Understanding Capital Volume II, John Fox, 1985

### Chapter 9: The Aggregate Turnover of Advanced Capital Cycles of Turnover

 "The aggregate turnover of an advanced capital is the average turnover of its various constituent parts." (p. 186 [262])

We have seen that different portions of advanced capital have different periods of turnover, circulating capital being turned over most quickly, and various parts of fixed capital being turned over more slowly and, generally, at different rates. The aggregate turnover of advanced capital may be represented as a weighted average of its components. As Marx points out, to render the different components comparable, it is necessary to reduce them to comparable quantities, that is, to money. Thus the development of aggregate turnover employs the circuit of money capital. We shall develop Marx's argument algebraically in order to present it more simply and compactly.

Marx's presentation may be formalized in the following manner: let C represent the aggregate of advanced capital, with aggregate turnover expressed as number of turnover periods per year, n (cf., Chapter 7). Let c1, c2, . . . , ck represent the components of advanced capital (expressed as amounts of money), with number of annual turnovers n1, n2, . . . , nk, consecutively. Then, C = cl + c2 + . . . + ck.

The amount of the first component of advanced capital turned over in a year is cln1, and likewise for the other components. The aggregate capital turned over in a year is given by c1nl + c2n2 + . . . + cknk = Cn.

The example presented by Marx on p. 189 [265] is summarized in Table 1.

Table 1. Calculation of Aggregate Turnover

 Component i Advanced Capital ci Yearly Number of Turnovers ni cini 1 25,000 1/10 2,500 2 12,500 1/2 6,250 3 12,500 2 25,000 Total 50,000 33,750

Here, the aggregate advanced capital is divided into three components: C = \$50,000 = c1 + c2 + c3 = \$25,000 + \$12,500 + \$12,500. The annual turnovers of the components are stated to be nl = 1/10, n2 = 1/2, and n3 = 2. Thus the total amount turned over in a year is Cn = cini + c2n2 + c3n3 = 25,000(1/10) + 12,500(1/2) + 12,500(2) = \$33,750, and the number of turnovers for the aggregate advanced capital is n = Cn/C = \$33,750/\$50,000 = 0.675. That is, a little more than two-thirds of the aggregate advanced capital is turned over in a year, or, put alternatively, the whole of the advanced capital is turned over in 1/n = 1/0.675 = 1.48 (about one and one-half) years.

Marx points out that although the durability of fixed capital tends to increase with advances in technology, the development of capitalist production also causes elements of fixed capital to become outmoded -- a process that he terms "moral depreciation." The end of an economic crisis is marked by large and general investments in new elements of fixed capital, providing a "material basis" for the business cycle. Crises, therefore, play a role in the physical as well as in the social restructuring of capital, a process described in Volume I.