DIME workshop Process, Technology, and Organisation: Towards a useful Theory of Production

Pisa, November 8-9, 2010

The Fund-Flow model: its foundations, extensions and usefulness for analysing technological change at the microeconomic level∗

Pere Mir-Artigues♦

The Fund-Flow model was first presented by Nicholas Georgescu-Roegen1 (1906-1994) at the Conference of the International Economic Association, held in Rome in 1965 (Georgescu-Roegen, 1969). Since then it reappeared in his work, without any appreciable changes, on numerous occasions. However, the last study specifically dedicated to this model was published in the mid-seventies. The three later decades, it has been improved and expanded by different contributors. Despite its originality, fertility and usefulness, the model still remains largely unknown. The present paper has been divided into three parts. Firstly, it examines the methodological foundations of the Fund-Flow model, offering a brief review. Secondly, it considers different extensions to the model as, for example, an adaptation to analyse the sources of productivity. Finally, it is suggested to use the model as a framework for exploring process innovations at the microeconomic level. 1. Foundations of the Fund-Flow Model The Fund-Flow model has the following prominent methodological and theoretical features:

1. It employs a naturalist approach to productive activities. 2. It is a partial interdependence model. 3. It refuses to be a simple black box. 4. Time is a fundamental dimension.

Let us take a detailed look at these points.

1.1. A naturalist approach

As it is known, production is a fundamental economic activity. Based on a microeconomic approach, production must be understood as the process of creating value by way of the co-ordinated execution of a given number of operations over a specific interval of time. Productive operations requires different amounts of resources and time to be executed, and encompasses a huge diversity of skills and, above all, social relations. Needless to say, it is possible to envisage a wide variety of different approaches to productive activities, and a similar range of associated models.

Models are stylised and incomplete representations of reality. They can be understood as a synthesis of the most important aspects of a system and, as is known, ∗ I would like to thank Josep González-Calvet for his valuable comments, particularly in chapter 2.2, and Malcolm Hayes for text revision. All errors that could be remained are my responsibility alone. ♦ University of Lleida and the Scientific Park of the University of Barcelona. 1 References to the life and work of Nicholas Georgescu-Roegen may be found in Zamagni (1982), Georgescu-Roegen (1989 and 1992), Maneschi & Zamagni (1997) and Bonaiuti (2001).

they proliferate in practically every field of scientific research. Amongst the criteria used to evaluate the quality of a model, the most outstanding is the condition that the set of the reffered real objects should not be empty. If this condition was not fulfilled, this model would be rejected as a simple metaphor. However, a given phenomenon can potentially be dealt with using different models, each characterised by a particular methodological approach and taking into account certain specific aspects rather than others. In this sense, on the one hand, the Fund-Flow model is characterised by its naturalist view and, on the other, as it is explained later, it is focused in analysing the temporal dimension of the production processes.

In a naturalist approach, only realistic assumptions that can be submitted to empirical scrutiny are acceptable. Or, put in other words, assumptions have to comply with the physical, chemical and biological laws.2 However, the Fund-Flow model defies the conventionalism of suppositions that guarantee appropriate economic behaviour, such as perfect substitution among factors, convexity and derivability. In fact, the Fund-Flow model is at the antipodes of the instrumentalism which characterises the mainstream approach to production. According to the logic of instrumentalism, the goal of the scientific inquiry is to build rules designed to manipulate reality, rather than to produce either a description or an analitycal comprehension of it. Instrumentalism stresses that hypothesis are acceptable, if they are useful, rather than necessarily realistic. On the contrary, in the Fund-Flow approach, what matters is truthfulness.3

1.2. A partial interdependence model

In the economic analysis of productive processes, two main approaches have largely been adopted:

1. Models focused on the creation, and distribution, of the value generated in the transformation process of given inputs into outputs. To a greater or lesser extent, such analitycal models tend to bring together the technical features of the process and the role played by the agents involved in it. As expected, very different types of models can be proposed according to the assumptions initially established.

2. The production process is understood as an articulated set of decisions, ranging from the design stage to the control of productive operations. This pragmatic view includes the detailed planning of tasks in order to achieve a specific goal (whether technical and/or financial) which is considered desirable by the managers. To this end, the results will be measured using generally accepted indicators.

There is an enormous variety of the first type of models. According to the methodological approach by which they are defined, it is possible to distinguish models of general and partial interdependence (also known as general and partial equilibrium models). The first category focuses upon the sectoral cross-requirements and tries to 2 This general condition can be partially relaxed in the case of facts that go beyond the scope of the model. As later explained, this is the case with the assumption of the constant efficiency of fixed capital. 3 It should be remembered that, despite the fact that he was very upset by the misuse of mathematics in maintream economics, Georgescu-Roegen did not consider formal elegance, the offspring of conventionalism and instrumentalism, to be the most important quality of an economic model. Indeed, although formal tools are useful for extracting certain required conclusions from hypotethical postulates, mathematics is unable to sustain specific concepts of an empirical discipline. Futhermore, although a formal filter is necessary, it is not enough.

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analyse the conditions for the reproduction of the economic system, as well as the distribution of the surplus (or net product) generated. Such models typically adopt a long-term outlook. Physiocratic and Classical school authors made different proposals, but the most refined and complete version is that of Sraffa.

The partial equilibrium approach is characterized by setting aside most of the reciprocal influences that exist between the different productive activities. These models articulate a set of hypothesis that relate to the internal configuration of the production processes (Tani, 1989 and 1993). Even though a certain protagonism is afforded to the most immediate environment (inputs and outputs markets) its role is reduced to that of simple data. Furthermore, partial analysis prefers a one-way view of production: it is only considered the direct and one-directional relationship running from the raw materials to the goods produced.4 Despite the undeniable advantages of such a restricted outlook, contextual shortcomings can give rise to some problems of logical consistency.

Bearing in mind the cost entailed by any classification, models of partial interdependence may be divided into two main types. The first type has a clearly normative goal: the pursuit and refinement of certain economic optimisation principles.5 In such a case, production processes are automatically assumed to be technically efficient and it is therefore pointless to study organisational aspects such as the division of labour, etc. This is a very wide-ranging group which includes the numerous formal variants of the production function (see, for example, Frisch, 1965; Ferguson, 1969 and Shephard, 1970).6 The second type proposes a very detailed description of the production process. Here, the nature of the materials used and of the operations to be performed merit preferential treatment. At the same time, special relevance is also given to the time dimension. This implies that organisational issues such as reducing idleness in the productive capacity of the involved agents and analysing the relationship between tasks and skills are two of the main concerns. The Fund-Flow model is the most important proposal in this line of work.7

It is important to be aware of the theoretical limitations of a partial approach. As it is well known, Georgescu-Roegen included some assumptions in his model that are difficult to accept (Kurz & Salvadori, 2003). These include the fact that the efficiency of fixed capital assets is held unaltered throughout the successive production cycles and 4 This process is continuous. Unfortunately, continuity is currently misunderstood as a transition with no significant changes. Nevertheless, between a caterpillar and a butterfly there is continuity although they are two very different phases of the same lifecycle. A process may therefore be continuous although it spans very different stages. 5 In such models the heuristic principle of maximisation becomes substantive theory, even though this is an epistemic fallacy. Indeed, the individual maximisation postulate should have been considered as a simple heuristic guide, that is, as a tool for formulating questions. Nonetheless, this principle is raised to total theory. According to this logic, every fact can be explained in terms of optimisation behaviour. Furthermore, rather than building the fundamentals of individual maximisation, the next step is to develop an axiomatic racionality. This is created from false suppositions, which should not be confused with abstract ones. Nonetheless, a conjecture can only become a theory if it has a factual content, heuristic fertility and it is consistent with accepted knowledge. 6 There are also some other theoretical proposals such as the so-called engineering production functions (see Chenery, 1949 and Whitehead, 1990, as well as the critical review by Mirowski, 1989: 327-332), the lineal activity analysis (Koopmans, 1951) and the (neo)Austrian approach to productive activities (Hicks, 1973 and Amendola & Gaffard, 1988). 7 There is also a model that considers the production process as a network of tasks (Scazzieri, 1993; Landesmann & Scazzieri, 1996a & b). Nonetheless, these same authors confess their intellectual debt to the Georgescu-Roegen’s work.

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workers do not experience any loss in their work capacity.8 However, the labour and machinery require an appropriate energy and material inputs to mantain their productive capacities at an acceptable level. Moreover, over time, they progressively and inevitably age. Despite the explanations given by Georgescu-Roegen, the entire model came under fire, as its assumptions were untenable. In any case, it should be stressed that these theoretical weaknesses of the model can not be overcome: they stem from the own methodological limitations of the partial equilibrium approach (see Mir-Artigues and González-Calvet, 2007: 38-47). Given such a situation, the only option is to be very cautious when exploring the analytical possibilities of the model.

1.3. Opening the black box

Georgescu-Roegen’s model includes a detailed inventory of all the elements directly involved in the production process. In this sense, his proposal may be considered as a major contribution to resolving the excessively simplistic treatment of the factors of production encountered in mainstream models. Indeed, from a methodological point of view, a production function is a black box representation of the productive activities. The production process is considered as a single unit, without any internal structure. Black box models only take into account external and global variables: net causes (inputs) and net effects (outputs). Only the quantities of inputs and outputs are considered, laying aside the operations between the former to the latter. Although outputs and inputs are intrinsically connected through a chain of transformation stages, the production function is built without considering this.

As is known, in economic theory there are a lot of black box models and their success can be explained in the three following terms:

1. The straightforwardness of their construction and use. 2. Their appropriateness to the statistical data availabe. 3. The fact that they are generally helpful for pragmatic uses.

But, in such models, what is most important is what is not seen: the specific mechanisms that remain hidden. It is not surprising that black box models give rise to many problems: low conceptual content, very limited heuristic capacity, and imperfect empirical validation because of their variable indistinctness and the fact that they fit very different data sets. It is therefore common to find this kind of approach in poorly developed scientific models and theories. But, what it is difficult to justify, it is not trying to open these black boxes and to shed some light on their internal mechanisms. This has always been a major task of scientific inquiry.

As has already been pointed out, the Fund-Flow model is an attempt to open the black box of the production function. Neverthesess, certain authors may consider that any detailed analysis of the productive activities belongs to the domain of (agricultural or industrial) engineering. This effort could therefore push the inquiry beyond the scope of economics. This question is not, however, well founded, because it is easy to see that, once the black box has been opened, various economic issues appear. In fact, this offers us the possibility to learn a lot about economies of scale, indivisibility, process innovation and temporal optimisation.9 Despite the inevitably fuzzy boundaries, the 8 Georgescu-Roegen also suggested that the impact of harmful by-products can be ignored because of they have no economic value. 9 It could be suspected that this argument is, in truth, a pretext to avoid undertaking a general revision of the theoretical guidelines of conventional models. Instead of embarking on a general revision of poor conceptual tools, it is easier to declare that certain issues remain outside of the sphere of the economic analysis.

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engineering approach and the Fund-Flow view are very different. Engineers make an exhaustive and meticulous examination of parts and components of a given devices. Their aim is to improve their performance which is measured according to shared technical indicators. Indeed, engineers are concerned with problems such as material fatigue, turbulences and friction. That level of scrutiny goes far beyond the analitycal reach of the Fund-Flow model. There is an enormous distance between a detailed look at the physical and chemical characteristics of materials and a simply list of all of the elements involved in a given productive activity.

Having metioned the differences between engineering and the Fund-Flow approach, it is worth noting that the aspect of the productive elements inventory depends on an important methodological option. Indeed, when attempting to model production processes, one possibility is to consider all elements as flows, while another is to combine funds and flows. The former was the option chosen for such diametrically opposed rivals as the von Neumann and Sraffa models, on one hand, and the production function and the Koopmans’s activity analysis, on the other. Georgescu-Roegen evidently preferred the latter. In his proposal, the classification of funds and flows is combined with the identification of the process boundaries. According to him:

“No analytical boundary, no analytical process. (…) where to draw the analytical boundary of a partial process –briefly, of a process- is not a simple problem. (…) a relevant analytical process cannot be divorced from purpose” (Georgescu-Roegen, 1971: 213, underlined in the original).

There are two types of boundaries: the frontier which, in analytical terms, separates the process considered from its surround environment at any point of time, and the duration of the process, or interval [0, Tp]. The distinction between funds and flows then emerges from their behaviour with respect the boundaries within the process. As expected, the co-ordinated elements of the production process have their own particular behaviour (entering, leaving or operating) throughout the process. Thus,

1. Funds furnish certain services over a given period of time and thereby enter and leave the process.

2. Flows either enter (inflows) or emerge from (outflows) the process. See the figure below.

The production process

Both funds and flows are cardinally measured. In the case of funds, four different types can be distinguished:10

10Established by Georgescu-Roegen (1969, 1971, 1990: 207ff.), this classification has been repeated by many other authors (see, for example, Tani, 1986: 200 and 1993; and Scazzieri, 1993: 110-112).

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1. The different kinds of workers whose services (also known as human work) form an essential part of all necessary, intentional transformation activity.

2. Land, understood in the sense established by Ricardo: the area on which productive operations take place and also the surface which sunlight strikes and is captured by.

3. The means of production: either previously manufactured equipment (such as tools or machinery) or constructions (such as premises or goods warehouses), or living beings that actively participate in the process (such as fruit trees or draught animals) or that are structurally required as facilities (such as trees acting as windbreaks).

4. The populations of natural organisms integrated within the ecosystem that, with their services, co-operate in the productive activity. An example would be the role of bees in crops pollination.

5. The process fund. This is comprised by all the units of output that are still within process.

Funds are not physically incorporated into the product. Furthermore, with the exception of the Ricardian land, the operative capacities of the human work fund and the means of production diminish as a result of the process. At the end of the process, the workers are tired and the fixed capital assets suffer wear and tear. For the sake of simplicity, and given the methodological limits of the partial analysis, the operations aimed at restoring, maintaining and repairing them are considered as separate processes and, as a rule, they will not be included into the model (Georgescu-Roegen, 1969, 1976 and 1990). Needless to say, when interpreting results it is important not to forget this strong supposition.

Flows may be divided into five categories: 1. Goods produced by previous processes, that is, raw materials, unfinished

products and components, seeds and energy. 2. Natural resources obtained at a positive or zero cost: sunlight, air, water,

minerals, and so on. 3. The main output (one or more products) obtained at the end of the process, or at

an intermediate phase within the production process. 4. Output produced that does not meet the minimum quality standards established

by the company at a given time. 5. Waste and other residual products and emissions (gases, particles, radiation,

etc.). The first two types of flow enter the process (inflows) and are incorporated into the different products that result from it. In contrast, the three types of output leave the transformation process (outflows) without ever having entered it.

1.4. Time and the deployment of processes In the Fund-Flow model, time is explicitly considered. There is therefore no such a thing as instantaneous production. Of course, time is understood in the Newtonian sense, that is, as a continuous, homogeneous and one-way displacement from an irrevocable past to an uncertain future.

As it is known, in Economics time is understood in two different ways: as a date to which facts and dees can be successively referred and as a duration which indicates the temporal persistence of a given economic activity. The Fund-Flow model is interested in time as duration. This can be incorporated into the model either by considering the whole production process as a unique period of time or by splitting it according its

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internal stages. In the first option, the participating elements are considered at each and every instant of the process and, in the second, there are several stages with their own duration. Georgescu-Roegen preferred the former, but most of his followers consider that the latter is better.

If the production process were taken into account at every moment of this duration, it would be possible to use suitable functions to represent the activity of the funds and flows. This would undoubtedly make things more visual, but it would also be very laborious. It is relevant to specifically consider (Tani, 1986: 200-2006 and Mir-Artigues and González-Calvet, 2007: 28-33):

1. The function Ik(t) which indicates the amount of the kth element (k=1, ..., K), that enters the process between 0 and t, for each instant t∈[0, Tp].

2. The function Ok(t) which shows the amount of kth element (k=1, ..., K), that exits the process between the initial instant and t, where t∈[0, Tp].

The functions Ik(t) and Ok(t) are accumulative and do not decrease during the interval in which they are defined, that is, [0, Tp]. It is assumed that Ik(0)=Ok(0)=0. It is evident that this representation is overabundant since it contains several functions which are identically nil. Indeed, in the case of flows they only appear on the input side (to be processed) or on the output side (emerging from the process). On the other hand, funds are both inputs and outputs, and comply with the following condition:

Ik(t) ≥ Ok(t) and Ik(T)=Ok(T), where t∈[0, T]. The awkwardness of this graphic representation led Georgescu-Roegen to propose a more manageable form. To start with, the flows, which are measured in their respective physical units, are denoted by the accumulative functions F(t) which are monotonic and do not decrease.11 With respect to funds, the proposed functions are Uj(t) (j=1, ..., J). These functions would be either equal to 0 when the jth fund is not active or to a positive number when it is operational. In this latter case, the number would indicate the number of units involved in the process. This kind of fund functions can be substituted by the functions Sj(t) (j=1, ..., J) which measure the accumulated amount of services rendered by a given fund between 0 and t. Functions Sj(t) do not diminish and are always continuous. As expected, Sj(0) = 0.

The next step is to represent a production process by an organised set of flow and fund functions. This representation is also called a functional. In such a case the relationship between the main output function and the collection of functions denoting the remaining funds and flows, can be written as the following formal manner,

⎥⎦⎤

⎢⎣⎡=

TTTtUtFtQ

000)(;)()( Ψ

This functional represents the “catalog of all feasible and nonwasteful recipes” (Georgescu-Roegen, 1971: 236, underlined in the original). Or, put in another word, the complete set of production processes from which one will be chosen according to certain criteria.

The modelisation explained, which was proposed by Georgescu-Roegen, has been considered too much complicated. Despite the fact that it is very rigorous, it does not seem very operational. In addition, it deals with the production process as a whole, although different stages can be distinguished within.12 There is no doubt that splitting the process could be of great analytical interest. Some of his followers have therefore

11 To simplify the representation, values are considered in absolute terms. 12 It must be underlined that Georgescu-Roegen was completely aware of the fragmentability of the production process, but he never into this question in any depth.

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suggested defining what could be understood as the smallest possible piece of a process: its elementary process. This concept refers to the set of productive or transforming operations which are necessary to obtain a unit of output at a given place (Scazzieri, 1993: 86, 94-97). Or, put in another way, the start-up of a certain number of elements which form a separable item. This is the smallest technical unit in a process (Morroni, 1992: 23). However, on one hand, a process on a smaller scale than an elementary process is not economically viable (for example, it does not make sense to produce half a car), albeit perhaps technically feasible. On the other hand, all the productive operations in an elementary process configure a given state of the technology. However, it should be underlined that an elementary process does not necessarily generate finished goods. Consequently, an elementary process may refer to the production of parts, components or pieces. In this case, further processing of these goods will be continued by other establishments belonging to the same filière.

In an elementary process, the human work fund and the means of production carry out highly diverse basic production operations. As a general rule, a productive operation is considered elemental when any attempt to further break it down merely succeeds in creating unnecessary additional work. Hence, an elementary operation is defined as the smallest possible unit of work. As it is well known, these elementary operations have been the subject of the time and motion studies.

For practical reasons it is pertinent to group all such simple operations into tasks (Landesmann & Scazzieri, 1996a: 195). Defining a task requires a verb denoting an action, coupled with the precise identification of the object and the way in which it is affected. Despite this definition, the identification of tasks remains rather arbitrary. A practical criterion is to identify them in the same way as the people who usually perform them.13

Tasks adjacent in time and space may be grouped in phases. Engineers are of great help for recognising such phases. In effect, technical manuals on production processes normally tend to consider the different forms of treatment applied to a specific item as stages or phases. For instance, chemical processes currently include such basic operations as pulverising, mixing, heating, filtering, precipitation, crystallisation, dissolution, and so on, which can be clearly differentiated, either by order in time or by the use of specific equipment. In short, phases coincide with the sequences of major transformation operations.

In summary, the concepts that we have just defined share the following relationships: Elementary operations ⊆ Tasks ⊆ Phases ⊆ Elementary process

As might be expected, the Fund-Flow model has been very successful at dealing with the temporal arrangements of the production processes. The most basic form of analysis revolves around the relationship that can be established between the forms of deploying the elementary processes and the efficiency levels subsequently achieved. This analysis demonstrated that the in line arrangement, compared more favorable than sequential and parallel deployment in the quest for an improved efficiency.14 13 It must be added that the instruments used in a task do not define it. In effect, the same task may be performed with different tools, according to the technical level of the process in question and the skill of the worker envolved. Conversely, identical tools may be used in a wide variety of different tasks. For example, hammers have a broad range of uses. 14This three castegory division was first proposed by Georgescu-Roegen (1969, 1971 and 1976). Since then it has been upheld by many other authors: Tani (1986), Landesmann (1986), Morroni (1992) and Scazzieri (1993). It should be pointed out that the term sequential has been chosen here instead of what Georgescu-Roegen, and his closest followers, called series activation. The reason for this conceptual change was to avoid confusion, given that in both

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In a sequential deployment, elementary processes are performed one by one. In this way, once an output unit has been completed the production operations corresponding to the next one can start. This method of production is associated with the craftwork activity. The problem with this type of deployment is that funds are unavoidably subjected to periods of idleness. Indeed, they remain inactive except for short lapses in which their productive services are required.

Parallel deployment is typical of agriculture. In such a case, production involves a large number of elementary processes, all carried out simultaneously. In effect, if each plant or tree were considered a separate process, a plot of land would be seen as an area in which the same type of elementary process is repeated many times. Elementary processes completely overlap and start and finish dates coincide.15

Line production is the way in which industry operates. It is also commonly known as mass or series production. The advantages of this form of deployment were acknowledged at the beginning of the 19th century, when it was known as the Factory System (Babbage, 1971; Leijonhufvud, 1989 and Landesmann & Scazzieri, 1996c). In this case, the units are produced in a continuous way and work on a given unit starts before work on previous units has finished. Many units may be on the conveyor belt simultaneously, but in-progress; this implies that each one is completed to a different degree. This arrangement guarantees that, once a certain task has been performed on an output unit, the next unit appears without delay, ready for the same intervention. This allows both machine and worker to specialise on a single uninterrupted task (welding, painting or whatever). It is worth noting that, the specificity and regularity of the tasks performed in line facilitate the establishment of procedural patterns, along with the control of the operating times of the funds involved. This practice is known as Taylorism.

Line production tends to be associated with extensive markets. In effect, compared to sequential or parallel processes, line manufacture multiplies the quantity of goods produced per unit of time. These items have been previously standardised and tend to be made of interchangeable parts of precise and invariable dimensions.

It should be stressed that there is a lot of room when productive activities are rearranged to pursue the least cost. Although all manufacturing processes can be deployed in-line, there are several clearly differentiated sub-types, including batch production and continuous flow production. Everything depends on the pace of the process and the amount and variety of the output units produced per unit of time (Spencer & Cox, 1995).16

common and academic terms, series manufacturing is the expression used to refer to industrial transformation in general. Conversely, and as proposed by Georgescu-Roegen, the term line production has continued to be used to refer to industrial production. 15It is important not to confuse parallel deployment with the well-known stratagem commonly employed by small workshops: to avoid breaks in the use of certain funds, several different elementary process, but which all belong to the same sphere of activity, are kept active at the same time. This is known as the functional or job-shop process (Mir-Artigues & González- Calvet, 2007: 61-63. 16 The analysis of in line efficiency has connected the Fund-Flow model with the classical analysis relating to the technical division of labour and its effects. This was an issue dealt with in depth by the British mathematician and engineer Charles Babbage (1791-1871). He put forward what has come to be known as Babbage’s Principle: specialisation allows separate tasks according to the degree of skill or strength required (Babbage, 1971: 175-176). He also suggested that the scale of line manufacturing is characterised by a particular form of discontinuity: having adjusted the amount and pace of activity of the specialised workers, if the

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2. Extensions to the model

There are several extensions to the Fund-Flow model, but only two which are of major significance receive attention here. The first relates to the table of elements and time. This is a very important concept which is directly related to the seminal ideas of Georgescu-Roegen. In fact, although not explicitly suggested by him, it was latently present in his work (Morroni, 1992: 75). The second involves key aspects of the Georgescu-Roegen’s approach that are used to build a microeconomic model that focuses on firm, or plant, costs. In this model, time is explicitly considered and can, furthermore, be adapted to include margins and prices. This is, of course, a second-order extension to the Georgescu-Roegen proposal. Althoug some researchers could repudiate this variation for straying too far from the core model, it can be used to obtain interesting results. 2.1. The table of elements and time It is very important to realise that an elementary processes can be represented by a table. Each element in the table will indicate the input/output rate of a flow, or the interval of time for which a fund is in operation, by task (or phase). The idea is to use the bi-dimensionality of a table to indicate the magnitude of the flows and/or funds present during the different stages (phases or tasks, as applicable) of an elementary process. The table clearly shows the basic technical and economic features of a production process. Any change in the materials used, in the operating times of the different machinery, or in any other component, will require a new table. The general form of such tables is shown below (the table presented is directly based on the work of Piacentini, 1995 and Morroni, 1992: chap. 7):

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

kskk

s

s

jsjj

s

s

aaa

aaaaaannn

nnnnnn

..............

......

......

..............

......

......

21

22212

11211

21

22221

11211

The table has two component parts. The top is devoted to the times the funds are activated during the phases (or tasks) of the elementary process. Elements (nj,s) indicate scale of production is extended, a multiple of the number of workers (and machines) will be required. If this rule is not followed, the unit costs of production will increase. This is known as the Multiple Principle (Babbage, 1971: 212). References to the life and work of Charles Babbage can be found in Berg (1987) and Stigler (1991). With respect to the principles, see Landesmann (1986: 308-9), Morroni (1992: 63-5) and Mir-Artigues and González-Calvet (2007: 68-85).

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the time for which the fund j is in service (j=1, ..., J) in phase s (s=1, ..., S). An empty position shows a stage during which a particular fund is not in use. As expected, the human labour fund normally appears in all stages, although with differing values. Plant (measured in hours of activity), on the other hand, is always present, but with the same value. Finally, one or more of the rows in the sub-table refer to the times at which the different stores are in use.17

The lower part corresponds to the sub-table of flows per phase (or task). It contains the elements (ak,s) that show the amount of flow k (k=1, ..., K) fed into, or produced during the stage s (s=1, ..., S). Given that the chronological order of the phases is to be maintained, the outflows appear in the final column of this sub-table. These outputs include the main output, by-products and residues, waste and emissions. In the case of outputs produced in the interim stages of the process, these sould be indicated using the final row of the table.

The rows of the table consecutively show the funds and flows required for the successive phases of the process, which are set out in the columns. It should be noted that row values that correspond to the same element employed by the process, can be added up, but with the exception of those shown in the last column, which refers to the outputs. Columns cannot be added due to the heterogeneity of the elements involved. Notwithstanding, this limitation has its own “silver lining”. Indeed, the simultaneity of different funds and flows at each stage of the elementary process underscores an essential feature of all productive activity: the different elements co-operate with each other. In other words, the complementarity of the factors of production is an earlier, and more basic, quality than any possible substitutive relationship that could occur (Daly, 1997). It is sufficient to read the table column by column to realise the essential relationship that exists amongst the different elements of production.

As previously stressed, the confines of the phases are established according to the analytical goals of each individual research project. However, it is not advisable to multiply the number of phases as this would adversely affect the main quality of the elementary process table: its ability to provide a view of the complete organisation of a production process at a glance (Piacentini, 1995: 471).

The table presented can be easily adapted to the applied analyses of the production process and, by extension, to any associated technical changes (Piacentini, 1997). Several researchers have already created and used adapted versions of the funds and flows model to analyse the efficiency of processes such as farming (Polidori, 1996 and Romagnoli, 1996), telecommunications networks (Marini & Pannone, 1998), or industrial activity (Birolo, 2001 and Mir & González, 2003: 57-64). However, it is to the work of Morroni (1992, 1996 and 1999) that merits the greatest attention. This includes a computer program called Kronos Production Analyser™ (Moriggia & Morroni, 1993 and Morroni & Moriggia, 1995), which was designed to systemise information relating to the basic technical and economic features of production processes. The output generated by this software consists of four tables showing the most significant features of the process studied, which is presented in a clear, ordered and exhaustive way. Although such a tool facilitates a better understanding of production processes and may help to improve the study of process innovations 17 Interim stocks appears because of the product in process needs to be decanted, settle, ripen, etc. and because of the phases are out of step. Apart from the stock held between phases, there are others which comprise the raw material prior to processing and stocks of finished products, ready to be sold within a reasonably short period of time. Both may be considered as phases of an elementary process.

11

(Loasby, 1995), as a general rule these latter could probably be examined by merely comparing two or more on the tables showing the elements and time. Any comparison must consider the coefficients and service times of flows and funds, as well as their position in the table (the task or phase in which they appear). In the first case, the volumen of an element can change due to the partial reduction of its use or its substitution and, in the second, it is the temporal organisation of the process what changes. There is also the question of new elements involved in the process, which could imply the elimination of previous ones. Finally, any technical innovation would be expected to have indirect effects, impliying changes in the quantities and times of some other elements.

Comparing different tables associated with a given elementary process, is the most obvious way of using the Fund-Flow model to analyse technological changes. The bi- dimensionalty of tables gives rise to a number of different possibilities: new inflows or funds, changes in the quantities of them required, altered times of flows incorporation or funds activity, changes in the layout and/or content of tasks (or phases), changes in the volume of in/outflows stocks and any combination of these different situations. There is no doubt that this kind of comparison is burdensome, but at the same time it is difficult to imagine how to obtain a more acute insight. 2.2 Costs, time and prices In this paragraph, a very different extension to the Fund-Flow model will be presented. It deals with costs and price determination at the firm level. This is a common chapter of any handbook on microeconomics. In this case, however, some basic ideas from the Fund-Flow model will be added to the different expressions presented.

As is known, the cost is the value of the resources required to perform a particular economic operation. Economic analysis has beeen traditionally concerned with the way costs react to changes in the level of production. When appropriately applied, the Fund-Flow approach helps us to delve into the behaviour of costs over time. This analysis of the costs is based on a simplified model with the following assumptions (Piacentini, 1989: 164-171 and 1995: 473-476):

1. The elementary process generates a single output. This assumption is maintained throughout the following pages.

2. It is assumed that the model refers to a firm with a single plant which has only one production line. If this supposition were relaxed, the cost expression would be accordingly modified without any problems.

3. For the sake of simplicity, it is assumed that the product is immediately sold after it is finished. Moreover, time lapses between the purchasing of flows and the payment of depreciation and wages, and the precise time at which these elements intervene in the process are not considered.

4. The length of the elementary process, or the time needed to produce a unit of output unit, is T. This period can also be called the cycle of production.

5. H indicates the duration of annual production activity, measured in hours. In turn, H=J·D, where J is the duration of the working day and D is the number of work shifts in a calendar year. As expected, J=β·J*, 0<β≤1, to encompass the number of effective working hours. Interruptions may occur for various different reasons which may, or may not, be programmed. It should also be added that D coincides with the number of working days, provided that there is only one shift per day.

12

6. Annual payments for the services provided by human work funds are called W.18 The total labour cost per unit of output is therefore w·T, where w is the total amount paid per hour in wages: w=W/H.

7. There are different tools and machinery. The vector [α1 , α2, ..., αj] represents the annual cost allocation for the use of the j funds (j=1,2, ..., J). The cost of the jth fixed fund is therefore equal to,

αj =Aj·T/Hj Aj is the charge for depreciation19 and Hj is the number of hours for which a given fund is used per annum (HT≥Hj, where HT=8,760 hours). It should be added that the main types of fixed fund are the premises and facilities, as well as all sorts of machinery and tools which are specific to the production line.

8. Some inflows are required to produce each unit of output. The cost of the inflows is given by,

∑ ⋅K

kk pf1

(k=1, 2, ..., K)

in other words, the technical coefficients of the flows entering the process (fk) multiplied by their respective given prices (pk). Generally speaking, the flows to be taken into account are energy, spare parts, raw materials and so on.

Considering all of the visible assumptions, the Average Total Cost (ATC) will then be given by,

∑∑∑∑

⋅+⎟⎠

⎞⎜⎝

⎛+⋅⋅=

⋅

⋅⋅++=

kkk

J

jk

kk

J

j

pfWH

TTH

pfTHWATC

1

1 11

1

αα

In this equation, the annual output produced (Q) is expressed as the outflow per unit of time multiplied by the annual number of hours of activity (H): THQ 1⋅= . For

example, if the duration of the elementary process was T=1/6 hours (i. e., each 10 minuts a new item was coming off the production line), the output per hour would be 6 units and, given H=1,800 hours of annual activity, the total output for a given year would amount to H·1/T=10,800 units.

From this expression it is obvious that the different factors that affect the cost per unit of output can be classified into one the following three types:

1. Attributable to time. Some institutional factors, such as the length of the working day (J) or changes in the annual working calendar (D) provide good examples. Others factors related to the internal organisation of the process and the capacities of the respective funds employed (which will alter the cycle of production, T) should also be added.

2. Those related to the efficiency of the use of materials. This is the case of the total amount of the flows absorbed per unit of output (fk).

18This remuneration includes the wages of all of the workers involved in the process from the top management and administration down to shop-floor workers and supervisors. The model has been simplified by not differentiating between the different remunerations. 19 The term Aj is equivalent to,

( )( ) 11

1

−+

⋅⋅+j

j

nj

n

r

Mrr

where Mj is the initial value of the tool or machine, nj the working life, expressed in years, and r the interest rate. For the sake of simplicity it is supposed that the residual value is zero.

13

3. Economic ingredients such as the prices of the labour (w) and flows (pk) or the factors (nj, Mj and r) that modify depreciation (Aj) and, in turn, their hourly value (αj).

From a static point of view, the description of the relationship between the average total cost and the volume of output per unit of time follows the standard division of the fixed and variable costs. Such a classification does not entirely fit with that of the funds and flows, although a simple link may be established between the two. Indeed, the fixed costs are those generated by the fixed funds, while the flows and human work fund account for the direct or variable costs. This relationship may be written as,

cc

kk

k

cc qq

pfw

qCF

qCVAFCAVCATC α

+⋅+

=+=+=∑

In the expression, qc refers to the amount produced per unit of time (an hour) at a normal (or standard) rate of activity (measured by cycle of production –c or T-) while the already familiar terms w and α denote respectively denote the hourly wage and the charge for depreciation. A standard working day is assumed (e.g. J=8 hours with one single shift and no weekend work). As is known, the burden of fixed costs increases when the level of production per unit of time diminishes. Furthermore, the average variable cost curve and the marginal cost curve are horizontal and overlap in their relevant segments. These short-term plant cost curves are shown in the figure below.

As is known, in the short term, the technical coefficients could be considered as fixed. There also is the normal level of production per unit of time (qc) which is lower than the theoretical, or hypothetical maximum capacity level, (q*). It should be pointed out that the normal production level accounts for a foreseeable degree of stoppage, due to both predicted breakdowns and to routine maintenance and repair. Beyond point qc, there are one or more steps up in the respective curves. Therefore, the highest level of production that it is technically possible to achieve is lower than q*, but very near to it. This q* can be understood as an absolute limit. For that reason, it is represented by a vertical section of the average total, variable and marginal cost curves.

Having presented the general cost expressions, the model can be extended in two related directions. Firstly, it is not difficult to build the expressions of price determination. The other option is to explore how specific curves can be drawn for particular processes that include services (see Mir-Artigues and González-Calvet, 2007: 226-241).

14

As is known, prices are determined by adding a margin to the costs. This is called the cost-plus pricing method. There are three ways to do this. The first variation is the mark-up pricing. This consists of adding a gross margin (γ) to the direct or variable costs. This margin includes the charge for depreciation. This simple principle is still used by small and medium-sized firms because to do so only requires a limited amount of accounting information. That is:

p=(1+γ)·AVC= ( )⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛ ⋅++

∑c

kk

k

q

pfwγ1 ,

The second method, which is the most realistic and widely-used, is the full-cost or normal pricing. It consists of adding a net margin (m) to the average total cost: p=(1+m)·ATC or,

p = (1+ m)·ATC= ( )⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛+

⋅++

∑cc

kk

k

qq

pfwm α1

It must be remembered that the normal average total costs is refered to the standard capacity used (qc) and incorporates all of the manufacturing costs, including depreciation and general administrative overheads. This price setting method is currently used by large companies. This practice has become increasingly extended as innovative accounting techniques have permitted general overheads to be allocated amongst the different goods produced.

The last method is the target-return pricing, which consists of establishing the level of gross, or net, margin according to a previously fixed target rate of return on corporate capital. This method calls for the use of sophisticated accounting tools as it implies working out the value of the capital employed by the company.

Let us take a detailed look at this pricing method, because it has an interesting theoretical consequence.20 To start with, the capital/output ratio shows monetary values in the numerator and physical units in the denominator. This ratio is defined as,

v=K/qc, with qc the amount of output per hour, associated to the normal capacity utilisation of the plant. In a partial equilibrium and short-term analysis, we can suppose that the value of the stock of capital, K, is constant (it only faces account depreciation). This value is given by,

∑ ⋅J

kjj pk

1

where kj denotes the physical quantities of the different capital goods (j= 1, 2, …, J) and their respective prices. For the firm, these elements are data and appear in its books

before the activity starts.

kjp

Now, suppose that r is the target of gross rate of profit. The profits pursued for the current period are given by r·K and, therefore, the required profits per unit of output must be equal to, 20 In Mir-Artigues & González-Calvet (2007: 210-212) this point was presented following Lavoie (1992: 131-133 and 2004: 47-48). However, the model included a very strong assumption: the capital/output ratio only involves physical quantities. Lavoie implicitly established this supposition when used the price of the output as the price of capital goods. Unfortunately, this assumption can only be admitted in a world with only one commodity, at the same time capital and consumption good.

15

vrq

Kr

c

⋅=⋅

The amount of profits per unit of output, following the mark-up pricing rule, is given by,

γ·AVC

The last two expressions should be equated to calculate γ. It is obtained, AVCvr ⋅=⋅ γ

Then, the gross margin added to the AVC, is:

AVCvr ⋅

=γ

From this expression it can be seen that,

01>=

AVCdrdγ

01>=

AVCdvdγ

An increase of the rate of profit, or the capital/output ratio, will lead to an increase of γ equal to 1/AVC times. Or, put in another way, the relationships between r and γ, and between v and γ, are linear. However, the factor of proportionality depends on AVC. This happens because the capital is expressed in monetary values.

If the price of output is given by, ( ) AVCp ⋅+= γ1

it can be written,

AVCvrAVCAVC

vrp +⋅=⋅⎟⎠⎞

⎜⎝⎛ ⋅

+= 1

It should be noted that AVC and r·v are, respectively, the remuneration of the variable inputs (wages and flows) and the fixed funds per unit of output. Therefore, the price is the sum of the flows and funds earnings.

In its full form, the expression of prices is given by:

c

kk

k

q

pfwvrp

⋅++⋅=

∑

This pricing expression can be connected to the Sraffian model of sectoral interdependence. Indeed, if the term AVC only includes the cost of the labour fund per

output unit, cqH

Wcw⋅

=⋅ , then,

vrcwp ⋅+⋅= This expression is directly and fully equivalent to the equation of the production prices in the Sraffian model which, as is known, are given by,

p = w n + r M p with p being the vector of prices, n the vector of the technical coefficients of labour and M the matrix of the technical coefficients of the means of production. In this expression, prices equal wages plus capital (variable and fix) remuneration.

It should be remembered that v is the monetary value of the capital needed to obtain a unit of output and, consequently, this unit of output can give rise to an amount of profits (r·v) proportional to the value of the capital. Therefore, r·v is the component of the price associated to profits, or capital income, while w·c is the portion of the price related to wages.

16

Perhaps, the connection between the Fund-Flow and the Sraffian models is not a surprise but it deserves to be highlighted. 3. The Fund-Flow model and sources of productivity In this chapter, following an analysis of costs at the firm level by adapting the basic ideas of the Fund-Flow model, it is proposed a very simple framework for studying productivity. In this general description, it is considered how modifications to elements, time and organisation, affects the productivity level in the productive processes. This is a very simple way to identify and classify the sources of productivity.

As is well known, the concept of productivity has many facets, although its definition seems apparently quite simple: Q/L. This concept of productivity suggests that the evolution of per capita income is related with the evolution of per-worker production, in both the medium and long term. Unfortunately, empirical calculations of productivity are very difficult. It should be very cautious about the nature and quality of the raw data collected and the statistical procedures used to process these data. Finally, productivity is frequently used as a very ideological subject. As is known, differences in productivity between countries, sectors and so on are currently employed to limit wages claims. In such cases, the productivity dynamic is seen as a factor shaping the evolution of wages. Real income will not increase if productivity does not, but this is only true form a historical perspective, because in the short-term improved productivity usually only means bigger profits. To put this in other words, the most important issue to be considered is the social distribution of any increased productivity.

Increasing productivity implies process innovation, whether technical or organisational. Nonetheless, any change in the number, and/or order of the tasks performed, and any changes in types or amounts of the funds and flows employed, originate problems of coordination within the process. Furthermore, incorporating innovations more often than not presents significant dilemmas:

1. The aim of benefiting as fully as possible from the latest technical novelties could cause problems if these new developments have not been sufficiently tested.

2. Complementarities between the different elements of production add limitations and require organisational adjustments.

3. Usually, existing equipment should be fully written off before it is changed, even though it may have become obsolete.

4. Changing methods and technique entail the loss of the accumulated know-how and experience.

For all of these reasons, changes into production processes tend to be only partial. Although comparing tables of elementary processes is the best way to become fully

aware of the complexity of the process innovations, here what it is proposed is just a general approach to the sources of productivity. The analysis starts from the equivalence,

TR = (W+B) + ATC that is, the total revenues of a firm is given by the sum of its wages, profits and average total costs which now only include depreciation and inflow consumption. Or, in other terms,

χT

HANAVT

Hp 11++=⋅

17

where p denotes the output price, χ relates to the consumption of flows per unit of output and NAV means the Net Added Value. If this expression is divided by the number of annual man-hours (H·L), it will be obtained

LT

LHA

LHNAV

LT

p χ⋅+

⋅+

⋅=

⋅11

As is known, a pragmatic definition of productivity (π) focuses on the NAV generated by each working hour, that is,

LHNAV

⋅=π

Substituing π and rearranging the terms,

⎟⎠⎞

⎜⎝⎛ −−=

THA

Tp

Lχπ 1 [1]

The first term is the inverse of the number of workers in the firm. This value multiplies a term (in brackets) composed of the ratio between price and the output per hour, minus the cost of depreciation per hour, minus the value of inflows divided by the output per hour. This expression evidently shows the factors that affect π. Therefore, an increase in π, or in the net added value per man-hour, will be obtained under the following circumstances:

1. The duration of the elemental process, or cycle of production, (T) is shortened. 2. The number of workers (L) is reduced without a corresponding reduction in the

level of output. 3. There is a reduction in the consumption of flows (χ) per output unit. 4. The annual cost of depreciation (A) is reduced. 5. There are changes in H, where H=J·D. 6. Any combination of the previous circumstances.

The value of π would also increase if the price of the outputs increased, but this possibility is excluded by the assumptions on which the model is based. The next paragraphs contain a brief discussion of these factors. 3.1. Changing the cycle

The duration of the elementary process could be changed in two ways:

1. By incorporating new knowledge such as, for example, new chemical developments that can shorten reactions or by introducing new feed formulae that increase the growth rates of plants and livestock. 2. By accelerating of the cycle of production using Taylorist and Fordist methods.

This second factor deserves more detailed attention, because of if the speed of the process changes, costs will also change immediately. To see this, it is considered a simple model containing the relevant technical and economic variables relating to a line process (adapted from the general cost expression previously presented and also incorporating some ideas that have been taken from Petrocchi & Zedde, 1990 and Piacentini, 1997). The average total cost per product unit is the annual cost of inflow and fund services divided by the total output produced for one year. That is,

kk

k

kk

k

pfH

AWcH

c

pfHc

AWATC ⋅+

+∗=

⋅++= ∑

∑

∗

∗

1

1

18

where c* is referred to the cycle time which synchronises the operating times available to the workstations for the completation of their tasks. This shared cycle guarantees that line production works regularly and smoothly. Thus, c* represents the minimum speed of a given production line. This temporal span encompasses the time required to carry out the work, including any periods during which some of the funds may remain idle moments.

If in this ATC expression w denotes the total wages per hour (w=W/H) and α the charge for depreciation per hour (α=A/H), it is obtained,

( ) kk

k pfwcATC ⋅++= ∑∗ α

Therefore, an increasing level of production could be attained by two ways: 1. By reducing c* from changing the lengths of the tasks, either directly by

stressing workers, or by implementing measures of a Taylorist type (motion improvement, strict time controls, etc.). Additionally, there is also the effect of the learning by doing process.

2. By reducing the cycle by accelerating the pace of the line. Or, in other words, by cutting the launch times of output units in process without changing the characteristics of the workstations tasks. In such cases, no changes are made to the internal organisation of the elementary processes. As is known, Fordism proposed to achieve this goal by pacing conveyor systems which according requirements, moving the output in progress between workstations.

The final expression to be considered is,

ATC = ( ) ⎥⎦

⎤⎢⎣

⎡⋅++ ∑∗

kk

k pfwcnc α with n>1 and 0<c<1

In this expression, c represents the gradually shortened cycle and n measures the acceleration of the line. It can clearly be seen that Taylorism and Fordism methods are assentially two sides of the same coin. One measure automatically reinforces another.

In addition to the abovementioned considerations, changes in production can also be related to storage. On a practical level, these may be of the greatest importance. Indeed, in many processes storage employs a great amount of time and therefore has a notable influence on efficiency and costs. Taking this consideration into account, interim outflows can be considered as another phase in the elementary process. These interim outflows are outflows for one phase and inflows for the next.21

Two forms of technical change may be considered with respect to the different storage phases:

1) A reduction in the time that goods in process are held as technical stock. For example, tanks with appropriate refrigeration accelerate the ageing process of wine.22

2) Holding smaller stocks of input or output flows. This may be achieved with more advanced stock control systems.

As can be seen form expression [1] if the elementary process is shortened, this will have a crucial effect, because of T is located in two terms of the expression.

Before ending this point, it must be stressed that ever-increasing improvements to and in the variety of features of the finished product, will also affect both the number and the complexity of the tasks (or phases) required. To cope with this, new funds and flows may have to be incorporated, which often requires a special effort in terms of 21 As has been indicated in note 17 there are different types of stocks. 22 It must be added that, in some occasions, innovation may consist of lengthening the period in which goods are stored. This is the case of fruits cold storing, meat and fish freezing and so on.

19

design and standardisation. At the same time, existing tasks could be rearranged to accommodate the new ones and, in such cases, part of the previously accumulated experience of the workers might be lost.

3.2. Inflows consumption

In the expression of factors affecting productivity, the term (χ) includes all inflows, their quantities and associated prices. Their burden can therefore change acoording to technical requirements and the evolution of prices. Leaving aside prices, the quantity of inflows can be saved, and productivity increased by: enhancing some natural processes, redesigning the product, and improving the energy efficiency of machinery, etc. Many of these goals can only be achieved by replacing some inflows by others. Such switches very often tend to require changes to be made to the methods and tooling used. They may also give rise to new varieties of outflows. Although many of these substitutions could be considered minor, there are indisputable exceptions. For instance, the same chemical product can be obtained using very different reagents, but this often implies making significant changes to production procedures.

Successive technical changes could lead to a reduction in inflows per unit of output. This saving (in energy, water, raw materials, etc.) can be quantified by collecting data relating to specific process innovations. The time pathway of this reduction can be highly diverse. As a hypothetical example, look at the stepped line in the figure below.

Quantity of flow k per output unit

In such a case, fk is the technical coefficient of a given inflow (k=1, 2,..., K) and the figure shows its reduction per unit of output associated with successive techniques over time. This temporal pathway can be estimated with the following function:

fk (t)= fk (0) e-δt, δ>0. This function describes the progressively decreasing amount of a given inflow per unit of output by means of a single family of production processes. Evidently, other forms of reducing the pathway would be equally plausible such as lineal, a progressively accentuated decrease, and so on.

Any accurate representation of changes in inflow rates should not only consider the direct, but also the indirect, effects. However, a complete picture would be highly complex. Futhermore, it should not be forgetten that anomalous cases would also be relatively easy to find: in other words, process innovations give rise to an increasing need for one or more flow inputs. A good candidate for such a case is, for example, the

20

direct consumption of electricity in the manufacture of many goods: this is a flow rate that has steadily increased over much of the 20th century.

3.3. Number of labour fund units The productivity level would sharply increase if the level of output was kept constant while the number of labour units was gradually reduced. As is known, labour funds can be replaced by mechanical machinery and, subsequently, by automated devices. When dealing with the replacement of the labour services by more hours of fixed fund activity, it should be remembered that this will probably lead to an increase in the consumption of certain flows, such as energy, and also to modifications in the mode and how long related funds are used. In any case, one major consequence of technological and organisational changes in production processes is a reduction in the amount of direct human labour in products.

In Economics, the analysis of labour substitution has a long history behind. However, this analysis usually neglects direct labour replacement due to organisational innovations. As has already been explained, the Fund-Flow model is very useful for studying the relationship between efficiency and the deployment of elementary processes. Nonetheless, the model can also be applied to take a detailed look at some particular issues relating to the manufacturing process. This is the case of the organisational rule “one post, one operator, one task” which is now disappearing. In recent decades, this Fordist principle has been replaced by workteams: a set of workers who share different tasks relating to a given stage of a certain production process. Prominent amongst the advantages that workteams offer firms is the way in which they increase the pace of production by reducing idle time. Indeed, workers and productive operations can be grouped and reorganised in such a way that there is no loss of continuity. This practice may even permit a reduction in the total number of workers required. This is how things could happen: Let us take a productive phase in which n workers perform their activities at individual workstations. This implies that tasks are performed in a rigid sequential order. If the cycle span is denoted by c, the total duration of the phase will be n·c: the length of the cycle multiplied by the number of workers. Moreover, as expected, each workstation has its processing (σ) and non-processing (φ) (load and unload machines, for example) intervals and lapses of inactivity (λ). The situation could therefore be expressed as,

∑∑ +++=+−=⋅n

ci

n

iccncn11

')1( λλφσ

In other words, the total working time available to perform the different tasks in a particular phase is the same as the sum of the three intervals considered. It should be noted that the amount of idle time has been split into λc, which is an interval equal to c, while λ’is the remaining inactive period contained in the phase. It is therefore clear that,

∑∑ ++=−n

i

n

icn11

')1( λφσ

This expression means that, if the different isolated workers were grouped together in a single workteam, the services contributed of one of the workers could be saved. This situation will tend to occur, to a greater or lesser extent, as long as,

cn

i ≥∑1

λ

21

Therefore, introducing a single workteam can lead to the elimination of some idle time due to the balancing delays that exist between different individual workstations. An organisational change can therefore result in a reduction in the number of workers. 3.4. Depreciation and the number of working hours

The expression of productivity also contains depreciation. As is well known, the depreciation of fixed funds is related to ageing, obsolescence and legal regulations. These factors justify the legal and accountancy operation of amortisation which firms schedule over time for convenience. Of course, whatever the depreciation programme is chosen it is necessary to take into account the price of machinery, the current interest rate and the hypothetical technical life of the fixed funds concerned. As is known, the study of all these circumstances has filled a huge number of pages in Economics and Management texts. From the Fund-Flow approach, the analysis would perhaps highlight the time profile of the fixed fund activity and its impact on the hourly cost of depreciation. At the same time, the annual number of hours during which a machine is correctly running will have a direct effect on productivity.23 However, extending the activity of fixed funds will probably shorten their life and, as a consequence, more attention will have to be paid to O&M operations. Therefore, there is room for process innovating pointed to increase the endurance of equipment and, simultaneously, reducing its faults and simplifying repair work. Unfortunately, it seems that until now no systematic research has been done on this subject.

In these pages, we only present a short analysis of the impact of working overtime and shift work on depreciation.24 To start with overtime, the expression of ATC should be expressed as follows,

( ) kk

k pfwcATC ∑++= ∗ α

This simplified version of ATC incorporates the number of hours of activity per year (H=J·D). Moreover, the term w denotes the total payroll (w=W/H) and α represents the charges for depreciation (α=A/H), both expressed per hour.

First of all, it can consider the average salary per hour for the whole of the working day (ω), i.e., the standard eight hours plus overtime. This can be defined as,

[ ]θ

ξθω+

++=

1)1(1w , θ>0 and ξ≥0

with θ being the lengthening of the working day, , and ξ the extra wages paid for overtime. This remuneration is assumed to be equal to, or greater than, the current salary. However, his assumption may change under different circumstances.

JJ )1(_

θ+=

The second step is to consider the depreciation of funds. If it is supposed that A does not change, the hourly depreciation will be,

23 Amongst the economic factors that help to extend H, growth in demand deserves special attention. As previously seen, in such cases, one option is to accelerate the pace of work. But, if it is not enough, other solution will have to be found, such as encouraging overtime (or enlarging J) and/or increasing the number of shifts (D). This can be achieved either by providing cover 24/24 or by working at weekends and shortening holiday leave. As a general consideration, it should be added that the annual number of working hours is also depending on institutional-related circumstances (for instance, the number of public holidays, wheter religious, local or national) and factors as the methods set up for controlling the compliance of the scheduled working day and absenteeism (see Landes, 2000). 24 The following paragraphs are based in Mir-Artigues and González-Calvet (2007: 212-217).

22

θαα+

=1

'

Finally, the average total costs with and without overtime are compared. The difference (π) between the two is given by the expression:

π = [ ] )(*1

)1(1* αΓθ

αξθ+−⎥⎦

⎤⎢⎣⎡ +

++++ wcwc

It must be pointed out that the flows related to the extra O&M operations (Γ) are included in this expression, because of in overtime this outlay will increase. It is therefore assumed that the rate of consumption of the other flows is not affected by the lengthening of the working day. The final result is,

( ) ⎥⎦⎤

⎢⎣⎡ +−

+= Γwc αξ

θθπ

1*

In this expression, the term θ

θξ+1

is bigger than θ

θ+1

, provided that ξ>1. Or, put in

other words, the overtime wage is higher than that for normal working hours. On the other hand, it is expected that Γ will have a low value. It is therefore quite possible that a lower α would be compensated by extra wage and maintenance costs. Hence, the average total cost curve including overtime would lie be only slightly above the normal ATC curve. In conclusion, firms cannot take any important advantage from overtime. However, this is a relatively quick solution to implement, it can be performed by the normal company workforce and it requires no changes in capital equipment.

With respect to shifts (each, presumably, of 8 hours and, therefore, a maximum of 3 per day), the analysis is somewhat more complex. To start with, increasing the number of shifts (D) will probably imply paying the workers at a higher rate for the personal inconvenience of the second and, especially the third, shift, along with those coinciding with weekends and holidays. These additional shifts will also require greater quantities of certain flows per unit of output. This is particularly the case of electricity, because on the night shift, the work area has to be adequately lit. But although this represents an extra cost, it may be partially or totally offset, as it is probable that power will be supplied at a cheaper rate at night.

Increasing the number of shifts also alters the hourly charge for capital depreciation. At this point, a distinction should be made between depreciation for functional wear and tear and for obsolescence. The former is measured in terms of calendar time according to the expected useful life of a given fixed fund and the number of shifts worked will not excessively affect this temporal rate. On the contrary, the forecast of obsolescence is independent of the time span of the fixed fund activity. Thus, the greater the number of hours used by the fixed fund, the lower the hourly charge for depreciation before the unit is withdrawn due to obsolescence. Finally, it is plausible to organise extra shifts carried out by less skilled workers, due to the extemporaneous nature of such working hours.

When comparing the costs associated with the first and second shifts the important point is that the option for setting up a second shift will be chosen if ATC2<ATC1 (where the superscripted number indicates the number of shifts), or in other words, when ATC1+π=ATC2. Having considered the appropriate expressions of costs:

[ ] ⎥⎦

⎤⎢⎣

⎡++−++−++= ∑∑

kkk

kkk fpwcfpwc )(*)1()1()2(

2* αϑαζεπ

is finally obtained in which the considered ATC2 has the following features:

23

1. The term ε≥0 represents the greater wages paid to the workers on the second shift: w+(1+ε)w, where w is the current wage rate. The global remuneration will therefore be equal to w(2+ε).

2. The element ϑ>0 indicates the higher expenditure for inflows per output unit. This amount is not broken down into individual flows because only the upper outlay is important.

3. The factor 0<ζ<1 shows the fall in the hourly charge for depreciation (α), due to the fact that more hours are worked.

4. The production is twice as high as for a single shift: 1/c*·J·2D. For this reason, the expression of average total cost is halved. This assumption simplifies the analysis, even though it is likely that the total production at the end of the working day will be slightly lower.

The final expression is,

[ ] ∑+−−=k

kk fpwc ϑζαεπ )1(2*

With respect to the value of the parameters in the above expression, it can be assumed that the extra salary (ε) paid will be more or less offset by the reduction in the charge for depreciation (α). At the same time, the presumably higher rate of consumption of flows into the second shift (assuming that their cost does not vary) will tend to increase the average total cost. 4. Exploring process innovations with the aid of the Fund-Flow model In this chapter, we present an example of how the Fund-Flow model can be used as a tool to describe the factors underlying technological trajectories in process innovations. There is no doubt that many other examples could also be found to illustrate that cost functions based on Georgescu-Roegen’s work are useful, because of the details that they include. They consequently offer a practical aid for systematising process innovation features.

More and more people are becoming worried about global warming. As is known, renewable resources of electricity could play a major role in the quest to make significant reductions in the emission of greenhouse gasses. These include solar photovoltaic systems, which have emerged as one of the most important technologies for generating green power (Boyle, 2004).

A photovoltaic plant is formed by several very different components. What can be seen at first sight are the arrays of panels (which more specialised texts refer to as modules). These arrays are normally at least one metre above the ground and, if required can be provided with sun-tracking gadgets. The arrays tend to be organised in clusters of flat panels, each with a surface area of around 1 m2. The cores of the modules are composed of several photoelectric cells, mainly made of crystalline silicon, which convert sun photon energy into useful power. The cells and the electrical contacts between them are embedded in EVA (ethyl-vinyl acetate) for protection, especially against moisture. This active layer is sandwiched between a pane of glass (at the front) and an aluminium cover (at the back). When manufacturing modules, exceptional care must be taken when sealing the frame edge. A connection box is the added and a set of wires carries the direct current (DC) generated by the cells to a sophisticated device, the inverter, which transforms it into alternating current (AC). Large grid-connected photovoltaic power plants also need other auxiliary devices, while self-consumption systems normally have batteries for storing electricity. As is known, photovoltaic power

24

plants promotion policies have established investment grants, fiscal advantages and premium prices for the purchase of generated kWh.

Photovoltaic cells and modules are manufactured in a long, complex and demanding process (Sauer, Rau & Kaltschmitt, 2007). To summarize, this proces starts with silica sand (SiO2) which is transformed into metallurgical grade silicon through an electrolytical process. Next, sophisticated and expensive steps are followed to purify this basic industrial input. Thus, silicon for photovoltaic uses, known as polycrystalline silicon, is obtained via the Siemens method, which converts metallurgical grade silicion into trichlorosilane gas. Through distillation and pyrolysis treatment, this gas is then laid down in convenient bars. However, by means of the Czochralki process, it is possible to obtain higher grade purity silicon, known as monocrystalline silicon. In this case, a crystall seed is dipped into the molten polysilicon in an appropiate furnace to produce cylindrical monocrystal bars, with an impurity content of below 10-9. This product meets the technical specifications required for microelectronic applications. If it is again transformed through other specialised processes, it can then be used in high-efficiency solar cells.

The next step is to cut the bars into wafers (250 µm, or less, thick) using a wire saw. These wafers are made of doped silicon (containing boron and phosphorus). They must be polished and cleaned with solvents. However, there is the alternative way of manufacturing silicon ribbons and sheets, which avoids the need to grow crystals, to cast ingots and to saw them. This process is known as edge-defined film-fed growth (EFG). In both cases, an anti-reflex coating is applied to the upper side to enhance light trapping. At the same time, electrical contacts are printed. The wafers then go into the furnace again for a last low termperature treatment.

There are several kinds of photovoltaic cells, but only two are manufactured on a commercial scale: the crystalline ones and the thin film type. Most of the latter are made of amorphous silicon but there are also cells that combine very rare semiconductor materials such as gallium, cadmium, tellurium, indium, selenium and other substances (Andersson, 2001; Green, 2009). In contrast, silicon is one of the most common elements on Earth.

With respect to cost and efficiency, crystalline silicon cells are more expensive than thin film ones, but their efficiency is higher. Indeed, the former have a power/light conversion rate of 13-18%, as opposed to the 8-12% of the latter. It is very important to add that there is a loss of efficiency of almost one third under real working conditions with respect to optimal laboratory conditions. This is due to such factors as intrinsic degradation, weather conditions, dust, DC/AC conversion, and wire resistance. Although things are perhaps changing, today nearly 50% of sold modules contain polycrystalline cells, around 40% monocrystalline silicon cells, and 10% are thin film modules. It must be also added that there exists the very dynamic field of research on multi-junction cells: cells with two or three layers of photoelectrical materials. This design can capture a broader range of the incoming light spectrum, but such cells are not yet commercially available.

From the 1970s onwards photovoltaic devices incorporated several technological improvements. They were first used in satellites to generate electricity on board. In that application, nobody was very worried about costs. Terrestrial uses allowed the relaxation of many operational parameters. Therefore, cells and modules made from cheaper polycrystalline silicon wafers now entered the market. This commercial application led to an increase in the size of cells and modules manufacturing plants. As a result, there was a significant reduction in the cost of producing cells and modules, as

25

shown in the figure below (adapted from Green, 2005; Swanson, 2006; Nemet, 2007: 144 and data obtained from <www.solarbuzz.com>).

0

10

20

30

40

50

60

70

80

90

100

75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 0 1 2 3 4 5 6 7 8 9

Year

S/W

p ($

200

7)

This evolution led experts on photovoltaics to use the experience, or learning, curve model as a forecasting tool (Wene, 2000; van Sark, 2008). However, this is a black box model and, for this reason, it is a very weak analytical instrument. To overcome its limitations, some authors have proposed more well-grounded alternatives. The bottom-up approach is the option which deserves most of the attention. In this case, the goal is to connect historic data on cost redutions with recognizable technical factors. The next paragraphs contain an example of how the Fund-Flow model can be used to improve the design of such models. To be more preciset, a detailed model of manufacturing costs is proposed with the aim of listing the different factors that influence cost reductions in photovoltaic systems. Although this work is still in progress, it is sufficiently developed to be presented as an example of the usefulness of the Fund-Flow concepts in this type of research.

To start with, it should be pointed out that the production of photovoltaic cells and modules has three main cost components:

1. Initial expenditure on designing the final output and the physical throughput of the pilot plants. These outlays in R+D should be considered as sunk costs.

2. Depreciation of equipment and direct labour costs. 3. Inflows expenditures (materials, energy, etc.).

As is known, in microelectronic components and information goods, the cost of making the first item (or copy) is extremely expensive. However, this sunk expenditure is not important in the photovoltaic sector because the basic and applied research and development stages have been able to take advantage of public money. As a result, this type of cost did not, and indeed still does not, represent a special burden for manufacturers photovoltaic products. This factor has therefore not been considered in the cost model.

The cost of manufacturing photovoltaic devices is normally dependent on output size: the expenditure related to producing a 1 m2 module, which is a standard size. Consequently, the following expression collects the most significant components of the cost of producing the cell and the modules:

26

( ) ( )z

Hψ

kpk kfepefspsfH

z

zHψ

AWm

ATC 11

1

112

⋅⋅−

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅∑+⋅+⋅⋅

+⋅⋅−

+=

The average total cost of manufacturing modules (per m2), or , is derived from the annual outlays in funds and flows divided by the quantity of finished modules, also measured in m2. The different symbols denote,

2mATC

1. W is the annual amount of wages paid for labour services. 2. A is the annual depreciation of fixed funds (machinery and tools used in the

manufacturing process). 3. The term fs·ps represents the quantity of silicon (grams) per unit of output

multiplied by its price. 4. fe·pe denotes the energy needed to produce a single unit of output multiplied by its

price. 5. (k=1, 2..., K) is the cost of the other k required flows (chemical reactives,

etc.) incorporated into the output.

kk

k pf∑

6. The term z denotes the duration of the module manufacturing process measured in units of time. Put in other words, this relates to the production cycle.

7. The factor (1-ψ) refers to the yield of the manufacturing process. Note that some elaborated modules do not pass quality tests. The proportion of non-functional modules that have already been produced is given by ψ (where 0≤ψ<1). Although some components could potentially be recuperated, these modules are not ready for sale.

8. H is the annual number of hours of plant activity. As is known, this is the daily worktime multiplied by the number of shifts in a year.

It is very important to understanding the meaning of the denominator. The annual output of the plant, measured in m2, is obtained by multiplying the percentage of modules of acceptable quality, the number of hours of plant activity and the cycle of production. For example, if a plant worked H=2,000 hours in a year, with a 1 m2 module coming off the line every 10 seconds, or z=1/360 hours, the production cycle would be 360 modules/hour. Finally, if only 1% of modules were rejected due to poor quality, the annual production of the plant would be 712,800 m2 (or, what is equivalent, 712,800 modules of 1 m2).

However, modules are sold at a given price based on STC power units (Wp or peak watt).25 Therefore, a link should also be established between the module value in terms of m2 and also in terms of Wp. This relationship is given by the expression:

2

2

/1000/€/€

mWmWp ⋅

=η

where η denotes its light/power conversion efficiency and 1,000 W/m2 is the maximum solar power irradiance.26 For example, a module with an efficiency of 12% and a price of 300 €/m2, would cost 2.5 €/Wp (=300/0.12·1,000).

25 STC denotes Standard Test Conditions. It relates the efficiency of cells under suitable laboratory conditions. Essentially, this means that the temperature of the cell should be 25 ºC. At the same time, any incident solar radiation should have a total power density of 1000 watts per square metre.

27

It is not difficult to incorporate module efficiency into the model. Thus, if the manufactured modules had a given maximum capacity of ω (or peak watt) this value would have to be understood as,

W1000⋅= ηω with all of the variables measured in m2. Plant production must therefore be specified in MW, if the quantity of m2 of modules produced is multiplied by this factor,

( ) Wz

H 100011 ⋅⋅⋅⋅− ηψ

In the example presented here, an output of 712,800 m2 would imply 85.536 MW, if the efficiency was 12%. As expected, the higher the efficiency, the higher the production of the plant in terms of its module capacity. Hence, given the same conditions in terms of field operation and financial requirements, higher efficiency would be expected to reduce the cost of generating kWh (Kaltschmitt, Schröder & Schnieder, 2007).27

The proposed cost expression for manufacturing cells and modules, including efficiency, can be used to identify and systematize the factors that affect the dynamics of the sector. The model is useful because it deals with the different building blocks of cost. As is known, cost is a single quantity which depends on a number of coordinated components, each of which has its own dynamics and each of which is capable of changing at a specific rate. This is a kind of information that cannot be given by a black box model for production and costs. Indeed, it considers a given production process as a very integrated system. On the contrary, the expression of cost based on the Fund-Flow model provides a useful framework for listing the technical and economic factors that drive technical change in the photovoltaic industry. This could be the first step towards building an exhaustive bottom-up model.28 It should be added that some scholars think that the learning by doing factor has never played a decisive role in photovoltaic dynamics (Nemet, 2007: 154). Conversely, this point of view stresses the importance of the research effort into cell efficiency and the process innovation.

Looking at the cost expression, the factors influencing cost reductions that should be taken into account are:

1) The efficiency of the modules (η). 2) The scale of the manufacturing unit (or plant) which is measured by the

production cycle (z). New lager plants, probably with higher levels of automation, that produce more output items per unit of time, imply lighter weights for labour, depreciation cost and general expenditures per unit of output.

3) Improvements in process yield (1-ψ): improvements in the percentage of output units reaching the end of the production line which can be sold.

4) The cost of labour and fixed funds services (W and A). 5) The materials saved, whether silicon (fs) or others (fk). This saving arises from

the fact that the wafers are cut thicker, which means smaller kerf losses of expensive ingot material.

26 The average input of solar energy irradiation is 5 kWh/m2/day. This implies a horizontal irradiation of 1820 kWh/m2/year and, for a south-facing tilt surface set at an angle according to the latitude, an irradiation of 1980 kWh/m2/year. 27 Several factors affecting the cost of the electricity generated by a photovoltaic installation. The most important factors to consider are the cost of financing, the life cycle of the modules, the solar irradiation at the site and the expenditure related to its construction and maintenance. 28 Others steps will be to collect historical data and to estimate an appropiate regression equation.

28

6) The price of silicon (ps). 7) Energy consumption per manufactured module (fe).

As additional information, the next paragraphs contain some imformation about the evolution of these factors. To start with, the figure below shows the STC efficiency of crystalline cells, monocrystalline (mono-x) and polycrystalline (poly-x), from the 1950s to the present day. As previously indicated, under real conditions, the efficiency tends to be 60-70% of these values.

Although efficiency has increased over the last six decades, and in fact the energy generated by a module has approximately doubled, the growth of efficiency seems to have finally stagned at a level which remains 5-10 points below the Wronski-Staebler limit for single junction cells. The alternative higher efficiency multi-junction cells are still very expensive and are not yet mass produced.

With respect to plant scale, from early 1990s to the middle of the last decade, the size of the new production units increased at a yearly rate that was slightly greater than 20%. As a result, unit costs decreased at an annual average rate of nearly 4%. Moreover, new plants have recently reached a production capacity of 100 MW/year; this implies that the annual rate of capacity growth has increased by up to 22%. Hence, the annual average rate of cost reduction must have risen by up to 4.5%. Nonetheless, it seems that bigger plants, those able to produce an annual volumen of output raging from 100 to 500 MW, have a similar unit costs (Nemet, 2006: 3222, n. 8). If this is true, it would imply that additional economies of scale in module manufacturing are unlikely to exist.

At this point, it should be added that the photovoltaic sector took advantage of the improvements in working with silicon achieved by microelectronics sector. This was also the case for thin film deposition. These knowledge spillovers made an important contribution to improvements in cells manufacturing. Today, the process of producing quality-photovoltaic silicon is a mature technology; as a result, there are probably few opportunites for reducing costs based on accumulated experience (Nemet, 2007: 156). The only possible way to significantly reduce cost ant further would probably be a technological breakthrough.

With respect to the cost of labour and investment in production facilities, it should be said that much of the investments in new manufacturing facilities has moved to emerging economies, such as China and other Asian countries. The costs of producing cells and modules have consequently been drastically reduced. However, this trend was,

29

to some extend, halted by the scarcity of silicon between 2006 and 2009. The rapid expansion of the photovoltaic sector around the world became greater than existing solar grade silicon capacity. This pushed up prices. Nowadays, however, new capacity has been incorporated and so prices are falling again.

With respect to the wafer tickness, this shrank from 500 µm to 150 µm over the studied period and it is now expected to be reduced to 120 µm in the coming years. This will suppose 3 g/Wp or less of silicon per wafer.

Regarding the price of silicon, it should be remembered that the cost of manufacturing silicon has fallen more than 12-fold since the 1970s. This trend has, however, been motivated by a mixture of very different factors. To start with, for years silicon manufacturers only produced a grade of silicon that was aimed at the semiconductor industry. Some of the material produced did no meet semiconductor specifications and was therefore categorised as fallout. This material was typically sold to, amongst others, to photovoltaic customers. Whereas high grade silicon was used for satellite communications, everyday users judged the efficiency of polysilicon to be acceptable. Moreover, the polysilicon module was cheaper. For this reason, polysilicon, which is also called solar quality silicon, has become the material most commomly used to produce cells.

Energy consumption in the manufacturing of cells and modules is the last of the factors highlighted. As is known, the energy payback time of a module relates to the operating time needed to recover the energy required for its manufacturing and field installation.29 Many years ago, the energy payback of a crystalline cell, especially of the monocrystalline type, was negative. However, the life cycle of modules and their efficiency have increased over time and various technical innovations have reduced the energy intensity of the manufacturing process. The energy payback time can be achieved within 3 years or less of operation, within a cycle life of almost 30 years. It can be added that the energy payback of thin-film modules is shorter.

Before ending this chapter, we should add that, results coming from a regression model which is very similar to the framework proposed here, have been relatively recently published. In this research the reduction in cost of the modules per Wp, measured by their selling prices between 1980 and 2001, was explained by the following independent variables (Nemet, 2006: 3222-3223 and 2007: 122):

1. The improvements in the energy efficiency of sold modules. 2. The size of manufacturing plants. 3. The proportion of functioning units available at the end of the manufacturing

process. 4. The percentage of all the manufactured cells made from polycrystalline silicon. 5. The evolution of the cost of silicon. 6. The silicon consumption per watt of photovoltaic module. 7. The wafer size.

The main result was that module cost reduction is explained by the rising size of the manufacturing plant (the economies of scale account for the 43% of the reduction), the cell efficiency (adding another 30%) and the price of silicon (12%). The other considered factors share the remaining impact.

5. Final remark

29 There is also the energy yield ratio: the times that the energy generated by a module in the course of its life is greater than that required for its manufacturing and installation.

30

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