طبقه و بهره برداری در اقتصاد عمومی مخروطی محدب

In this paper, we examine what appropriate formulations for labor exploitation are, in order to explain the emergence of class and exploitation status in capitalist economies. Given the well-known controversy pertaining to plausible formulations for labor exploitation in joint production economies, we propose an axiom, Axiom for Labor Exploitation (LE), which every ‘appropriate’ formulation of labor exploitation should satisfy. Using this axiom, the necessary and sufficient condition for plausible formulations of labor exploitation is characterized to verify Class-Exploitation Correspondence Principle (CECP) ( Roemer, 1982). According to this, CECP no longer holds in general convex cone economies if the well-known formulations of labor exploitation such as Morishima (1974) and Roemer (1982; Chapter 5) are applied. Therefore, we propose two new definitions of labor exploitation, each of which verifies CECP.

Exploitation of labor is the difference between labor hours an individual provides and the labor hours necessary to produce commodities the individual can purchase via his income. This notion has been one of the prominent key-concepts relevant to capitalist economic systems, particularly in a number of debates, ranging from analyses of labor relations, especially focusing on the weakest segments of the labor force, such as women, children, and migrants (see, e.g., ILO, 2005a, ILO, 2005b and ILO, 2006). This has been seen as the cornerstone of Marxist social theory, but it is also extensively discussed in normative theory and political philosophy (see, e.g., Wertheimer, 1996, Wolff, 1999, Bigwood, 2003 and Sample, 2003). In addition, this notion deserves recognition in contemporary economics for understanding one of the essential characteristics of market economies with private ownership of wealth, given the recent and common trends of growing disparity in income and wealth and the increase in poverty among advanced countries. In fact, though, traditionally, the Marxian social theory has described capitalist society as that the capitalist class exploits the working class, it is Roemer (1982) who discusses, by applying the standard general equilibrium analysis, that this phenomenon is shown as a formal theorem called Class-Exploitation Correspondence Principle (CECP), 1 as opposed to a mere descriptive theory. Given this CECP, an appropriate formulation of exploitation can be seen as relevant to the inequality of opportunities which are generic in capitalist society. This is because CECP shows that the wealthier agents are exploiters, and they can rationally choose from all classes of society to belong to the capitalist class, whereas the least wealthy agents are exploited and relegated to the working class being that there is no other available option. Thus, the exploiting agents of the capitalist class tend to have a myriad of options, whereas the exploited agents of the working class have far fewer options: the existence of labor-exploiters and labor-exploited agents reflects unequal opportunity of life options, due to unequal access to productive assets. 2 Furthermore, interestingly, an appropriate formulation of exploitation can perhaps be seen as an index for capturing ‘unjust’ distribution of well-being freedom in the following sense: As discussed by Rawls, 1971, Sen, 1985a and Sen, 1985b, etc., well-being freedom implies an individual’s ability to choose to pursue the life she values. 3 There are two crucial factors which stipulate the degree of an individual’s well-being freedom: one is the amount of income she can spend to purchase the commodities necessary to achieve her goals, and the other is the amount of time she has to sacrifice as labor supply in order to purchase such commodities. Then, the rate of labor exploitation can represent her degree of well-being freedom, or indeed un freedom, since it measures the difference of these two factors by using labor hours as a numéraire: if this value is negative for the individual, she is exploiting the free hours that some other agents sacrificed as labor supply for the production of the commodities she can purchase. If the value is positive, she is exploited in the sense that some of the free hours she sacrificed as labor supply to purchase the commodities are appropriated by somebody else. Granting the normative relevance of labor exploitation, the well-known formulation of this notion was proposed by Okishio (1963) in the simple Leontief-type model, and given this model, CECP holds true under this definition of exploitation, as Roemer (1982; Chapter 4) illustrated. However, once a more general convex cone model such as the von Neumann model is applied, the Okishio (1963) formulation is known to be ill-defined, as Morishima (1973) and Steedman (1977) argued. Given this difficulty, two alternative formulations were respectively proposed by Morishima (1974) and Roemer (1982; Chapter 5), which are indeed well-defined in more general models. However, as this paper will point out below, neither the Morishima (1974) nor the Roemer (1982; Chapter 5) definition could preserve CECP as a theorem in general convex cone models. This is indeed problematic for both the definitions, since, as Roemer (1982) forcefully argued, the central relevance of CECP in exploitation theory implies that it should be epistemologically considered as a postulate, by requiring that any satisfactory definition of exploitation preserves CECP. Given this background, our main concern in this paper is to discuss what formulations of exploitation are appropriate. Regarding this issue, previous publications on exploitation theory, including Morishima (1974) and Roemer (1982), have repeated the process of criticizing the existing formulations while proposing an alternative one that to some, could be seen as more appealing. However, since there is potentially an infinite number of formulations for exploitation, we may find it difficult to come to a consensus on which formulations could be deemed appropriate if we were to continue this argument. In contrast, this paper introduces an axiomatic method which is a completely new approach to the exploitation theory. By taking an axiomatic approach, this paper suggests to start from the very basic principles which represent the normative intuitions behind exploitation theory, thus explicitly identifying the class of proper formulations for exploitation. To be precise, in this paper we first propose a plausible axiom, Axiom for Labor Exploitation (LE), which is a minimal necessary condition for any formulation to be considered as an appropriate one. By using this axiom, we characterize what kinds of formulations can verify CECP as a theorem in general convex cone economies. Based upon this characterization, we show that, in contrast to the above mentioned two traditional definitions, the two new definitions of exploitation satisfy LE and preserve CECP: one is a refinement of Roemer’s (1982; Chapter 5) formulation and the other is an extension of the so-called “New Interpretation” ( Duménil, 1980 and Foley, 1982) formulation of exploitation (originally defined in Leontief models) to general convex cone models. Both of these definitions formulate the exploitation index as the difference between one unit of labor supplied by an agent per day and the minimal amount of labor socially necessary to achieve the agent’s income per day. We could also resolve, by using the two new definitions, most of the difficulties that Marxian economic theory has faced. That is, the difficulty of Fundamental Marxian Theorem (FMT) in the general convex cone economy that was discussed by Petri (1980) and Roemer (1980), is resolved. In the following paper, Section 2 defines a basic economic model with convex cone production technology, and an equilibrium notion. Section 3 introduces alternative formulations, including our new definitions, for labor exploitation. Section 4 discusses the robustness of CECP in general convex cone economies by using the various definitions of labor exploitation, while Section 5 discusses the performance of the new definitions in terms of FMT. Finally, Section 6 provides some concluding remarks.

We have characterized the condition for the plausible formulation of labor exploitation to verify CECP, as well as proposed two new definitions of labor exploitation, each of which performed well in terms of both FMT and CECP. However, the new definitions have exclusively distinct characteristics in comparison with the previous definitions such as those proposed by Morishima (1974) and Roemer (1982; Chapter 5), which may give us new insights on theories of labor exploitation. First, Roemer (1982) claimed that prices should emerge logically prior to labor values so as to preserve CECP as a theorem in general convex cone economies. Though he failed in proving this claim with his own price-dependent labor value formulation (Definition 4 in this paper), Theorem 2 in this paper proves that his claim itself is true. In fact, in order to verify CECP as a theorem, any formulation of labor exploitation satisfying LE must be price-dependent, as we discussed in Section 3. This implies that the classic transformation problem in Marxian economic theory is no longer worth investigating, since any price-independent labor value formulation causes the failure of CECP. In other words, according to Theorem 1 and Theorem 2, the scope of the classical Marxian perspective on labor exploitation (that the exploitative relationship between capital and labor was considered to be logically prior to the prices that constitute an equilibrium in the capitalist economy 15) must be limited to models with Leontief technology. Second, in the classical Marxian argument, labor exploitation was explained by using the concept of the labor value of labor power, which was defined in the Morishima (1974) framework as the technologically minimal amount of direct labor necessary to produce the subsistence consumption vector as a net output. In such an argument, the subsistence consumption vector plays a crucial role. In Definition 6 of this paper, however, the labor value of labor power might be defined as the minimal amount of direct labor socially necessary to achieve workers’ income by which they can respectively purchase at least the subsistence consumption vector. Also, in Definition 7, the labor value of labor power might be defined as the minimal amount of direct labor socially necessary to achieve workers’ income, which is evaluated via the actually used social production point. In both of these formulations, the subsistence consumption vector is used, at most indirectly, to define the labor value of labor power. Thus, the labor value of labor power also no longer emerges logically prior to the price of labor power (wage income). Hence, the concepts of labor value in these new definitions are irrelevant to theories of exchange values of commodities and labor power. In spite of such a significant difference of these new definitions from the classical Marxian notion of labor exploitation, they would be justified, according to the scenario Roemer (1982) offered, since both FMT and CECP hold true for these new definitions. Note that we still need further argument as to which of Definition 6 and Definition 7 is more appropriate. This problem is relevant to the issue of characterizing the unique appropriate formulation of exploitation by applying the axiomatic method. Recently, Yoshihara and Veneziani (2009) proposed, in subsistence convex cone economies, four axioms as the necessary conditions that any appropriate formulation of exploitation should satisfy, and then showed that the Definition 7 formulation is the unique one satisfying all of these axioms. Since this result is obtained from subsistence economies, it could not be directly applied to the accumulation economies studied in this paper. Indeed, it is an ongoing problem in the model of accumulation economies to identify the unique formulation for exploitation by utilizing the axioms. We leave this issue for future occasions. Note that there have been recently some papers published, such as Skillman (1995) and Veneziani (2007), which address the issue of whether the class and exploitation structure is (logically) persistent or not in the long run. They argue that if the possibility of savings is introduced in intertemporal models, then positive profits and exploitation tend to disappear over time. Though we did not address this issue in this paper, because our objective was to discuss proper definitions of exploitation for explaining the emergence of class and exploitation in a simple temporary equilibrium model, it is worth commenting on. To be precise, Veneziani (2007) showed, assuming an intertemporal Leontief model of subsistence economies, that any price vector of the stationary equilibrium converges to the vector of labor value, which drives the rate of exploitation to zero over time. This result indicates that if all agents are indifferent between the current consumption and the future consumption in the sense that the discount factor is equal to unity, then the class and exploitation structure disappears in the long run, due to the profit rate converging to zero. In other words, it may be possible that if the discount factor of all agents is less than unity, then the positive profit rate of the stationary equilibrium as well as the class and exploitation structure persist. This is indeed true even in more general intertemporal models with convex cone production sets, as Veneziani and Yoshihara (2009) show. In contrast, although these results focus on the stationary equilibrium where any agent no longer has an incentive to save, it is easily conjectured that in the out-of-stationary-equilibrium state, the positive profit rate and the class and exploitation structure are not persistent. This is due to, as Skillman (1995) and Veneziani (2007) pointed out, the introduction of savings without population growth easily diminishes the scarcity of capital relative to labor in the process of capital accumulation, which drives profits and the rate of exploitation to zero over time. To take this issue seriously, we should introduce, in addition to savings, the factor of population growth explicitly in an intertemporal model. This kind of perspective is also shared with the classical Marxian argument for the progressive production of a relative surplus population, which is beyond the scope of this paper.