The Homogenization of Labor Services and Determination of Labor Compensation
Moving forward from consideration of the Walrasian/Paretian production function to evaluate Walrasian/Paretian treatments of the factors of production, we need to emphatically question the notion that we are dealing with homogeneous units that can be readily aggregated to generate determinate quantities of output from given factor combinations. In this manner, we are after the ready quantification of inputs to production in forms that can be easily combined and amenable to calculations to yield marginal contributions to the output of the firm. Bearing in mind that we are, once again, dealing with a rigorously rationalist body of theory that constructs ideal, abstract models and validates them in reference to their explanatory power in relation to real markets and real production processes, it would not be fair to argue that abstract homogenization of labor, land, and capital presents an unrealistic portrait of real production inputs. Reality is not at stake in Walrasian theory - the capacity to explain reality through an abstract model in a persuasive manner is. In these terms, we need to examine the particular ways in which the Walrasian/Paretian theory of the firm homogenizes the production factors and illuminate the particular consequences of such theorizations.
Beginning with labor, homogeneous representations of labor services are ubiquitous within multifarious shades of economic theory. The English Classicals approached labor as a common denominator in the production of value. For Adam Smith, labor appears as a generalization of human activity, subject to development through the technical organization of production processes and acquisition of skill and dexterity through experience. As such, task divisions of labor at the minute level in individual production processes (e.g. Smith's pin factory) had the effect of sharpening the particular skills of laborers at particular tasks at the expense of diffusive, complex experiential knowledge of a larger production process. This developmental understanding of labor appealed to a particular imagery of labor through which abstractly unskilled laborers could be transformed to enhance individual and collective productivity, without simultaneously developing an integral understanding by workers of the broader range of tasks involved in commodity production. In this sense, Smith's comprehension of labor incorporated a transition from abstract universality to dynamical particularity, characteristic of an age in which the social utilization of human labor was rapidly changing, from small scale, localized artisan production of goods to technologically transformed manufacturing of goods under a task division of labor, and gradually and unevenly to introduction of machinery and artificial sources of power that could entirely replace the skills and energy of human laborers. In the end, however, for Smith, labor commands a universalized dual significance as both the transformative process through which natural endowments could be transformed into objects of consumption and the source of value underlying such objects.
Almost half a century later, David Ricardo sharpened Smith's understanding of labor by distinguishing between the notion of labor time expended in the production of goods as the source of marketable value in most commodities and the notion of labor services as a marketable commodity commanding a wage. Later in the Nineteenth century, Karl Marx offered the most rigorous formalization of Ricardo's insights, homogenizing the understanding of labor time embodied in the production of goods and services as a socially necessary average calculation, conveyed and standardized through the operation of markets and the force of competition, and formalizing the concept of marketable labor capacity as labor power, as a fundamental ingredient to production under capitalism. As such, the Marxian counter-homogenization of abstract social labor time and labor power represent the theoretic apogee of the Classical tradition beginning with Smith.
These Classical formulations of the homogeneity of labor differ in important ways from the understanding of labor that emerges within the Neoclassical tradition, either for Walrasian theory proper or for Austrian and Marshallian variations. Preeminently, developmental concerns with labor disappear, subsumed within the unseen technological contours of the production function. In particular ways, the Neoclassical tradition reintegrates the role of labor in value creation with the question of compensatory rates, simultaneously undermining certain aspects of labor considered exceptional for labor by the Classicals in relation to the other factors of production. Emphatically, labor time loses its primacy as the source of value in exchange advanced by the Ricardians and the Marxists. Moreover, the Neoclassicals implicitly depreciate the Classical emphasis on income distribution between classes. If the Classicals, from Smith to Marx, are preeminently concerned with the distribution of income between classes defined overwhelmingly in accordance with ownership of divergent productive assets, then the Neoclassicals, from the early Marginalists into the Twentieth century, are preeminently concerned with questions of technical efficiency in the employment of substitutable factor combinations and how such considerations, seen through the prism of relative factor scarcity and market competition, reflect upon the ethics of compensation. In these respects, marginal productivity factor pricing theory, as anticipated or otherwise implied by Walras in his early elucidations of general equilibrium theory and refined into a full-fledged theoretic doctrine by the American J.B. Clark, is above all as much an ethical proposition about wage rate determination as it is a technical condition of profit maximization/cost minimization. My considerations on labor homogeneity and compensation here, are, thus, bound up with marginal productivity factor pricing although my account does not expressly offer a critique of the latter.
The homogenization of all factors of production is predicated on the need to calculate the marginal product from adding additional increments of each factor. Such calculations can only make sense if each additional unit of each factor is virtually identical to every other unit of the same factor already employed or capable of being employed. Considered in this manner, we need to establish both the technical boundaries of the production process and the manner in which labor services are technologically integrated with other factors in order to generate output. These pieces of information can inform the theoretic homogenization of labor services to the extent that they posit the level to which concrete variations in real labor activity can be erased in the effort to define a given homogeneous factor input.
Fundamentally, we need to differentiate between two distinct senses of homogenization with regard to labor services. On the one hand, there is the real simplification of labor processes, related to the concept of scientific management and the reorganization of industrial tasks through subdivision and, at least in part, automation. Conceptions of homogeneity in labor services along these lines emphasize the real interchangeable character of human labor, enabling a radical reduction in basic necessary skill levels to perform industrial tasks. Arguably, such a real simplification of labor services goes far beyond what Walrasian/Paretian theory has in mind. Rather, in my view, we are pursuing an abstract theoretic homogenization of labor services, through which even the most complicated tasks in a complex production process can be conceptually related to more basic tasks, perhaps, in certain circumstances, by reinterpreting a particular form of labor services as a composite of labor and (human) capital. In this manner, the boundaries between labor and capital may become blurred, but such ambiguities are likely inevitable when we attempt to make calculative generalizations concerning something as heterogeneous as the performance of labor.
If we pursue the abstract homogenization of labor services to its logical extreme, then we would reduce labor services to a single factor of production, contained within a vast array of production processes in varying proportions in combination with a single homogeneous substance called capital. Such a conception of labor services manifests itself within certain aggregate production functions, conceived on a macroeconomic level. Such theoretic devices, again, operate beyond the range of inquiry contained by this document - we are interested in developing an understanding of production functions and factors within the limited theoretic framework of the firm, abstracted, in part, from the dynamics of the wider general equilibrium economy within which it is contained. Briefly, however, labor at this extreme level of abstraction detaches from the particular technological contours of individual production functions/individual firms to represent an abstract substance commanding a rate of return related, somehow, to its marginal productivity across all production processes and all commodity markets. In short, it represents an attempt by Neoclassical macroeconomic theory to come to terms with the general rate of return to labor as a productive asset and, thus, to explicate short run or long run patterns of change and/or stagnation in real wages relative to technological factors across an entire macroeconomy. Without elaborating further, such theorizations expand the explanatory power of theoretic tools within the Neoclassical tradition far beyond their logical limits!
Returning to the bounded level of abstraction contained within this document, it is at least conceivable that we could homogenize labor services adequately to establish a particular relationship between a production process utilizing labor services in combination with particular forms of capital and the compensatory rate offered to labor for performance within the production process. Through the prism of Walrasian/Paretian theory, such a relationship would involve the equalization of the marginal revenue product of labor, derived from the individual firm's production function, with the market wage rate for labor services. The relationship is, in turn, grounded in the process of tâtonnement. That is to say, households on the commodity consumption side of the firm's production problem establish the prices that they are willing to pay for given quantities of the firm's output commodity, defined on the market level at which all firms are subject to rigorous price competition. On the factor supply side, households determine how much of each factor of production they are willing to supply to the firm for each rental/wage rate, again defined on the market level at which the firm must likewise accept the position of price taker in competition with many, many other firms.
Relative factor prices enable the firm to determine, through the objective technological contours of the production function, what combination of factors will achieve profit maximization/cost minimization. At a factor combination characterized by constant returns to scale/constant costs, the sole remaining question concerns how much of each factor will be rented by the firm to harmonize output market demand at operative costs per unit of output (where the marginal cost for the last unit of output must equal the average cost across all units of output) with factor market supply at operative compensation rates (where each factor will be compensated in accordance with its marginal productivity), consistent with the firm's financial constraint (i.e. its capacity to rent money capital at given rates of interest to compensate the factors). Again, the results of this balancing act is, in turn, technologically (pre-)determined for the firm by its production function. Under the constraints of perfect competition/perfect information, Walrasian/Paretian firms can only react to the market outcomes they face.
With this process in mind, is it really necessary to abstractly reduce labor services to a single factor of production if, on the one hand, technological subdivisions of the production process can be readily defined within the contours of the production function and, on the other hand, such subdivisions are mirrored by the presence of readily separable factor markets with divergent compensation rates? If we accepted a certain level of heterogeneity in the definition of production factors and in the equilibration of marginal revenue products with factor market compensation rates, then we might obtain a more accurate and nuanced portrait of the production process. This approach is implied in the suggestion by Gérard Debreu, one of the theoretic fathers of contemporary Neo-Walrasian general equilibrium theory, that we need to recognize a much
greater degree of heterogeneity between commodity markets based on divergent,
contingent conditions of exchange (see Debreu (1959), The Theory of Value: An
Axiomatic Analysis of General Equilibrium, 28-32. New Haven, CT: Yale University Press, at: http://digamo.free.fr/debreu59.pdf).
The point of Debreu's argument, in this respect, is that a range of heterogeneous conditions structure individual contexts within which commodities are exchanged and that this range of heterogeneities actually constitutes boundaries between commodity markets. As such, for every individual moment in which a fully integrated economic system arrives at a general equilibrium, the set of commodity markets that equilibrate is different from the set of commodity markets that equilibrates at some other moment. If a continuity exists in the realization of general equilibrium, such a continuity is expressly manifest in the process of tâtonnement without which we would lack any meaningful explanation for market clearing where the commodities offered in trade are, by contextual structuration, continuously changing. The timeless character of a general equilibrium economy would be taken to its extreme at which every continuity in objects of exchange would disappear except as an object of memory/simile in the minds of consumers.
Debreu's definitive conditioning of the meaning of commodities offers us a relevant means for sidestepping the problem of theoretic homogenization for labor services. If the labor services supplied by each individual can be readily distinguished from the labor services supplied by every other individual, or, conversely, if the labor services demanded by firms at each stage of a production process can be readily distinguished from those demanded at all other stages, then we would have to admit of a multiplicity of labor markets. Each labor market would, in turn, realize an equilibrium in which the marginal revenue productivity derived from each individual form of labor services would determine the compensatory rate for each respective form of labor services. That is to say, different markets might exist for the labor services offered by every individual and the marginal productivity of each would be calculated in reference to a set of temporal units of labor services offered by the individual where all other conditions for the utilization of labor services (e.g. quantities/qualities/varieties of capital employed) are held equal.
If Debreu's redefinition of the commodity offers us a way out of abstract homogenization, then we need to develop the implications of pursuing such an alternative. Notably, accepting Debreu's radical heterogeneity of labor services, we can no longer talk about the simple two-factor production function, characteristic of most Walrasian/Paretian theorizations of general equilibrium. Rather, every production function would have to embody multiple vectors of production factors in which each individual offering labor services would enter as a distinct factor to the production process, each with its own marginal productivity. Such radical heterogeneity may exceed the practical limits of our theory of the firm, but it remains as an asymptotic imagery of what Walrasian/Paretian economics might be able to pattern theoretically if it concedes that real firms must negotiate the real heterogeneities evident in the employment of diverse individual laborers, including divergent internalized skill sets and market conditions at the time of employment. Theoretically, all such conditions would have to be subsumed within either the technological contours of the production function or defined within the cost function by virtue of market processes/tâtonnement.
Developing the implications of radical heterogeneity further, two salient and linked concerns become evident. First, if every discrete manifestation of labor services constitutes its own market, then how can we evaluate the influence of competition between households/individuals in mitigating compensatory rates charged to firms? Second, if we expand a production function to include an indeterminately large vector of individual labor service factors, then how large would such a vector have to be and how would we deal with combinations in which certain factors remained unused? At the intersection of these two concerns exists the problem of substitutability as a practical matter for the firm in selecting between relatively homogeneous labor services.
The first of our concerns here can be reduced to the determination of market boundaries. Again, theoretically speaking, we can opt for Debreu's radical heterogeneity of commodities/factors, but accepting such radical heterogeneity would imply that every supplier enjoys a strict monopoly in the provision of their services. As such, in order to evaluate the effects of competition between suppliers of labor services, we would have to acknowledge that a broad range of substitutes exists for every particular manifestation of labor services demanded by a firm. Every discrete labor service factor, therefore, would have to exhibit some degree of substitutability in relation to every other factor, expressed as an elasticity, where unitary elasticity would reflect perfect substitutes. If the average elasticity of substitution between labor services suppliers approached unity across all suppliers accessible to a given firm for a given production process, we might conclude that the firm faced something approaching a single market for labor services, characterized by perfect competition (with perfectly homogeneous labor services). Considered in this manner, the question of boundaries between markets is intimately linked, for the firm, to the contours of its production function in relation to each individual labor services factor, and, again, as technological compatibilities reduce the necessary degree of heterogeneity between individual labor service factors, the boundaries constituted by discrete, individual skill sets erode and collapse, constituting singular labor markets for exchange of relatively homogeneous labor services. Recognizing the potential for near-perfect substitution of labor services between discrete individuals, in most cases, as an outcome of technological compatibility across a range of possible substitutes, the question of boundaries between markets for labor services reduces, in part, to a technological matter framed by the firm's production function.
If we concede the point that technologically-induced compatibilities in the substitution of labor services between individuals can break down individual differences between skill sets, then we must simultaneously concede that legitimate and insurmountable differences between individual skill sets are liable to remain, more prominently in certain production processes than in others, and, consequently, such differences must continue to structure labor market boundaries. In real economies, many of these market boundaries appear subsumed within the institutional boundaries of the firm as internal labor markets, As individuals employed within firms accumulate greater quantities of workplace-specific experience in the performance of a given occupation, their development of an occupationally-specific skill set differentiates them from potential new hires in ways that are apt to be reflected by the firm's production function through enhanced productivity at the temporal margin. Thus, at least asymptotically, more experienced individuals would command higher rates of compensation than new hires for reasons of skill-based differentials in marginal productivity. Such differences must appear, within structure of the firm's production function, as differences between two or more distinct forms of labor services, each with its own discrete market.
More generally, it would stand to reason that the set of individuals competing for positions in the labor market for home healthcare assistants would differ from the set competing for positions as paralegal aids for reasons not limited to the particular forms of training required to participate in these fields. If we can reasonably conclude that investment in particular training processes, as a form of human capital, differentiates individual labor market participants, then we should also conclude that the nature of labor services performed in particular fields differentiates participants prior to the accumulation of human capital. Individual physical attributes and motivational proclivities for particular forms of work can both determine the scale of particular, discrete labor markets, per se, and the extent to which individuals will invest in occupationally-specific forms of training as human capital, in the limit based on the expectations individuals have that they will enjoy a positive return in relation to other individuals by investing time to accumulate occupation-specific skills.
Finally, if we were to consider the scale of discrete labor markets faced by real firms for particular production processes, we have to evaluate the basic ontological dimensions of temporality and spatiality encountered as such firms undertook production decisions. Notably, what are the temporal conditions of the production process for which labor services are required? How long will employees engage in production before final commodities are generated for exchange? What subsequent conditions might govern the possibility for contractual renewal across multiple iterations of a particular production process? Such questions must condition the temporal length of any labor contract, however structured or implicit. Conversely, how geographically expansive will be the search for suppliers of particular labor services? Is there an expectation that suppliers with a particular skill and/or training/experience set can be found within areas proximate to the site of production or should firms engage in wider searches? All of these conditions must structure the scale and skill/qualitative dimensions of particular markets for labor services, in turn determining the degree to which labor services of a particular, detailed form can be considered homogeneous in relation to relatively close substitutes. As each market manifests a greater degree of homogeneity between individual suppliers, we would expect that competition between suppliers would propel real wage rates to approach some mutually acknowledged compensatory minimum, however defined, if only because the presence of readily available substitutes would tend to dampen the expectations individuals have for compensation.
From the perspective of the firm, framed by the technological contours of its production function, insurmountable differences between the labor services offered by particular individuals or sets of individuals would, again, have to be patterned as differences between discrete factors of production, contained by discrete markets for labor services and included as discrete mathematical arguments in the firm's production function. Differences between individual employees with substantial quantities of on-the-job experience and new hires would constitute the terms by which the firm would compare divergent factors of production to achieve profit maximization/cost minimization. As suggested, such differences might, invariably, be patterned as differential accumulations of human capital, and, as such, particular employment decisions by the firm might involve combinations of "pure" labor services and accumulated training/experience as human capital. In these terms, it is possible that a firm, undertaking a given production process, might enjoy multiple, discrete profit maximizing/cost minimizing factor combinations along a continuum defined by its production function. Moreover, it is possible that certain forms of labor services, defined within the firm's production function, might remain entirely unused within its selection of a profit maximizing/cost minimizing combination of production factors. Finally, respecting the possibility that production decisions by a range of firms within a given market context with multiple, technologically-driven profit maximizing/cost minimizing combinations might have some impact on demand for particular labor services, it is at least conceivable that demand side decisions by firms in discrete factor markets will shape the process of equilibrium price determination. We need to evaluate each of these conclusions.
To begin, the basic presence of heterogeneities between labor services implies that firms face a vector of alternative labor services factors, where each factor must vary slightly before we even begin to account for accumulations of human capital by individuals. Theoretically, considered across all production processes within an integrated general equilibrium economy, such vectors might be defined to include all labor services factors offered for rent within the economy (i.e. the labor services of all individuals within the employable labor force). In practical terms, such a situation is unrealistic - the employment decisions of firms, patterned as vectors of available labor services factors, are limited to those individuals who expressly offer their labor services or might otherwise be recruited by a firm because of their physical/mental attributes and/or their particular accumulations of generalized or occupationally-specific human capital. As such, the labor services vector faced by each firm is limited in its scale and scope by a range of possible considerations.
This limitation of the range of available labor services factors simplifies the employment decisions of the firm to at least some degree, but it can never reduce the problem to one of selecting the appropriate quantity of homogeneous labor services in relation to some quantity of homogeneous capital. In order to achieve profit maximization, the firm is still constrained to select between diverse combinations of relatively heterogeneous labor services and heterogeneous capital, including training/skill acquisition by potential employees as human capital. That is to say, a firm engaged in some production process, say dining services, must select between available labor services offered by some individuals with little experience and no training at relatively low compensation rates (reflecting diminished expectations on marginal productivity), other individuals with multiple years of experience preparing foods and accumulation of formal training at relatively high compensation rates, and individuals with various quantities of experience and training in between. If each of these possibilities corresponds with a different factor combination on the set defined by its production function, then the firm must decide which combination will maximize its profits (assuming, for our purposes, that such a decision takes the production function as an objective, determinate formula for the production of outputs, even if our previous critique of the production function casts doubt on the firm's ability to do so!).
With regard to the firm's labor services vector and its set of technologically available factor combinations from its production function, two general outcomes arise for profit maximization/cost minimization: an internal solution exists in which all labor services factors in its vector are utilized in positive quantities by the firm, and a corner solution in which some factors are used in positive quantities while others are wholly unused. The former case, which becomes less likely as the labor services vector expands and the elasticities of substitution between discrete labor-human capital combinations approach unity, might at least afford the possibility that marginal productivity calculations for each factor obtain strictly through differentiation of a production function rigorously corresponding to Walrasian/Paretian assumptions. Conversely, if the firm's production function incorporates a labor services vector in which certain factors are utilized in zero quantities, then it becomes impossible to gauge the marginal productivity of any other factor by means of differentiation. Rather, we would be compelled to maximize profits through linear optimization in which the factor compensation rates are determined through price imputation.
As suggested in the previous section on the production function, there is nothing innately wrong with imputed factor pricing so long as we recognize that, if we are operating within a general equilibrium framework, then both factor and output market prices are subject to simultaneous determination through tâtonnement. On the other hand, we should further concede that, even to the extent that we realize product exhaustion, price imputation divorces factor pricing from technological productivity, manifest strictly as a mathematical outcome of differentiation (i.e. obtaining a marginal product calculation by differentiating a production function characterized by continuous substitutability and constant returns to scale). As such, we cannot obtain the marriage of technological efficiency and ethical distributive justice implied in J.B. Clark's formalization of marginal productivity factor pricing theory. The latter simply cannot stand if we have to diverge from strict reliance on differentiation of simple production functions with homogeneous factors.
Concluding this section, I want to emphasize that the abstract theoretic homogenization of labor services, prescribed by Walrasian/Paretian production theory as a means to account for direct human labor within the firm's production function, is entirely possible and, perhaps, necessary if we want to achieve all of the useful insights of general equilibrium theory regarding the efficiency and distributive justice of integrated, unregulated market/cooperative economies relative to rent and utilization of production factors. This reduction of labor services to a homogeneous factor is not equivalent to the real simplification of labor processes in industrial production of goods and services, however the pervasive breakdown of differences between threshold occupational skill sets in different production processes may shape our capacity to envision labor services as a homogeneous factor. Moreover, the capacity to view labor services, as a basic factor, in combination with accumulated skills, experience, and training as human capital, further facilitates our ability to reduce labor to a homogeneous common denominator entering into to labor process.
Conversely, if we proceed in the opposite direction by recognizing radical heterogeneities in individual labor services, then we introduce a more nuanced, if not "realistic," imagery of employment decisions involved in profit maximization by the firm. Such employment decisions concern the selection between ranges of discrete labor/human capital combinations with (relatively) independently determined compensation rates and expectations on productivity at the temporal margin (i.e. as we increase the number of labor hours utilized from a given, relatively heterogeneous factor, holding all other variable factors constant). On the other hand, the incorporation of heterogeneity between labor services available to the firm complicates the mathematical process of profit maximization and, at least to some extent, undermines the ethical distributive claims associated with marginal productivity factor pricing.
In the end, I want to emphasize that the importance in choosing between strict, abstract homogenization of production factors and the introduction of radical heterogeneity between discrete factors pertains to the overall discursive/argumentative/rhetorical aims of the theory. We invariably return to the question of what the theory means to tell us about the reality that it is theorizing. In these terms, incorporation of relative heterogeneity may simply constitute a means through which Walrasian/Paretian general equilibrium theorizations can connect a little more persuasively with the radical heterogeneities of real economies.
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