A dynamic model of socioeconomic systems based on hierarchy theory and its application to...

STRUCTURAL CHANGE AND

ECONOMIC DYNAMICS

ELSEVIER Structural Change and Economic Dynamics 8 (1997) 453-469

A dynamic model of socioeconomic systems based on hierarchy theory and its application to sustainability

M a r i o G i a m p i e t r o a, K o z o M a y u m i b,,

a Istituto Nazionale della Nutrizione, Roma, Italy b Faculty oflntegrated Arts and Sciences, University of Tokushima, 1-1 Minamijyosanjima,

Tokushima City 770, Japan

Abstract

Socioeconomic systems are seen as complex, adaptive, dissipative systems, stabilized by informed autocatalytic cycles. The energy budget of society is determined by a dynamic equilibrium between the supply and demand of useful energy per hour of labor. Parameters affecting this equilibrium belong to different hierarchical levels (individuals; economy; environment). Improvements in 'efficiency' can only be defined at a particular point in time and space (quasi-steady-state view). Improvements in 'adaptability' can only be defined from an evolutionary perspective. Short-term and long-term perspectives cannot be reduced to a single description. Technological changes imply trade-offs between efficiency and adaptability rather than 'absolute improvements'. © 1997 Elsevier Science B.V.

Keywords." Hierarchy; Dynamic modelling; Efficiency; Adaptability; Sustainability

1. Introduction

A system is hierarchical when it operates on multiple spatiotemporal scales, that is when different process rates are found in the system (O'Neill, 1989). In other words, systems are hierarchical when they are analyzable into successive sets of subsystems (Simon, 1962, p. 468) or when alternative methods of description exist for the same system (Whyte et al., 1969). Human societies and ecosystems are perfect examples of complex hierarchical systems and this represents a major complication in their analysis, especially when dealing with the issue of sustainability (Giampietro, 1994a; Giampietro, 1994b).

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Components of hierarchically organized systems can be called 'holons' (term introduced by Koestler, 1969). A holon has a double nature (Allen and Starr, 1982 pp. 8-16): it is at the same time a whole made of smaller parts (e.g. a human being is made of organs, tissues, cells, molecules, etc.) and a part of some greater whole (an individual human being is a part of a family, a community, a country, the global economy, the biosphere). Therefore, hierarchical systems have an implicit duality: holons have their own composite structure at the focal level, but, because of their interaction with the rest of the hierarchy, they perform functions that contribute to so-called 'emergent properties'. These emergent properties can only be seen from higher levels of analysis.

The problem in dealing with these entities is that the space time closure of their structure (the holon seen on the focus level from the lower level) does not coincide with the space time closure of their role (the holon seen on the focus level from the higher level).

Because of the peculiar functioning on parallel scales, hierarchical systems can be studied either in terms of structures or in terms of functional relationships. Established scientific disciplines rarely acknowledge that this unavoidable and prior choice of 'perspective' implies a bias in the description of complex hierarchical systems and this represents a major complication in their analysis, especially when dealing with the issue of sustainability (Giampietro, 1994a; Giampietro, 1994b). For example, analyzing complex systems in terms of structures implicitly assumes: (i) initial conditions (a history of the system, which is affecting its present behavior) and (ii) a stable higher level on which functions are defined for these structures in order to make them meaningful and stable in time. Similarly, to have functions at a certain level, one needs to assume stability at the lower levels where the structural support is provided for the function (Simon, 1962). Hence, no description of the dynamics of a focus level, such as society as a whole, can escape the issue of structural constraints (how--what is going on at lower levels?) or functional constraints (why--what is going on at the higher level?).

The purpose of this paper is to present a model based on hierarchy theory that establishes a relation between the description of socioeconomic systems at one particular level (the focal level) with the description of the corresponding higher hierarchical level (e.g. the ecological level) and the lower hierarchical level (e.g. the individual perspective of humans operating within the society). Equations, simulations and validation of the model with data from our database are not presented here, but references to published work are given in the text.

Owing to the hierarchical nature of socioeconomic systems, which implies a complex behavior (parallel processes detectable on different space-time scales) when dealing with the sustainability of interactions, we must analyze the process of self- organization of society in a dual way: (i) thermodynamic stability of present dissipative structures--related to the congruence of mechanisms of dissipation (technical coefficients describing the socioeconomic system) and availability of gradients of free energy (characteristics of boundary conditions)--system seen through a snapshot picture; (ii) stability of the functions--related to the ability of the information system providing the controls in keeping the congruence of the mechanisms

M. Giampietro, K. Mayumi / Structural Change and Economic Dynamics 8 (1997) 453-469 455

of dissipation with changes in boundary conditions (evolutionary view)-- (Giampietro, 1997a).

In practical terms this translates into a dual reading of a socioeconomic system: (i) on the process side, by assuming the system as in a quasi-steady-state and studying the pattern of investments of useful energy (this is provided in Section 3); and (ii) on the control side by studying the profile of human time allocation (a proxy for control capacity assessed at the societal level) between efficiency and adaptability from an evolutionary perspective (this is provided in Section4). A general overview of the possible applications of this model along with concluding remarks is given in Section 6.

Based upon a hierarchical reading of the system, we choose the society--seen as a whole--as the focal level of analysis. Such a black box can be described by variables such as level of energy dissipation, GNP, population size, life expectancy at birth, etc. which are defined and assessed at the hierarchical level of the entire society. The corresponding higher level, the ecological level, can be seen as the ensemble of biophysical processes on which society depends. At this higher level, we assess the scale of the processes of natural self-organization of ecosystems seen as dissipative systems based on solar energy (this class of systems was first investi- gated by Prigogine's school--e.g. Nicolis and Prigogine, 1977; Prigogine and Stengers, 1981) by using a set of variables which can be defined and assessed only on a larger scale than the one used for describing society. These variables refer to the amount of solar energy and biomass used in self-organization, and the size of ecosystems directly and indirectly exploited. As the lower hierarchical level one could choose individual economic sectors, specific social groups, or individuals, using those variables which describe the characteristics of the interaction with the societal level that are of interest in the analysis.

2. Theoretical framework

Humans alter the ecosystems in which they live with their technology in order to increase the 'efficacy' of the process of production and consumption of goods and services in society. They attempt to stabilize and 'improve' the structures and functions of society according to a set of internally generated values in face of a set of given boundary conditions. The process of self-organization of society can be described in terms of two different types of activity: that related to 'efficiency' and that related to 'adaptability'. This has to do with two functions in the evolution of the system (Schneider and Kay, 1994): (i) sustaining the short-term stability of the process by taking advantage of existing favorable gradients. That is, efficiency according to present boundary conditions (Conrad, 1983); and (ii) sustaining the long-term stability of such a process by maintaining a high compatibility in the face of a changing environment. That is, adaptability defined as the ability to be efficient according to unknown future boundary conditions (Conrad, 1983).

The main idea of the model of analysis presented here is that technological development of a society can be described in terms of an acceleration of energy throughput in the primary sectors of its economy generating a decoupling between

456 M. Giampietro, K. Mayumi / Structural Change and Economic Dynamics 8 (1997) 453-469

the profile of human time allocation (human time seen as a proxy for the available capability of control) and the profile of exosomatic energy allocation (exosomatic energy seen as a proxy for investment of useful energy). Exosomatic energy is the useful energy throughput outside human bodies as opposed to endosomatic energy (the energy metabolized by humans) as proposed by Georgescu-Roegen (1971). In modern societies, a smaller and smaller fraction of total human time is used for running the primary sectors of the economy (e.g. food security, energy and mining, manufacturing), whereas the material throughput in these sectors has increased dramatically.

A scheme presenting an overview of the parallel allocation of (i) exosomatic energy (ET) and (ii) human time over different compartments of the economy is given in Fig. 1. The overall flow of exosomatic useful energy (ET) and the total amount of human time (THT) are used: (i) to procure and transform energy input in the energy sector and to procure raw materials (ii) to build and maintain exosomatic devices (manufacturing sector), (iii) to guarantee food and environmental security, (iv) to provide services in the service sector and (v) to support human activities outside work in the household sector. Activities (i), (ii) and (iii) have been defined as CI activities (Circulating Investment stabilizing the steady-state). The sectors using exosomatic energy going into CI activities are indicated as: E&M (energy and mining), B&M (building and maintenance), FS (food security), ES (environmental security). All together these sectors absorb an amount of working time assessed by C. Activities (iv) and (v) have been defined as FI activities (Fixed Investment increasing adaptability). The flows of exosomatic energy going into FI activities are indicated as: SS (service sector), HH (households), whereas the human-

/ ~ H ° u s e h o l l d ( H H ) " l - - ~

JFI ac t iv i t ies~/ r ~

\\

I "l ''c"vi"esl \ / [ ' ' X~i, Building & P , / \ - - ~ /

~ Maintenance(B&M)/~ x x V ,-rw T~r

. Mining(E&M) ~ ~\ I I I - " . - " , , I I . ~ ' _ f " _, ,,~X I

(exosomafic ~ . T ~, ~ endosomatic ~devices i | energy | i devices i i L,=.< ines, j c sources J L ,,.m.n.> j

Fig. 1. Parallel allocation of exosomatic energy and human time.


time allocated in these two sectors is respectively, B and A. Clearly: ( E & M + B & M + F S + E S + S S + H H ) = E T on the energy side and ( A + B + C ) = THT on the human time side.

By assessing the flows and parameters presented in Fig. 1, we can describe, for any defined society, the particular autocatalytic loop of exosomatic energy in terms of demand of labor WS = B + C (determined by the labor productivity in different economic sectors) related to the stabilized flow ET. A parameter called SEH-- 'Strength of the Exosomatic energy Hypercycle'--measures the supply of energy accessible to society per unit of working time in the primary sector of the economy. SEH can be expressed as a combination of technical coefficients.

On the other hand, if we change perspective, moving from a biophysical analysis of technical coefficients (the matrix of inputs and outputs of energy and labor in different sectors of the economy as depicted in Fig. 1 ) to a socioeconomic perspective, we can still describe the relation between energy demand and labor supply, but this implies an inversion of the terms 'demand' and 'supply' with respect to 'useful energy' and 'labor time'. The demand of exosomatic energy consumed by society per unit of working time allocated in the primary sectors of the economy has been called BEP (Bio-Economic Pressure). Several variables (referring to different perspectives of the socioeconomic system) can be used to characterize such a pressure and they can be aggregates into this numerical indicator (e.g. age structure, level of education, labor load, etc.). Such a pressure is generated by societal activity aimed at improving material standard of living. BEP tends to push faster and faster energy and matter throughputs within the economic process (e.g. producing and consuming more goods and services per capita).

According to the scheme in Fig. 1, the energy throughput (the level of energy dissipation--ET) at which society's energy budget can be stabilized (when require- ment is equal to supply) is defined by: (i) characteristics of the society determining the level of consumption of energy per unit of human time; and (ii) characteristics of the interaction technology/natural resources determining the supply of energy per unit of human time.

Putting this in a hierarchical perspective we have that, at the focal level, society can be seen as a dissipative system whose energy budget must be balanced: the energy consumed by society to stabilize its structure and functions must be made available through its interaction with the environment. However, simply matching energy demand and supply does not necessarily guarantee stability for the system. The energy balance defined on the focal level is stable only if it is compatible with both: (1) lower level constraints related to the 'biophysical' (food requirements, labor supply) and cultural dimensions (minimum level of material standard of living which is considered as acceptable and social equity acceptable to members of society) of socioeconomic organization; and (2) higher level constraints, that is compatibility with 'ecological' boundary conditions.

2.1. Check on the interface focus~lower level (intensive variables only)

Is the current material standard of living: (i) technically feasible; and (ii) culturally acceptable?

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By adopting our model we can translate this question into a problem of congruence of two parameters: (i) is it possible to have a BEP (wanted by people)=SEH (achieved by technology)? (ii) is the current BEP above the minimum acceptable value (BEP*) defined by current cultural identity?

It should be noted that BEP, even if defined in terms of a set of measurable characteristics defined at the level of the society as whole, provides indications about material standard of living as perceived by lower level holons (Pastore et al., 1996).

2.2. Check on the interface focus/higher level (intensive and extensive variables)

Is the dimension of the total energy throughput dissipated by society compatible with the stability of boundary conditions? Put another way, is the amount of inputs taken from the ecosystems and the amount of wastes dumped into the ecosystems compatible with the stability of the processes of self-organization occurring in the ecosystems with which the society is interacting?

In order to answer this question we have to first define the concepts of Environmental Loading and Critical Environmental Loading. The concept of Environmental Loading was first introduced by H.T. Odum (1996) as an attempt to put in perspective human interference with the activity of self-organization of those natural systems with which humans interact.

(i) Environmental loading--indices of Environmental Loading, defined as human interference on the activity of natural systems, can be obtained by comparing (i) assessments of the scale of human activity (e.g. input demand and waste production) to (ii) assessments of the scale of ecosystem activity (e.g. regenerative capacity and absorbing capacity); or, alternatively, by comparing (i) densities of matter or energy flows induced in the ecosystems by human alteration to (ii) densities of matter or energy flows in a natural ecosystem in the absence of human alteration.

(ii) Critical Environmental L o a d i n ~ t h e maximum level of Environmental Loading which is still compatible with the stability of the process of self-organization of ecosystems with which society is interacting.

Note that any attempt to compare the scale of activity of human societies to the scale of activity of ecosystems implies a combined use of intensive variables (such as level of energy dissipation per unit of control--e.g. W/kg of humans in society and W/kg of biomass in ecosystems) and extensive variables (such as 'control capability' available in the information system--e.g, population size for human society and total biomass for ecosystems).

The check on this interface is totally different from the one made about the focus/lower level check. In that case the optimization is related only to what happens within the system (optimal allocation of economic resources according to marginal costs). This is the point made by Daly (1992) about standard economic analysis which focuses mainly on optimum allocation. This carries the risk of overlooking the effects of the size of the economic system on the stability of boundary conditions.

The question about the compatibility focus/higher level can be translated into the following condition:

Is current EL <critical EL?


2.3. The dynamic system

This model looks at human societies as dynamic systems based on the resonance between controls generating useful energy and useful energy generating controls. This follows the intuition of Herbert Simon (1962) about the functioning of complex systems--recipes inducing processes and processes making recipes--and that of Prigogine (1978)--DNA making metabolism and metabolism making DNA. This conceptualization fits perfectly with the general model of resonating self-entailment proposed for living systems by Rosen (1991).

Describing the process of self-organization of human society in terms of a dynamic system provides a direct link between the characteristics of input-output of the economic process (technical coefficients achievable on the process side according to technology and natural resources) determining SEH and the set of cultural and social characteristics of the society determining BEP.

The balancing of the energy budget implies that the exosomatic energy consumption must be met by the exosomatic energy supply. Therefore, the two readings of the socioeconomic system according to the concepts of BEP and SEH establish a link among variables referring to different types of analysis: (i) physiological variables, (ii) socioeconomic variables, (iii) technological variables, and (iv) indicators of environmental stress (Giampietro, 1997b; Giampietro et al., 1997).

3. Society seen as in steady-state

In his analysis of ecosystem structure, Ulanowicz (1986) finds that the network of matter and energy flows making up what we call an ecosystem can be divided in two parts. One part that generates a hypercycle and the other part that has a purely dissipative nature.

The former part is a net energy producer for the rest of the system. Since some dissipation is always 'necessary to build and maintain structures at sub-compartment level' (Ulanowicz, 1986p. 119) this part comprises activities that, taking advantage of sources of free energy outside the system (e.g. solar energy), generate a positive feedback by introducing degradable energy into the system at a higher rate than it is consumed. The role of the hypercyclic part is to drive and keep the whole system away from thermodynamic equilibrium.

The latter part comprises activities that are net energy degraders. However, this dissipative part is not useless for the system. It has the role of providing control over the entire process of energy degradation and stabilizing the whole system. An ecosystem made of a hypercyclic part alone could not be stable in time. Without the stabilizing effect of the dissipative part, a positive feedback 'will be reflected upon itself without attenuation, and eventually the upward spiral will exceed any conceivable bounds' (Ulanowicz, 1986 p. 57).

A similar approach can be used to describe society from the process side. Society consists of two compartments, one of which is hypercyclic (a net producer of useful energy for the rest of society) and the other purely dissipative (a net consumer of

460 M. Giampietro, I~ Mayumi / Structural Change and Economic Dynamics 8 (1997) 453-469

useful energy). Getting back to Fig. l, where the exosomatic energy consumed by society in different sectors is allocated to three types of activity: HH (Household services), SS (Service Sector), and CI. The total flow of exosomatic energy consumed by society (ET) is divided into two types of investment: the circulating investment (CI) that is needed to stabilize the steady-state (efficiency), and the fixed investment (FI = HH + SS) needed to make the system adaptive in the face of changing boundary conditions (adaptability).

The different nature of the use of the energy flows FI and CI can also be seen in terms of hierarchy theory. The energy in the energy-supply system (CI flow) main- tains the dynamic energy budget in the short term on the time scale of operation of the energy converters, that is through feeding and replacing them. The 'spare' useful energy allocated to activities elsewhere (FI flow) affects the dynamic equilibrium of society in the long term, for example by accumulation of knowledge and capital and expansion of human potentialities. Thus, by analogy with economic terms, the circulating investment (C1 flow) refers to energy spent directly in the primary and other sectors responsible for guaranteeing the steady-state, and with effects detectable on a short time scale, whereas the fixed investment (FI flow) refers to energy spent in the maintenance of the rest of society's activities with effects detectable only on a longer time scale.

It may be clear that the quantity of useful energy that any society can allocate to the stabilization of its structure in the long term (FI flow) depends on the efficiency of the energy-supply system (ET/CI). Hence, we have here a biophysical constraint, given boundary conditions and a defined performance of technology, on the fraction of useful energy that can be allocated, at the level of society, to 'adaptability'. A higher efficiency of the energy-supply system is indicated by a lower demand of useful energy consumed for its own operation and maintenance per unit of ET (high ratio ET/CI).

4. Society seen as an evolving system

In their social interaction, humans experience limits that 'are related to the fact that a human being is more nearly a serial than a parallel information-processing system' (Simon, 1962, p. 476). When the capacity for interaction among humans is saturated, the system faces an internal constraint on its further expansion (e.g. since it takes time to care for a friend, one cannot have an infinite number of friends). Hence, the limited ability of humans to exert control over flows of useful energy allocated to various activities is a fundamental factor in shaping the process of self- organization of human society. Redundancy in the demand of human control reduces the ability to expand the set of activities performed by social systems.

In using an analogy between ecosystems and human societies, we face the problem of defining an equivalent of 'species' in ecosystems for the organization of human society. A reasonable candidate would be 'labor positions' or 'roles'. In fact, a labor position in society, like a species in an ecosystem, reflects the ability to perform an encoded activity (an activity that has proved useful for the system from past

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experience). However, labor positions alone are not sufficient to regulate flows of matter and energy in society. During labor time, humans control only flows of resources that are used in the economic process of production (the supply side). In ecosystems, it is well known that autotrophs (primary producers) need heterotrophs (herbivores, carnivores and detritus feeders) to degrade their by-products (e.g. pre- venting accumulation of oxygen in the atmosphere) and to recycle nutrients such as nitrogen. The rate and the pattern of primary production in ecosystems are controlled not only by the activity of primary producers, but also by the activity of consumers and decomposers. Actually, the more developed is the ecosystem, the more consumers and decomposers play a key role in the regulation of the overall flow of solar energy (Odum, 1971). In order to produce more and better, plants must be 'eaten' at a higher rate by heterotrophs.

The same applies to the economic process. In order to be able to produce more, society must be able to consume more. As with the heterotrophs, the amount and pattern of human consumption directly affects the amount and pattern of production.

The direct biophysical relation between autotrophs and heterotrophs in ecosystems implied by the word 'eaten' is intriguing when it comes to socioeconomic analyses. In order for society to be more productive and efficient, labor hours must be partially 'eaten', that is reduced in number, by becoming part of the consumer compartment (to expand HH). In other words, at the level of society, labor time has to be sacrificed in favor of consumption if more products and services and higher wages are to be obtained. Here the distinction between 'roles' and 'incumbents' (Bailey, 1990) is particularly useful: when society goes through a phase of economic development, it can change the allocation of human time among different roles (decreasing time in production and increasing time in consumption) with the same endowment of incumbents (same structure of population) simply by changing socioeconomic variables (e.g. work load). Even though, sooner or later, one should also expect changes in the distribution of the population among age classes (Giampietro et al., 1993; Giampietro and Bukkens, 1996).

In order to boost the performance of an economic system we not only need more diversity and more efficiency in labor positions (roles), but also more diverse and better consuming roles. As noted earlier, labor positions and a consuming role are defined at the hierarchical level of society (above that of individuals), since their existence is independent of the incumbent at the particular moment (Bailey, 1990).

Increasing the time allocated to leisure has an important effect on the ability to consume and then on the ability of a society to produce added value (Zipf, 1941). Moreover, labor roles due to organization can be seen as replicated actions (Bailey, 1990, p. 179) and, therefore, reflect what happened in the past. Also, leisure time tends to be allocated to an 'established' set of leisure roles (that is, individual choices are constrained by cultural identity: for instance, Europeans play soccer whereas Americans prefer football). However, the fidelity to leisure roles is less strictly enforced by society than for labor roles. This allows more freedom of decision for individuals and, hence, more variability in the set of activities performed during leisure time.

Fig. 1 depicts the profile of human time allocation among a set of several activities.

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Within the available resource 'total human time' (THT = population size × hours in a year) we can define a fraction of human time allocated to CI activities (C/THT) that has to do with 'steady-state efficiency' and a fraction of human time allocated to FI activities [(A + B)/THT] that has to do with 'evolutionary adaptability'. The former fraction refers to repetitive encoded activities based on experience accumu- lated in the past needed to stabilize the required flow of inputs. The latter fraction of time allocation is aimed at building up cultural identity and stimulating innovations that will benefit future adjustments in the set of activities in society.

4.1. The issue of scale." environmental loading and the need for adaptability

The larger is the energy throughput (ET) in the system, the larger the size of the process of energy degradation (destruction of available favorable biophysical conditions). This translates into a faster depletion of stocks and filling of sinks. An increased difference between the speed at which favorable conditions (e.g. gradients of free energy) are generated by biophysical processes in natural ecosystems and the speed at which favorable conditions are destroyed because of the self-organization process of society implies a decrease in the sustainability of the socioeconomic process under the 'ceteris paribus' hypothesis. That is, a lower life span of known resources and the consequent need to find substitutes for limiting resources at an increasing speed. A larger ET of society within a defined ecosystem results in a higher stress on boundary conditions and then in a more pronounced need for adaptability in the social system. Hence, high levels of energy dissipation when coupled to large size of population require a greater investment in adaptability both in terms of energy allocation (increase in the ratio FI/ET) and human time allocation (increase in the fraction of non-working time). This could be a biophysical interpreta- tion for the process of post-industrialization that tends to affect all developed societies.

5. The double autocatalytic loop: human control, exosomatic power, and environmental services

The autocatalytic loop of human activity can be described from a hierarchical perspective in terms of division of human control over 'efficiency' (short time scale, regulating the interface between focus/lower level assuming fixed boundary conditions) and 'adaptability' (long time scale, regulating the interface between focus/higher level assuming a given history of the system). Such a 'triadic' reading (Salthe, 1985) is illustrated in section (i) of Fig. 2. The human control (time/activity) available to the socioeconomic system can be allocated to three levels: the focus, upper and lower levels. Indeed, humans have to pay a tribute, in form of time allocation, to all three hierarchical levels: • tribute paid to the higher hierarchical level in the form of A activities. This tribute

is necessary to guarantee adaptability in the long term. This higher level relates to society in a historic perspective: A activities in the past provided society with


A = ( T o t a l H u m a n T i m e - W S )

Control allocated to

M•m adaptability

am mm mm mm mm m a c mm am mm mm mm mm mm mm ma mm am mm mm mm u mm R ~

WS = B + C (Work Supply)

B Control allocated to ( i ) manufacturin - Services efficiency

m M m m

(ii) E&M

FS

ES

I •

Useful energy allocated HUMAN MASS to control:

• Household (HH) • Service Sector (SS)

" " " " " " " " " " "E 2;s 7s" ,~ B&M Useful energy allocated

to the autocatalytic loop B&M = Building& Maintenance

I I plus: MASS OF • Energy & Mining (E&M) ----~- EXOSOMATIC DEVICES -- • Food Security (FS)

• Environmental Security (ES)

m m ml lUl n I m m R n m ~ Iim u ~ m m l l i u m m m J m ~ I

j Energy throughput used m tai Loading Ratio for self-organization

I ~ e.g., Er/Area = Environm. ! oading

< B I O P H Y S I C A L P R O C E S S E S )

Fig. 2. The double autocatalytic loop: (i) human activity; (ii) exosomatic power.

'initiating conditions' (cultural identity, knowledge, technological capital and reproduction of human mass). The present generation has to take care of the initiating conditions for future generations; tribute paid to the focus level in the form of B activities to ensure the every-day maintenance of the structure of human mass. B activities provide the system of controls over the network of matter and energy needed by society; tribute paid to the lower hierarchical level in the form of C activities to guarantee efficiency in the set of every-day operations. C activities guarantee the needed flow of inputs from the environment.


The autocatalytic loop generated by exosomatic devices (machines) has two distinct interfaces (see section (ii) in Fig. 2), one with humans and one with the environment. Regarding the former, machines represent a cost for humans in terms of human labor demand (they need a certain amount of human time allocated to their control), but machines pay back in terms of a net supply of useful energy for human use. Regarding the latter, machines alter boundary conditions with their activity through the withdrawal of inputs and disposal of wastes. Given a particular area, the scale of machine activity (exosomatic energy dissipation which measures the amount of energy conversions controlled by machines) relative to the scale of ecological activity (the amount of solar energy 'used' by ecosystems for their self- organization, which assess the energy conversions controlled by ecosystems) defines a certain environmental loading ratio.

When describing the autocatalytic exosomatic loop from a hierarchical perspective, as is illustrated in section (ii) of Fig. 2, we see that exosomatic devices too have to pay a tribute to the three hierarchical levels involved in the description of their functioning: * tribute paid to the higher hierarchical level in the form of FI useful energy. This

is the disposable useful energy that humans obtain in return for the construction and maintenance of machines;

• tribute to the focus level in the form of B&M. This is the useful energy generated by machines needed to build and maintain their own structure;

• tribute paid to the lower hierarchical level in the form of useful energy invested in mining (energy and other material), food security, and environmental security. This is the useful energy generated by machines that is needed for the stabilization of inputs of matter and energy and waste disposal into the environment. Within this framework, we may define the following indicators: (i) an indicator of technological development equal to the exo/endo energy ratio;

this assesses the ability of technology of making a better use of natural resources by amplifying the societal metabolism well above the sum of energy controlled through human metabolism;

(ii) an indicator of technological efficiency equal to the ratio FI/ET; this assesses the fraction of useful energy which can considered as 'disposable energy income' for adaptability;

(iii) an indicator of the relative weight of adaptability and efficiency in society equal to the ratio (A+ B)/THT; this assesses on the control side the allocation of the capability for control on long-term and short-term investments;

(iv) an indicator of material standard of living or technological development BEP; this indicator correlates well with all the major indicators of development (Pastore et al., 1996) and therefore assesses, at the societal level, the material standard of living coupled to a particular combination of socioeconomic characteristics;

(v) a family of indicators of environmental stress (Environmental Loading Ratios); these indicators can be chosen according to the limiting set of resources (either on the input or the sink side) that are considered in the analysis of environmental compatibility.


6. Applications of the model and conclusion

Several applications of this model have been explored to check its validity as a theoretical tool in the field of ecological economics. Some examples follow.

6.1. Analysis of demographic behavior of socioeconomic systems

The classic demographic transition hypothesis can be seen as a movement from one metastable equilibrium of the energy budget to another, involving three phases. (1) A metastable equilibrium in which energy demand matches energy supply under the conditions of low labor productivity (SEH) and low bioeconomic pressure (no growth and no development). (2) A transitional phase, in which an increase in strength of the autocatalytic loop of exosomatic energy increases the average energy return of labor (SEH), thus generating an energy supply that exceeds the demand. The energy surplus is initially absorbed by an increase in population size (extensive variable) while the bioeconomic pressure (intensive variable) remains close to the original value. Later, also the bioeconomic pressure will increase and its effect will dominate toward the end of this phase. (3) A new metastable equilibrium will be reached after a certain lag time required to 'settle' the values of the variables determining the bioeconomic pressure. At this point, any new surplus of energy (increases in ET/CI) is absorbed by adjustments in the bioeconomic pressure keeping constant the population size (zero population growth, post-industrialized society).

According to this model it can be concluded that the classic hypothesis of demographic transition of all developing societies is problematic for three reasons. (1) The increase in bioeconomic pressure that led to the completion of the demographic transition in the industrialized world was, and still is, based on the unique characteristics of fossil energy: huge levels of power per hour of labor and the possibility to purchase fossil energy by creating monetary debts. Similar performances cannot be achieved with known alternative energy sources. (2) Gradients in bioeconomic pressure, both within and among countries, generate gradients in fertility rates and migration flows (kilograms of biomass are produced where they have a lower biophysical cost--where BEP is lower--and then they tend to move where they provide a higher return--where SEH is higher). This can neutralize the mechanism stabilizing the 'phase-3-equilibrium'. (3) A halt in population growth through reduced fertility decreases significantly the labor supply through graying of society. Therefore, the stability of this equilibrium requires a slow but continuous increase in labor productivity (SEH) which is more and more difficult to obtain in an overcrowded world (Giampietro et al., 1997; Giampietro and Bukkens, 1996).

6.2. Feasibility checl~ on alternative energy sources

The level of development of society depends on the characteristics of the autocatalytic loop of exosomatic energy. These characteristics are defined by two distinct factors: (i) ET/CI =energy return (related to the output/input ratio or the energy cost to get energy inputs and the quality of conversion of energy input into useful


energy), and (ii) CI/C=the level of power under human control (related to the speed of the flow of useful energy in primary sectors of society).

These two factors have to do with the two types of energy efficiency involved in the scientific debate on the 'maximum power principle' (Odum and Pinkerton, 1955): one referring to output/input and another referring to the speed of the output (Mayumi, 1991). Maximum speed of output (ET/C) implies a loss of efficiency in terms of output/input ratio (ET/CI) and vice versa. The particular level of BEP and environmental loading at which a society is operating will define if a particular source of energy is feasible according to the set of biophysical constraints implied by the equations describing the energetic budget (Giampietro et al., 1997).

6.3. Theoretical analysis of the sustainability of human development

The equilibrium between demand and supply of the energy budget can be expressed using not only intensive variables but also by using extensive variables (e.g. by using equations that also include ET or total population mass).

The values assumed by CI/C and ET/CI, the two parameters characterizing the autocatalytic loop of exosomatic energy (the values of SEH), are scale-dependent. CI/C tends to increase with size (economies of scale and specialization), whereas ET/CI after an initial positive correlation tends to decrease with a further enlarge- ment of the size of society assuming fixed natural capital. The combination of these two effects is useful to explore concepts such as 'carrying capacity', which is the maximum population size for which an equilibrium between demand (BEP) and supply (SEH) is still possible, at a defined level of technical and natural capital, and at a particular value of BEP, and 'optimum population', which is the population size that according to a defined level of technical and natural capital generates a maximum in BEP (Giampietro and Mayumi, 1996). The parameter BEP can also be used as an indicator of development according to the human perspective. The correlation of this indicator of material standard of living (range 16MJ/h to 1600 MJ/h), tested in our analysis in over 107 countries of the world comprising more than 90% of world population, is very similar (actually slightly better) to that obtained by using GNP (Pastore et al., 1996).

6.4. Conclusion: implications of th& analysis in view of sustainability

From an anthropocentric point of view, it would be desirable if technology could continually increase ET/CI to continually improve the standard of living. However, labor productivity in the energy sector is also affected by limited supply of resources and the limited ability of natural systems to absorb waste disposal and be resilient to other perturbations caused by technological processes. Here the scale of the system is fundamental to determine the feasibility of possible solution.

Low labor productivity and low standard of living are the basic problems facing the people in developing societies. They exploit mainly energy funds. In contrast, in developed, 'oil-based' economies the return of labor and standard of living are high, due to the use of fossil energy stocks and abundant technology driving towards


unsustainability (Mayumi and Giampietro, 1997). The desire for high, 'Western' standard of living, improvement in BEP (>500MJ/h) is rapidly spreading worldwide. Adoption of this high material standard of living must be coupled to a high level of human power amplification and use of fossil energy. This harms the traditional energy sector of developing societies that are based on energy fund exploitation.

The interaction of two types of socioeconomic system operating at widely different rates of energy throughput, one being based on stock exploitation and the other on fund exploitation, inevitably generates friction. Interacting, in one way or another, with oil-supported economic activities provides members of developing societies with the opportunity to amplify the return of labor (SEH) well above the traditional return based on biophysical conversions. When this occurs, farmers abandon their labor intensive, low remuneration jobs, even if this implies a major decrease in the efficiency of using natural resources and higher environmental loading ratios.

In fact, it is much easier to reach a high exo/endo energy ratio (a larger SEH) by depleting energy stocks, and consequently ignoring the sustainability issue, than by managing in a sustainable way the available energy funds. This provides an unfair edge to Western economies over subsistence economies: despite the better ecological performance and higher sustainability of many traditional subsistence economies, their job opportunities provide a too low return per hour of labor. Subsistence societies cannot afford a high BEP.

Subsistence societies when operating at a low population density are ecologically sustainable (low EL), but economically unsustainable (too low BEP) when there is an opportunity to interact with the Western world. On the other hand, Western societies are economically competitive (high BEP), but ecologically unsustainable (too high EL).

The model presented in this paper is an attempt to deal with the biophysical roots of these contrasts. Clearly, our model does not provide a definite answer to solve these contrasts, but at least establishes a link between different perspectives (e.g. ecological, social, economic, etc.). This link, we believe, provides useful information for dealing with the issue of sustainability of human development.

Acknowledgements

The authors wish to thank Professor Gowdy, editor of this special issue, for his editorial help and stylistic advice. However, we alone are responsible for any remaining errors.

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