Proceeding beyond the limited abstract terms by which we have heretofore leveled a critique of Walrasian/Paretian conceptions of the firm in a general equilibrium economy, we need to approach a critical ontological problem concerning the dimensionality of economic processes. Is it fair to characterize a general equilibrium economy as either timeless or spaceless?
In order to answer this question, we need to, first, clarify exactly what we have advanced as a portrait of general equilibrium. However we specify the particular mechanisms of price adjustment in a general equilibrium economy, we have assumed that the conditions exist to ensure that such an economy exists in permanent and continuous equilibrium. That is to say, any changes in factor supplies, production technologies, household preferences, etc. must induce an instantaneous and smooth readjustment of relative prices. The instantaneous character of the process of tâtonnement (i.e. bargaining between households over prices across all markets) implies that the process is, itself, continuous. Households never emerge from price negotiations with other households. Tâtonnement goes on and on and on forever. In this sense, the identification of any particular, momentary equilibrium outcome constitutes a singular static outcome in the never ending adjustment and readjustment of prices to guarantee that all markets clear at every moment in time. Therefore, we do not need to inquire into the temporal structure of market price determination. Every moment in time is an instance of tâtonnement.
At the outset, I want to acknowledge that the theory mirrors real economic processes here in certain ways. If we acknowledge that real households engage in recurring and temporally overlapping evaluations of final commodity and factor prices in relation to their own preferences and that these evaluations collectively determine market pricing outcomes (i.e. forcing firms to periodically readjust prices in relation to shifts in final consumer demand or factor supply), then we would have to conclude that, in the aggregate, new offers and counter-offers in commodity and factor pricing are repetitively being issued across all markets in ways that suggest that a continuous, non-stop auction metaphor might not be far from the truth. In this sense, general equilibrium theory merely simplifies the overarching complexities of discontinuous readjustment processes between subsets of households and firms by positing that the entire process can be treated as if the readjustment process was actually continuous for the entire integrated system. Again, as I suggested in the previous section of this critique, such a result can be entirely unsatisfying to economists proceeding from a decidely more empiricist/positivist epistemological standpoint, for whom the analysis of real decisions by households must take temporal variations (e.g. seasonal shifts in demand for certain goods and services, long term factor supply contracting, etc.) into account.
The particular focus of this larger document on firms and the economics of production raises more pointed concerns with regard to time, introducing problems that extend beyond the continuous nature of tâtonnement to muddy the larger connection of Walrasian/Paretian commodity producing entities to firms in real economies. As argued, Walrasian/Paretian firms exist as contingent assemblages of production factors in which individual households continue to supply their production factors only to the extent that doing so achieves utility maximizing outcomes. Unlike real firms, Walrasian/Paretian firms lack tangible property in infrastructure and fixed capital. If, in these terms, we can asssume that infrastructure (e.g. roads, rail networks, buildings/facilities) and fixed capital (durable machinery) exist, then we must simultaneously divorce the ownership of such physical components from the purely contingent and transitory existence of firms. We would, thus, need to envision of world of fixed capital and infrastructure in place, where firms rent fixed capital, rent labor, purchase circulating raw materials, and rent the money capital to pay for all of the other factors, subject to reimbursement in accordance with the marginal revenue products for each of the production factors (i.e. conforming to product exhaustion). This imagery effectively separates the notion of capital accumulation from the existence of firms - firms do not accumulate capital, households do by virtue of their deferred consumption of income.
Proceeding from this imagery of spatially displaced/free-floating firms (an imagery of which I will subsequently pursue a spatially-oriented criticism!), we have a theoretic basis against which to approach the temporal framework of production. Insofar as firms do not accumulate capital but only rent capital from households, there is no basis for considering temporal frameworks within which firms shift between diverse scales of production by accumulating new capital. Firms do not need time to invest in new fixed capital or build new plant/infrastructure because firms do not undertake such investments. If accumulated masses of fixed capital exist to be rented from households by firms and rates of interest are adequate to reimburse households for use of their fixed capital by firms, then firms can always achieve given scales of output, supported by household demand for final commodities, at any given moment in time. If an existing production facility or quantity of fixed capital (machinery) is inadequate to produce quantities of output desired by consumers, then a firm can always move to larger production facilities or rent new fixed capital to produce desired output quantities, increasing the total expenditure on factors of production but simultaneously increasing total revenues by an equivalent quantity.
Rounding out the implications arising from our assumptions about firms in general equilibrium economies, if firms are continuously dealing with homothetic production functions, with constant returns to scale and constant average total costs per unit of output, then any change in scale should be effected smoothly, with compositions of labor and capital corresponding with profit maximizing marginal rates of technical substitution. In this manner, firms never have to depart from their expansion paths as they either increase or decrease their scales of production. Appropriate infrastructures and quantities of fixed capital must always exist in place for firms to rent in order to produce quantities of output that maximize profits/minimize costs. This continuous availability of infrastructures and fixed capital for firms enables us to argue that there is no differentiation between a short run and a long run in the Walrasian/Paretian theory of the firm. By contrast, we will find that such a differentiation exists for firms within Marshallian theory simply because Marshallian firms have to invest in fixed capital and infrastructures to alter their scales of operation, and such investments are costly in terms of time - new manufacturing plants or other facilities cannot be built overnight!
Thus, our assumptions regarding the transitory existence of firms and the homotheticity of production functions lead us to a world in which households continuously invest in new fixed capital and new infrastructures, available for rent by firms in accordance with their respective scalar requirements for fixed capital and infrastructure. Such investment processes (suitably adjusted to account for depreciation and technological obsolescence) can be patterned through a variety of different economic growth models (e.g. the Solow model), conforming to all of our assumptions about general equilibrium economies. Growth models of this kind perform the function of a dynamical bridge from the static mechanism of tâtonnement to the multi-scalar shifting of macroeconomic production possibilities and sectoral responses to changing household preferences over time. And this temporal consideration is critical. General equilibrium economies change because households invest savings into new capital and new infrastructure. In the absence of such investments (and in the absence of either capital depreciation, technological change, or changes in household preferences) a general equilibrium economy would operate as an infinitely reproducing, never ending repetition of identical market outcomes.
At this point, I want to reassert that, approaching from a strictly rationalist standpoint, general equilibrium theorizations are not identical to the real economies that they attempt to mirror through theory. Rather, they simply posit abstract models in an attempt to generate predictions on the workings of market systems as if the system functioned in accordance with their abstract models. In these terms, there is absolute nothing wrong with the timeless character of static equilibria in a general equilibrium system as long as models of this kind continue to produce relevant insights into the functioning of real market systems, and I am not going to contest that, in certain respects, they do. On the other hand, we have to confront the peculiar ontological characteristics of the market systems theorized by Walrasian/Paretian economics.
Through macroeconomic growth theory, the logic of capital accumulation attains a sort of abstract existence separated from particular production processes or aggregate demand for outputs of final commodities, per se. In some respect, household investment in capital must be wholly speculative. On the other hand, within a general equilibrium system, such speculation has to be supported by demands for new capital and infrastructure by firms. Any income saved must be capital invested to produce larger quantities goods and services that will be instantaneously demanded by households as increased consumption possibilities. Alternately, if we assume some level of depreciation, there must be some basic level of investment in new capital and infrastructure to replace depreciating implements in order to preserve a constant level of consumption possibilities over time. But here we run into the problem that investment in capital and infrastructure take time to come on line as productive assets.
As such, our Walrasian/Paretian theory of economic growth (introduced to harmonize our assumptions on changes in scale by firms with the static/timeless nature of tâtonnement) runs squarely into a quintessentially Keynesian concern: expectations about the future under conditions of uncertainty. Why would utility maximizing households undertake investments in fixed capital and infrastructure if these investments enjoyed an inherently uncertain rate of return? This question transcends the unique boundaries of Walrasian/Paretian general equilibrium theorization to become a universal concern in economic discourse. Moreover, theorization of subjective probability distributions on future income possibilities from investments notwithstanding, there is no meaningful way to answer this question.
To summarize where we have ventured to this point in considering the role of time/timelessness in Walrasian/Paretian general equilibrium theorizations, we have argued that the process of tâtonnement is continuous and, thus, timeless/static. At any moment in time, a general equilibrium system must generate a vector of relative prices that will bring all markets within the system into equilibrium. If such a system is not, however, to be a truly stationary system (i.e. a permanently unchanging economy), then there must be some mechanisms by which changes in household preferences for final commodities and/or changes in production technologies can circulate throughout the system. Insofar as our theory of the firm precludes the possibility that firms occupy a role as anything other than a means for efficient production of commodities, households must be the agents enacting such shifts in production, including overall increases in consumption possibilities over time. Thus, the role of households in achieving smooth transitions in production over time leads us to the problem of capital accumulation and speculative investment with uncertain future returns. It almost certainly, likewise, necessitates that speculative investments in capital and infrastructures by households may result in the accumulation of fixed capital and infrastructures that, at the time of their completion, remain totally idle, awaiting conditions in which they can be inserted into production processes at rates of return satisfactory to their household owners (rates that may never arise!). That is to say, the household owners of physical capital invest to accumulate capital for the sake of accumulation, without any guarantee that their investment will yield a return, in order to ensure that the larger system will have adequate reserves of capital to smoothly transition to higher quantities of output or to maintain existing levels of output under depreciation. For a theory that assumes that households are pure, self-centered utility maximizing agents, the idea that households should invest speculatively to secure the needs of the larger system seems just a little quixotic! I will revisit this idea in this critique when I directly confront capital as a factor of production.
The second dimension of interest in this section is space/spatiality. Like time, spatiality implicates itself in every facet of commodity production and market exchange. If commodity production has a time and, hence, a temporal relationship (e.g. a unique and unalterable sequencing) to processes of exchange and household consumption, it must simultaneously have a place and a spatial relationship (e.g. colocation) to exchange and consumption. As I have argued in this section, the notion that firms should be able to continuously readjust their scales of production in response to changes in demand requires that reserves of fixed capital and infrastructure be readily available in place. This necessarily implies the existence of spatial distribution/dispersion of fixed capital and infrastructure, defining a spatial relationship between the various assets utilized by a firm at a given moment in time (i.e. the spatiality of firms renting multiple production facilities at different locations). Moreover, contemporary innovations in online marketing notwithstanding, exchange processes must have both temporal and spatial dimensions that can be identified and related temporally and spatially to other processes. If I purchase a textbook online with my laptop in a coffee shop in Massachusetts from a textbook supplier in Oregon and receive the textbook through the U.S. Postal Service four days later, then we have a more complicated temporal and spatial distribution to the process than would have obtained had I purchased the same textbook from a bookstore down the street. However, as a matter of ontological necessity, space and time are universally implicated in all economic processes, no less in this case than in any other.
We know from our analysis above that Walrasian/Paretian general equilibrium theory deals with time by denying its influence on theoretic structures. Rather, the theory imposes on market exchange and commodity production a peculiar timelessness, manifest in the capacity of firms to perfectly adjust to changes in commodity demand, factor supply, or technology instantaneously. This imposition has particular consequences, most emphatically evident in the necessity that households engage in continuous speculative investments in fixed capital and infrastructure at uncertain future rates of return. I will argue now that Walrasian/Paretian theory does not deny (or contort) spatiality as much as it ignores spatiality as a problem outright. At no point in our analysis of the firm, for example, did I elaborate on the problem of transportation costs under circumstances where sites of commodity production are physically/geographically distinct from points of exchange and/or consumption. Such considerations might serve to illuminate important decisions made in the operation of real firms. On the other hand, I will argue that any considerations on the location of production facilities and/or transportation costs holds the potential to undermine key assumptions on competition in the functioning of a general equilibrium economy.
Specifically, the relative proximity of competing firms to sites of market exchange must necessarily impose differential transportation costs, generating centripetal pressures in the location of production facilities relative to key markets. Such a conclusion assumes, importantly, that market exchange articulates a particular, centralized geography. It, further, assumes that the average total cost of transportation services consumed by firms remains constant per unit distance as the distance traveled by commodities from production facilities to sites of market exchange increases. If these conditions hold, then, given the absolute finitude of land-space, firms must compete for spaces closer to relevant market sites. In turn, firms closer to markets must enjoy lower average total costs, taking transportation costs into account, than firms farther away. In a system predicated on the principle of perfect competition, firms located at greater distances from given markets must, therefore, be competed away. In the limit as firms select locations at infinitesimally small distances from market sites, limitations on the availability of space must undermine competition, thereby enabling firms to exercise market power in determining commodity prices.
Thankfully, there is a way out of this quandry. Insofar as land-space exists as a factor of production owned and rented out by households and the marginal utility of holding land-space for divergent uses in proximity to market sites diminishes with distance from such places, it must be the case that households will charge higher rents closer to markets. Thus, firms that choose to minimize their transportation costs by locating closer to a relevant market site will encounter higher land rents eliminating their cost advantages in relation to firms that locate at greater distances from markets. As such, the centripetal pull of transportation cost minimization must be counterbalanced by a centrifugal push of differential land rent minimization, ensuring that firms will be indifferent in making location decisions. We can formally pattern such a relationship between land rent and transportation cost for an economic space delineated by a even circular plane with a market site at the center by means of a von Thünen model, named after an early Nineteenth century German pioneer in geographical economic analysis. This model is elaborated in figure 27.
Elaborating in reference to the general equilibrium theorization of firms that we have developed so far, this model posits that, for some arbitrarily large economic space with a single basin of attraction for market activity, land rents should decline monotonically as we approach the economy's periphery. By contrast, transportation costs should be expected to rise monotonically over the same interval. Assuming that net revenues for all firms are adequate to compensate labor and capital in accordance with their marginal productivities irrespective of locational decisions by each firm, the model defines net revenues to the exclusion of factor payments for land. Thus, we arrive at product exhaustion via the additional step of accounting for land rent and transportation costs. That is to say, firms will always arrive at product exhaustion/zero profit. Our land rent model simply explains the ratio of transportation costs to land rent that each firm will encounter as it selects a spatial site for production such that each firm will be perfectly indifferent in selecting locations because the balance of land rent and transportation expenditures will exactly exhaust net revenues after labor and capital have been compensated. As such, land rent is derived as a residual after we have accounted for the cost of transportation from each distance within our monocentric economy.
Consequently, if we assume that all markets operate with such a spatial pull-push mechanism, then we can ignore the influence of spatiality as a determinant of market pricing and a potential source undermining perfect competition. Any advantageous locational decision made by a firm in relation to its targeted markets will be eliminated by the countervailing imposition of land costs, bringing us right back to product exhaustion. On the other hand, it is one thing to assume, within a theoretic model, that geography/spatiality will exert no influence on relative prices. It is another thing to actually articulate the arguments that might lead to such a result and lay bare the assumptions against which such arguments might seem to mirror economic reality. That is to say, if economists want to conclude that space does not matter, then we should always provide a persuasive explanation to justify our conclusion.
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