The Marxian account of exploitation is a theory of how surplus labour is extracted, and the form that this takes as profit. In formalisations of Marxian theory, the relationship between surplus labour and profit is expressed by the 'fundamental Marxian theorem' (FMT) that the existence of surplus labour is necessary and sufficient for the existence of profit. In a recent article in this journal, Kliman (2001) has argued that in any interpretation of Marx's value theory in which prices and values of inputs and outputs are determined simultaneously, the extraction of surplus labour is insufficient, and in general unnecessary, for the existence of positive profit. He calls such interpretations 'simultaneist' and argues that because in such interpretations the FMT fails, they are all incompatible with Marx's theory. By contrast, a 'temporalist single system interpretation' (TSSI) does indeed imply that surplus labour is both necessary and sufficient for positive profit. Elsewhere, for example in Kliman and McGlone (1999), it is argued that all of the major propositions of Capital can be replicated by the formalism of the TSSI, and that this is not true of any other interpretation in the modern literature. Consequently, the claim is that of all modern interpretations only the TSSI adequately represents the theory presented in the three volumes of Capital.
It is important to be clear about what is being asserted. Kliman is not assessing the adequacy of any theory, whether this theory be his own, Marx's, or some other. While desiderata of a theory might include meaningfulness of assumptions, logical coherence, elegance, insight and testable implications, none of these is at issue here. Kliman is only presenting an interpretation of the theory of Capital. In order to decide between rival interpretations, the criterion he employs is whether an account can derive the major propositions of Capital (the 'replication criterion'), and he sees this as a straightforward test that can decide between rival interpretations.
This paper focuses on Kliman's claim that the TSSI can support a logically robust FMT, that is, one that is valid 'under completely general conditions' (Kliman 2001, p. 106, emphasis in original). For convenience, the paper identifies the TSSI with Kliman's writings (as both single and joint author), but further references can be consulted in Kliman (ibid.). Section 2 recalls Kliman's argument, using his notation and terminology. The next section emphasises that his argument depends upon two assumptions. These are stated (ibid, p. 106, immediately before and after equation (7)), but it is easy to miss their significance. Adherents to what Kliman calls the 'standard interpretation' reject both of these assumptions; adherents to what he calls the 'new interpretation' reject one of them. Without both of them, Kliman's demonstration of the FMT fails. The fourth section focuses on his definition of the 'monetary expression of labour-time' and shows that this definition requires the two particular assumptions. Section 5 outlines the TSSI method. The following two sections consider whether a non-TSSI FMT is possible, and whether the TSSI proof of the FMT is valid according to the TSSI method. The answers are first, that Kliman has not conclusively shown that the demonstration of the non-TSSI FMT is flawed, and second, that if the non-TSSI FMT is flawed, then so too is the TSSI FMT, and for exactly the same reason. A short conclusion summarises, and suggests that issues of rival interpretation are not perhaps the best focus for the construction of a coherent theory of today's world.
The TSSI FMT
Consider the TSSI as outlined by Kliman. Time is considered discretely in the following manner. Time t is a period in which inputs are purchased at the outset and then used continuously during the period. The period ends immediately prior to the appearance of output, and the appearance of output denotes the start of period t + 1. Output is instantaneously sold, providing profit to the seller and enabling the instantaneous purchase of inputs. A second period of production then ensues. Thus in the present context, temporality refers solely to an insistence that it takes time to produce commodities, so that the price of a commodity as input may be different from the price of that same commodity as an output.
The following notation is used.
C(t) is the total expenditure on used-up means of production at the start of period t, measured in money.
V(t) is the total wage bill advanced at the start of period t, measured in money.
P(t+ 1) is total revenue received from the sale of output (called 'total price' in the Marxian tradition), measured in money.
[[pi].sup.N] is nominal profit, measured in money, and defined as
(1) [[pi].sup.N] = P(t + 1) - C(t) - V(t)
[[pi].sup.R] is real profit, measured in money, and defined as
(2) [[pi].sup.R] = [[P(t + 1)]/1 + i] - C(t) - V(t)
where i is the discount factor which commensurates monetary magnitudes through time.
[tau](t) is the monetary expression of labour-time at time t, or the amount of money that represents one hour of socially necessary labour-time at time t. Its inverse is the value of money, the number of hours of socially necessary labour-time represented by one unit of money at time t.
L(t) is total labour purchased at the start of period t. While he is not explicit, Kliman assumes that this is also the labour-time performed in production during period t. It is therefore measured in hours of socially necessary labour-time. This assumption is not at issue for the argument of this paper.
S(t) is surplus labour-time, measured in hours of socially necessary labour-time.
Kliman's argument is as follows. Surplus labour-time is the difference between total labour-time and the labour-time equivalent of the wages paid:
(3) S(t) = L(t) - [V(t)/[tau](t)]
Kliman wants to show that this surplus labour-time is necessary and sufficient for the real profit of equation (2) to be positive. Now in the present specification, the only reason why a discount factor is necessary in equation (2) is that the monetary expression of labour-time might change. So define the discount factor as the period by period rate of change of the monetary expression of labour-time:
(4) i = [[[tau](t + 1) - [tau](t)]/[tau](t)]
(5) 1 + i = [[[tau](t + 1)]/[tau](t)]
Substituting for 1+I in equation (2),
(6) [[pi].sup.R] = [[P(t + 1) [tau](t)]/[tau](t +1)] - C(t) - V(t)
and substituting for V(t) from equation (3),
(7) [[pi].sup.R] = [[P(t + 1)[tau](t)]/[tau](t + 1)] - C(t) - [L(t) - S(t)][tau](t)
(8) [[pi].sup.R] = [[[P(t + 1)]/[[tau](t + 1)]] - C(t)]/[tau](t)] - L(t)][tau](t) + S(t)[tau](t)
Kliman then asserts that value added in terms of labour-time is the difference between the labour-time equivalents of total revenue (total price) P(t + 1)/[tau](t + 1) and expenditure on the means of production C(t)/[tau](t), and this difference is equal to the living labour extracted L(t), since the latter generates all new value (ibid. p.107). Hence the expression in the large brackets in equation (8) is identically zero, whence
(9) [[pi].sup.R] = S(t)[tau](t)
Now consider again the large bracket of equation (8). Since for Kliman this is zero, it can be written as
(10) [[P(t + 1)]/[[tau](t + 1)]] - [C(t)/[tau](t)] = L(t)
and hence in time 1,
(11) [P(1)/[tau](1)] - [C(0)/[tau](0)] = L(0)
Assuming that P, C and L are each positive and finite in all time periods, then as long as [tau](0) is positive and finite, so must [tau](1) be positive and finite. Hence so is every member of the [tau] series. Therefore [tau](t) in equation (9) is positive and hence positive surplus labour is both necessary and sufficient for real profit to be positive.
3 TSSI definitions
However, in addition to the assumptions stated, this...