If we accept the idea that Marshallian firms operate under multiple, concentric, overlapping temporal frames, each shaped by differential capacities to alter or amend their rental/contracting/investment and integration/utilization of production factors, then we should be able to specify a schedule under which the relative variability of each production factor can be assessed. Accordingly, any change in short (or very short) term market conditions, anticipated repetitions in cyclical patterns, or long term imperatives in strategic planning of market engagement/penetration should be accompanied either by a relatively truncated or a relatively expansive list of variable factors, mapping into the firm's production function. At any moment within the longer history of the firm's engagement with its relevant markets, its entrepreneurial decision-maker(s) would stand in the shortest operative period within which to make relevant production decisions, but the firm would also exist at the cusp of future periods in which it could bring new assets to bear in commodity production. Thus, the firm's decisions on factor utilization might continuously reflect its most truncated lists of variable factors, but it must simultaneously account for investment in factors that it will, only at some designated point in the future, treat as fixed.
It is at this moment that we are critically turning a corner on the temporal problem underlying the Marshallian firm and separating such firms from the abstract theoretic manifestation of a timeless, spaceless Walrasian/Paretian firm. If both Marshallian and Walrasian/Paretian firms must be viewed as rational, profit maximizing/cost minimizing agents, then only the latter receive the privilege of realizing global profit maximizing/cost minimizing solutions in relation to the mathematical terms of their production functions. Marshallian entrepreneurs operate as rational agents bounded by temporal and spatial constraints through which global profit maxima may be unattainable for any (or every) given production period. Marshallian firms negotiate technological and market conditions marked by continuous change in which their investment strategies may never bear fruit if, by the time capital investments come on line, production processes and/or consumer preferences have decisively changed. As such, we will argue, over the course of this section, for a perspective on capital investment grounded in the post-Keynesian conception of fundamental uncertainty.
Let us approach the problem here with an example. Say that we have a firm engaged in fabricating plastic forms through injection molding, a common industrial operation to manufacture a range of plastic components of various sizes and specifications. The firm in question operates on short term contracts with numerous downstream manufacturers in automotive, energy, transportation, and consumer product industries, specifying the volume and delivery timelines for each respective production run. It generates proprietary molds in house for each production run through wire electrical discharge machines (EDM) from detailed specifications supplied by contracting firms. Some of its production runs are relatively small, producing finite quantities of customized components for detailed manufacturing projects by one of its clients. Others involve repetitive contracting on reasonably constant design specifications for regular returning clients, where continuities in mold design over consecutive production runs generate cost savings for clients. With a mix of simultaneous production runs for recurring designs and customized short run projects, the firm is able to regulate its operations to maintain a fairly constant stream of production across multiple projects on a weekly basis. Its primary variable production factor on a weekly basis remains not labor but plastic intermediate materials. Generating products from a range of thermoplastic materials (e.g. acrylic, polypropylene, polycarbonate, etc.), the firm must manage inventories of molding materials based on weekly production schedules. In the mold production process, it must likewise manage supplies of aluminum and other composite metals for forming in the EDM process.
The firm's management of human resources, by contrast, figures as a relatively longer term constraint on the firm's ability to maintain continuous production. The most highly skilled personnel work in the design shop, utilizing three-dimensional computer design/printing technologies to generate detailed mold designs from computer aided drafting (CAD) blueprints supplied by clients. Beyond the mold design process, human resources utilized by the firm tend to include largely semi-skilled machine tenders. The wire EDM tool-making process is automated and the injection molding process itself is automated, with minimal involvement by machine operators and tool-setting staff. Training time in the latter processes is minimal but not inconsequential. Errors in programming wire EDM machinery in the mold production process, in setting up A and B side tools on injection mold machines, or selecting appropriating clamping force for the charge materials used can lead to significant costs from damage to materials or machinery and defective products. An extended on-the-job training protocol is maintained for all production personnel, with detailed supervisory training as new technologies are integrated in fabrication and production control. It suffices to say that the firm may be able to procure more polycarbonate granules for the injection process overnight if production operations leave its supplies depleted, but it cannot as easily replace the labor services of a few machine operators or tool setters if they become unavailable either because of a work stoppage or acute retention problems.
Then there is machinery. This firm, like every other manufacturing firm in the fabrication of plastics, is automation intensive. In the mold production process, the firm operates a number of EDM die sinking and wire EDM machines to produce precisely detailed aluminum and composite molds to the exact specification demanded by clients. In the molding process, it operates twelve separate injection molding machines of divergent clamping force ranges. Precisely, it may not be an industry giant, but it is capable as an actor within its own geographic and design market niche. On the other hand, as committed entrepreneurial actors, the firm's proprietors seek to expand beyond its specific limitations by investing in new machinery and more advanced technologies and by expanding their base of clients to realize a return on their investments. In this manner, the firm manages its long term market strategies around the integration of new capital equipment, enabling it to undertake projects that it is currently incapable of completing and to take on multiple concurrent projects of larger sizes.
Patterning the firm's production function around the availability of its current supplies of intermediate plastics and aluminum plates, the availability of diverse forms of skilled/semi-skilled labor, and the integration of existing and new machinery, we get a series of nested temporal optimization processes that, invariably, become collapsed into overlapping frames of decision making by the firm's proprietors. For our purposes, however, we can break down the separate optimization processes in order to define, separately, what the firm is actually doing to maximize profits and minimize costs, subject to fixed factor limitations, at each temporal frame. To begin, if we generalize the intermediate materials (plastic granules, aluminum plate, etc.) as a single, homogeneous factor of production m that exists in a continuously variable form, then we can set up an initial stage of a broader optimization process by arguing that the firm varies its quantities of intermediate materials against a relatively fixed quantity of labor services l and a fixed quantity of capital machinery k. We can pattern this problem graphically below, with quantities of the factor m on the horizontal axis, outputs as a function of m, l, and k, on the vertical axis, and quantities of l and k held fixed at all points along our total product curve.
Figure 17: Total Product Varying Intermediate Materials m Against Fixed Labor l and Fixed Capital k
In this manner, we vary intermediate materials to four separate levels as multiples of a base level. Intuitively, we might reason that initial increases in marginal productivity of the factor m arise as a result progressive utilization of the fixed factors l and k. At very low levels of employment of intermediate materials, skilled and semi-skilled labor may remain idle of significant portions of the work day and EDM and injection molding machines may remain wholly out of use. As we increase quantities of intermediate transformative materials, we increase the productivity of labor and machinery and, in conjunction, the marginal productivity from additional quantities of intermediate materials increases. This subset of the optimization problem necessarily has a maximum, where the average product of the factor m is equal to its marginal product. In this case, the maximum occurs around level four, as illustrated by a ray from the origin, denoting the highest attainable locus of constant average products of m, which is tangent to the total product curve at a single, highest point, in figure 18.
The point of tangency of the ray from the origin with the total product curve in figure 18 indicates that we have a unique global profit maximum/cost minimum for this level of capital k and labor l, varying quantities of intermediate materials m alone. Beyond this maximum, increases in the integration of transformative materials can only generate a diminishing stream of marginal products. Logically, the accumulation of larger and larger inventories of intermediate materials, beyond the capacity of labor and capital to transform into finished outputs, must lower both the average and marginal products of m, even if it does not reach a point where marginal products become negative.
This problem, conceivably, constitutes the daily, weekly, or, at most, monthly decision set for the firm, as it decides what quantities of intermediate materials it needs to hold in inventories for production beyond longer term considerations on staffing and long run investments in machinery. Acknowledging the relative simplicity of this decision, problems arise as we integrate successive higher/longer time frames. Again, the firm operates within a context where its production planning horizon is strictly limited. Any decision that it makes on the transformation of scale, through investment in its longer term factors of production, must be supported by some expectation that it can reap a return on its investments by increasing its sales volumes to existing clients or by bringing in new clients. Conversely, it may be the case that the firm's proprietors recognize that some investments can be made, under its current and recurring portfolio of projects, to improve its efficiency of operations, reducing factor costs per unit of output. This is a recognition that the firm, within a Marshallian theoretic, undertakes a recurring reexamination of operations to determine whether it is at a global profit maximum/cost minimum in relation to all production factors under circumstances where technological possibilities for production efficiencies are simultaneously changing. In one conceivable circumstance, the firm's proprietors may determine that they can reduce average costs per unit of output by increasing the quantity of labor services employed and achieve gains from greater specialization of existing production staff. Such a strategy hearkens back to the image of the Smithean pin factory and to Frederick Winslow Taylor's dogma of scientific management. If we superimpose a set of total product curves against our existing total product schedule for the factor m, where each new total product curve represents the change in the total product schedule as we undertake discrete and proportional increases in the quantity of labor employed by the firm, then we can come to some graphical approximation of how the firm might be able to make gains in output by substituting discrete quantities of l for m.
The suggestion here is that our initial short run profit maximizing/cost minimizing outcome in terms of m does not take into account the extent to which the firm can gain outputs by substituting discrete quantities of a relatively less variable factor over longer time frames for quantities of its most variable factor. If the quantity of labor hired by the firm is relatively less mutable at very short run intervals than the quantity of intermediate, transformative materials, then our firm can always vary the quantities of plastics and aluminum plate in its inventories but can only alter the quantity of labor it uses subject to its capacity to reorganize the utilization of labor in production and to supply new hires with the rudimentary quantities of training they will need to undertake their roles in production. However, when it does integrate new workers and reorganize production, it can increase total output while reducing waste in the use of intermediate materials. In accord with figure 19, the firm can raise total product and reduce total use of intermediate materials by making five proportional increases in labor, ending at level li6.
The manner in which I have drawn figure 19, further, seeks to make an argument with regard to the substitution of labor for intermediate materials. For every discrete, proportional increase in the quantity of labor services in figure 19, the total product curve in terms of m pivots inward total the quantity axis, denoting the fact that our substitution will yield an increase in total product for every quantity of m consumed as a result of our integration of increased quantities of labor services. These increases in total product are not, however, proportional for each of our discrete changes in l. That is to say, our first increase in labor services yields more additional output than our second increase, and so forth (i.e. the marginal productivity of labor services against a fixed base of capital machinery diminishes as we substitute labor services for intermediate materials). Even as we decrease the amount of m required to produce higher quantities of output, our capacity to substitute l for m is diminishing as we proceed, and it is likely that we will reach a maximum at which no additional increases in labor services relative to intermediate materials, under a fixed base of capital machinery, will yield increased outputs.
The relationship between l, m, and total outputs could similarly be patterned in three dimensions by means of isoquant level curves that would be convex with respect to the output origin, tailing off asymptotically toward the m and l axes into infinity for each level of total output (figure 20). Here, holding to an assumption that the firm's financial constraint (i.e. its total budget for hiring factors of production) remains fixed as we substitute one set of production factors for another (and, thus, holding relative factor prices constant, we remain on a single isocost curve), selection of relatively more efficient factor combinations leads us to a point of tangency between the isocost curve/financial constraint and the highest attainable isoquant curve (I3 in figure 20). Thus, for every set of relative prices for the production factors, we must have a global profit maximizing/cost minimizing point for every temporal interval in which we can treat each of the factors as variable.
Figure 20: Labor and Intermediate Materials Factor Optimization Problem Expressed through Isoquant/Isocost Curves
Finally, we have to expand our analysis to incorporate successive factor substitutions on longer and longer time frames. That is to say, the firm must always be attentive toward the possibilities for investment in new capital machinery of the sort that will potentially enable it to bid on new projects, expanding its base of short term and regular clients. Precisely, the injection molding machines currently utilized by the firm may be especially conducive to a certain range of products that the firm regularly fabricates for clients. No doubt, some other fabrications may be entirely beyond its capacity to manufacture if, for example, the clamping force of its machines is incompatible with the technical specification of manufacturing certain parts. In the end, the firm's proprietors are continuously considering how to deal with manufacturing problems in the injection molding process and the EDM/wire EDM manufacture of molds/tools in order to achieve long run growth in the firm's client base or, in the very least, to ensure that the firm will be capable of maintaining its current repertoire of clients in the event that its available machines require replacement.
Having already conveyed two distinct graphical representations on factor substitution in a two-factor case, adding a third factor to assess the differential impacts of adding new capital equipment becomes conceptually more difficult. Approaching this problem both abstractly and in reference to the potential real effects of investment in new machinery, let us say that the firm's proprietors conclude that, given present demand for the firm's outputs and expectations for increased demand for plastic fabrications among the firm's current client base, they could stand to profit from investment in a new hydraulic injection molding machine with a clamping force around 175 tons. Investing in such a machine will, optimally, demand three to four new machine operating staff over the existing production schedule, increase the use of intermediate plastic materials by ten to fifteen percent per day, and increase the use of aluminum and composite materials in mold production by ten to twenty percent, contingent on the realization of new production contracts or expansion of existing ones. Conversely, they expect that such an investment will increase gross revenues (accounting for potential increased contracting) by around twenty percent and revenues net of increased operating costs by three to five percent. Finally, the incorporation of a new hydraulic injection molding machine will only be realized in three weeks time. The model, itself, may be relatively generic, but it must still be spatially integrated into the firm's production facility and connected to existing infrastructure. Beyond the basic market reality of the machine's purchase by the firm, these details take time, as will formal training in the operation of the new machine to the firm's machine tenders by staff from the manufacturer.
Holding in mind these expectations on the firm's performance relative to its potential new investment, we can conceivably sort through a set of abstract differential relations, mapped out by the firm's unspecified production function. In the most abstract sense, the firm's production function can be denoted as:
With marginal products:
Where a is the marginal product of intermediate materials, b is the marginal product of labor services, and c is the marginal product of capital machinery. We can safely assume that, within relevant ranges of output, each of these marginal products has a positive value, even if values approach zero or become negative on other ranges, holding other factors constant. Moreover, we can assume that the second order partial derivatives for each of the factors, in terms of itself, will be negative for relevant ranges (i.e. diminishing marginal productivity). However, assuming that each of the factors operates as a relative complement to the others, in a three factor case, the situation with mixed partials becomes cloudy.
If the firm adds a new injection molding machine, in the absence of any changes to labor services hired or intermediate material inventories, it may increase total outputs but the substantial addition of new machine hours to its production schedule will introduce a steeply diminished marginal productivity of capital. That is to say, without additional staffing, machine tenders and tool-setters will have a more difficult time operating an additional machine and regulating use of plastic intermediate materials for optimal efficiency. There may be more waste of plastics and, in any case, the firm will more rapidly diminish its existing inventories of plastics in the absence of some increase in purchasing. Fundamentally, an increase in capital machinery must be accompanied by both an increase in purchasing of intermediate materials and an increase in staffing if the firm is to maximize profits from its investment. Here, again, as suggested above, the firm's proprietors already have entertained the possibility that investment in a new injection molding machine will require higher utilization of labor services (three to four machine tenders) and intermediate materials, both for plastics (ten to fifteen percent per day) and metallic plates (ten to twenty percent). It is conceivable, in this respect, that multiple profit maximizing factor combinations exist for the injection molding process at different production scales and that this firm has simply selected one possible multi-factor expansion path, but, having selected this particular expansion path, it must now manage its multi-factor investment and utilization schedule over time to ensure that it is maximizing profits, particularly with respect to the factors that are least variable over time and, hence, constitutive of its hardest constraints on output variation.
The idea that there may be multiple profit maximizing combinations, involving, especially, different ensembles of capital equipment and skilled or semi-skilled labor services, potentially takes us beyond the image of the Walrasian/Paretian general equilibrium system in which all firms in a given production process select identical profit maximizing factor combinations. The latter idea constitutes a rationalist oversimplification, but if we concede a certain level of nuance to production processes for relatively homogeneous goods and services, we have to recognize that variations in production factors must exist, and that such variations may generate marginal cost advantages for certain firms. If, at every moment, all firms in a given market are attempting to achieve all available reductions in production costs, the innate imperfections of information on production technologies in a Marshallian economy must constitute an experiential environment in the selection of particular combinations of labor and capital. Remaining on the theme of plastic injection molding, for example, certain firms overwhelmingly utilize hydraulic injection molding machines while others have updated to incorporate partial/hybrid or fully electric models. Selection between such models is highly contextual, with fully electric models enjoying an advantage for certain high volume, high precision processes and in regions where rates for electric power are relatively low. Firms specializing in plastic components for medical procedures where consistency tolerances are extremely tight tend to utilize fully electric injection molding machines. Production for certain other downstream processes are more readily handled by hydraulic machines. The mix of clients involved for individual firms, thus, determines the particular technologies employed, but, to the extent that overlaps exist between subsets of the larger market in plastic fabrications, it may be true that certain firms select factor combinations that are relatively efficient given their in house capital equipment even such factor combinations are not globally efficient across the larger industry for the particular components manufactured. In the end, capital investment decisions by particular firms at every temporal period must reflect the particular range of their client portfolio, in injection molding and in every other business field.
Integration time is another important consideration here. That is to say, we need to consider how long it take the firm to fully incorporate any particular capital investment. In the case of intermediate materials, investments are incorporated immediately - plastic pellets and metallic plates can immediately be injected into their respective role in the production process once they are received by the firm. In the case of labor services, there has to be some nominal on-the-job training period to integrate staff into their roles. In the case of new equipment, integration of machinery is a prolonged process, from purchase to manufacture, in accordance with specific details, to transportation, to installation, to training of staff, to full formal utilization. In the case of our firm, we have posited the possibility that the machinery purchased conforms to a standard model, without any detailed changes. Even accepting such conditions, the integration of new capital machinery is an extended process, especially where its use significantly reshapes the operation of the firm.
Emphatically, in our case, if the purchase of a new injection molding machine increases the range of production processes open to the firm, then formal integration sets the timeline in which personnel can procure new contracts for projects not available to the firm before the machinery was purchased. On the other hand, at the time in which the firm's proprietors make the decision to invest in new machinery, the potential to realize new projects that will make their investment profitable remains fundamentally uncertain. The proprietors cannot fully diagnose the profitability of an investment that may take several months or longer to integrate into production based on market conditions that do not exist at the time in which the investment was made. Under such circumstances, the proprietors, as investors, are constrained to undertake as much research into contemporaneous technological and market conditions that will enable them to make an educated guess as to whether they are apt to profit from procuring new machinery. The insoluble nature of risk here ultimately constitutes a singular justification/rationale for the existence of normal profit as a return to willingness of entrepreneurs to undertake capital investments under inherently risky/uncertain conditions.
Reflecting briefly on the image of differential expansion paths shaped by investments in particular very short, short/intermediate, and long term variable production factors, liquidity is a significant concern for the firm's proprietors as they move forward. Every investment in production factors transforms a relative liquid capital asset (e.g. retained cash earnings) into a relatively illiquid asset (e.g. an inventory of polycarbonate and polypropylene pellets, liability to pay a week's earnings for an additional machine tender or to pay contractual salary obligations for mold designer, sunk investment costs for an additional injection molding machine inclusive of interest on financing). In some way, the total product generated by each investment in an illiquid asset must at least equilibrate the potential return for alternative uses of liquid capital assets (e.g. lending through financial intermediaries or purchase of debt or equity-based securities). At this point, our analysis of the Marshallian firm begins crossing the threshold into the derivative terrain of traditional Keynesian theory and, even more, of post-Keynesian theory, where we acknowledge that the microeconomic contexts in which firms operate are situated within and mediated through financial systems in which alternative uses of capital must shape very basic business decisions for firms on every level of an economy. It might be easy for our firm in this section to regulate its investment in human resources over the course of one or two months in response to shifts in profitability of its production processes, but how easy it is to disinvest in a new injection molding machine? A ready market may exist for used industrial equipment, but how fully can the firm expect to recoup its initial investment by liquidating an asset through such a market? Likewise, the firm probably can rely on wholesale suppliers of intermediate materials to buy back unused, non-perishable inventories, but at how much of a discount? The fact that every investment in illiquid factor assets constrains the firm to utilize them productively over a particular temporal period over which the firm does not manifest perfect knowledge on market conditions means that the firm must simultaneously concern itself with the capacity of each asset to be liquidated in the future.
The critical point is that none of the investment decisions here can be made in the abstract. They are all outcomes of an analytical process, undertaken by the firm's proprietors, to evaluate the potential for increased revenues against increased costs under different mixes of production factors, variable in accordance with different temporal frames, all considered in relation to the firm's portfolio of client projects and the potential to gain returns from alternative (non-productive/financial) uses of capital. We should not, in this manner, construe that entrepreneurial decisions are either the outcomes of intensive, determined research or that such decisions are factually simplistic and mechanical. Rather, the work of entrepreneurs in planning capital investments, on divergent and overlapping time frames, is continuously practical to the work of their businesses and, as such, reflects the recurring degrees of skill and intellectual ability manifest in the day-to-day negotiation of particular market contexts.
Summarizing the arguments of this section:
1. Planning of investments in production factors by entrepreneurs is continuous and involves overlapping temporal frameworks, with certain factors more variable along shorter timelines than others.
2. The basic framework of production analysis (i.e. production functions with multiple, discrete factor combinations and roughly determinate output ranges), accounting for differential temporal variability of individual factors, constitutes the foundation for analysis of capital investments along divergent timelines.
3. On shorter timelines, firms are more capable of deploying contemporaneous information on production technologies, consumer demand, and competition to determine the profitability of a discrete investment in new production factors that can be readily integrated in production in short order.
4. On longer timelines, firms encounter fundamental uncertainty, manifest in an incapacity to forecast technological and market conditions that do not yet exist. As such, investments in factors that require longer timelines to fully integrate into production are accompanied by uncertain estimations on profitability.
5. The relative liquidity of any given capital investment, considered in relation to alternative investments in productive capital and/or non-productive financial investments, must be taken into account by entrepreneurial decision makers, in the event that capital investments that take time to integrate into production come on line under technological and market conditions that render them less profitable than previous estimations would have indicated. The existence of market institutions (e.g. markets for used capital equipment) can function as a buffer against the relatively illiquid nature of certain investments.
