A Marshallian Theory of the Firm III (Microeconomics)

Generalizing Short Run Time Frames: Management of Variable Factors Against Rising Marginal Costs

Short run time periods, for Marshallian firms, are defined by the presence of separate sets of fixed and variable production factors.  As in our elaboration of the Walrasian/Paretian "pure" Neoclassical firm, we will proceed in this section with an assumption that we can, at least for purposes of presentation, homogenize the factors of production utilized by the firm, reducing entrepreneurial decisions on factor combinations to a two factor (labor and capital) case, even as we acknowledge the potential to analyze a wide array of heterogeneous factors with different temporal degrees of variability.  In this sense, the critical differentiation here relative to Walrasian/Paretian firms remains the idea that for Marshallian firms certain factors must be held fixed in short run periods.
              Drawing from our hypothetical firms in the previous section, for example, our interurban bus operator faces certain short run constraints on the provision of transit services.  If there is a rapid and unanticipated increase in passengers on one route, the firm cannot adjust by placing additional buses on the route if these are unavailable in its fleet.  If it takes a prolonged period, say four months, to order new buses and take delivery from the manufacturer, then the firm may be constrained to deal with a short term increase on one of its routes by diverting certain vehicles from planned maintenance, renting buses from other firms in the industry with unused capacity, and increasing the number of drivers in its weekly schedule to deal with increased ridership.  To the extent that these measures enable the firm to deal with a temporary increase in ridership, the firm still needs to evaluate the source of the increased demand and determine whether it may be permanent.  Additionally, evaluating the cost structure involved in its temporary ameliorative, the firm will likely face an increase in costs for each additional bus route scheduled, especially if it rents vehicles from other firms in place of using its own.  If the firm anticipates a long term shift in ridership, then it will want to invest in new buses in order meet higher demand at a lower cost per scheduled route.  This scenario demonstrates the problem of short run adjustment to changing market conditions for firms that face constraints on increasing certain factors in the short run.  In the long run, the bus operator may be maximizing profits/minimizing costs like a Walrasian/Paretian firm with continuous factor substitutability and constant returns to scale.  In the short run, however, it cannot adjust at least one critical factor, the scale of its fleet of buses.  Consequently, as it tries to adjust to new short run market conditions, it incurs increasing marginal costs, as its variable factors exhibit diminishing marginal productivity relative to the fixed factor.
             In certain respects, our bus case is more complicated than the general model that I intend to elaborate in this section.  There, the entrepreneur is selecting between different means of adjustment among higher cost alternatives (renting buses from other firms) to increase services if new physical capital (new proprietary buses) cannot immediately be incorporated into production to maintain an optimal profit maximizing combination of production factors.  In our basic elaboration, we will deal with a two-factor, labor and capital model, in which labor will be considered variable in the short run and capital fixed.  Otherwise, we will proceed with the same sort of theoretic elaboration involved in our Walrasian/Paretian theory of the firm, developing theoretic tools to analyze physical productivity, cost structures, and market engagement from the insular frame of an individual firm in competitive conditions.

The Short Run Production Function

Our understanding of the production function in Marshallian theory will technically mirror its equivalent in Walrasian/Paretian general equilibrium economics, with the noteworthy exception that here we will have to account for the effect of holding factors fixed in the short run.  Thus, in a Walrasian/Paretian economy, where agents in possession of perfect information on technology and market conditions can instantaneously adjust to changes, we represent production through the following function:



Where the quantity of commodity i is represented as a function of the quantities of labor l and capital k utilized in its production.  For the Marshallian firm, in the short run, the quantity of capital available to the firm in the short run is fixed.  We, therefore, represent the firm's production function as:



Where k-bar denotes a fixed quantity for capital.  Thus, for the Marshallian firm, the entrepreneur is constrained, in the short run, to vary quantities of labor in response to changing market conditions, increasing labor services utilized if demand from consumers increases and decreasing labor services utilized if demand from consumers decreases.
             As we increase the use of labor services against fixed quantities of capital, we presume that, to some degree, the additional productivity derived from adding each additional labor hour will decline.  The extent of this decline in the marginal productivity of labor services will be reflected by the firm's short run production function.  To conceptualize this, reflecting back on the process of profit maximization for Walrasian/Paretian firms, let us say that we are dealing with a firm that has a suitably constructed production function with the desirable properties from our previous theoretic approach (e.g. continuous substitutability/differentiability of the production function, linear homogeneity/homotheticity).  Under relatively stable output and factor market prices, these properties enable our firm to arrive at a profit maximizing combination of production factors that will hold for all respective scales of output, absent changes in relative prices in factor and output markets.  Figure 2-1 represents two output scales at two total cost levels represented by isocost curves IC1 and IC2 under a profit maximizing combination (ki*, li*), defining expansion path EP*.

  Figure 1: Profit Maximizing Combinations of Labor and Capital for Firm Operating with Full Factor Substitutability 
The problem, in forging a transition from the theoretic vision of Walrasian/Paretian general equilibrium to a Marshallian economy is that our firm cannot instantaneously shift from point A to point B (or vice versa) in response to changes in consumer demand in its market.  In a Marshallian world, capital is not ready, in place, to be utilized to transition between production scales.  It takes time to invest in new capital and to bring such investments on line for production at higher scales of operation for a firm.  Our bus operator needs time to bring in new buses.  Our producer of remanufactured master brake cylinders needs time to invest in new boring machines/lathes and bring them on line for production.  If our feedlot needs to construct new pens to accommodate an increase in the scale of its feeder cattle stock, such an investment takes time.
             Assuming, in this regard, that the firm in figure 1 is stuck, in the short run, at capital level ki1*, any change in output demand can only be addressed by increasing the quantity of labor services committed to production.  Rather than bring new machinery on line, our brake cylinder remanufacturer can only add more labor hours with existing machinery to increase the quantity of master cylinders ready for sale to satisfy increasing demand.  As he does so, his costs for each additional unit of output must rise.  We can think of this increase in marginal costs in multiple different ways.  He may simply be working his existing staff longer hours, during which time the productivity of each worker declines as they work the last few additional hours of the day.  He may be hiring new workers who are less experienced at the job of remanufacturing master brake cylinders than his regular staff.  Whatever causes the additional productivity of workers to decline as he raises the total number of labor hours committed to production, it is becoming more expensive to produce each brake cylinder as quantities increase beyond what the firm was capable of producing at its optimal factor combination A.  Figure 2 attempts to come to terms with this decline in the marginal productivity of labor services and rise in marginal costs as we move from point A to point C.

     Figure 2: Short Run Adjustment to Increased Output Quantity by Firm with Fixed Capital Constraint
Elaborating on figure 2, in relation to the conception of production functions that we have already developed in examining Walrasian/Paretian firms, the increase in output quantities represented by a shift from isoquant I1 to I2 would satisfy the firm's objective profit maximizing conditions if the firm could remain on its expansion path EP*, effecting, in this regard, a shift from point A to point B.  Our point here is that, if such a change is entirely conceivable in a timeless and spaceless Walrasian/Paretian world, then it is inconceivably for the world in which Marshallian firms operate.  Being stuck at capital quantity k1*, the firm in consideration can only hope to transition to output xi2 by increasing its employment of labor services to li2' to arrive at point C.  Point C's location on IC2', at a total cost level/isocost curve that intersects its relevant isoquant curve at two points, indicates that the combination of production factors utilized here is suboptimal - the firm could produce the same quantity of outputs at a lower cost if it could obtain a larger quantity of capital and could employ fewer labor services. At point C, the absolute value of the slope of the isocost curve IC2' (i.e. the relative price of labor in terms of capital, Pl/Pk) exceeds that of isoquant curve li2' (the marginal rate of technical substitution (MRTS) of labor into capital, MPl/MPk), meaning that the additional productivity of labor at the margin of employment relative to that of capital is less than the relative price of labor in terms of capital. This implies that the last dollar spent renting labor earns less additional output for the firm than if it could spend the same dollar renting additional capital, which it is restricted from doing in the short run. Effectively, as the firm diverges from its long term profit maximizing expansion path to adjust to short term market conditions, the marginal productivity of its variable factor(s) diminish relative to their fixed factor(s). We can better illustrated this situation, for the firm in figures 1 and 2, by depicting the firm's short run production function in output-labor space as a two-dimensional curve, defined as a function of variable labor quantities and a single, fixed quantity of capital. We can label such an illustration of the production function in two-dimensions with fixed capital a total product curve. This is illustrated in figure 3.

Figure 3: Short Term Production Function (Total Product Curve) with Fixed Capital ki1* and Variable Labor
As drawn, this function has a number of quintessentially Marshallian features related to the average and marginal products of labor. The marginal product of labor can be represented by tangent lines to the curve, reflecting the instantaneous rate of change of output as we move along the surface of the curve. With this in mind, addition of the first units of labor demonstrate a pattern of increasing marginal productivity. Intuitively, if we have a fixed quantity of capital ki1*, represented by some mass of tools and equipment needed to undertake a production process, to which we begin adding units of labor, then the first units of labor added to this mass of capital equipment must provide a surge of output from zero to some positive quantity. As we proceed down the curve, however, the marginal productivity of labor must peak and then decline continuously. Again, if we continue to add additional units of labor services to a fixed mass of capital equipment, at some point, the additional product that we get from adding more labor must start to diminish.  
The other relevant feature of the curve concerns the average product of labor and its relationship to the marginal product. The average product of labor can be represented graphically by drawing rays from the origin, the slopes of which equal the average product of labor at each point where the rays intersect with the production function. The average product of labor attains a maximum value along a ray that intersects the production function at a single point of tangency. Such a ray is drawn in figure 3, intersecting with the production function at the point A. At this point, the average product of labor equals the marginal product of labor. The reason for such an equality should be intuitive. If additional quantities of output from the rental of additional units of labor continue to exceed the average product of labor, then, mathematically, they must force the average product to increase. As soon as additional quantities of output are less than the average, the average must itself decline. Assuming the production function itself is continuously defined such that discrete additions of labor services can always generate a definite output quantity, and given the initial increasing range of marginal productivity and its subsequent continuous decline, it must be the case the average product of labor reaches its maximum where average product is equal to the marginal product. In figure 4, I have attempted to represent the average and marginal products of labor in relation to our figure 3 short run production function, adding point E to represent an inflection point in the production function where the marginal product of labor reaches its maximum value and starts to diminish.  

Figure 4: Marginal and Average Products of Labor Services in Relation to Short Run Production Function with Fixed Capital
The representations of the average and marginal products of labor in figure 4 definitively attempt to convey the idea that, as we had discrete quantities of labor to a fixed capital base, we initially achieve complementarities between production factors that raise marginal productivity as we add successive discrete units of labor to production. Such complementarities must, however, be exhausted at some point, evident in the upper panel at point E. Beyond this point, marginal productivity diminishes with each additional unit of labor rented by the firm. This pattern of marginal productivity similarly mandates that the average productivity of labor must initially rise, reach a maximum level (at which average and marginal productivity are equal), and decline monotonically. Thus, graphically, the marginal and average productivities of labor are represented as inverted "U"-shaped curves.
In reference to our short run production function, it would be entirely valid to conclude that, at some point, the marginal product of labor becomes negative, indicating that progressive addition of labor hours to a production process with a fixed capital base will cause diminution of total output beyond some maximum value. Thus, it might be the case that a firm hires so many employees in the short term to deal with increased demand that they end up getting in each others way, ultimately diminishing the total production that might have been produced by a smaller number of employees. As such, we may confront a larger definition of capacity utilization, in relation to diverse fixed factors, where saturation of a work place with superfluous variable factors becomes an actual impediment to increasing outputs to meet demand. On the contrary, I am content to allow the production function to reach an output limit, beyond the range that I have illustrated, at which the marginal product of labor reaches a zero value and average productivity approaches zero asymptotically. In any case, the larger point here is that production functions in the short term reach limits, shaped by the diminishing marginal productivity of variable factors against fixed factors. The particular contour of short term production functions, moreover, shapes the contours of short term marginal and average cost curves for Marshallian firms and reflect demand functions for variable factors.
Having defined the marginal and average product schedules for labor, as the firm's variable production factor, we can further relate the firm's marginal product schedule for labor to its demand for labor in factor markets. In doing so, we will make the initial assumption that the firm operates as a price taker in a relatively competitive factor market context. If it does so, then, as a profit maximizing entity, the firm will seek to rent successive units of labor and capital to maximize the return that it receives from each successive unit of each factor subject to both the factor market price for the factor and the price of the outputs produced by the factor. This reasoning simply reiterates the general conditions for profit maximization that we introduced for the Walrasian/Paretian firm on the theme of product exhaustion. In that context, we treated both labor and capital as variable factors, against which the mutual determination of factor and output market prices enabled us to determine an objective profit maximizing/cost minimization combination of factors realizing product exhaustion. Here, however, the capital available to the firm is fixed in the short run. Thus, the firm can only choose quantities of labor in order to maximize its profits and minimize costs relative to changes in the output or factor market prices.  
With these limitations on profit maximization and the necessity of adjustment to short run market conditions in mind, Marshallian firms face a somewhat different profit maximizing condition. In the short run, Marshallian firms will rent labor services from households up to the point at which the last unit of labor employed returns an additional/marginal value product equal to its compensatory rate, determined by the equilibrium wage in the factor market for labor services. We define this value product as the marginal revenue product of labor services (MRPl), calculated, as previously defined in regard to the Walrasian/Paretian theorem of product exhaustion, by multiplying the marginal product of labor by the output price of the commodities produced by labor. Thus, short run profit maximization by Marshallian firms maintains the following condition:



We can, further, qualify this condition with respect to our arguments concerning the short run marginal productivity of labor for Marshallian firms constrained by fixed quantities of capital. To the extent that Marshallian firms operate with marginal productivity schedules for labor characterized by ranges of increasing and diminishing marginal productivity, the short run labor demand schedules of Marshallian firms are represented only by the range of marginal revenue productivity values where values are less than or equal to average labor productivity and diminishing. This range is represented graphically in figure 5.  

Figure 5: Marginal and Average Revenue Product Curves with Labor Demand Subset Accented  
Intuitively, the reason why the firm should only demand positive quantities of labor services in this range, under the condition that it pays labor a wage equal to its marginal revenue product, is because it is only in this range that the firm can receive, from each additional worker, a return that will equal or exceed the wage rate that it pays in order to hire the last additional worker. For all preceding points on the marginal revenue product curve, the average revenue product of labor is less than the marginal revenue product - the average return from hiring labor must be less than the compensation rate paid to workers.  
Before concluding this sub-section, I want to elaborate to an element of continuity between Walrasian/Paretian and Marshallian conceptions of the production function. My initial approach to the short run production function for Marshallian production functions attempts to make use of the Walrasian/Paretian architecture of isoquant and isocost curves, instruments largely superfluous to an explanation of production in the theory of Marshallian firms, at least in the short run. In arguing graphically, moreover, that the short run Marshallian production function reaches an equality of marginal and average productivity of labor at a point at which we realize an objective profit maximizing/cost minimizing combination of production factors, consistent with Walrasian/Paretian production analysis, I have sought to contextualize Marshallian theory in relation to the Walrasian/Paretian approach. For Walrasian/Paretian firms, we concluded that, for every conceivable scale of output, the firm, characterized by a linearly homogeneous production function, will operate at a combination of production factors where compensation of each production factor in accordance with its marginal productivity will precisely exhaust the total revenue product of the firm. As such, the marginal products of each factor will be proportional to their average products.  
For the Marshallian firm, we concluded that short term production is apt to diverge from an objective profit maximizing combination of factors because the firm is constrained in its ability to rent certain factors that are relatively scarce for certain periods of time. Recognizing this point, it is conceivable that Marshallian firms would operate with constant returns to scale, in the same manner as Walrasian/Paretian firms, but this is a special case. The Marshallian firm constitutes a more generalized production analysis, in which certain firms will be characterized by global decreasing returns to scale, others by global increasing returns, others, like Walrasian/Paretian firms, global constant returns, and still others, characterized notably by Viner's formalization of Marshallian production analysis, by discrete regions with increasing, decreasing, and constant returns to scale. Such differentiations and their larger consequences in production analyses will have to await a long term portrait of the Marshallian firm, but, more generally, they are formative to the more complex macroeconomic portraits emerging from Marshallian theory, especially along the developmental progression of Keynesian analyses.

A Marshallian Theory of the Firm II (Microeconomics)

Production Across Diverse, Overlapping Temporal Frames

Marshallian firms operate in simultaneous, overlapping temporal frames that vary in length given the nature of the firm's production and exchange processes.  Such considerations involve differences in production technologies, constraints on the integration of new capital investments, fluctuations on the growth of available factor supplies, and exogenous regulation of the entry or expansion of given firms.  Each of these issues depends on the particular context of firms in relation to input and output markets, where such considerations emphatically respect geographical specificities and levels of competition between supply side agents and between consumers.
           Fundamentally at stake in the definition of temporal frames is the problem of adjustment by firms to changes in technology, factor market supply, and output market demand.  For Walrasian/Paretian firms, such adjustments are continuous and instantaneous.  For Marshallian firms, we have to consider how firms make adjustments over prolonged periods and how prolonged adjustment periods affect production costs and, as such, market pricing.  At the level of individual firms, we are concerned with the relative variability and relative fixity of production factors over each temporal frame.  At the level of individual markets, we are concerned with the variability of market shares as firms adjust factor utilization and output levels, enter, and/or exit.
           If we were to approach these problems by respecting the rigorously empirical character of Marshallian theory, then we would need to evaluate a range of divergent cases of real firms in which the nature of production and market engagement caused the temporal frames of each firm to vary widely.  Such a broad investigation of the effects of time on production, investment, and exchange and the capacity of such processes to construct conceptions of the short run and long run would reveal the latent complexities involved in the entrepreneurial management of production scale and scope over time.  This section will not offer such a detailed analysis of how real firms construct their own temporal firms.  On the other hand, it will offer a speculative account on how particular types of firms in particular industries might develop strategies for managing short term variable factors and output quantities, undertaking intermediate term investments to increase operative scales and incorporate consideration of an increasing range of variable assets, and facilitating long term investments in large and/or complex infrastructures or human resources to alter the scale and/or scope of operations.  As such, we will posit how a particular set of imagined firms in particular industries might approach entrepreneurial decisions over a set of overlapping time frames in order to understand how each approaches time in a different way.
          With this in mind, let us consider the following set of hypothetical firms:
1.  A small producer of aftermarket remanufactured automotive brake master cylinders.
2.  An interstate supplier of commercial workers' compensation insurance.
3.  An interurban operator of passenger buses.
4.  An independent operator of a beef cattle feed lot.
5.  A South Asian cafe in a small college town.

1.  Remanufactured automotive brake master cylinders:  The firm in question undertakes a single, four stage manufacturing process through which brake master cylinder housings are chemically cleaned, bored, and relined to produce a serviceable after-market, replacement master cylinder.  The process requires chemical solvents, precisely sized stainless steel tubing, adhesive materials, and boring and drilling machinery.  Labor resources utilized in the process typically do not require significant development through classroom training, but tend to demand substantial "learning by doing" - dexterity and precision at the various stages of the remanufacturing process, especially boring the housing of the master cylinder, demands that individuals involved demonstrate substantial proficiency or else recycled housings may be damaged beyond repair or reuse.  Most critically, the firm requires a steady supply of used master cylinders of sufficient quality that they are capable of being rebuilt in order to realize a serviceable product at the end of the remanufacturing process.  Spatially, the firm's manufacturing process occupies a relatively small space, just under 2,000 square feet.  Storage facilities and office space additionally account for 1,500 square feet.  The entrepreneur, a sole proprietor, owns the machinery and raw materials, but rents space and hires labor services, varying staffing in accordance with the availability of materials and orders from wholesale purchasers of remanufactured auto parts.  He also operates with an open line of credit from a local financial lender to ensure that suppliers of raw materials and employees can be paid in a timely fashion, regardless of fluctuations in revenue from sales.  The entrepreneur contracts on a discontinuous, recurring basis with both a set of suppliers of used master cylinders (wholesale suppliers of disassembled automobiles) and a set of wholesale purchasers of remanufactured equipment.  Both factor and output markets are relatively competitive on both the producer/supplier and consumer sides.  The technologies required to remanufacture master cylinders are relatively well known and a wide array of auto parts wholesalers readily stock remanufactured master cylinders, contributing both to demand for used master cylinders and stable output market prices.  In these regards, the entrepreneur's operational and investment time frames are configured in relation to the availability of ready sources of used master cylinders, capacity of suppliers for other raw materials (solvents, adhesives, stainless steel tubing) to make materials available on demand, the availability of labor services including training for new employees, the adequacy of production and storage space, the adequacy of available tools and machinery including specialized lathes and drill bits, and the presence of ready wholesale purchasers for finished outputs, either speculatively or under contract.  The discontinuous nature of the firm's contracting with both suppliers and purchasers means that the entrepreneur's operational decisions on production schedules operate on a short run horizon, with new supplies of used master cylinders arriving weekly, production schedules for use of labor and other raw materials determined on a weekly basis, and output sales driven by the weekly availability of new outputs and cushioned by available stocks of inventory.  Intermediate term variables may be driven by seasonal patterns of raw material supply (contracting with new wholesale jobbers for used parts) or anticipated, defined contracts with wholesale purchasers.  In either case, such dynamics may require increases in staffing, to include training of new personnel, procurement of larger supplies of other raw materials and replaceable parts for wear of tools and machinery, and procurement of alternative, possibly temporary, storage spaces for new inventories.  Conversely, the anticipated loss of contracts or suppliers may drive reductions in staffing or other raw materials and replacement parts.  Finally, long term horizons, driven by larger anticipated changes in output markets (e.g. major technological change in master cylinder technologies) and/or entrepreneurial efforts to expand or contract market share relative to competitors, or to expand scope of production to include other, related products, involve spatial expansion and/or relocation of production and storage facilities, purchase of new specialized machinery, and transformation of engagement with output markets, possibly including the development of specialized sales staff.  Such changes may necessitate development of new financial lending resources to cover investment expenditures, with or without assurances that investment strategies will yield positive rates of return for the entrepreneur and for capital lenders.  Alternatively, the entrepreneur may be able to achieve expansions of scale and/or scope through reinvestment of retained earnings over a longer period.  In either case, the developmental horizon for such changes may extend for two or more years, a period over which no expectations enjoy any degree of certainty.

2.  Workers' Compensation Insurance:  This firm is an insurance corporation with multiple divisions catering to a range of household and commercial products.  The division in question operates as a wholesale underwriter of workers' compensation insurance policies, although the corporation previously operated as a retail insurer with hundreds of local offices handling all product lines.  Over time, it had grown in scale to a point at which its board of directors decided that shareholders would benefit from a policy of contracting policy issuance through local commercial insurance agents in exchange for a nominal commission per policy.  Afterward, the corporation's multi-service local sales staff were eliminated.  The workers' compensation division retains a staff of service representatives, field accident investigators, underwriters/actuaries, information technology specialists, and legal specialists/litigators.  Employees in each of these sections have invested in substantial quantities of specialized human capital through advanced education.  In certain cases, such human capital investments occurred prior to employment.  Other investments take place on a recurring basis as on-the-job and specialized classroom developmental coursework at the firm's expense.  Its major physical capital expenses derive from information and communications technologies, including annually updated in house and outsourced data management software programs.  The division also expends resources developing publications for client firms reinforcing workplace accident prevention/mitigation and information updates on changes in statutory/administrative rules on workplace safety in key industries.  Spatially, the workers' compensation division operates a free-standing call center in rented office space and proprietary office space at the corporation's headquarters facility, and numerous field staff, particularly accident investigators and litigators, telecommute, working from home offices and conducting field work such as on site investigations over accident claims.  Financially, the critical constraint facing the division's growth remains its underwriting margin, measured as the ratio of expenditures (claim losses plus administrative expenditures) to premium-based revenues.  As a consequence of jurisdictional differences in workers' compensation requirements, policies governing claim reimbursement, and competition with other insurance carriers, the workers' compensation division maintains relatively small positive or slightly negative underwriting margin on policies.  As such, the corporation has pursued a bundling of policies to commercial clients, in order to boost premium revenues in relation to losses from claims, pronounced in workers' compensation.  Evaluating the entrepreneurial temporal frames faced by the corporate board of directors, executives at the corporate level, and directors within the workers' compensation division, key strategic variables, even in human resource management, appear to assume a more prolonged character.  In most circumstances, the recruitment and development of new staff personnel requires years of formal education and a prolonged hiring process, especially evident in the hiring of in house litigators/legal staff.  This focus on the management of advanced human capital, in turn, shapes a broader long term focus on institutions, in particular statutory constructions of workers' compensation policy in individual governmental jurisdictions, through which the corporation seeks to reconfigure the conditions in which it offers, underwrites, and compensates claims to individual policy holders.  In effect, the long run for the corporation constitutes a prolonged conversation with jurisdictional authorities concerning its capacity to generate profits by satisfying the legal requirement for employers to carry insurance against workplace injury or death.  Conversely, management of physical capital and physical space appear secondary to the overall purposes of the corporation and its workers' compensation division.  If information technology updates and new publications arise on an annual basis, and call centers relocate periodically in relation to real estate costs, then these investments tend to simply structure the conditions under which the corporation generates revenues in workers' compensation.  Properly speaking, the corporation's short run and long run in workers' compensation are, respectively, shaped by its efforts to maintain and service its existing portfolio of policies and to expand the ranges of policy portfolios in divergent jurisdictional regions and industrial/sectoral categories.  If the short run is, thus, configured in relation to annual renewal of existing insurance contract and the mitigation of risks through underwriting adjustments, then the long run concentrates on a broader strategic evaluation of existing and potential markets and on transforming the conditions for market penetration in order to create, by statute or juridical precedent, potentially profitable markets.  In these terms, differences in temporal frames are immediately constructed into the firm's organizational structure, reflecting differentiations in demand for particular, heterogeneous production factors to perform distinct subsets of the larger process of producing and exchanging insurance services, as the conditions shaping markets for such services are in flux and susceptible to direct intervention by insurance carriers.

3.  Interurban Buses:  This privately held corporation operates interurban buses on twelve fixed routes, servicing forty separate terminals with five major intermodal hubs including its own central facility, which houses local and interurban buses, interurban and regional commuter commuter rail, express services to two local passenger air terminals, and substantial quantities of short and long term automobile parking.  Rental incomes from various components of its central facility, including parking revenues, constitute a single and lucrative subset of the firm's larger operation, but we are principally interested in its interurban bus operations.  The firm maintains forty-four buses, normally operating thirty-six in its daily schedules.  Some of this rolling stock operates with a wide array of up-to-date technological amenities, including on board wi-fi connectivity and extra passenger leg-room.  Seventeen of the buses are older models without amenities and incapable of accommodating significant modification.  The firm tends to utilize the latter buses on predominantly rural routes to smaller terminals, not associated with a large flow of business passengers with whom the firm tends to be more attentive in response to other, competing modes of transit.  As such, the firm focuses particular attention on the flow of business customers on three of its routes to local and more distant air passenger terminals, where passengers can substitute lower rates on long term parking at the firm's central hub for higher rates in closer proximity to the airports.  The production of interurban transit services involves the actual transit process but additionally incorporates significant quantities of vehicle maintenance and logistical control and communications to maintain continuous control over vehicles in operation.  The firm has a single logistical/control/dispatch facility but employs field staff at all of its terminals both to facilitate forward control and handle ticket sales.  In recent years, moreover, the firm has been compelled to take a more sober approach to vehicle and terminal security.  All of its field personnel and drivers are advised and trained on security/anti-terrorism procedures to maintain passenger and vehicle safety.  The firm provides security staffing as well at fifteen of its terminals, in coordination with governmental anti-terrorism authorities.  With these processes in mind, the firm employs a significant range of specialized personnel.  Drivers are exclusively hired with prior licensing and training in the operation of commercial passenger vehicles.  In these terms, incoming drivers are responsible for their own investments in specialized human capital.  Similarly, maintenance staff typically come to the firm with substantial training in automotive repair and experience in the servicing of commercial passenger buses.  Hiring practices emphasize a general preference to minimize training of drivers and/or automotive technicians to brief orientations on the operation and/or maintenance of vehicles, otherwise reinforcing background proficiencies.  The same may be said in regard to information technology personnel, servicing logistical/control and human resource management hardware and software.  On the other hand, driver and field staff orientations do include substantial reinforcement of customer service guidelines in order to project an amicable corporate persona in the treatment of passengers.  Security staff undergo rigorous training in conjunction with government security/anti-terrorism authorities.  Vehicle maintenance is continuous for the firm.  At any given moment, the firm has at least five of its vehicles undergoing quarterly full service maintenance and other vehicles undergoing repairs to correct technical problems/deficiencies, often arising with high technology features.  Spatially, the firm's proprietary central terminal facility occupies 90,000 square feet in the central business district of its home city, including office space and rented concession outlets, with an additional 120,000 square foot of short and long term parking.  It also maintains a separate 58,000 square foot proprietary maintenance and vehicle storage facility at a peripheral industrial park in the same city.  Office and ticket counter spaces in other terminal facilities on its routes are rented from local proprietors or otherwise operated under agreement with local proprietors and/or governments.  With regard to physical capital, the firm maintains information technology hardware and software to handle logistics/control, human resource management, cost and financial accounting, and ticketing/sales.  Most software programs are updated on an annual or biannual basis.  The multi-use functionality and compatibility of computer hardware has expanded substantially over time, allowing the firm to prolong the useful life of assigned desktop and laptop computers.  Computer diagnostic terminals for automotive repair need to be updated on a more regular basis.  Further, the firm, in its capacity as landlord, has to make periodic capital upgrades to the rental spaces in its central facility.  However, its rolling stock remains it predominant category of physical capital expenditure, and these expenditures are a day-to-day investment, consuming a constant stream of circulating capital, encompassing expenditures on fuel, recurring vehicle maintenance, and labor (drivers and maintenance staff).  With these considerations in mind, the firm's corporate executives and supervisory staff operate on differential layers of temporally-focused decision frames.  In the super-short/immediate term, daily operating schedules have to incorporate spot readjustments on vehicles and drivers and to adjust routes in response to weather conditions or other emergency circumstances arising on an hourly basis.  The short term frames itself around weekly planning of route schedules for drivers and assignment of vehicles to routes or for periodic maintenance.  Month to month, the firm adjusts its schedules in accordance with changes in seasonal demand on particular routes.  Such adjustments also incorporate detailed assessments on fuel expenditures in relation to ticket sales on particular route schedules.  Fluctuations in fuel costs, thus, constitute a significant constraint on the number of scheduled buses for routes on both weekly and monthly time frames.  Over daily, weekly, and even monthly temporal periods, the firm is axiomatically focused on the changing details of its transit operations because this is where the relevant variables can be manipulated.  Likewise, pricing for transit reflects short term frames, with discounts applied in inverse relation to the duration between time of purchase and time of departure - ticket purchases at the time of departure are marked at full price.  On a year to year basis, revenues generated from rental contracting can be varied in relation to changing market conditions.  Additionally, longer term capital expenditures, including technological upgrades for its bus fleet, the purchase of new buses, rental of space in new terminal facilities, construction or purchase of increased maintenance and storage space, and development of new routes to new transit markets can be contemplated.  

4. Beef Cattle Feedlot:  This firm is a family owned independent farm operator of a beef cattle feedlot, located on forty-eight acres in a highly rural state.  It regularly operates with six rotations of one hundred twenty to one hundred forty head, each in 72,000 square foot pens.  The farm additionally maintains 30 acres planted in a combination of feed corn and alfalfa, contributing, in part, to its feed operations.  Notwithstanding, the bulk of feed grains, proteins, and roughage demanded by the feeding process is contributed by purchases on contract with wholesale marketers of cattle feed.  As such, fluctuations in the market prices of feed grains and other dietary components in the feeding process constitute substantial constraints on the farm's operations, impacting the total finishing period for feeding cattle prior to marketing (and, hence, the total weight per head/carcass at the time of sale) and regulating the total occupancy of each feeding pen.  To the extent that pricing along the larger stream of the beef cattle supply chain constitute the primary regulatory variables for the firm over its annual schedule of operations, including market prices for live (pre-finished) cattle stock and feed grains, market prices for finished feeding cattle, and variations between spot market pricing and hedged/future contract prices, the farm is still able to regulate other variables, including staffing.  In addition to family members, the farm employs ten to fifteen cattle hands to assist in the daily operations of the farm, including daily feeding operations and seasonal cultivation of feed crops.  Further, the farm expends significant resources to contract outside veterinary services, a necessity if the farm is to maintain the overall health of each feeding pen and mitigate mortality rates.  While some feedlots operating on this smaller scale actively manage nutritional requirements for cattle through recourse to a staff nutritional professional, this farm is incapable of affording the expense.  In this manner, sub-optimal nutritional mixes of grain and dietary proteins promote ratios of daily feed to weight gain per head for the farm's cattle that tend to be substantially higher than industry averages, incorporating the much lower averages of large, corporate-owned/managed feedlots.  Further, use of beta-agonist medications, promoting increased and more predictable muscle growth in the later stages of cattle finishing, follows a more irregular pattern than in feedlots incorporating day-to-day nutritional management, resulting in longer total feed times and less uniform weights per head.  While the farm's land is wholly owned, like numerous other feedlots of this scale, it maintains a non-negligible debt burden to finance its yearly operations.  Given the smaller scale of the feedlot in relation to corporate operators, it is difficult for the farm to actively engage in financial risk management through futures/forward contracts, rendering it continuously subject to the risk of fluctuations in negotiable market prices per finished head at the time of sale to packers.  Finally, the farm is reliant on outside contracting for transportation of finished cattle to packinghouses at the point of sale.  In this regard, fuel costs, incorporating consideration of distances from the feedlot to purchasers, constitute a relevant variable for the farm.  All of the above considerations shape the particular ways in which the farm is either subject to or capable of manipulating time.  At the outset, the farm is most capable of regulating its particular utilization of local labor services, in which it tends to rely relatively little on the accumulation of substantial investments in specialized human capital.  Most farm hands have a long history of employment with the farm or with other farms in the area, but do not command an excessive return for education or the accumulation of privilege experience, and the farm is able to regulate its employment schedule in relation to seasonal demands, pointedly related to its cultivation schedule.  Its management of physical capital, both as a matter of day-to-day maintenance of farm equipment and investment in new equipment/infrastructure, follows a predictable pattern.  The farm has a collection of proprietary farm equipment that it attempts to maintain for multiple successive years of production, both in feedlot operations and in crop cultivation, but older equipment does have a tendency to require more intensive maintenance.  In good seasons, when market prices for finished cattle are relatively high, the farm is able to save and eventually reinvest savings as capital into new equipment purchases, but this is a multi-year cycle.  In dire circumstances, particularly at harvest times, the farm may be compelled to rent certain capital implements to make up for deficiencies when it would be impractical at best to purchase a new tractor or other heavy equipment outright.  The critical seasonal operational variable, however, obviously concerns the scale of live cattle purchases from breeders, considered in relation to sales prices from breeders, contemporaneous and expected future prices for cattle feed, expected internal outputs from cultivation of feed crops, expected transportation/fuel costs, and expected future sales prices to packers at the conclusion of a finishing period of indeterminate length.  Insofar as all of these considerations figure into the compositions of each of the farm's feeding pens and, thus, the scale of its total operations at any given moment in time, it operates as the primary constraint on the firm's revenues, over a cycle that, for this farm, typically takes thirteen months from purchase to sale.

5.  South Asian Cuisine:  This cafe is a family operation started by an immigrant entrepreneur who initially began by operating a food cart in the downtown of this small college community.  He subsequently invested in a second food cart, renting space on the floor of the college's campus center and preparing a range of food items for sale at both sites in the kitchen of his apartment, a practice that was discontinued when he received greater scrutiny from the local municipal health department.  Faced with the inability to continue operations entirely out of his home, but otherwise awash with free cash from retained earnings from operation of both food carts, he sold one of the food carts and rented a commercial kitchen off the main thoroughfare downtown, with a small store front, allowing him to introduce counter service with limited seating, retaining, as well, the rented food cart space at the college.  After several years of operation and maintenance of a sustained loyal clientele, the entrepreneur took the risk of relocating to a full-size restaurant space, with 1,100 square feet of seating space and a 950 square foot commercial kitchen, fully equipped in compliance with local health standards to provide food items for the restaurant and for the campus food cart.  The majority of the kitchen staff are members of the entrepreneur's extended family, with the exception of one assistant chef and two cleaners.  By contrast, the restaurant maintains a staff of eight to twelve table servers/hostesses, only one of whom is a relative.  During the course of the school year, part time serving help is readily available in the area from students seeking variable weekly shifts.  A son and nephew of the entrepreneur manage and staff the campus food cart.  In provisioning the restaurant and previous manifestations of the business, the entrepreneur has relied largely on a single wholesale food services provider for non-perishable legumes, canned vegetables, miscellaneous ingredients for proprietary sauce recipes, and relatively inexpensive cuts of fresh poultry.  Increasingly, since the opening of the larger restaurant, he has sought to increase local sourcing of fresh vegetables in season in an effort to appeal to demands of clientele for local ingredients.  This move to local food sourcing has raised the cost of several menu items, but the loyalty of repeat customers has maintained a robust demand for the restaurant's production, notwithstanding a wide array of alternative culinary options in the downtown area.  Demand for the restaurant's services varies predictably in relation to the academic schedule of the college.  From mid-May to early September, as students and some faculty and staff leave the area, business declines slightly and the campus food cart is retired entirely.  In turn, the restaurant scales down the number of table staff to a minimum.  Considering seasonal fluctuations of demand and innate geographical limitations on the scale of the market (i.e. steep decline in customer base at the community's periphery), the entrepreneur confronts a relatively static long term horizon for growth of operations.  To the extent that the entrepreneur maintains an amicable relationship to the landlord of the rented space of the restaurant and few alternative rental opportunities exist in the downtown area to improve on monthly rental expenses, there is little prospect that the business will relocate from its current space.  The entrepreneur focuses, for the most part, on diligent maintenance of kitchen equipment (e.g. stoves, small cooking implements, refrigerators, etc.) and accumulation of a share of retained earnings as a replacement fund to deal with depreciation.  Purchase, use, and depreciation of higher cost kitchen equipment represents a multi-year cycle.  Replacement of kitchen staff also occupies the entrepreneur's mind as family members leave the area or embark on other projects.  Tasks in the kitchen manifest a prolonged practice of on the job training in the preparation of proprietary recipes meeting optimal consistency and product quality.  As such, hiring and training of staff for the kitchen represents a palpable investment of time.  Regulating the number of available table servers, by contrast, to adjust to seasonal fluctuations of demand is relatively easier for the restaurant.  Insofar as the restaurant does not serve alcohol, it confronts relatively few restrictions on table staffing beyond compliance with child labor laws.  If staffing issues remain a seasonal, short term variable of concern for the restaurant, then the super-short/immediate term represents itself in weekly or even daily staffing and persistent control of perishable product inventories to ensure both the optimal freshness of prepared dishes and full utilization of purchased fresh produce and poultry items, realizing that any effort to utilize questionable materials in the kitchen is apt to not only bring scrutiny from local health department officials but damage the restaurant's strong reputation within the community.  With this in mind, the day-to-day practice of provisioning, especially when local produce items are in season and available, constitutes the most important and continuous variable in the operation of the business.

The rationale behind this extended elaboration of hypothetical firms has been to imagine circumstances in the operations of conceivable enterprises in which divergent engagements with markets heterogeneously structure entrepreneurial decision sets in relation to time.  In approaching these decision sets, we might emphasize the subjective and strategic nature of entrepreneurial activity in relation to market competition and cooperation/defection by separate agents within the firm.  Such an approach will occupy us in developing a strategic/game theoretic approach to the firm.  Conversely, the accounts above sought to stress, on the one hand, the innate complexity of decision sets even to the extent that, on the other hand, entrepreneurial activity can be reduced to manipulation of a changing/overlapping set of variables against a changing/overlapping set of objective constraints.  In some way, shape, or form, all of the above firms negotiate the complexities of an environment structured by the exogenous determination of critical variables.  While this might be most apparent for the operator of a small cattle feedlot, sandwiched between other producers in a longer supply chain for beef products in which the entrepreneur is utterly incapable of affecting output prices, it is no less true for a corporate workers' compensation insurance carrier, subject to market structures determined, in large part, by statutory and judicially-mandated requirements for commercial insurance coverage.
           Moreover, it is critical to the larger focus of the theory that, over longer temporal periods, each entrepreneur can affect a wider range of variables, but the extent to which each can shape the firm's engagement with markets always depends on the context.  Our feedlot operator is probably least able to shape his long term engagement with the farm's market, but the potential still possibly exists for collaboration with other small operators in his region in order to achieve more predictable output prices by means of financial futures/forward contracting.  Our bus operator can, conceivably, expand the range of terminals serviced by the firm, but this will rely on investment in new rolling stock and in new terminal facilities, with all of the attendant increases in labor, spatial/rental, and capital expenditures to increase the scope of current operations.  With these considerations in mind, I will move to develop a generalized theoretic conception of Marshallian firms in different temporal frames, hoping to maintain a connection to the hypothetical elaborations in this section.