The Transformation of Values into Prices: Formal Analysis

C. The Transformation of Values into Prices: Formal Analysis

The source of profits, for Marx, is surplus or unpaid labor time. To appreciate his analysis we must first establish the fact that Marx’s “prices of production” are equivalent to classical long-run cost prices, as formulated by the Physiocrats, Smith, and Ricardo: “The price of production includes the average profit. We call it price of production. It is really what Adam Smith calls natural price, Ricardo calls price of production, or cost of production, and the physiocrats call prix n´ecessaire, because in the long run it is a prerequisite of supply, of the reproduction of com- modities in every individual sphere. But none of them has revealed the difference

between price of production and value” (MECW 37: 197). 8 And he affirms that the traditional focus on costs rather than labor values can be explained by its con- venient superficiality from an ideological perspective: “We can well understand why the same economists who oppose determining the value of commodities by labour-time . . . always speak of prices of production as centres around which mar- ket prices fluctuate. They can afford to do it because the price of production is an utterly external and prima facie meaningless form of the value of commodities, a form as it appears in competition, therefore in the mind of the vulgar capitalist, and consequently in that of the vulgar economist.”

As for the matter of distribution, the main objection to orthodoxy is well expressed in Capital 3, Chapter 48 on the so-called “Trinity Formula,” where Marx rejected any conception of factor returns which suggested that they “grow out of the role played by the land, produced means of production, and labour. . . .” (812). On this false view, “profit and rent . . . appear independent with respect to wages, and must arise from sources of their own, which are specifically different and inde- pendent of labour; they must arise from the participating elements of production, to the share of whose owners they fall” (813), whereas in fact “[c]apital pumps the surplus labour, which is represented by surplus value and surplus product, directly out of the labourers” (808); similarly: “capital is a perennial pumping-machine of surplus labour for the capitalist, land a perennial magnet for the landlord, attracting

a portion of the surplus value pumped out by capital, and finally, labour the con- stantly self-renewing condition and ever self-renewing means of acquiring under the title of wages a portion of the value created by the labourer and thus a part of

7 On the stability of the profit-equalization process, see in particular Nikaido 1983. 8 A note refers to Malthus, presumably his statement that “the cost of production itself only influences the prices of . . . commodities as the payment of this cost is the necessary condition of their continued supply in proportion to the extent of the effectual demand for them” (1836: 71; see also 78).

18 Value and Distribution

the social product measured by this portion of value, i.e., the necessities of life” (809).

According to Marx then, the source of profits is excess (or unpaid) labor time. Assume a ten-hour work day of which five hours are devoted to the production of the wage basket, and the remainder to commodities constituting profits, in the sense that five of the ten hours generate sufficient revenue to compensate the employer for his outlay on wages. The ratio of “surplus” to “necessary” labor, or s/v, is defined as the “rate of exploitation” or the “rate of surplus value,” which in this instance amounts to 100 percent (MECW 35: 225). The various sectors of the economy are supposed to require different “compositions of capital” or constant capital (machinery, structures, materials) relative to variable capital (wage goods), or c/v ratios. Since the ratio c/v is non-uniform between sectors (e.g., 311), but s/v is assumed to be uniform, it follows that if – as is the assumption throughout Capital

1 – commodities exchange in proportion to labor values, including labor embodied in the net value added (v + s) as well as in the constant capital used up during the process (c ′ ), then the rate of profit or s/(c + v), will also be non-uniform. For the same total capital (c + v) in two industries yields differing s, and therefore, differing profit rates on the total, depending on the fraction of capital devoted to the maintenance of labor (v); the more “labor intensive” the industry (in modern parlance) the greater will be s and the greater accordingly will be the rate of profit. That a uniform s/v but differing c/v between industries implies different profits rates can easily be seen if the profit rate s/(c + v) is written as:

s /v

1 + c /v

Note that only if the wage rate is constant will v – which represents the “value” of (or labor embodied in) wage goods capital – vary with the current labor input and serve as an index of labor-capital ratios, and even this will not suffice if technical progress should be reducing the labor cost of producing wage goods.

Marx refers in Capital 1 to “[t]he law demonstrated above” whereby “the masses of value and of surplus value produced by different capitals – the value of labour power being given and its degree of exploitation being equal – vary directly as the amounts of the variable constituents of these capitals, i.e., as their constituents transformed into living labour power” (311). But non-uniform profit rates are not typical of competitive capitalism: “This law clearly contradicts all experience based on appearance. Everyone knows that a cotton spinner, who, reckoning the percent- age on the whole of his applied capital, employs much constant and little variable capital, does not, on account of this, pocket less profit or surplus value than a baker,

who relatively sets in motion much variable and little constant capital.” 9 “For the 9 See also: “We have in fact assumed that price = values. We shall, however, see in Book III, that

even in the case of average prices the assumption cannot be made in this very simple manner” (MECW 35: 229n). Also 608, cited below p. 44.

19 solution of this apparent contradiction,” Marx continued, “many intermediate

C. The Transformation of Values into Prices: Formal Analysis

terms are as yet wanted . . . .” The “solution” was published posthumously, but he certainly had it on hand when composing Capital 1. 10

As expressed in Capital 3, the apparent dilemma is that the empirical evidence drawn from the world of general equilibrium or the “circulation process” – “what- ever may be the surplus value extorted by capital in the actual production process and appearing in commodities, the value and surplus value contained in the com- modities must first be realised in the circulation process” (MECW 37: 814) – appeared to favor the orthodox view; in particular: “the equalization process of capitals . . . divorces the relative average prices of the commodities from their val- ues, as well as the average profits in the various spheres of production (quite aside from the individual investments of capital in each particular sphere of production) from the actual exploitation of labour by the particular capitals. . . . Normal aver- age profits themselves seem immanent in capital and independent of exploitation” (815–16).

The solution is given in Capital 3, Chapter 9: “Formation of a General Rate of Profit . . . and Transformation of the Values of Commodities into Prices of Produc- tion.” It is to allow cost prices to diverge from labor values in such a manner as to assure a common profit rate. This Marx does by calculating the average profit rate (in the labor or Capital 1 scheme) as the total of surplus values in all sectors relative

each sector, namely to the used-up constant capital and variable capital. This yields “prices-of-production” which now diverge from labor values, the deviations of course cancelling out to zero. The ratios of surplus (now in price terms) to variable capital also diverge from sector to sector, the labor-intensive industries subsidizing, so to speak, the capital-intensive industries. These conceptions are summarized in Tables 1.1 and 1.2.

These tables implicitly assume all industries to be of equal magnitude. But this is only to simplify exposition; the general profit rate will usually have to take account of sectors differing in quantitative significance: “The general rate of profit is, therefore, determined by two factors: (1) The organic composition of the capitals in the different spheres of production, and thus, the different rates of profit in the individual spheres. (2) The distribution of the total social capital in these different spheres, and thus, the relative magnitude of the capital invested in each particular sphere at the specific rate of profit prevailing in it; i.e., the relative share of the total social capital absorbed by each individual sphere of production” (162).

10 Writing in May 1885 in the Preface to Capital 2, Engels observed that Marx “had resolved this contradiction already in the manuscript of his A Contribution to the Critique . . .” referring

to the Economic Manuscripts 1861–63. “According to the plan of Capital, this solution will be provided in Book III” (MECW 36: 23). As we show in Chapter 9, Marx had in fact already solved the “contradiction” in the Grundrisse 1857–58.

20 Value and Distribution Table 1.1

Rate of composition

Organic

Rate of

Used up

Cost Value profit of capital by

Surplus

capital

price (c ′ + (s/[c + v]) industry

[Order

Surplus value

(c ′ )

(s/v)(%) [arbitrary] (c ′ + v) v + s) (%) I 80c + 20v

by v/c]

60c + 40v 0.66 (1)

10 15 20 5 390c + 110v

Source: MECW 37: 155.

Marx’s concern is to convey the notion that “the sum of the profits in all spheres of production must equal the sum of the surplus values, and the sum of the prices of production of the total social product equal the sum of its values” (172). These identities – in fact the two conditions reduce to one, each implying the other – are insisted upon so frequently that they must be taken very seriously. For example, on the identity of total surplus value and total profit: “surplus value and profit are identical from the standpoint of their mass . . . there [is] difference of magnitude only between the rate of surplus value and the rate of profit . . . .” (166); “ . . . the average profit can be nothing but the total mass of surplus values allotted to the various quantities of capital proportionally to their magnitudes in the different spheres of production. It is the total realized unpaid labour, and this total mass, like the paid, congealed or living, labour, obtains in the total mass of commodities

Table 1.2

Organic composition of

“Price of Deviation capital by

production” (c ′ of price industry

Rate of

Cost

profit a price b Value b + v + p) from value I 80c + 20v

22 15 20 37 + 17 Source: MECW 37: 156.

b From table 1.1.

21 and money that falls to the capitalists” (173). As for the second identity: “Since

C. The Transformation of Values into Prices: Formal Analysis

the price of production of the commodities of the average capital remained the same, equal to the value of the product, the sum of the prices of production of the products of all capitals remained the same as well, and equal to the sum total of the values produced by the aggregate capital. The increase on one side and the decrease on the other balance for the aggregate capital on the level of the average social capital” (200).

The Transformation procedure has been subject to an unceasing flood of com- mentary, but one particular objection does not stand up, namely that the aggregate amount of profit cannot be said to equal aggregate surplus value – that the com- parison itself is meaningless – because the former is a number of dollars whereas the latter is a number of man-hours; the two concepts are measured in differ- ent dimensions (e.g., Itoh 1976). But the comparison is in fact legitimate, for the reason that all units, values as well as prices, are expressed in money terms. For example: “If, e.g., the necessary labour amounts to 6 hours daily, expressed in a quantum of gold = 3 shillings, then 3s. is the daily value of one labour power. If, further, the rate of surplus value be = 100%, this variable capital of 3s. pro- duces a mass of surplus value of 3s., or the labourer supplies daily a mass of surplus labour equal to 6 hours” (MECW 35: 307). Again: “If we are to assume all the time that £1 stands for the weekly wage of a labourer working 60 hours, and that the rate of surplus value = 100%, then it is evident that the total value product of one labourer in a week = £2. Ten labourers would then produce no more than £20. And since £10 of the £20 replace the wages, the ten labourers can-

not produce more surplus value than £10” (148). 11 Moreover, a constant “value” (labor input, direct and indirect) is assumed to rule in the case of the monetary commodity; and where changes in the value of money are allowed, the consequences are purely nominal (138, 324). A second condition is that the monetary commodity should require the mean organic composition of capital, as will shortly become clear.

We return to the formal Transformation. The limited nature of Marx’s own pro- cedure – that only outputs are transformed from values to prices and not inputs (c’s and v’s) – has long been the focus of discussion. 12 Marx himself recognized

11 More than the use of a monetary unit as a matter of convenience is involved; a distinct external monetary measure of “value” was regarded by Marx as a sine qua non for the capitalist scheme

under investigation. (See below, Chapter 13.) 12 There are several “closures” of the Marxian system. These include the Bortkiewicz’s 1907 solu-

tion, for a simplification of which see Sweezy 1942: 115–25; see also Howard and King: “ . . . it is in fact easy to prove that the Bortkiewicz procedure will generate a positive rate of profit if and only if there is a positive rate of exploitation. It follows that exploitation is a necessary and sufficient condition for the existence of positive profits. This result has come to be known as the Fundamental Marxian Theorem. In addition it can be shown that the rate of profit varies directly with the rate of exploitation” (1985: 139). The Winternitz 1948 solution is elaborated

22 Value and Distribution

that prices might diverge from values not only in the case of final goods but in that of means of production as well: “the cost price of a commodity may already contain a deviation from the value of the means of production consumed by it, quite aside from a deviation of its own which may arise through a difference between the average profit and the surplus value” (MECW 37: 204). Furthermore,

he recognized that such may be true of the commodity produced by “mean” factor proportions. But he only asserted that this complication “does not detract in the least from the correctness of the theorems demonstrated which hold for commodi- ties of average composition” (205). Profits are still identified with surplus value in the case of the commodity produced by mean factor proportions – despite the subtle change in meaning of this conception – and by implication, total surplus value with total profit: “The quantity of profit falling to these commodities [of average composition] is equal to the quantity of surplus value contained in them.

For instance, in a capital of the given composition 80 c + 20 v , the most important thing in determining surplus value is not whether these figures are expressions of actual values, but how they are related to one another, i.e., whether v = 1/5 of the total capital, and c = 4/5. Whenever this is the case, the surplus value produced by v is, as was assumed, equal to the average profit.” Similarly, the iden- tity of value and price in the case of the commodity produced by mean organic composition – again, by implication, of total value and total price – is also reasserted for the complex case: “since [surplus value] equals average profit, the price of pro- duction = cost price plus profit = k + p = k + s; i.e., in practice it is equal to the value of the commodity.” 13

in Meek 1967. See also Kayali and Sari 1989. And there is Seton’s solution which extends to the n-product case and beyond simple reproduction (Seton 1976 [1957]).

Of high interest in their own right and for coverage of the literature, are Samuelson 1971, Meek 1975, Desai 1991. Morishima’s sympathetic treatment justifies Marx’s position but only in the absence of joint production and alternative manufacturing processes, leading him to recommend “a Marxian economics without the labour theory of value” (1973: 181), on which matter see our concluding chapter.

Reference may also be made to the so-called “new solution” to the Transformation pro- pounded inter alia in Dum´enil 1983–84; Foley 1982, 1986: 42–4; Lipietz 1982. Here the value of variable capital or of “labor power” is taken not as labor embodied in a given commodity wage but as the product of a given money wage and the “value of money.” The “solution” disallows a transition from values to prices, since the set of prices must be known before the rate of commodity wages can be established. For criticisms of this and various other “Marx- ian” interpretations, see Sinha 1997; Hunt and Glick 1987; Howard and King 1992a: 276–80; Cavalieri 2005.

See further notes 29 and 36 below, which point to fortuitously common features between our own interpretation and “the new solution.” 13 For the simple case involving partial transformation, the two identities insisted upon are mathematical alternatives, either of which can be used to complete the equational set of simultaneous equations describing the transformation. In the complex case, however, the two identities are no longer alternatives, but generate different solutions (cf. Meek 1975: xviii f).

D. The Transformation and the Allocation Mechanism