DEMATERIALISATION, TIME ALLOCATION, AND THE
SERVICE ECONOMY
Mario Cogoy
Department of Economics - University of Trieste - Piazzale Europa 1 - 34127 - Trieste - Italy
Phone: ++39040-6767041 / Fax: ++39040-567543 - email: mario.cogoy@econ.univ.trieste.it
Abstract
This paper investigates the role of human capital and knowledge-based services in determining the
materials intensity, and therefore the environmental impacts of consumption. The model presented
generates a stylised structural dynamics of the economy: a phase of growing materials throughput is
superseded by a phase of dematerialisation and service-intensive consumption. It is assumed, that
consumption is a time-requiring activity, and that knowledge-based services play an important role in
shaping the material requirements of consumption. The accumulation of human capital can therefore
enable consumers to substitute service-time for commodities as the economy develops. In this way, both
the allocation of time and the material intensity of the life-process is endogenously determined in a
dynamic model of economic development.
Keywords: Dematerialisation; Time Allocation; Consumption Activities; Human
Capital; Service Economy
JEL Classification: D90; J22; O30; O40
1. INTRODUCTION
In the present state of industrial societies, welfare is dependent on the production of
considerable amounts of waste. Clearly, the environmental impacts of waste not only
depend on its magnitude, but also on its chemical and toxicological composition, and on
disposal technologies. It seems unlikely however, that socio-economic systems can for
longer periods feed on abundant flows of energy and materials, which are ultimately
transformed into waste, without causing considerable disruption to the environment. For
this reason, environmental economists are presently not only concerned with the
reduction of particular kinds of harmful pollutants, but also with the problem of
reducing the overall energy and materials intensity of human activities.
Dematerialisation of the economy has become therefore an important field of research
(Ausubel/Sladovich, 1989; Bernardini/Galli, 1993; Quadrio-Curzio/Fortis/Zoboli, 1994;
Vellinga/Berkhout/Gupta, 1998; Haake, 1999), and sustainable policies of economic
development can meanwhile rely upon a vast literature on dematerialisation, showing
that a considerable body of knowledge and technology is actually available
(Ayres/Ayres, 1996; Weizsäcker/Lovins/Lovins, 1997; Schmidt-Bleek, 1997;
Weizsäcker, 1998; Reijnders, 1998), which could be used in order to radically reduce
materials and energy requirements, without impairing present levels of welfare.
The literature on dematerialisation is mostly concerned with relative materials intensity
of economic activities1. Favourite examples often include such items as a comparison of
the material content of an early ENIAC computer at Pennsylvania University with a
modern laptop (Ayres/Ayres, 1996, p.9) or historical data on the steel content of an
average car (Herman/Ardekani/Ausubel, 1989, p.59) or statistics on the requirements of
selected raw-materials per dollar of output (Bernardini/Galli, 1993; Fortis, 1994). Such
information, although interesting and important for analysing the internal structure of
industrial processes, does not imply by itself that the economy is dematerialising in
absolute terms. A reduction of materials and energy inputs per unit of output, or of
consumption service (relative dematerialisation), will not necessarily lead to a global, or
absolute, dematerialisation of the economy, if the gains in terms of ecological efficiency
are neutralised by the overall effects of economic growth (De Bruyn, 1998). It is
necessary to distinguish therefore between relative and absolute dematerialisation, the
first expression denoting a reduction in the flow of materials and energy per unit of
2
output, or of consumption service, and the second denoting the final overall result, after
the economy has dynamically adapted to the stimulus represented by the original
increase in ecological efficiency. Since the overall impact of human activities on the
environment depends on the absolute level of materials and energy flows mobilized by
the economy, it is absolute, and not relative dematerialisation that contributes to
sustainability, and it is therefore absolute dematerialisation that will be studied in the
present paper in the framework of a dynamic model of the economy.
Different mechanisms leading to dematerialisation processes have been suggested in the
literature, for example industrial ecology (Ayres/Simonis, 1994; Ayres/Ayres, 1996;
Erkman, 1997; Fischer-Kowalski, 1998; Fischer-Kowalski/Hüttler, 1998), or ecoefficiency (Schmidt-Bleek, 1992, 1997; Weizsäcker/Lovins/Lovins, 1997; Reijnders,
1998; Weizsäcker, 1998). In this paper, I shall attempt to explore the possible role of
human capital and consumption services on dematerialisation processes within the
economy. The central assumption is, that knowledge not only increases efficiency in
commodity production, but also in consumptive processes, in which life-enjoyment is
extracted out of commodities and time (Becker, 1965; Michael/Becker, 1973).
Consumption will be considered therefore as an activity, transforming commodities,
consumptive knowledge, and service-time into time-dimensional enjoyment of life.
If time and commodities are substitutable in consumptive processes, and I shall assume
that they are (Spreng, 1993), the proportion of time and commodities, used in
consumptive processes will depend on their relative productivities in view of the lifeenjoyment target of consumers. I also assume, that knowledge influences the relative
productivity of time and commodities, and that the accumulation of knowledge
privileges time in the form of knowledge-based consumptive services, as compared to
commodities, at higher levels of the socio-technical evolution. In this way, a possibility
of substitution of knowledge-intensive service-time for commodities, and therefore a
possibility of dematerialisation, arises for advanced stages of the socio-economic
system.
The following sections present a model, based on the previous considerations. Section 2
describes stationary optima, and section 3 develops the full dynamic model. Section 4
concludes.
3
2. STATIC ALLOCATION OF HUMAN CAPITAL AND TIME
In this paper I shall neglect the survival sector of the economy, and I shall assume that
the target of consumption activities is to spend time in a pleasant way. I shall call this
kind of pleasant time-expenditure: enjoyment time. In order to make time enjoyable,
consumption activities require different kinds of inputs as: commodities, services and
knowledge, and imply the choice of an effort level, i.e. a basic decision on how complex
and expensive activities yielding a unit of enjoyment time have to be. Hiking requires,
for example, less inputs per hour than sailing. Inputs must be paid for by working, and
working requires time. If equal wages are assumed, a person choosing sailing will have
to work longer, in order to pay for the inputs, and have therefore less time left for
sailing, than a person choosing hiking. The choice of a level of effort can be interpreted
as a choice of lifestyles, a higher level of effort corresponding to a more expensive
lifestyle. I shall model aggregate social consumption activities therefore in the
following way (for a more detailed discussion of this approach, cf. Cogoy, 1999a,
1999b):
E   1C  SH 
1
0    1;
0  S,   1
(1)
where E is enjoyment time,  is the chosen level of effort (or an index of aggregate
social lifestyles), C are consumption goods, S the fraction of disposable time allocated
to consumption services (population and total disposable time are taken as constant, and
total disposable time is normalized to 1), H is human capital, and  the fraction of
human capital augmenting the efficiency of consumption services. SH is therefore
knowledge-augmented service-time. H is exogenously given in this section, and will be
endogenously accumulated in the research sector of the economy in the full dynamic
specification of the model presented in the next section.
Equation (1) is an aggregate description of the consumption sector of the economy and
 represents therefore the aggregate intensity of lifestyles in the overall economy. The
equation states that, once lifestyles are chosen, a longer time of enjoyment ( E ) requires
more inputs (commodities and/or knowledge augmented service time) in a similar way
as an increase of physical output requires more inputs in the production sector. (1) can
4
be interpreted therefore as a production function of enjoyment time, relative to a choice
of lifestyles. In the production of enjoyment time, commodities, time, and knowledge
are assumed to be substitutable (Spreng, 1993). The enjoyment production function has
been taken to be Cobb-Douglas for simplicity, but, clearly, other specifications are also
possible. The two productive factors are: commodities ( C ) and assisted service labour
time ( SH ). This means, that technical progress in consumption is of “enhanced labour
type”, where service labour is multiplied by a productivity factor equal to human capital
available to service activities. Service labour is therefore skilled labour and
encompasses all kinds of time-consuming activities (preparing, organising, cleaning,
cooking, etc.), which are necessary for enjoyment, but are not reckoned to enjoyment
themselves. If human capital accumulates, all other inputs remaining equal, consumers
have the choice of either extending enjoyment time (which is only possible, if other
types of time-expenditure are reduced), or of increasing the lifestyle-index of
consumption.
Commodities are produced by labour and human capital only:
C  PH
0  P,   1
(2)
where P is the portion of labour and  the portion of human capital allocated to
commodity production. PH is therefore knowledge-augmented production labour.
(1) and (2) imply that physical capital both in production and consumption is neglected.
Since the dynamic model in section 3 is driven by the accumulation of human capital,
the introduction of physical capital would not contribute additional insights to the
model.
Obviously:
 
(3)
P  S  E 1
(4)
(4) is the time-budget constraint of the economy, implying that if we want to extend
enjoyable time, we have to reduce the time allocated to production and/or to services.
5
I assume that consumers have preferences over enjoyment time and lifestyles, since
both, a longer time spent in enjoyable activities, and more elaborate lifestyles contribute
to welfare. I model preferences, therefore, as:
U  U E,  
U E  0; U EE  0; U   0; U   0
(5)
For a given endowment with human capital, an optimal allocation then
solves:
max U E, 
(P1)
subject to (1) to (4).
First order conditions are:
 
(6)
  1 
(7)
P   1  E 
(8)
S  1  1  E 
(9)
UE


U  E 1  E 
(10)
Making use of (2 ), and (6) to (9), the consumption technology constraint (1) becomes:
E   11  E H
(11)
where:
   2 1   
2 1 
(12)
(10) and (11) yield the optimal values of  and E . (11 ) can be interpreted as a
technological enjoyment-time/lifestyle-intensity transformation curve, yielding efficient
points  for given E and H .
Diagram 1
6
The relevant feature of this transformation curve in enjoyment-time/lifestyle-intensity
space is its concavity. Consumers can efficiently trade enjoyment time against lifestyleintensity along the transformation curve. Feasible consumers’ choices include two kinds
of extreme options.
On the one hand, consumers can set   0 and E  1 (implying C  P  S  0 ). This
means, that consumers enjoy pure time, without making any use of commodities or
services. I shall call this extreme option: the pure leisure case.
On the other hand, consumers can set    and E  0 . This means, that consumer will
accumulate commodities and services, but allocate no enjoyment time to their
consumption activities, which will consist of “having” instead of “doing”. I shall call
this second kind of extreme option: commodity hoarding.
Pure leisure and commodity hoarding are at any point in time technologically feasible
options for consumers2. The reason, why consumers will not adopt these extreme, but
feasible, options is based on consumer preferences, which must be such, as to rule out
an optimal choice in one of the extreme points. For this reason, I shall now formulate
conditions on consumer preferences generating an interior solution ( 0  E  1 ) for
(P1).
I shall model preferences as:
U
E

1

 1    

 1
(13)
Using the enjoyment/intensity transformation curve (11), utility can be expressed as a
function of enjoyment time alone:


1 
 1 E 
U  E  1   H  
 
 
 E  
(14)
It is easy to see, that for   0 , commodity hoarding ( E  0 ) is the optimal option.
For   0 however, utility maximisation will yield an optimal interior solution for E .
In this case (14) is an inverted U-shaped curve with U   for E  0 and for
E  1 . The unique peak of this inverted U-shaped curve can be found by deriving (14):
7
H 
dU
 E  1  1    1 
1 
dE
E 1  E 

Setting
E

(15)
dU
 0 , one obtains:
dE


H 
 1    
1 
E 1  E 
(16)
(16) has a unique interior solution, as shown by the diagram:
Diagram 2
where a = E



H 
and b = 1    
1 
E 1  E 
.
For the above stated reasons, I shall assume in the following:   0 . This means, that
enjoyment time and lifestyle intensity are bad substitutes. This is quite a resonable
assumption, since it implies, that consumers are only moderately disposed to trade
enjoyment time against consumption intensity, and that they are not willing therefore to
solve their maximisation problem by opting for commodity hoarding.
3. A DYNAMIC MODEL OF HUMAN CAPITAL AND DEMATERIALISATION
I shall now proceed to extend the results of the preceding section to a dynamic model of
an economy accumulating human capital and thus endogenously increasing its
technological capabilities.
Since I am more concerned with the possible substitution between commodities and
services, than with the ecological quality of commodities, I shall assume physical
homogeneity of output through time. This means, that a fixed quantity of materials and
energy is embodied in a unit of output, and that absolute dematerialisation is therefore
only possible, if physical output declines. In traditional dynamic models, a decline in
output with constant population is tantamount to a decline in welfare, but this is not
8
necessarily the case, if consumption is conceived as an activity, and if commodities can
be substituted by services in consumption activities.
In analogy to Lucas (1988), I assume that human capital is accumulated with the aid of
skilled research labour:
H  RH
0  R  1;   0
(17)
where R is the portion of time allocated to research.
The time-budget constraint becomes therefore:
P  S  E  R 1
(18)
(1), (2) and (3) also apply to the dynamic case.
Since H  H  H , (17) implies that the sum of human capital in production and
consumption acts as an externality in assisting labour in research.
Equation (17) is a rather simple means of introducing an engine of technical change into
the model. Although the process of generation of technical change is certainly much
more complex, than can be represented by (17), the choice of such a crude
simplification is justified in the present context, since the focus of this paper is not so
much on the complex texture of social interactions implied in the generation of
technical progress, but rather on the effects of technical progress on the structure of time
and on the flow of energy and materials supporting economic activities.
The central assumption I now make is that the parameter of the consumption technology
 depends on knowledge, and therefore on human capital:
   H 
(19)
The main idea is that, at a low level of knowledge, the relative productivity of
commodities increases, since commodities can better suit the requirements of
consumption activities of a lower degree of complexity (“commodification”, Manno,
19993). As knowledge accumulates, after a turning point, the relative productivity of
skilled services rises to the detriment of commodities (“service economy”, Stahel,
1994). Examples of how an increase in knowledge, information and related services can
better contribute to welfare than an increase in the endowment with commodities,
include such items as: integrated transportation systems based on using instead of
9
owning (Stahel, 1994), locally tailored energy supply systems, prevention oriented
medical care, etc. Knowledge does not only pertain to the best way of producing things,
but also to the best way of conceiving, organising, and planning social networks that
contribute to a more intelligent use of things. For this reason, when society is already
endowed with a satisfactory quantity of commodities, social and organisational knowhow, mostly ignored in models of economic growth, becomes more productive than
material goods in the satisfaction of human needs.
This idea can be captured by using a bell-shaped function for ψ(H), for example:
     e  H  
2
 ,   0;     1;  ,   0
(20)
where  H  has a maximum value equal to    at a turning point, characterised by
H   , and a lower bound    . A larger value of  corresponds to a “bell” with
steeper sides. In this formulation, constant returns to scale in commodities and skilled
service-labour are preserved for the production function of “enjoyment” at any point in
time, but the relative productivity of commodities and skilled service-labour changes
with the accumulation of human capital.
I assume, that the social planner is aware of (20) and that she knows therefore in
advance how  will change as the consequence of the accumulation of H . An optimal
path then solves:

max  e  t
0
 E

1


 1     dt
(P2)
subject to (1), (2), (3), (17), (18) and (20).  is the rate of discount.
First-order conditions are:
HP   1    
(21)
  1  
(22)
S  1  P
(23)
1     P  E   PE 
(24)
10

P
 P 
   R   1  2  H ( H   )    log 



 S 
(25)
where  is the shadow-price of human capital.
The transversality condition is:
lim e rt H  0
(26)
t 
First-order conditions, together with the constraints, determine the optimal dynamics of
the system.
From (3), and (22) we get:
 
(27)
  1 
(28)
and from (18), and (23):
P   1  R  E 
(29)
S  1  1  R  E 
(30)
This means, that the relative shares of the productive and service use, both of labour and
of human capital, are determined by the dynamics of H .
 P

 
 S 1 
(31)
Diagram 3
Eliminating P , S ,  ,  and  , one gets:
H 1  R   E 
(32)
1   1  R   H    1  R  E 1 E 2
(33)
C   2 1  R  E H
(34)
11


    1  E    1  R  E F log

1 
(35)
where:
F ( H )  4 H H       
(36)
( H )   2 1   
(37)
2 (1 )
Taking time-derivatives of all variables, eliminating  , and considering that:
  
F H
2 H
(38)

  F log  H

1  H
(39)
one gets a dynamic system in H , E , R , and C :


E
R


    1  R  E 1  F log
E 1 R
1 




1   R  R1  F log 
2E 1   E
R




E
1 R  E 1 R 1 R  E
1 

 F
C
R
E


 R1  
C 1 R  E 1 R  E
 
(40)



(41)
(42)
It is now possible to study the dynamics of this economy, using phase-diagrams. (40) to
(42), together with (33), (34), and (17) yield a system of 6 equations in 8 variables: H ,
E , R , C , and their time-derivatives. Setting the time-derivative of one variable equal
to 0, the system yields loci of stationary points for that variable. The system cannot be
solved explicitly, but commonly available software (e.g. the Solver tool in EXCEL®)
can be used to compute stationary loci of the variables for given values of the
parameters. I shall not discuss all possible outcomes, in dependence of various possible
combinations of parameters, but only pick a particular set of values, which generates a
stylised dynamics of C : an increase of C in a first phase, characterised by a low value
of H (“commodification”), and a second phase of absolute dematerialisation, after a
12
critical value of H has been reached (“service economy”). Such a set of values is, for
example:   0.1;   0.5;   0.01;   8;   0.5;   0.5;   2.5;   1 .
It can be first remarked, that the dynamic system has a stationary point. Setting all timederivatives equal to zero, one gets from (33) and (40):
1     H 

  1  E 
   1  E 1  F log

1 
E 2
(43)
 

1   
(44)
(43) and (44) determine the stationary values of E and H . The solution can be
represented in a diagram, for the given values of the parameters.
Diagram 4
I shall now discuss phase-diagrams in C / H , E / H , and R / H space. The phasediagram in C / H space is:
Diagram 5
The diagram shows the loci: C  0 and H  0 , and the optimal path, represented by
--
- - - . In order to better understand the properties of the stationary state, it is useful to
zoom in on Diagram 5 in the neighbourhood of the stationary point.
Diagram 6
As can be seen from Diagram 6, the optimal path crosses the C  0 locus, before
approaching the stationary point from below. The optimal path experiences therefore a
short spell of rematerialisation, before settling down in the optimal stationary state.
13
Before I discuss the reasons for rematerialisation, I shall present the phase diagrams for
the time-related variables. The phase-diagrams in E / H and R / H space are:
Diagram 7
Diagram 8
As can be seen from the diagrams, the basic trend of a decline in research time as the
system approaches the stationary point, and a consequent shift of time allocation to
enjoyment, is modified by the “wave” generated by equation (19).
The commodity intensity of knowledge-based services can be determined from (28),
(30) and (34) by the expression:
 
C
 
SH  1  



2
(45)
Diagram 9
Declining commodity use, increasing enjoyment time and knowledge-based services
characterise the final phase of the structural development of the economy (service
economy: Stahel, 1994).
The reasons for a curb on rematerialisation are rooted in two basic assumptions of this
paper. The first basic assumption is contained in equation (19), which generates a
“wave” in the relative shares of commodities and services, as human capital
accumulates. When the effects of the wave taper off, and  approaches its lower level
(which has been assumed to be grater than zero), the economy begins to enter a path of
proportional increase of commodities and knowledge-assisted services. At this point,
the second basic assumption of the paper comes into play: since the elasticity of
14
substitution between intensity and time is lower than unity, individuals do not consider
a further accumulation of commodities, given the fundamental shortage of time (Linder,
1970), to be a target worth to pursue, and therefore the economy comes to a standstill. It
is therefore essential for the results of the present paper, that a low degree of
substitutability between enjoyment time and lifestyle intensity chokes off the process of
growth early enough, so as to prevent the economy to move along a path of proportional
growth, and to rematerialise, after the effects of the “wave” begin to subside.
A lower value of  extends the effects of the wave into a longer period of time. If
  0 , commodities do not play any role in the very long run, and consumption tends
therefore to zero, as H tends to infinity. Although it is very difficult to say what
happens in the very long run, I have preferred to neglect the case   0 , and to set a
low, but positive, value for  . When the dynamic system approaches this positive
value, it behaves in a similar way, as an economy with a constant  . At this point the
economy begins to rematerialise.
As Diagram 4 shows, for the chosen value of the parameters the stationary point lies to
the right and in the neighbourhood of the “wave”. If  rises, the graph of equation (43)
shifts downwards, and the stationary point shifts to the right, further away from the
“wave”. The process of growth is extended into a longer period of time, and an
opportunity for a longer period of rematerialisation arises. When  approaches zero,
the stationary point tends to infinity, and in this case dematerialisation is only possible,
if   0 .
4. CONCLUSIONS
The mechanism generating dematerialisation in the service economy is based on the
substitution of services for commodities in consumption activities. Welfare is not set
equal to the consumption of commodities, but is the result of complex consumption
activities, where commodities, combined with social and organisational knowledge and
service labour, yield “enjoyment time”. The accumulation of organisational know-how
enhances the productivity of services relative to the productivity of commodities in
consumption activities and, in this way, a substitution of knowledge-based services for
15
commodities is induced. The basic structure involved in the dematerialization process is
the structure of time. Time is structured in four parts in the present model: enjoyment,
production, services and research. If time is allocated to research, human capital
accumulates, and this induces a shift of disposable time from production to services.
This shift is the time-structural basis of dematerialisation.
It is important to note, that in the present model individuals are not assumed to derive
utility from dematerialisation. It is not concern for the environment that triggers off the
dematerialisation process, but only the fact that individuals enhance more effectively
their welfare by means of services and knowledge than by means of commodities. This
implies, that there are reasons for dematerialising the economy, which are completely
independent from environmental concerns. Dematerialisation may be a good idea even
for non-ecologists, since, with the growth of knowledge, increasing the endowment of
individuals with commodities may not be the best way of increasing welfare.
The present paper attempts to focus on one possible source of dematerialization, and not
to give a comprehensive picture of all possible mechanisms, that could lead to an
overall reduction of the materials and energy flows within the economy. Other
candidates could be, as already noted, industrial ecology, eco-efficiency, etc. Obviously,
also environmental preferences of individuals would have to play an important role, not
studied in this paper. A more comprehensive picture could be obtained by combining
different possible dematerialization mechanisms, but the purpose of the present paper
was only to argue that knowledge-based services could play an important role.
A satisfactory theory of dematerialisation cannot exclusively rely on an analysis of
relative dematerialisation in selected economic sectors, or on the assessment of a
potential improvement of ecological efficiency. Dematerialization can only become a
credible strategy for reducing the distance to sustainable development paths, if it is
possible to identify dynamic mechanisms of absolute dematerialization, which are
rooted in a comprehensive picture of an evolving economy.
16
Notes
1
Different measures have been suggested in the literature for quantifying relative
materials intensity, depending on the theoretical points of view of the authors: materials
and energy intensity per dollar of GNP, per given commodity, per unit of consumptive
service, etc. (Bernardini/Galli, 1993; Fortis, 1994; Herman/Ardekani/Ausubel, 1989;
Schmidt-Bleek, 1992).
2
As a matter of fact, pure leisure is only feasible, if the consumer has already solved
the problem of survival, but I consider survival to be granted in the framework of the
present model.
3
Commodification denotes a bias towards material commodities instead of services and
knowledge in the satisfaction of human needs (Manno, 1999). I prefer the expression
“commodification” to “commoditization”, used by Manno, for purely aesthetic reasons.
17
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20

E
0
1
Diagram 1
21
b
a
E
0
1
Diagram 2
22
P/S
H
Diagram 3
23
1
E
(43)
0,5
(44)
H
0
0
10
20
30
40
Diagram 4
24
2
C
C'=0
H'=0
1
C'=0
C'=0
0
0
10
H
20
30
40
Diagram 5
25
0,105
C
H'=0
C'=0
H
0,1
28
29
30
Diagram 6
26
1
E'=0
E
H'=0
0,5
0
H
0
10
20
30
40
Diagram 7
27
0,5
0,4
R
0,3
0,2
0,1
R'=0
0
-0,1 0
10
20
30
H
40
Diagram 8
28
2,5
C/(SH)
2
1,5
1
0,5
H
0
0
10
20
30
40
Diagram 9
29