2. Historical accounts on the organization of work and the divergence of productivity patterns in the US and the UK at the beginning of the twentieth century

The rise of the large firm is probably best understood by taking a comparative historical approach. Here we compare historical accounts of the development of UK and US firms at the beginning of the twentieth century. Lazonick Reference Lazonick1981, Reference Lazonick1983, Reference Lazonick1990 and Elbaum and Lazonick (Reference Elbaum1984) have argued that in this period British industry lost its role as the workshop of the world to the United States because of its failure to re-equip production processes with modern technology. These contributions show that capitalists were unable to adapt the UK's economic structure, which was still based on the competitive model of the nineteenth century. The transition to a model of corporate or managerial capitalism like that developed in the United States did not take place due to institutional inertia in the organization of industry, which in turn determined a specific arrangement of the labor process. As a consequence of their competitive mindset, British decision makers failed to make a collective effort to alter these institutional constraints as US capitalists did.

The managerial organization and technologies employed by late nineteenth-century UK firms were comparatively simple. They were mainly run by owner-proprietors or close family associates. Managerial and administrative staffs were small, as methods of cost accounting and production control were crude or not used at all. A specific development in the British industry in the second half of the nineteenth century was that many groups of workers consolidated their control over the production process. Individual industrialists, engaged as they were in unsettling competition with other firms, opted to collectively accommodate unions of skilled and strategically positioned workers rather than jeopardize the fortunes of their firms through industrial conflict. During that time the labor movement also made important legislative gains which enhanced the ability of workers to organize unions and stage successful strikes. Even when skill-displacing technical change took place, the power of the unions had become so great that it had little effect on costs, as wages could not be cut.

For British managers this system of craft control had a number of advantages. The reliance on shop-floor labor to coordinate production involved low organizational and capital costs. The large administrative overhead and capital-intense production that characterized corporate capitalism could be avoided (Lazonick, Reference Lazonick1990: 181 ff). It was also a very effective mode of recruitment and supervision, as it was decentralized and built on personal relations. In the competitive environment in which firms operated, these features of craft control proved advantageous as firms had a very limited ability to experiment with different organizations of production. In any event, this organization of production allowed them to compete against and resist high fixed cost competition for some time.

The disadvantages of this arrangement were eventually responsible for the British industry falling behind that of the United States as they certainly delayed or altogether inhibited the adoption of new technologies. As (Lazonick Reference Lazonick1981) argues in his study of Lancashire cotton spinning, when technical change threatened their privileged position, skilled workers often cooperated with managers to increase their work effort in order to cut unit costs and overcome the expected net advantage of the new technology. As a consequence, the diffusion of new technologies was extremely slow. In many cases skilled labor also controlled the technical adjustment and tuning of machines. This created a situation where no two pairs of otherwise identical machines worked the same way. This lack of standardization made crafted workers less disposable. Together with favorable labor legislation, a strong collective organization in handling labor-related issues, and the power to execute important managerial tasks such as the organization of production and the hiring and firing of workers all ensured that British craftsmen would be in charge whenever the relation between work effort and pay was determined. Firms could only threaten to introduce new machinery from time to time in order to elicit more effort, but the power of the workers remained largely untouched. Lazonick's work suggests that the failure of British managers and proprietors to take control of the production process was a major factor in long-term British decline.

The ‘aristocratic’ position of craftsmen also had an effect on the labor market and the workers themselves. As they were in charge of hiring and firing, they could not only establish the relation between work effort and pay, but they could also prevent general labor market conditions from working against their own interests. The unions repeatedly and successfully opposed attempts on the part of management to interfere with hiring and firing of workers (Lazonick, Reference Lazonick1981: 502; Lazonick, Reference Lazonick1983: 228 – 229). At the same time most crafted workers retained their jobs for a very long time. This meant there were more skilled workers available than the labor market could absorb. However, as it was the insiders who did the hiring, labor market pressure rarely translated into wage cuts. Outsiders either had the option to seek low-paid unskilled work, remain unemployed, or emigrate to the United States. This persistent insider – outsider problem had the same effect on wages as an undersupply of workers. As a result, the chances of a skilled worker of finding identical work after being dismissed were low, but this had no effect on the level of the insiders' wages.

The US initially had a similar system of craft control, which characterized the American System of Manufactures (Lazonick and Brush, Reference Lazonick and Brush1985). However, unlike in the UK, American businessmen's reliance on inside contracting, i.e. skilled shop-floor labor, to coordinate production activities was generally short lived. In contrast to British managers, they lacked neither the individual nor collective means to alter the prevailing institutional constraints. They developed technological and organizational alternatives to leaving skills, and along with them the control of work, on the shop floor. In particular, the economic downturn at the beginning of the 1880s and the immigration waves in 1880s were used to vigorously break the power of the unions and gain control over the production process (Montgomery, Reference Montgomery1987: chapter 1). ‘By employing unskilled immigrants from Eastern and Southern Europe, by investing in deskilling technological change, and by elaborating their managerial structures to plan and coordinate the productive transformation, US industrial capitalists attacked the craft control that workers – typically of British and German origin – had staked out during the 1870s and 1880s’ (quoted from Lazonick and O'Sullivan,. Reference Lazonick, O'Sullivan, Chandler, Amatori and Takashi1997: 501).

As (Chandler Reference Chandler1962) has shown, the rise of corporate capitalism in the US went hand in hand with the rise of the ‘large’ enterprise. These were essentially firms that had developed large administrations which were used to control the production process in order to cut production costs and control the market in order to evade competition. Unlike British firms, American firms changed their industrial structure in such a way as to reduce the pressure of competition. They integrated and merged operations, pursuing strategies to segment the market through marketing. On the cost cutting front initial attempts to introduce new management methods like Systemic Management took place as early as the 1870s (Litterer, Reference Litterer1963). These developments foretold what would develop from the late 1880s onward. Many authors have argued that the introduction of management methods that relied on Frederick W. Taylor's Scientific Management principles were a core ingredient in breaking the power of the unions and gaining control of the shop-floor (e.g. (Clawson, Reference Clawson1980; Montgomery, Reference Montgomery1987). It consisted of breaking the work process down to its most elementary tasks and using closely monitored unskilled workers to execute them. This favored the standardization of work routines (Noble, Reference Noble1977: chapter 5) and the development of cost measures to control activities (Levenstein, Reference Levenstein and Temin1991). The gathering and evaluation of information on production and sales increased sharply, thereby increasing the importance of administrative activities. Eventually the information flows generated in this way swelled to such a scale that it became necessary to apply the very same principles to office (Beniger, Reference Beniger1986; Yates, Reference Yates1989; Reinstaller and Hölzl, Reference Reinstaller, Hölzl, Foster and Hölzl2004).

Although crafted workers tried to collectively organize and resist these developments in the 1880s, the combined effects of the racial segmentation of the work force, the firms' resolute use of strikebreakers (mostly immigrants), the tactic of locking out workers and an important High Court ruling to outlaw workers' control ensured that craftsmen failed to gain control over the production process (Montgomery, Reference Montgomery1987: chapter 1). The division of labor that ensued as a consequence of modern management methods and the resulting allocation of work warranted that no crafted worker was able to control an entire production process. By the early years of the twentieth century most industries had completely abandoned methods of production in which craftsmen made the products and laborers fetched and carried parts. The new industrial system with its extreme division of labor broke up the crafts, replacing skilled workers with cheaper machine operators. Most skilled workers indeed ceased to be production workers. They became engaged in ancillary tasks like planning and tool making, while the actual production was carried out by specialized operatives (Montgomery, Reference Montgomery1987: chapter 5).

The consequence of this development was that management was very much in charge of determining the relation between work effort and pay. ‘Breaking down company operations into component parts . . . provided executives with an accurate standard against which to measure the performance of each unit of operation’ (quoted from (quoted from Noble, Reference Noble1977: 282). With these figures at hand they could more easily determine who was performing under par and fire these workers – even more so, as the weakened unions could not oppose such policies. On the other hand, managers also understood perfectly well how an abundant labor supply could work in their favor. The existence of a continuous flow of low-skilled or unskilled workers ensured that deskilling technical change would also allow wages to be cut. With the unions unable to control wages, dissatisfied skilled workers needed to leave the firm in order to avoid the consequences of technical change or accept substantial wage cuts.

American industrialists were neither constrained by too fierce competition nor unable to change the institutional factors that constrained British firms. Consequently, they could opt for techno-organizational designs that maximized productivity. As Lazonick and O'Sullivan (Reference Lazonick, O'Sullivan, Chandler, Amatori and Takashi1997) have argued, the productivity growth experienced by US manufacturing in the early twentieth century could not have been achieved without managerial success in gaining control over work organization on the shop floor. The importance of this development is studied in the following simulation model.

3. The model

In this section we present a simulation model that captures some of the aspects we have discussed in the first two sections of the paper. In this model, economic growth is conceived as flowing from an increasing division of labor. The near-decomposable structures that emerge from this process are dynamically efficient in that they encourage learning by doing. On the other hand, as we model the interaction between management and workers, smaller and more specialized routines are also easier to monitor. Therefore, firm owners and management have an interest in organizing production in a near-decomposable way, while workers have an interest in opposing this, as it implies a loss of control over the production process. Over time, in dependence on the institutional arrangements governing the relationship between workers and capitalists, firms learn about the best techno-organizational design and adapt their innovation strategies accordingly. A simulation exercise of this analytically untractable model then demonstrates that the pace of technical advance will depend on the balance of power between management and workers.

3.1 Techno-organizational designs and innovation

Figure 1 shows how the technology and organization of a firm is conceptualized in the model. It is assumed that the activities of a firm produce an output with certain technical characteristics. These in turn generate services and eventually value to the customers of the firm (Saviotti and Metcalfe, Reference Saviotti and Metcalfe1984). In Figure 1(a) these technical characteristics are represented by θ₁ to θ₄ which are produced by routines m ₁ and m ₂. Footnote ² More generally, we will say that the technology of a firm consists of a set of n _t routines m _i grouped by means of n _t−1 administrative routines m^a_j into a techno-organizational design that produces a given vector Θ of k technical characteristics of the final output. As the division of labor is allowed to vary over time n_t carries the time index t.

Fig. 1.

Decomposition in the technology-characteristics map: (a) a simple map with four technical characteristics θ₁ − θ₄, four tasks grouped into two activities m ₁ and m ₂. (b) Neutralizing the effect of feedback loops through decomposition and introduction of the coordination (administrative) routine m^a ₂

Together, the technical characteristics meet defined customer needs in the market where the firm operates, and we assume that a product is viable in the market if, and only if, all the technical characteristics are delivered. Hence, production is subject to the condition that all produced technical characteristics θ_h must correspond to the market vector Θ, or ∪^k_h=1〈θ_h〉 = Θ. The set corresponds to one techno-organizational design out of a finite design space in use at time t, which the firm explores by changing the organization of production. Each of the m_i routines present in a design consists of λ_i, d_t tasks, . The number of tasks λ_i, d_t is allowed to vary across routines and it is directly proportional to the number of technical characteristics produced by that routine. So, if a routine produces λ_i, d_t characteristics, it will consist of the same number of tasks.

Near-decomposability and performance In order to introduce the idea of near-de-com-po-sa-bi-li-ty, we assume that, on the one hand, the performance of a routine m_i is not affected by any other routine m_l, l ≠ i. On the other hand, we posit that all λ_i, d_t tasks comprising a routine are non-separable, i.e. the performance at time t, , of any task h in routine m_i affects the performance of all other tasks in this routine, while its own performance is in turn affected by all other tasks in m_i. Therefore, on the level of routines, optimization by stages is excluded as positive and negative feedback loops between the tasks exist, while across routines it is possible. This reflects a situation that is, for instance, typical in team production as discussed in the introduction. So, if one member performs under par, the work efficiency of all other members is affected. However, entire teams can be replaced. Figure 1 summarizes these assumptions. If the performance of the task producing characteristic θ₃ in routines m ₂ is changed, feedback loops may cause the performance of the task producing θ₄ to change as well, making any improvement of the performance of the entire routine m ₂ more difficult.

We assume that the performance η_h,t of every task h in any production routine in the firm is measured by a productivity index such that η_h,t ∈ [0, 1]. We also assume that there is a fixed general technological frontier which is equivalent to saying that the technological landscape does not change over time but that the division of labor is a means to explore it. Consequently, simulations for different parameter settings are directly comparable, and no rescaling of past performance draws is necessary. Given these conditions in the simulations we then draw the performance value η_h,t for each task from a uniform random distribution such that η_h,t → Uniform[0, 1]. The performance of a task represented through its labor augmenting effect is then calculated as and the average productivity for a given labor input in routine m_i is then the average over all tasks, .Footnote ³ The assumption of non-separability in a routine requires that if the firm tries to improve the performance of any of the λ_i, d_t tasks in a routine, λ_i, d_t values have to be re-drawn and a new has to be calculated.Footnote ⁴ Routines consisting of a higher number of tasks are therefore more difficult to improve than smaller ones. The number of routines n_t is then a measure of the degree of decomposition of a specific design d_t.

Hierarchy and new coordination routines In Figure 1 (b) the problem of strong complementarity within routine m ₂ is resolved by splitting it into two distinct routines, m′₂ and m ₃, each focused on exactly one task of the original routine. Hence, any attempt to change the performance of m′₂ producing θ₃ will leave m ₃ producing θ₄ unaffected. This implies that an optimization by stages is now possible for these two routines. The ensuing coordination problem between the two new routines, which was formerly internalized in routine m ₂ is solved by introducing a coordination mechanism such as an organizational and/or technical interface that neutralizes the feedback. One can think of these as administrative routines needed to coordinate and control the operations of two shop-floor processes. In Figure 1 they are represented by the coordination routines m^a_j. Thus, ‘architectural’ knowledge on a production routine is moved to the management and integrated in an administrative routine, m^a_j. The subset of coordination routines therefore captures the ‘architecture’ of an organizational design d_t, i.e. the knowledge about the relation between single production routines m_i. There are n_t−1 coordination routines m^a_j, as we assume that one administrative task is required to coordinate and neutralize the feedbacks between any pair of production routines. Given this assumption, at any time the total number of routines in a design is then n^tot_t = 2n_t − 1.

With the increasing decomposition of the production routines, the weight of coordination tasks as related to productive activities increases. If these are costly, then overhead costs resulting from the process of decomposition will rise relatively to the cost of productive activities. We will assume that the overhead costs are an increasing function in the number of coordination routines, and that this happens at an increasing rate. These costs are bounded from above by the maximum decomposition of the production routines, n^max=k. Hence, the more production routines have to be coordinated, the more knowledge about the production process itself is required on the level of the administration, and the more expensive the administration becomes. In what follows we will ignore potential problems of interdependence and feedback mechanisms on the level of the administrative or coordination routines.

Exploration of the design space by the firm The management of the firm is assumed to use a set of innovation strategies to explore the space of techno-organizational designs . The strategy space S=(s ₁, s ₂, s ₃) consists of three innovation activities, each of which is used with probability μ_j,t at each time step t. The three strategies are given by learning by doing, s ₁, by the decomposition (or splitting) of a routine into two smaller ones, s ₂, and by job-enrichment (or integration) strategies where two routines are reorganized into a larger one, s ₃.Footnote ⁵

Learning by doing may be thought of as management measures aimed at improving the skills and knowledge of team members. This strategy leaves the structure of the techno-organizational design untouched, i.e. the number of activities and the set of technical characteristics influenced by each does not change. Furthermore no capital investment is needed. The improvement is the result of a cumulative process. The performance of existing routines is simply improved by a ‘learning’ draw for all tasks in a routine. If the performance improves, it is adopted – a decision rule known as hill-climbing in the original NK-model (Kauffman, Reference Kauffman1993).

The second and third innovation strategies change the techno-organizational design of the firm. In the case of the decomposition strategy, the management increases the separability of its production technology by identifying and neutralizing complementarities that bind tasks in a routine. If the overall performance of the firm improves, the new design is kept. These performance improvements may be due to the reduction in hold-up problems in production and, as a consequence, of a more efficient utilization of workers and machinery as well as a higher learning rate on the job due to the specialization of productive activities and the use of more specialized and effort-saving technical equipment (Lazonick, Reference Lazonick1990: 333ff). Finally, the job-enrichment or integration strategy involves the selective acquisition of links between routines. It is the reverse operation of splitting. Performance improvements under this strategy may be thought of as the realization of synergies. In terms of Figure 1, this implies that the two distinct routines, m′₂ and m ₃ in Figure 1 (b) are rejoined to m ₂, and m^a ₂ is removed to get Figure 1 (a). However, the performance values of routine m ₂ after enrichment are redrawn and performance is recalculated. Therefore, enrichment or integration is not just a simple reversal of a splitting operation.

Investment and innovation When the firm changes its techno-organizational design as a consequence of splitting and enrichment strategies, it will have to invest, i.e. it will either need to upgrade existing machinery or replace old capital vintages altogether. This implies that the capital equipment in use is always commensurate to the degree of specialization of the routines. In the present model, specialized capital equipment is a catalyst for the introduction of changes in the techno-organizational design. We will assume that the firm starts with an initial capital stock K ₀ given by a specific capital-output ratio which reflects the technological base of the industry in which the firm operates. We define K ₀ = R ₀κ, where R ₀ is the initial revenue of the firm and κ is the assumed capital-output ratio. In order not to overburden the model with details, we assume that the management continuously replaces the existing capital stock, given by the initial capital stock and past net investment, because of wear. Net investment takes place only as a consequence of splitting and enrichment strategies. We also assume that output and capital in this case grow at the same rate. Therefore, the investment required to install a new techno-organizational design d′ is given by

where the index τ indicates that net investment takes place at irregular points in time τ, q_t is the physical output produced at time t, and E[q _t+1] is the expected output at time t+1 if an innovation is adopted. This way of modelling the relation between output growth and net investment implies constant returns to scale. At some point in time t the value of the capital stock is then given by K_t = K ₀ + ∑_τI _τ, where τ are the points in time in which net-investment has taken place. I _τ may also be thought as of capturing the fixed cost for developing a specific techno-organizational design, that also requires capital of a specific quality.

3.2 Workers' effort choice

Once the management has chosen an innovation move, we assume that this is announced to the staff and the workers then decide upon the effort they want to put into their work if the innovation is adopted. The effort choice of workers is specified following the general ideas outlined by Bowles (Reference Bowles1985). Workers may oppose innovation through the reduction of work effort or even sabotage.

To model this, we have to specify how wages are set. We assume that the average wages paid per unit of output in a routine i, w _i,t, are a function of the number of technical characteristics λ_i,dt produced in it, which captures also its skill profile. Therefore, more-qualified workers, i.e. those able to carry out a larger number of tasks, get a higher wage. The firm can control this variable endogenously by changing the division of labor and simplifying the work. The level of wages also depends on a parameter σ ∈ [0, 1] that reflects the labor market situation. It represents the extent to which the outside labor market situation affects the bargaining position of workers within the firm. We specify it here as the risk of not being able to find a job with another employer for the same qualification profile. If, for instance, σ is small, a firm will find it more difficult to impose wage cuts or find workers with similar skills if the staff quits.Footnote ⁶ Finally, we also assume that mechanisms are in place which enable workers to oppose attempts by the management to fire employees. This is captured by parameter pr_out ∈ [0, 1], which reflects the probability of being dismissed if one is found disobeying the directives of the management. Depending on how powerful these mechanisms are, or how powerful workers are in relation to the management, the chances of a worker being dismissed if found to be shirking will vary. If, say, legislation is in place that makes hiring and firing difficult, the probability of a worker being dismissed if found to be shirking is low. Alternatively, if the workers' response to management actions is individualistic, the management can fire workers whose performance is below average or who hinder changes to the production process. Whereas, if the response is ‘collective’, for instance in the form of repeated collective and simultaneous exits, the sacking of workers for inadequate performance may be prohibitively expensive. Therefore, parameter pr_out captures the relative power of the management, as opposed to that of the workers, to control the relation between work (effort) and pay. Wages will be higher when the probability of being fired is lower. Wages are therefore a function of the skill profile of an activity, the labor market situation and the power relation inside the firm, w _i,t ≡ w(λ_i,dt, σ, pr_out). The following restrictions are imposed in order to have a well-behaved wage setting function. We assume that w(λ_i,dt, σ, pr_out) increases with λ_i,dt at an increasing rate and that it is bounded from above by the maximum number of technical characteristics k a firm produces, sup w_i,t = w(λ_i,dt = k,σ,pr_out). Furthermore, for every given λ_i,dt wages fall if unemployment increases at a decreasing rate. Hence, wages are bounded from below by inf w_i,t = w_min, where w_min is the income/unemployment benefit the worker would gain with certainty if dismissed.

To summarize, given that the innovation choices of the management affect wages, workers have two options for reacting to an unwanted innovation decision made by the management. First, they may opt to quit the firm and seek employment elsewhere. The value of the ‘exit’ option depends on the labor market situation captured by σ. Workers will be more willing to accept wage cuts if the chance of not getting an equally well-paid job in another firm is low and they will be more likely to quit if it is high. The second option is to stay in the firm and reduce their work effort. This will be contingent on three factors. It will depend on the management's capability to detect shirking workers, its capability to fire a shirking worker, which depends on how well organized labor is on the shop-floor, and the cost to the worker of being fired. Hence, we call this the ‘voice’ option.

The link between the innovation choices of the firm and the wage-setting mechanism is modelled as follows. Assume that the probability of detecting shirking workers depends on the complexity of the routine of which they are part. Simpler routines are easier to monitor, while the performance of more complex ones is difficult to assess. Then, the probability of being detected, pr ^δ_i,t, is given by the probability that workers' behavior is observed by the employer, pr ⁰_i,t. This probability is directly proportional to the complexity of the routine in which they are employed. If we define a variable ν_i,t ≡ λ_i,dt/k, then the probability of observing workers not complying with management directives is given by pr ⁰_i,t ≡ (1 − ν_i,t). Hence, the probability of the management detecting idle workers in activity i after an innovation is then pr ^δ_i,t+1 = pr ⁰_i,t+1(1 − e _t+1), where e _i,t, e _i,t ∈ [0, 1], is the average effort by workers in routine i.

The cost of dismissal to workers in routine i depends on the probability of finding a comparable job outside the firm and the probability of not finding such a job and having with certainty to settle for a lower-paid job or unemployment benefits, i.e. the expected wage if dismissed is given by E[w^exit _i,t+1] = ((1 − σ)w _i,t − σw_min). The expected wage in activity i is therefore

where the first term is the expected wage if not detected, the second term is the wage if detected but not fired, and the last term represents the wage if detected and consequently fired. The value of w _i,t+1 is determined through the innovation strategy announced by the firm at the beginning of the period. If the disutility of work to workers is quadratic and given by , and the expected pay-off is given by , then pay-off maximizing workers will choose a work effort

(1)

in each activity i. The restriction e*_i,t+1<e_min reflects the assumption that for every techno-organizational design a firm is able to elicit some minimum effort from workers. Parameter w_s corresponds to a subsistence wage. Working up to this income level will not be felt as a burden. Given a specific effort level e*_i,t+1 the labor coefficient per unit of production in activity i is then determined by l _i,t+1 = 1/e*_i,t+1.

3.3 The cost and adoption of new designs

The specification of the technology and organization of the firm, as well as the labor process presented in the two previous sections is now embedded into a standard model where the firm faces a downward-sloping demand curve and Say's law holds. The firm maximizes profits in each period for given the costs. As we exclude rational expectations, the firm reinforces the innovation strategies that have yielded the highest cost reduction in the past. Hence, the behavior of the firm over time is given by a changing probability distribution over her three actions, s_t = [μ_1,ts ₁μ_2,ts ₂μ_3,ts ₃]′, with μ_1,t + μ_2,t + μ_3,t = 1. The probability distribution changes as the innovation policy mix evolves through reinforcement learning, given some initial probabilities μ_j,t=0. The dynamic decision problem of the firm is then to find a sequence of adoption of techno-organizational designs that maximizes the flow of profits over time.

Cost of production for a given design d_t We get the variable costs of production by aggregating the unit cost of production in a routine over all routines. It is weighted with the number of technical characteristics affected in relation to the total number of technical characteristics produced, i.e. with λ_i,dt/k. Taking into account overhead costs, we get

(2)

where is the weighted average unit wage in all routines, is the weighted average labor coefficient, and is the weighted average performance factor in shop-floor routines. As the division of labor changes and new coordination routines are introduced, the total number of routines increases and their relative weight in unit cost as compared to production cost changes. Therefore, the cost terms in (2) need to be weighted as well. For this purpose we introduce z_t, which is defined as z_t=k/(k+(n_t−1)).

In each period the firm incurs capital costs. If capital prices don't change and capital costs are debt financed and paid off in annuities, capital prices to the firm remain constant over time as long as interest rates and pay-back periods also remain constant. If the pay-back period is also equal to the scraping period, then, for a given capital stock K_t, an annuity

(3)

is paid each period, where r is the interest rate and Δt is the duration of the pay-back period. If the interest rate is also equal to the discount rate, then the revenue generated by an investment I _τ and the cost of this investment are valued at the same rate, and discounting issues can be neglected. The annuity form in equation (3) implies that the sum of interest and amortization charges are equal in each period and capital costs are therefore equal over the life of the investment.

Profit maximization and the adoption of new designs The profits for any given techno-organizational design d_t are

(4)

and the inverse demand the firm faces is given by

(5)

Is is a constant reflecting the intercept of the demand function and ε is the price elasticity of demand with ε>1. During each period t the firm sets quantities in order to maximize its profits, i.e. ∂Π_d,t(s_t)/∂q_t = 0, such that the optimum quantity of production is given by

(6)

Hence, the maximized profits for a techno-organizational design d_t at time step t are given by

(7)

The decision to adopt an innovation will depend on its profitability. If the firm discovers a new organizational design d′, it compares its expected pay-off given the expected reaction of workers to the announced innovation project with the pay-off it is able to make using the old design d_t

(8)

From this follows the adoption rule for any organizational innovation. The firm compares the pay-off of the current techno-organizational design with the pay-off it expects from using the innovation. The adoption rule is then given by

(9)

i.e. whenever the expected profits from using an innovation are larger than those for the given techno-organizational design, then the innovation will be adopted.

Reinforcement of successful strategies The management learns about the best strategies for reducing costs in the space of techno-organizational designs, as it explores the design space. The reinforcement learning we apply is identical to the one studied by Arthur (Reference Arthur1993), where each of the strategies is allocated strength based on its past contribution to the performance of the firm

(10)

where ΔΠ*_t = Π*_t − Π*_t−1 indicates the change in the performance improvement between two time steps t and t−1 where strategy s_j was used. Equation (10) reinforces the strategies that best maximize the stream of profits.