Why One Investment Can Expand a Firm
The Census study's two-margin pattern needs a mechanism. This chapter explains why custom software can make a multi-establishment firm cheaper to operate even when labor and physical capital must be repeated at every site. The useful judgment is not that software automatically creates scale, but that within-firm reuse changes the marginal value of adding an establishment and leaves the firm to balance that benefit against the costs of governing a larger organization.
The cost of a shared input
The model begins by treating a firm as a collection of establishments. Each establishment produces its own variety, and the firm chooses how many establishments to operate. That setup matters because it makes the firm boundary an economic decision. The question is not simply how much output a business produces. It is whether output is produced through one large operating unit, through many units under one owner, or through separate firms that cannot share the same internal capability.
For a non-adopter, the production inputs are labor and capital. If the firm operates two establishments, it needs the labor and capital required at the first site and the labor and capital required at the second. If it operates ten, those rival inputs must be provided across all ten. The firm may obtain better purchasing terms or managerial efficiencies in practice, but the baseline model captures the basic physical constraint: one worker-hour or one machine cannot perform the same task simultaneously at every establishment.
An adopter adds custom software to that production process. The paper's key assumption is that the firm pays for the software once and can use the same quantity of it simultaneously across its establishments. The software cost therefore does not multiply by the number of establishments in the way rival labor and capital costs do. The distinction is not that software is free. It is that the relevant investment is shared within the firm.
Consider a deliberately simple illustration. A firm develops a system that coordinates inventory and replenishment. The first establishment uses the system, along with workers, storage, and equipment. When a second establishment joins the same firm, that site still needs workers, storage, and equipment. It may need training and some adaptation as well. But it does not necessarily need a second, independent development project of equal scope. The original capability can support both sites. The average software burden associated with each establishment can therefore fall as the network grows, even if total software spending rises.
This is why the model treats custom software as a variable input that is non-rival across establishments rather than hiding it entirely inside a fixed cost. A fixed cost is paid once and then sits outside the production decision. A reusable input continues to affect production, but its cost is not repeated in proportion to every operating unit. That distinction allows the model to ask how a firm's software, labor, and capital shares change as its scope changes.
The cost difference appears in the model's unit-cost curves. For a non-adopter, unit cost is constant with respect to firm scope in the baseline: adding establishments does not make the labor-and-capital recipe cheaper merely because the firm has added sites. For an adopter, the effective price of the capital-software bundle falls as scope increases because the software component is shared across more establishments. The adopter's unit cost can therefore decline with scope.
In plain terms, the model compares two kinds of cost. The rival portion grows with the number of establishments: more sites require more labor and capital. The software portion is paid at the firm level: the same investment can support the larger network. As the network expands, the software cost is divided across more operating units, while the rival costs continue to be counted site by site. The model does not need software's sticker price to fall for this effect to appear. The effective cost falls because the firm is using the same input over a wider scope.
This is also why the relevant object is the firm's unit cost rather than the software bill alone. A firm might increase software spending when it expands, because it needs more integration, maintenance, or complementary capability. Yet the cost of producing each unit of the firm's combined output can still decline if the additional establishment makes better use of the existing software base. Conversely, a firm could spend little on software and still have a high total cost if it must repeat every important input at every site. The mechanism is about how costs scale together, not about ranking firms by software dollars.
The model's treatment of the software-capital bundle makes the intuition more precise. Software is not assumed to replace all physical capital. It is combined with capital, and that bundle is then combined with labor. A firm still needs equipment and workers at each establishment; the reusable capability changes the price of the combination. This matters for later factor-share results: if software becomes more valuable as a shared input, the firm can change the relative use of capital and labor rather than simply adding software on top of an unchanged production recipe.
The result is an increasing return to scope. It is not the same as saying that producing more of one identical product is always cheaper. The gain comes from organizing more establishments under one firm and allowing a non-rival capability to serve them all. The paper's model makes the distinction precise by letting establishments produce differentiated varieties. Adding an establishment may broaden the firm's presence rather than simply increase the output of an existing site.
The mechanism also has an organizational boundary. The baseline assumes that software is non-excludable within the firm but excludable across firms. A firm can reuse its own system across its establishments, while another firm cannot simply appropriate it. This creates increasing returns inside the firm without assuming that the same software creates free, economy-wide increasing returns. The source of the advantage is shared access within one organizational boundary.
That assumption is powerful, so it should be read as a condition rather than a universal description of software. A vendor may charge by site or by use. A system developed for one establishment may require substantial adjustment before another can use it. The paper explicitly identifies licensing and establishment-specific adaptation as reasons why real reuse may be partial. The mechanism is strongest when the software, data, processes, and contracts travel together at relatively low additional cost.
The core causal chain can be shown without the model's formal notation:
The diagram is intentionally asymmetric. Rival inputs create a cost that follows each establishment. Non-rival software creates a benefit that can be spread across them. The firm does not choose scope by looking at either side alone; it compares the cost of another establishment with the additional revenue and the software-enabled reduction in effective cost.
Scope is a choice, not a free lunch
Once scope is a choice, the firm has to consider more than the cost of inputs. An additional establishment can earn profits by serving a new location or variety. But its contribution is reduced by within-firm cannibalization when it competes with the firm's existing establishments for overlapping demand. The model also includes a span-of-control cost for maintaining multiple establishments. That cost represents the managerial burden of coordinating a wider organization, even though the baseline does not attempt to describe every real management practice.
The firm therefore compares four forces. First, an additional establishment can bring additional profits. Second, the non-rival software input can reduce the effective cost of operating a broader network. Third, the new establishment may take sales from the firm's existing establishments rather than create entirely new demand. Fourth, the cost of supervising and coordinating the larger network rises with scope. The optimal firm is where the marginal benefit of another establishment is no longer greater than the combined marginal costs.
The word “marginal” is doing important work here. The software benefit is not the total amount the firm has saved since it first adopted. It is the additional value that the existing capability creates when one more establishment can use it. That value can be high at first, when the investment is spread over only a few sites, and then diminish as the network becomes larger. At the same time, the next establishment may be harder to manage or more likely to compete with existing sites. A firm can therefore have increasing returns to scope over part of its range without having an incentive to add establishments forever.
Cannibalization also makes the market side of the choice explicit. If two establishments offer similar varieties to overlapping customers, moving one sale from the old site to the new site does not create the same benefit as reaching a new customer. The firm must count the effect on its own internal demand, not just the revenue observed at the new location. In this setting, software can lower operating cost while the product-market return to expansion still falls. The technology changes one term in the decision; it does not remove the others.
Span-of-control costs supply the organizational counterpart. A firm can share data and software across establishments, but it still has to set priorities, monitor performance, resolve conflicts, and adapt common processes to local conditions. The model represents these burdens with a cost that rises with scope. It does not claim that every management cost has the same form, only that a realistic scope decision needs some force that makes additional establishments progressively harder to coordinate. Without it, the model would mistake technical reusability for organizational capacity.
This balance explains why non-rivality creates a scaling incentive but not an instruction to keep expanding. If management costs were zero and every new establishment reached new customers, the cost-sharing mechanism would dominate too easily. If cannibalization were severe, the firm might not add sites even when software is reusable. The model retains both forces so that the software advantage changes the scope decision without eliminating the scope decision.
The same logic also clarifies the difference between an adopter and a non-adopter. For the non-adopter, adding an establishment brings another round of rival inputs without the software-related decline in unit cost. For the adopter, an added establishment can make the existing software investment more valuable by spreading it over a larger base. Holding productivity and other conditions constant, the adopter has a reason to choose a larger scope than the otherwise comparable non-adopter. The paper's model uses this difference to connect adoption with firm boundaries.
That comparison does not mean that every large firm must adopt or that every adopter must be large. The model includes heterogeneous firm productivity and an adoption decision. A highly productive firm can support more establishments, making the software cost-sharing benefit easier to realize. A small or less productive firm may not operate enough sites for the same investment to pay off. The detailed threshold is the next question, but the direction is already visible: the value of a non-rival input depends on the number of places over which it can be used.
There is also a subtle feedback. A firm may choose a larger scope because software makes that structure more attractive, but a larger scope can in turn make the existing software investment more economical. This is not a claim that adoption and expansion happen in a single predetermined order. In the model, the choices are made jointly. The feedback means that the firm evaluates the technology and the organizational form together rather than asking first whether to buy software and only afterward whether to add establishments.
This joint choice is why the paper's mechanism is different from a simple statement that “large firms use more technology.” That statement could describe a correlation with no explanation. Here, scope changes the effective cost of the input, and the input changes the payoff to scope. The relationship runs through the cost function and the firm's optimization problem. It still depends on assumptions about demand, productivity, management, and reuse, but it supplies a reason for the direction of the observed pattern.
The model also gives a first explanation for the apparently opposite data patterns. A broader firm is more likely to adopt because it can spread the non-rival investment across more establishments. Once it has adopted, however, the same sharing can mean that additional growth relies more heavily on rival physical capacity and complementary inputs. Total software spending may rise while software's share of total capital expenditure falls. The adoption margin records access to the shared capability; the intensity margin records how the complete firm is assembled after access.
That interpretation should not be mistaken for a complete proof. The model is stylized: establishments are treated as identical in the baseline, and many contractual, organizational, and technological details are abstracted away. Its contribution is to show that the Census pattern can arise from a specific interaction between a non-rival input and a scope choice. The model does not establish that this is the only mechanism in the data.
The next task is to make the selection logic explicit. If the software advantage grows with scope, there should be a point at which a firm finds adoption worthwhile and another point at which factor proportions change as scope expands. That threshold and changing factor mix will explain why the same reusable input can benefit firms differently even before its effects are aggregated into market concentration.