the transformation problem 2

This is an illustration of some accounts figures for a single capitalist firm or aggregate of firms, with the red lines illustrating the ratios between these figures

a - accounting rule: assets equals liabilities

b - rate of profit on capital

c - capitalisation rate

d - mark up, or rate of surplus

e - rate of exploitation

f - organic composition of costs (Marx's "organic composition of capital" relates wages to total assets)

Samuelson's argument involves an example in which firms' capitalisation is equal to their total costs over the period in question. This is the same assumption that Marx makes in his example of production price calculation in Capital part three. In reality, capitalisation rates are likely to vary between industries depending on the turnover of stock, depreciation of assets and funding for new assets, cash to pay wages etc, credit extended and received, "good will".

Samuelson proves that for the "hard" version of the labour theory of value to hold, given a positive rate of interest, the rate of exploitation would have to be the same for all firms. It could be argued that different sorts of work cannot possibly produce the same rate of exploitation. For example, if someone packing boxes could be made to generate 10% more profit for the same remuneration, how could the same transformation apply to different sorts of work, like driving a van, sewing shirts, repairing car engines? Or, if we can be sure that some firms have some monopoly power, won't this show up in higher rates of exploitation?

Samuelson's example suggests another reason, that because a, b and c are fixed ratios, d (mark up) must be a fixed ratio. If e (rate of exploitation) is also a fixed ratio then f (organic composition of costs) must also be a fixed ratio. This is a different thing from Marx's "organic composition of capital", which represents the ratio between labour costs and total capital.

Because of this "tradition" of drawing up examples where capital is taken to be equal to costs, certain commentators, like the Soviet Union analyst Alec Nove, sometimes discuss Marx's "organic composition of capital" as if this meant the same thing as "organic composition of costs". This is not the case if rates of capitalisation vary.

Marx's concepts of constant and variable capital aren't really tenable, because a firm's fund out of which labour costs are paid, and which represents the capitalisation of these costs, isn't necessarily distinct from the firm's other cash funds. The same bank account will generally be used for non labour costs and taxation. Hence, variable capital, taken as the average amount of the labour fund isn't really measurable. Also, labour isn't an "asset" in capitalism, it's merely funded out of a firm's stock of cash, which is.

A further disparity occurs in public companies, where the profit rate ought to relate to the market value of the stock, whereas the organic composition of capital will relate to the company's assets, which could be much less. Although arguably, the market value of companies' stock should only exceed the value of their assets in conditions of complete or partial monopoly.