Turnover Time and Its Relation to the Rate of Profit
Hyun Woong Park UMASS,Zhun Xu UMASS
2010 Oct 17
Economy of time, to this all economy ultimately reduces itself.
Marx, Grundrisse, p.173
- Introduction
The rate of profit is the major Marxian variable that indicates overall workings of the capitalist economy.[1]And its falling tendency in relation to crisis has been a subject of intense debate in Marxian literature. Yet there has been no agreement on the determinants of the tendency. Profit squeeze theory (Weisskopf 1979, Wolff 1986, etc.) and rising organic composition of capital (Marx 1981, Shaikh 1978, Weeks 1981, etc.) have been the two most widely accepted approaches. The increase of the ratio of unproductive labour to productive labour as a major determinant of the falling rate of profit was also discussed as an alternative explanation (Moseley 1990, 1997). In addition, the increase in the rate of surplus value was pointed out as a main factor that generates a counter-tendency.[2]However, one important element which plays no less important role in Marx’s discussion of the rate of profit and crisis has been more or less downgraded in the literature: i.e. turnover time.
In various places in Capital Volume II Marx indicates turnover as one of the most important categories in direct relation to profitability.As is well-known, the major theme of Volume II is the circuit, the life cycle, of capital comprising the production process and the circulation process in their unity. The gist is to conceive capital as a process which spans a certain time period. And turnover is introduced as a fundamental concept that reflects the time structure of capital. An implication is that, simply put, it takes time or has to risk time to produce and realize surplus value since the variable capital generating surplus value has to go through a certain time period of circuit along with its constant counterpart. Therefore a conclusion is derived that turnover time is one of the factors that significantly affect the profit rate of capital.
An implication that follows is that manipulating the turnover time is what capitalists can rely on at times when the profitability conditions get deteriorated. In this regard Marx’s demonstration of turnover provides an insight in understanding characteristic phenomena of the modern industrial capitalism where various cutting-edge technology areintensively utilized in time-management so as to affirmatively respond to the aggravating environment for the business, and to acquire more profit in a given period of time; as Dell founder Michael Dell says, “The closer you get to perfectinformation about demand, the closer you get to zero inventory. It's asimple formula. More inventories mean you have less information, and moreinformation means you have fewer inventories.”Indeed, turnover is one of the categories that distinguish Marx’s theory of capitalist production from that of neoclassical economics which does not consider time structure.[3]
Given such an important theoretical status and implications of turnover within Marx’s theory, it is quite striking to find that the concept has not drawn due attention in the literature. Among a few articles that came to our view, Webby & Rigby (1986) and Fichtenbaum (1988) were the ones that directly deal with turnover time in their empirical study of the trend of profit rate. In large, we adopt their method in constructing the turnover rate and extend their results, which cover pre-Neoliberal era, into quite recent years. In this way we could compare the trend of turnover rate in the so-called Golden Age capitalism when the business environment was rather ‘peaceful’ and in the Neoliberal era when all-round competition among capitalists drastically increased.
The paper is presented in the following order: In section two weexamine Marx’s discussion on the turnover and its relation to the rate of profit throughout Capital. And in section three Webby & Rigby (1986) and Fichtenbaum (1988) are discussed. Explanations on the method and data set adopted in this paper will be given in the fourth section. And the empirical results will be presented in section four. In the last section we provide a case study of food industry as our conclusion of this paper.
II. Turnover and its relation to the rate of profit
In this section we examine Marx’s analysis of the concept of turnover and its relation to the profit rate.
Marx on turnover
(i)Theory
The most systematic demonstration of the concept can be found in Part Two of Capital, Volume Two. In particular Chapter 7, 8, and 9 need a careful examination. There the most difficult aspect of the concept arises when considered in relation to the fixed capital. In Chapter 7 Marx introduces the concept of turnover with an assumption of the absence of fixed capital, and in the following chapter discusses the distinction between fixed capital and circulating capital. And in chapter 9 the concept is analyzed with the fixed capital taken into account. Throughout these discussions two conceptually different approaches to ‘turnover’ seem to emerge:
-1st notion of turnover: ‘the sum of the time of circulation and that of production’; or, ‘the interval between one cyclical period of the capital value and the next.’
-2nd notion of turnover: time taken for the advanced capital value to return to its initial form recovering its initial amount.[4]
Both definitions emerge from the analysis of the circulatory nature of the capital circuit of the forms (the circuit of money capital) and (the circuit of productive capital). Namely, the capital value advanced returns to its initial form (either the money form or the form of productive elements) in order to repeat the same process; what is more, it repeats the same process in order to be perpetuated and valorized.[5] Capital value that has ‘perpetuated valorization’ as its nature is subject to a circular movement, constantly returning to its initial form after a series of processes. Marx writes “[This] circuit of capital, when [it] is taken not as an isolated act but as a periodic process, is called its turnover.”[6] One period of cycle which the advanced capital value goes through and recovers its initial form at the end is consisted of production and circulation process. From this it necessarily follows that the two definitions of turnover coincide with each other. In other words, the capital value advanced is recovered with surplus value only after it has gone through the combined cycle of production and circulation process. However, this holds only with an unrealistic assumption: the absence of fixed capital.
The distinction between circulating and fixed capital as resulting from the circulatory aspect of the capital lies in that the circulating capital goods enter both the labour process and the valorization process in their entire physical shape, while this is the case for the fixed capital goods only in the labour process.[7] So to speak, contrary to the circulating capital goods, the fixed capital goods transfer their value to the final output only gradually. Obviously, the time for the fixed capital goods to completely recover their initially advanced form cannot be identical with, but should be longer than, the time lasting for one cycle of production and circulation.
Marx recognizes this so well, and it is in Chapter 9 where he analyzes “how two new forms which capital obtains as a result of the circulation process [i.e. fixed capital & circulation capital] … affect the form of its turnover.”[8] Now if the first definition of turnover is adopted the turnover time wouldn’t be affected by the existence of the fixed capital. However when we take the second definition, the problem arises how to conceptualize the notion of turnover and its duration in case of the capital constitutive of both circulating capital goods and fixed capital goods with various turnover times. Marx’s solution is ‘the average turnover of its different component parts.’[9] But he merely cites an ‘American economist’ Scrope’s numerical example of the calculation of the average turnover rather than providing his own case. We briefly reproduce it here with numbers changed.[10]
A total capital value advanced is $100,000. One half of it is invested in the first fixed capital goods which turn once in twenty five years; four tenths of it is invested in the second fixed capital goods which turn once in five years; the remaining one tenth is invested in circulation capital goods which turn four times in one year. Then the capitalist’s annual expenditure would be
______
.
From this Scrope calculates that the average turnover of the various components of the capital is 2 years by reasoning that the capitalist’s ‘annual expenditure’ is $50,000, and that the total capital advanced is $100,000.
The fallacy of this approach is immediately obvious. The pinpoint here is the difference between capital ‘expended’ and capital ‘advanced.’[11] In Scrope’s case, capital is said to turn over when its initial total value is expended in the process of capital circuit regardless of whether it completely recovers its initial form. Accordingly, turnover time is conceived as time taken for the entire expenditure of the amount identical to the total capital value. However, this is not what the second definition of turnover refers to. It is the time taken for the capital value to recover its initial form in its initial magnitude. The correct calculation would be as follows: The entire value of circulating capital goods of $10,000 is always recovered at the end of each cycle and advanced again in the next cycle, and thus the same is true at the end of each year as well. For the fixed capital goods, $10,000 (depreciation of the first fixed capital goods $2,000 + that of the second fixed capital goods $8,000) would be recovered at the end of each year. Therefore, at the end of year 9 the capitalist would have in her pocket $10,000 of circulating capital returned and $90,000 of fixed capital returned. The entire capital value initially advanced $100,000 is fully recovered in 9 years. Thus the correct turnover time should be 9 year.
Whether Marx approves Scrope’s method is somewhat vague since he merely cites it and does not make any comment on the calculation itself. Yet despite the incomplete and rough nature of Volume II and the difficulty, as Marx himself admits, of the issue itself, we think the core idea of the second definition of turnover and of the average turnover time is clear enough. And according to it, Marx would have rejected Scrope’s approach.
One problem with Marx’s (incomplete) theory of turnover is that he seems to think that the consideration of fixed capital modifies one concept of turnover to the other. This is also true with Engels. Observing that “In commercial practice, the turnover is generally worked out only roughly,” he comments “It is assumed that the capital has turnovered over once as soon as the sum of commodity price realized reaches the sum of the total capital applied. But the capital can have completed a whole cycle only if the sum of the cost prices of the commodities realized equals the sum of the total capital.” (Capital III, p.334-5)
However, better way to theorize turnover is to conceptualize its two distinctive definitions as referring two different types of turnover. To put it differently, whether or not fixed capital is existent, we can conceive without any hinderance those two different types of turnover. Of course they would coincide with each other only in a special case when there are no fixed capital goods. And we can also measure at least conceptually the first definition of turnover even when there are fixed capital goods. Actually, this approach is what Marx and Engels seem to take, as can be verified in their discussion of turnover in relation to the rate of profit in Volume 3. That is, with the term ‘turnover’, they solely refer to the first type of turnover (as a sum of production time and circulation time). Measurement issue as well is confined to this type of turnover, to which we now turn.
(ii)Measurement
First of all, the main problem with measuring the turnover cycle as a sum of production time and circulation time is that it is not immediately known; indirect ways to calculate it using accounting data need to be devised. As mentioned above, Engels makes a comment in an editorial note that “In commercial practice, the turnover is generally worked out only roughly.”
In Chapter 4, Volume 3 written by Engels, it is suggested to calculate the number of turnover during the year by dividing the annual expenditure of variable capital by variable capital advanced. That is,
(1)
where n: the annual number of turnover, V: annual expenditure, and v: variable capital advanced at the start of the year. Actually, this approach is adopted by Marx already in Chapter 16 of Volume 2 where the turnover of variable capital is discussed. The problem of this approach however is that, as Engels rightly complaints, “The capitalist himself does not know in most cases how much variable capital he employs in his business …. Even if he were to keep a separate record for wages paid, this would simply indicate the total sum paid at the end of the year, i.e. vn [=V], and not the advanced variable capital v itself.” (Capital III, p.167) In a word, it is almost impossible to get data for the variable capital advanced; this is true even to this day!
Since “the only distinction within his capital that impresses itself on the capitalist as fundamental is the distinction between fixed and circulating capital,” Engels comes up with an unique way to calculate v so as to eventually measure n as follows: Since circulating capital (), which is consisted of constant part of circulating capital () and variable capital (), is known,[12] the ratio by which circulating capital () is consisted of and would be identical to the ratio of the annual expenditure on constant part of circulation capital () to that on variable capital (), both of which are also known data. Thus,
(2).
Combining equations (1) and (2) we finally get the annual number of turnover as:
(3).
In words, if the sum of the annual expenditures on the constant part and variable part of the circulating capital is divided by the circulating part of the total capital advanced, we would get the annual number of turnover.
Marx on the relation of turnover and the profit rate
Marx’s systematic discussion of the relation between the turnover and the rate of profit is found in two places throughout Capital[13]; Chapter 16 of Volume 2 and Chapter 4 of Volume 3. To begin with, the rate of profit is measured as an annual rate with the annual production of surplus value divided by the capital value advanced at the start of the year not by the capital expended or turned over during the year.[14] That is, the profit rate measures the ratio of the annual flow of surplus value on the stock of capital value. Here the turnover time affects the rate of profit by directly influencing the magnitude of surplus value produced during the year. Let us examine Marx’s analysis more closely.
First of all, the relation between turnover and production of surplus value is discussed in Chapter 16 of Volume 2 titled ‘The Turnover of Variable Capital’. As the appropriation of surplus value is directly associated with the employment of the variable capital in the production cycle, the more frequently the variable capital goes through the production cycle along with the constant capital the more surplus value would be appropriated. Thus we have:
(4)
where S: annual appropriation of surplus value, s: appropriation of surplus value in only one production cycle. Now dividing both S and s by variable capital advanced v gives us:
, (5)
where S’: annual rate of surplus value and s’: real rate of surplus value, using Marx’s terminology.
Then the discussion is expanded to the rate of profit in Chapter 4 of Volume 3 titled ‘The Effect of the Turnover on the Rate of Profit.’[15] As noted earlier, Marx constructs the annual rate of profit as an annual flow of surplus value over the stock of capital value advanced as follows:
(6)
Where c: constant capital advanced, v: variable capital advanced.[16] Now in order to grasp the influence the turnover has on the rate of profit, combine (4) and (6) and we have
, (7)
The positive relation of the turnover to the rate of profit is evident in the equation. However, Marx himself ignores it in Part 3 of Volume III where he analyzes the tendencies and counter-tendencies of the rate of profit to fall.
In Chapter 13 of Volume III a rise in the organic composition of capital () associated with a technological development is discussed as major determinant of the tendential fall of the rate of profit; whereas in Chapter 14, Volume III the rate of surplus value () comes at the center of the analysis of the counter-tendencies. But no word is given to turnover. Marx does not distinguish surplus value appropriated during the whole year (S) and that during one production cycle (s). As an editor Engels makes a supplementary remark in a parenthesis that Marx is assuming that S is identical to s which is the same thing to assume capital turns over only once during the year. (Capital III, p.334-5)[17]
The implication is not small. If we are confined to such assumption, our behavioral analysis of the capitalist in counter-acting to the tendential fall of the profit rate would be confined to the management strategies within the production site. The elements Marx discusses in Chapter 14 as counteracting factors all belong to this category.[18] The problem with this is that other possible capitalist strategies related to the circulatory nature of the capital circuit as a periodic process constituting various phases of production and circulation escape from our attention. It is our argument that increase of the velocity of capital should have been included as one of the major counteracting factors to the tendential fall of the profit rate.
One last comment on Engels’s treatment of turnover in Chapter 4 of Volume 3 relates to another important issue of fixed capital. Notice that when fixed capital is taken into consideration the rate of profit is constructed as follows: