## Thursday, 20 March 2014

### Capital II, Chapter 15 - Part 8

Having set Marx's example out on this simpler basis, let's apply this to Marx's actual example.

 Table I CAPITAL I Periods of Turnover Working Periods Advance Periods of Circulation I.1st - 9th week 1st - 4th ½ week £450 4th ½ - 9th week II. 10th - 18th " 10th - 13th ½ " £450 13th ½ - 18th " III. 19th - 27th " 19th - 22nd ½ " £450 22nd ½ - 27th " IV. 28th - 36th " 28th - 31st ½ " £450 31st ½ - 36th " V. 37th - 45th " 37th - 40th ½ " £450 40th ½ - 45th " VI. 46th - [54th] 46th - 49th ½ " £450 49th ½ - [54th]”

 CAPITAL II Periods of Turnover Working Periods Advance Periods of Circulation I. 1st - 9th week 4th ½ - 9th week £450 10th - 13th ½ week II. 10th - 18th " 13th ½ - 18th " £450 19th - 22nd ½ " III. 19Th - 27th " 22nd ½ - 27th " £450 28th - 31st ½ " IV. 28th - 36th " 31st ½ - 36th " £450 37th - 40th ½ " V. 37th - 45th " 40th ½ - 45th " £450 46th - 49th ½ " VI. 46th - [54th] " 49th ½ - [54th] " £450 [55th - 58th ½] "

In 51 weeks (taken as the year) Capital 1 goes through 6 working periods, ending in week 49.5. It advances £100 per week = £450 in a 4.5 week working period. So, its output in a year equals 6 x £450 = £2,700. Note, it does not produce even a portion of output in weeks 49.5 – 51, because this is its circulation period, where we are assuming that the capital lies fallow. Similarly, it does not advance any capital during that period.

Capital 2, goes through 5⅓ working periods. That is its last working period begins in week 49.5, and ends in week 54. At week 51, it has gone through 1.5 weeks of a 4.5 week working period i.e. ⅓ of a working period. So, its output in the year equals 5 ⅓ x £450 = £2,400. In total, £5,100 of output is produced (£2,700 Capital 1, and £2,400 Capital 2).

The aggregate capital advanced by Capital 1 and 2 is £450 (Capital 1) and £450 (Capital 2) = £900. Using the propositions previously set out then, we have the number of working periods. That is £5,100/£900 = 5⅔.

“Hence the total advanced capital of £900 has functioned 5⅔ times throughout the year as productive capital. It is immaterial for the production of the surplus-value whether there are always £450 in the production process and always £450 in the circulation process, or whether £900 function 4½ weeks in the process of production and the following 4½ weeks in the process of circulation.” (p 273)

We can then look at how things stand from the perspective of the turnover of the advanced capital.

Looking at the capital returned it is less than the value of the output produced, for the simple reason that the turnover period extends beyond the working period. So, Capital 1 receives a return of capital in weeks 9,18,27 etc. and Capital 2 receives a return of capital in weeks, 13.5, 22.5 and so on. Capital 1 turns over 5⅔ times in 51 weeks, because it only completes the sixth turnover in week 54. Capital 2 only turned over 5 1/6 times, because it only completes its sixth turnover in week 58.5.

So, the actual capital turned over is 5⅔ x £450 + 5 1/6 x £450 = £2550 + £2,325 = £4,875. So, the aggregate capital turns over 4875/900 = 5 5/12 times.

This is mathematically always true, in the sense that if we assume continuous capitalist production, and recognise that the working period and the circulation period form one whole of the circuit of capital, the capital in circulation is, in whatever form, proportionally through its period of turnover. Of course, the fact that this capital is part way through a period of turnover, does not mean that a proportion of it actually has been turned over, in the sense that it has returned in the form of money-capital, ready to be used again.