumption. These consumption goods, representing a portion of the annual product created by the workers' own labor, serve to reproduce the workers' labor-power. The working class depends for its existence on the continued sale of its labor-power to the capitalist class.

Marx notes, in this context, that it is inaccurate to say that capitalists exchange variable capital for labor-power (although this expression is sometimes used in a "shorthand" fashion). Rather, latent variable capital in the form of money is exchanged for labor-power, which functions as variable capital in the process of production. The capital remains in the capitalist's hands; it merely changes its form. In the hands of the worker, money wages simply represent (that is, are exchanged for) the worker's subsistence; wages are not capital for the worker, whose exchanges (LP--M--C) have the form of the simple circulation of commodities.

In most of his consideration of simple reproduction, Marx ignores the special characteristics of fixed capital, stating simply that only the part of fixed capital that wears away during the year contributes value to the annual commodity-product. In actuality, some of fixed capital expires (that is, completes its useful life) during a given year, while the remainder continues to function. Only the fixed capital that expires is replaced out of the annual product. Fixed capital that is not wholly worn away during the year, however, yields a money return to the capitalist, even though it is not replaced in kind in that year. This money, as was explained in the section on turnover, is hoarded against the day when the fixed capital must be replaced.

For simple reproduction to take place, the money that is drawn from circulation for hoard formation must equal the money re-entering circulation to replace fixed capital expiring during the year, money which partially represents previous years' hoards. Moreover, Marx argues, because simple reproduction means an identical scale of production from one year to the next, and because, therefore, identical circulating capital is required from year to year, the amount of fixed capital wearing away annually cannot change. Marx regards this as an unrealistic requirement.