## Friday, 1 August 2014

### The Rate Of Turnover, Profit and The Transformation Problem

In Capital III, Chapter 9, Marx describes the process of transformation of exchange values into prices of production. The process is basically to take the total social capital, and calculate an average rate of profit on it, and then apply this average rate to the cost-price (laid out constant and variable capital plus wear and tear of fixed capital) to obtain a price of production. The process by which these prices of production and an average rate of profit is established, is via competition. Capital tends to move from areas where the rate of profit on the advanced capital is low, and into those where it is high. As a result, the supply of commodities in the former sphere declines, and market prices rise, whilst supply of commodities in the latter sphere rises, and market prices fall.

If cost price is equal to k, and the rate of profit is p', the price of production is k + kp'. Marx points out that this only applies, however, where the advanced capital turns over just once during the year. As, for individual spheres of capital, this is virtually never the case, it is impossible to determine a price of production mathematically on this basis, because the cost of production and the advanced capital will always be different.

There is a fairly simple solution to this problem. Marx points out that for the total social capital, the problem of different rates of turnover does not exist.

“Since the general rate of profit is formed by taking the average of the various rates of profit for each 100 of capital invested in a definite period, e.g., a year, it follows that in it the difference brought about by different periods of turnover of different capitals is also effaced. But these differences have a decisive bearing on the different rates of profit in the various spheres of production whose average forms the general rate of profit.”

The price of production for any individual sphere, however, can only be calculated by taking the cost of production, and adding the average profit calculated, not on this laid-out capital, but on the advanced capital. For example,

“Take, for example, a capital of 500, of which 100 is fixed capital, and let 10% of this wear out during one turnover of the circulating capital of 400. Let the average profit for the period of turnover be 10%. In that case the cost-price of the product created during this turnover will be 10c for wear plus 400 (c + v) circulating capital = 410, and its price of production will be 410 cost-price plus (10% profit on 500) 50 = 460.”

This is clearly different than a price of production calculated as k + kp', which would be, 410 + (410 x 10%) = 41, giving a price of production of 451.

The following table sets out how different rates of turnover affect the mass of profit generated in each sphere, the rate of profit in each sphere, the formation from this of the average rate of profit, and the formation of prices of production for each sphere. The price of production here is the price of the whole production not per unit.

 Sphere Fixed Capital C V Wear & Tear S Rate of Turnover Total S P' % Price of Production Profit Margin 1 60 20 20 6 20 3 60 60 172.25 37% 2 50 20 30 5 30 2 60 60 151.25 44% 3 40 20 40 4 40 1 40 40 110.25 72% 4 30 20 50 3 50 0.5 25 25 84.25 122% Total 180 80 140 18 140 185 46.25

Its assumed here that the fixed capital lasts on average for ten years, thereby giving up 10% of its value each year as wear and tear, and that the rate of surplus value is 100%. Because, the rate of turnover in sphere 1 is 3 times per year, the total surplus value produced in that sphere in a year is equal to 3 times the surplus value produced in the turnover period, i.e. 3 x 20. The same applies for each of the other spheres. In sphere 4, the advanced circulating capital turns over once in 2 years, thereby only turning over 0.5 times in a year. This would be the case, for example in an industry such as shipbuilding, where capital must be advanced for labour-power and materials, during the whole of a two-year period, whilst the ship is being produced, and is only turned over, when at the end of that period, the ship is finished and sold.

The total social capital advanced is then equal to 400 (180 fixed capital + 80 circulating constant capital + 140 variable capital), and the total surplus value produced during the year is 185, giving an average rate of profit on the total advanced capital of 46.25%. The amount of profit to be added in each sphere is then £46.25. However, as Marx sets out above, this amount of profit is added to the cost of production, not the advanced capital. The cost of production is the advanced circulating capital, multiplied by the rate of turnover, plus the wear and tear of fixed capital. In sphere 1, therefore, this is (20 c + 20 v) x 3 = 120 + 6 = cost price of 126. Price of production is then 126 + 46.25 = 172.25.  In other words, it is the total laid out capital for the year, plus the wear and tear of fixed capital.

What becomes clear here is that as the rate of turnover rises, the mass of surplus value increases, and so the annual rate of profit for that sphere rises, but the profit margin is simultaneously reduced, because this given mass of profit is spread across a larger mass of laid-out capital. This is, in fact, also the situation described by Marx in Capital III, Chapter 18, dealing with the effect of the turnover of Merchant Capital.

Marx points out that the mass of profit accrued by merchant capital, depends on the general rate of profit, and the mass of capital advanced by the merchant capital. He then demonstrates that unlike productive-capital, the mass of profit does not rise as the rate of turnover of capital rises, because merchant capital can only share in the surplus value actually produced by productive-capital. Consequently, as the rate of turnover of the merchant capital rises, so that the mass of laid-out merchant capital rises, or put it another way, its cost of sales, so this mass of surplus value is spread across a greater mass of commodities, a greater cost of sales, and so the profit margin per unit must fall.

But, this is analogous to the situation described above where for the year, the mass of surplus value is already determined, and what is being compared is how this mass of surplus value is spread across the laid-out capital in each sphere, according to the different rates of turnover.

Marx writes,

“But, assuming the relative magnitude of merchant's capital to total capital to be given, the difference of turnovers in the various branches of commerce does not affect either the magnitude of the total profit falling to the share of merchant's capital, or the general rate of profit. The merchant's profit is not determined by the mass of commodity-capital turned over by him, but by the dimensions of the money-capital advanced by him to promote this turnover. If the general annual rate of profit is 15%, and the merchant advances £100, which he turns over once a year, he will sell his commodities at 115. If his capital turns over five times a year, he will sell a commodity-capital he bought at 100 at 103 five times a year, hence in a year a commodity-capital of 500 at 515. This gives the same annual profit of 15 on his advanced capital of 100. If this were not so, merchant's capital would yield a much higher profit, proportionate to the number of its turnovers, than industrial capital, which would be in conflict with the law of the general rate of profit.”

(Capital III, Chapter 18)

This is the same as the situation described above. It demonstrates that in those spheres where the rate of turnover of capital is high, for an average rate of profit to be established, and for prices of production across the economy to be established on the basis of it, the profit margin must be continually reduced.

If we take Capital 4, in the original example, and assume that its capital turns over 10 times faster, i.e. 5 times a year, as opposed to 0.5 times, we obtain the following result, on the basis of the previously calculated rate of profit. Its advanced capital remains 100, but its laid-out capital, its cost of production for the year, becomes 350 + 3 = 353. Adding in the average profit due to it, on the basis of its advanced capital 46.25, this gives a price of production of 399.25. But, if we calculate the profit margin for this production it is 46.25/353 = 13%, which is significantly lower than the original figure of 122%.

Obviously, the other thing that occurs with an increased rate of turnover of capital is that the actual volume of production also increases. If we assume that an advanced capital of 100, produces 100 units of output in each of the four cases, set out in the example, purely for the purpose of elaborating this point, then the more times this capital turns over, the more times it produces these 100 units during the year. This necessarily affects the price per unit.

So, Capital I produces 300 units per year, giving a price per unit of £0.57 per unit; Capital 2 produces 200 units per year giving a price per unit of £0.76; Capital 3 produces 100 units, giving a price of £1.10 per unit; and Capital 4 produces 50 units resulting in a unit price of £1.69.