The Ambiguity of Capital: A Brief Introduction to an Insoluble Theoretic Problem
If heterogeneities between diverse manifestations of labor services, even in a single production process, complicate the notion of homogenizing labor in ways that might make it amenable to marginal productivity calculations as we add successive quantities of labor to a production process, then the idea of homogenizing capital to calculate its marginal productivity is complicated by the absence of any clear conception of what capital is, per se. In the same way that labor has held a ubiquitous place in the history of economic theory as divergent theoretic traditions have attributed a different significance to direct productive human activity, multifarious opposing conceptions of the meaning and significance of capital reside across opposing traditions.
For the Classicals, including Marx, capital had been synonymous with the ownership of particular assets that conferred on capital the capacity to organize the employment and utilization of labor in the production of goods and services. In these terms, the capacity of capital to command a rate of return beyond the cost of its own reproduction (i.e. surplus, in a Marxian sense) defines the class structure called capitalism. By contrast, for the Neoclassicals, again, capital represents a purely technical argument in a theory stressing productive efficiency across ranges of substitutable factor combinations. While it, thus, makes sense to discuss capital as a household asset capable of being rented out to firms as a factor of production, the notion of representing the collective body of households owning capital as a class with collective interests and a collective political disposition and power extends beyond the theoretic frontier of the Neoclassical tradition. To the extent that we can discuss capitalism within Neoclassical theory, the term amorphously encapsulates free market exchange, individual consumer choice, and the freedom of entrepreneurs to engage in innately uncertain investments without any discernible connection between such a system and theories of production and exchange except as an implicit background for the latter. As we shall see, moreover, such a background is not even entirely evident for Walrasian/Paretian theory, insofar as general equilibrium theorizations operate with an implicitly decentralized, cooperative, non-entrepreneurial, quasi-non-market structure.
If Neoclassical theory, in general, operates with an unclear conception of capitalism, then it confounds the problem by having unclear conceptions of capital, as a factor of production, in the heart of its theorizations of technological efficiency in production. Such a problem is succinctly evident for Walrasian/Paretian theory, which embarked on several years of theoretic conflict against a collection of left-leaning Marshallian/Keynesian and Neo-Ricardian/Marxian theorists over the meaning of capital and the significance of compensation rates for the owners of capital (i.e. the so-called “Cambridge controversy” of the 1950s and 60s). To the extent that these debates ended with no conclusive consensus in academic economics over its subject, it would, at least, be worthwhile to posit, as a point of criticism, that the theoretical ground on which Walrasian/Paretian general equilibrium economics is situated remains perilously unstable! In this respect, we might benefit from a brief diversion from Walrasian/Paretian approaches to capital in order to develop an understanding of alternative approaches within the Neoclassical tradition. Most emphatically, Austrian theory can be credited with the development of the most theoretically rigorous conception of capital in Neoclassical economics.
As a discursive introduction, let us say that we are operating in a rudimentary economy in which individuals undertake the production of goods and services independently. In order to produce the goods and services that they want to consume or to exchange with others, each individual has full access to a primordial common allotment of natural resources that can, for our purposes, be assumed infinitely expansive relative to the capacity of individuals to withdraw its materials. No tools or machinery exists to assist in production, but, importantly, the knowledge necessary to build such machinery is universally available. However, if an individual chooses to produce a tool or machine to aid in production, the tool will be completely consumed in a single production process. Therefore, in deciding what to produce, each individual is faced with a set of productive technological choices. Should they utilize a technology maximizing direct human labor to achieve the desired output or should they take time out to build some tools that might allow them to produce more of the good or service they desire?
Critically, the issue for Austrian production theory is about time. It takes time to produce output enhancing tools and machinery that might otherwise be spent producing the thing that you want to consume with universally available, minimalistic technologies that will generate minimal outputs. Individuals who choose to produce goods and services utilizing more “roundabout” techniques will enjoy larger quantities of such outputs and will, thus, create more wealth in objects of consumption. For Austrian theory, capital is constituted in the utilization of production techniques that are more roundabout, and, thus, capitalism, as a system of technologically-driven production, consists of a pervasive drive to make production more roundabout. As such, Austrian theory attributes the greater wealth of capitalist economies to the willingness of individual entrepreneurs, engaged in production, to defer their desire to consume in order to take the time necessary to develop the technologies that will expand the quantity of outputs available under more rudimentary, minimalistic technologies.
If we take this theoretic definition of capital a step forward toward the problem of compensation, the relationship between time and output quantities remains key. Roundaboutness in production always involves a deferral of desired consumption possibilities. This deferral constitutes a real material cost, measurable through time. In order to induce an individual to engage in the production of tools/machinery that will expand output beyond output levels that he would be able to consume with existing technologies right now, he must receive a quantity of outputs at some indeterminate time in the future that will compensate him for the inconvenience of having to defer consumption. This conception of a future reward on deferred contemporaneous consumption defines the Austrian conception of the rate of interest on capital investments, where the compensatory payment for capital is defined as a rate of interest. In accordance with the broader understanding of capital investment in Austrian theory, the reward for deferring consumption must increase as a function of time. On the other hand, if we assume that individual utility functions discount future consumption possibilities relative to contemporaneous consumption (i.e. individuals would rather eat their cake today than eat the same cake tomorrow), then, as production processes become more and more roundabout, the interest rate would have to increase to account for the fact that more prolonged deferrals of consumption command a steadily declining level of marginal utility for individual entrepreneurs/investors as a function of time.
The thing that unifies capital as a concept and renders it susceptible to homogenization in the interest of analyzing its marginal productivity is its temporal relationship to production under abstractly rudimentary technological conditions. In the same sense that the time taken to produce a fishing pole represents a capital investment in relation to the practice of catching fish with ones bare hands, the time taken to learn accepted teaching practices for younger/primary aged students in particular subjects represents a capital investment relative to the practice of amateur home-schooling by untrained parents. The return to each of these capital investments, conceived as a rate of interest, compensates different manifestations of the same species of production factor (i.e. mechanical capital v. human capital). Acknowledging the genealogical commonality of these two investments as capital, each presents us with a problem in anthropological economics - can we universally conceive of an abstractly rudimentary labor process converted by a capital investment to a state of greater roundaboutness enabling the enhanced productivity of labor?
The fishing example might work exceptionally well in demonstrating an Austrian conception of capital and, in particular, for measuring the comparative productivity enhancement from increased roundaboutness. Maybe we can say the same thing about the training of primary school teachers in relation to home schooling, if only by means of a qualitative comparison on the range of knowledge and relative pedagogical efficiency of trained educators. On the other hand, how do we make meaningful comparisons between the industrial production of structural steel in basic oxygen furnaces relative to some rudimentary practice of steel production (e.g. puddling of wrought iron in a primitive clay furnace)? In regard to human capital investments, can we really make a serious comparison between the legal training of jurists under the bar or the medical training of brain surgeons relative to some imaginary rudimentary juridical practices or brain surgery by amateurs?! At some point, in a wide range of production processes for goods and services, we have to concede that we lack a convincing rudimentary baseline against which to evaluate the gains from increasing roundaboutness because the most rudimentary practices in question happen to be extremely capital intensive. In this regard, we need to amend our initial definition of capital to recognize that capital represents a continuum within which we can identify successive degrees of roundaboutness and, further, comprehend production processes that demand significant levels of roundaboutness to enable production to take place at all. In fact, to the extent that we approach our image of firms in a general equilibrium economy from a standpoint in which all profit maximizing factor combinations are points of tangency between an isoquant and isocost function with positive quantities of both labor and capital, we have to conclude that some level of roundaboutness in production is implicit within our basic understanding of a Walrasian/Paretian firm.
Proceeding henceforth from a basic Austrian definition of capital as temporal roundaboutness in production, on the further conclusion that all roundaboutness is relative (and need not reflect a connection to some primordial rudimentary labor-intensive process), we need to further inquire into the determination of compensatory rates for capital. Acknowledging that such compensation rates, especially for human capital, may embody a degree of ambiguity, enforced by intense degrees of complementarity between divergent production factors (e.g. basic homogenized labor services and human capital, manifest as occupation-specific training), the resulting compensation rate received by a given household supplying capital to the firm may exist as composite of multiple interest rates (for diverse. heterogeneous manifestations of capital) and wage rates (for labor services distinct from the accumulation of human capital by individuals). As with labor services, the homogenization of capital is complicated by innate heterogeneities. In fact, the more that labor services are simplified through reorganization and automation of labor processes, the more we will have to contend with heterogeneous composites of labor services and capital, insofar as reductions of basic skill levels in labor processes effectively demand inputs of technical learning on the structuration of production processes manifest as human capital. All of this leads us to the basic conclusion that capital is heterogeneous and commands divergent rates of interest as compensation, dependent upon the relationship of particular forms of capital to particular production processes.
If capital, thus, exists as a heterogeneous set of factors, incorporating divergent temporal displacements in the production of goods and services collectively resulting in some degree of roundaboutness, then, as with labor services, the firm encounters a vector of capital factors, each manifesting a certain, defined elasticity of substitution with other all other factors varying between 1 (perfect substitutability) and -1 (perfect complementarity). In this regard, the same comments and criticisms applied to the problem of heterogeneity in labor services also applies to heterogeneity in capital. Our simplistic, two-factor production model has to give way to a production model with multiple vectors in which certain labor services are intimately tied to particular forms of capital, especially human capital, and, given a particular vector of compensatory rates for diverse forms of labor services and capital, firms may achieve profit maximization with factor combinations that leave certain types of labor services and capital wholly unused. And, again, such outcomes may result in product exhaustion without offering a continuously differentiable production function through which we would want to calculate the marginal productivities of each form of capital. As such, compensatory rates for capital would certainly be determined by imputation from output market pricing, conventional to Austrian theory (which, in any case, rejects the whole project of mathematically deriving marginal productivities as a basis for factor compensation).
In certain respects, Walrasian/Paretian theory has taken the lead of Austrian theory in interpreting capital as deferred consumption, commanding a rate of interest through future expanded consumption possibilities. As such, we may view Austrian theory as the implicit backstory/prequel underlying the Walrasian/Paretian tale of an integrated general equilibrium economy governed by tâtonnement. On the other hand, significant inconsistencies arise when we introduce this conception of capital into our theory of the firm. Most notably, introducing capital, in an Austrian sense, as a factor of production defined by a temporal relationship between entrepreneurs and particular processes of production, becomes innately problematic in a body of theory noteworthy for its timeless character. The Walrasian/Paretian theory of the firm presented in this document requires that firms be continuously and instantaneously capable of adjusting scales of production to account for changes in output demand. Again, such a requirement demands that capital be readily available in place if firms need to readjust to larger scales of output - there is no time in a pure general equilibrium economy to invest in producing the capital needed to expand scales of output if it is not already available to firms that need to expand. Implicitly, for the Austrian theory of capital to be consonant with Walrasian/Paretian general equilibrium theory, (entrepreneurial) households have to incidentally invest in capital assets, necessary to expand output levels, without any certainty that the capital assets being produced will ever actually be rented by firms at a positive rate of return/interest. As argued earlier, such uncertainties may not be a problem for either Austrian or Marshallian (and Keynesian) theories of capital investment, where future outcomes in market economies exhibit inexplicable elements of risk, but they have no place in a Walrasian general equilibrium system.
Approaching the incongruities between Austrian and Walrasian/Paretian conceptions of capital from a slightly different focus, the idea of roundaboutness, critical to Austrian theories of capital and interest, reflects differences between relatively labor intensive technologies and relatively capital intensive ones, where the theory manifests an implicit productivity bias for the latter by definition. That is to say, as implied by Austrian theory, entrepreneurs should only invest in more roundabout production technologies if they are expected to yield positive returns, evident as increased outputs for the same expenditure of labor. It is possible that this deduction overstates the Austrian emphasis on roundaboutness relative to profit maximization to some degree, however. I have no doubt that an Austrian theorist would concede that an entrepreneur seeking to maximize profits in an economy with relatively abundant supplies of unemployed laborers and a consequentluy depressed compensation rate for labor services should select a relatively labor intensive technology. The point for Austrian theory, in this sense, is not that a theoretic preference for roundaboutness as a formula for increasing the material wealth of an economy should override the contextual advantages of utilizing relatively abundant factor resources.
At this point, I want to once again address the particular balancing act implied by the accumulation and investment of capital. In neither a Walrasian/Paretian nor an Austrian sense is capital equivalent to savings/retained incomes or wealth. The difference between savings and capital resides in the active character of the latter - capital is actively invested in production to explicitly expand output by means of roundaboutness. Savings is simply a stock of retained income or wealth, manifest in diverse material forms that lies fallow, awaiting consumption or investment. In a fully integrated general equilibrium economy, utility maximizing households will only retain income that could otherwise be consumed to enhance contemporaneous utility if and only if there is some future reward that will justify deferring their consumption. The problem is complicated further by the notion that households have a time preference/temporal dimension to their utility functions through which they discount future consumption possibilities. In this manner, all household savings must be invested as capital - Keynesian considerations on liquidity preferences in the maintenance of positive, non-interest earning cash balances by households have no place in Walrasian/Paretian or Austrian understandings on the relationship between savings and investment.
On the other hand, the possibility of a future return on retained incomes demands knowledge on the technical possibilities of future enhanced material returns. In order to fully act rationally, households must have knowledge of a set of technological and/or market conditions that do not presently exist in order to be satisfied that deferred consumption today will result in more consumption or more satisfying consumption tomorrow or next month or five years hence. Such information cannot possibly exist. To borrow a page from post-Keynesian macroeconomic theory, the future outcomes of capital investments are characterized by fundamental uncertainty. Considered in this manner, every retention of incomes by households in forms that might subsequently be employed as capital reflects a subjectively formed belief, on the part of the household, that by deferring consumption today, they will earned more or better consumption tomorrow. Capital formation always demands a digression from strictly rational behavior through which saving households come to believe in the possibility that they will be better off not consuming all of their incomes in the present.
Transplanting this imagery of imperfectly rational households into our portrait of the firm in a general equilibrium economy, our linking of savings to capital investment remains the (entrepreneurial) backstory to the static, technologically-determined profit maximizing behavior of the firm (absent an entrepreneur). The peculiarity of the story resides, however, in the fact that it has to be told across multiple periods of time as if everything was occurring simultaneously. The accumulation of capital must begin at some moment in the past at which its future rate of return was merely an expectation in the minds of the households that deferred consumption in order to accumulate it. The present equilibration of marginal productivity from utilization of a given quantity of a particular capital asset (within a vector of capital assets) to a particular rate of interest must imply that the past expectations for augmented future incomes of saving households were either satisfied or those expectations were updated to reflect unexpected changes in economic conditions. In either case, the entire act through which savings was converted into usable capital and usable capital was injected into a production process reflects a slew of uncertainties and expectations that cannot be redeemed by any recourse to the strictly rational behavior of the household agents.
Finally, I need to reiterate the point that the Austrian backstory to Walrasian/Paretian general equilibrium is unabashedly entrepreneurial in nature, while entrepreneurship is thoroughly vacated from the Walrasian/Paretian firm, which remains a simplistic, technologically determined profit maximizer. The palpable lack of an entrepreneur in Walrasian/Paretian theory is, in many ways, the most important point of contrast with Austrian theory and the principle reason why it would be disingenuous to argue, without addenda, that the theory of the firm presented here is a self-consciously Austrian theory rather than a theory that seeks to borrow judiciously from certain Austrian themes and influences. To the extent that Austrian theory readily engages in a conception of free market activity, capital formation, and investment in productive roundaboutness in a world of acknowledged uncertainties, entrepreneurial risk, and, to utilize the terminology of Austrian theorist Joseph Schumpeter, creative destruction, a thoroughly Austrian economy might actually be described as capitalist, by the terms with which it labels capitalism. By contrast, the mechanistic character of firms and implicitly cooperative nature of tâtonnement between utility maximizing household agents renders any attribution of the term capitalism to a general equilibrium vision of market economics inherently murky and ambiguous.
Having concluded that the Walrasian/Paretian conception of capital is, at best, a caricature of Austrian theory, I want to further elaborate two additional points on compensation to the owners of capital. First, we have argued so far that firms seek to maximize their profits by renting production factors up to the point at which the marginal revenue product derived from renting the last unit of each production factor equals the factor market price for this last unit, under circumstances where, due to competition, the firm accepts both output and factor market prices as given. This result is given in our consideration of the product exhaustion theorem, and it applies not only to our two-factor case but also to cases in which the firm is utilizing n >2 distinct factors of production. As such, any multiplication of production factors to account for greater heterogeneities must still require the firm to equalize its marginal revenue products to the factor market price for each factor of production in its labor and capital vectors. Alternatively, if we cannot strictly derive marginal revenue products through differentiation of the production function, then the output price-imputed value derived from the last unit of each factor rented must similarly be equated to the factor market price for this unit. If this must be the case and we can otherwise clearly determine how much output the firm receives from the last unit of each capital factor it rents, then what is the conceptual significance of the factor market compensation rate that it evaluates in order to realize profit maximization? That is to say, how does this factor market price relate to our quasi-Austrian theory of capital, where the compensation rate for capital is a rate of interest for deferred consumption?
In answering this question, we are interested in numerous details about the particular factor under consideration. What is its durability (i.e. can the unit be injected in multiple iterations of the production process or is it completely consumed in one iteration)? Can it be readily reproduced beyond the exhaustion of its productive life? Is the factor usable in a wide range of production processes or is it restricted to an extremely finite range of processes? How many units of the factor are available to firms (i.e. is the supply available to firms restricted in some way that will tend to enhance the market power of household agents in possession of the factor)? Beyond these concerns, we are, again, evidently concerned with the expectations that households have regarding compensation? What rate of interest would be sufficient to compensate the household for investing in the production of capital?
I want to give a more detailed explanation on these questions when I explicitly elaborate on household agents in a Walrasian/Paretian general equilibrium economy, but, for now, the simple answer that I want to advance is that the compensatory rate that households must demand from firms will reflect their expectations with respect to both the total quantity of compensation they expect to receive for their capital investment and their expectations regarding how long their capital asset will be usable and, hence, productive for renting firms. In this sense, households in possession of capital assets approach firms in factor market contexts with subjectively formed expectations regarding how much they should be willing to receive for their asset today if their asset will be available at the same factor market price for t expected periods into the future, sufficient to realize the equality:
tΣi=1(pkiki) = I(1+r)^t
where pki = Market price of a capital asset k at time i
ki = Quantity of capital asset k rented at time i
I = Total investment in production of capital asset k
r = Rate of interest expected by household from investment in k
t = Total periods in expected rental life of k
Without giving too much away from subsequent critiques of household utility maximization, no objectively verifiable means exists to enable household agents to determine whether they will be capable of securing a sufficient return over t periods to realize the total future expected value of a capital investment over t periods. Moreover, borrowing again from the Austrian theoretic account from which the Walrasian/Paretian conception of capital owes its inspiration, there is no way to determine a priori the number of iterations t through which a capital asset will continue to earn interest for its owner. The determination of this number is an outcome of the diversity of production processes and firms to which the capital asset may be rented, the degree to which the productivity of the capital asset depreciates over time and the extent to which the owner is faced with competition from investors in newer, more productive substitute capital assets, and the extent to which technologies change, rendering this particular capital assets obsolescent. Here, again, we encounter the Austrian theme of creative destruction, manifest in the prolonged or swift reduction in the relative productivity of a capital asset in relation to newer technologies. All such considerations must, in some way, reconfigure the production functions of firms and, as such, reshape the context within which Walrasian/Paretian firms achieve profit maximization.
Lastly, a critical point of departure in terminology between the Classical and Neoclassical traditions regarding capital remains to be discussed. Namely, theorists in the Classical tradition, at least, to some degree, until the development of Marxian theory, regard the rate of return to capital as a rate of profit. The reasons why such a return might accrue for the owners of capital are entirely unclear before Marx. Notably, for Ricardo, profit appears, for lack of a specific explanation, as a natural rate of return for investment of capital, distinguished from land and labor. As such, Ricardo's most detailed attempt at an explanation for the origins of profits on capital concern agricultural investments tied to naturally occurring variations of the productivity of land. For Marx, profit is expressly attributable to the exploitation of labor power/capital capable of varying its rate of value productivity in relation to its socially determined reproductive expenses. Thus, in order for profit to exist, direct human labor must generate a surplus value in excess of the expenses accrued by firms to hire/rent labor power.
In the Neoclassical tradition, the definition of compensatory payments to the household owners of capital changes starkly, in ways that hold significant ethical consequences. As shown, the Austrians regard the rate of return to capital as interest, accruing both as a function of deferred consumption and enhanced roundaboutness of the production process. In this manner, the ethical consequences of capital accumulation are transformed to accommodate both the frugality of investors (in relation to prodigal segments of the population in an economy for whom poverty and an absence of discretionary income to employ as savings is a character flaw!) and the technological savvy of entrepreneurs. The conceptual significance and ethical consequences of profit, by contrast, relate emphatically to variations in market conditions, generating static divergences in the prices that firms may receive for their goods and services. Such an explanation of profit readily applies to Austrian theory and, as we shall see, to the Marshallian conception of the firm, where short term variations on market conditions and the capacity to vary certain factors while others remain fixed are pertinent. To the extent that these approaches are mutually sensitive to the effects of short term variations in market conditions on the revenues realized by firms, the conception of firms as profit maximizing entities exudes something more than a bland, mathematically-determinate significance. Moreover, in reducing profit to a short run market phenomenon (in contrast to long run returns to scarce or otherwise restricted resources defined as rent), profits lose a substantial degree of ethical significance. Can entrepreneurs really be blamed today for profiting from short term appreciations in market demand for goods and services that might be competed away tomorrow?
To the extent that Walrasian/Paretian general equilibrium theory avoids the developmental consequences of capital accumulation by taking the quantities of capital available to firms in a given temporal context as given, we can entirely avoid the ethical consequences of our respective terminologies for the compensatory returns of capital. Rather, insofar as Walrasian/Paretian firms operate in a timeless/spaceless environment where any short term variation in demand for goods and services will instantaneously be resolved to realize a continuous zero-profit condition across all markets, the theory of the firm presented in this document dispenses with the possibility of profit entirely. Thus, we are left with our Austrian inspired conception of interest as the default alternative in assessing the virtues of supplying capital to production.
To conclude this section, the conception of capital contained within our Walrasian/Paretian theory of the firm remains, in certain respects, unclear. As with labor, we have to acknowledge a substantial degree of heterogeneity in capital, susceptible to patterning through vectors of discrete capital factors incorporating tools, equipment, and machinery but also human capital, manifest as experiential or education/training-driven knowledge. The common thread connecting these factors remains the capacity of each to enhance the productivity of a given production process by making the process more temporally roundabout. On the other hand, capital introduces complementarities and complications that we will continue to sort out across subsequent theoretic approaches to the firm.
No comments:
Post a Comment