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TEVECON: Description of Model
Pier Paolo Saviotti1, Andreas Pyka2, Bogang Jun2
SECTION 1
1.1) Introduction and Conceptual background
The TEVECON model of economic development was created by Pier Paolo Saviotti and
Andreas Pyka, starting from 2000 to the present. In 2014 Bogang Jun started collaborating
with the development of TEVECON. TEVECON is not a finished product but it is in
continuous evolution by the addition of new variables, new interactions between variables and
new aspects of the economic system to be explored. As a consequence this documentation
will need to be regularly updated.
The initial versions of TEVECON were programmed in Turbo Pascal. Following the
entry of Bogang Jun into the development team the subsequent versions of TEVECON will be
programmed in Java. The present document does not contain any code but it is based on
concepts, equations and graphic representations. A version containing the code will be
published in the near future. The graphic representations depend on the variables, interactions
and parameters of TEVECON. The diagrams shown are examples corresponding to particular
settings of model parameters. Different settings of model parameters can give rise to
considerably different results and diagrams. We have chosen results obtained in a wide range
of conditions of our artificial economic system produced by a correspondingly wide range of
model parameters.
1.1.1) Conceptual background
TEVECON is a model of economic development in which the main determinant of economic
development is the emergence of new sectors. Each sector is created by an important
(pervasive) innovation. TEVECON is a model in which structural change is a determinant of
economic development. During development the composition of the economic system
changes as result of the emergence of new sectors. In the versions developed so far there is no
extinction of older sectors. The main motivation for the development of the model came from
the idea (Paolo Saviotti 1996) that variety growth is a necessary requirement for the long-term
1 Faculty of Geosciences, Cross-faculty “Institutions” program, sub-theme “innovation”, Utrecht University,
2 University of Hohenheim, Economics Institute, Wollgrasweg 23, D-70599 Stuttgart, Germany
TEVECON : Description of Model (no code)
2
continuation of economic development. In TEVECON the variety of the system is
(approximately) given by the number of sectors existing at a given time.
In TEVECON the economic system is constituted by an endogenously variable
number of sectors, and each sector is constituted by a number of firms which varies in the
course of time
Adjustment gap
In this model a new sector is created by a pervasive (Freeman 1991; Verspagen 2002)
innovation, that establishes an adjustment gap, that is a potential market (Gualerzi 2002). At
the time the innovation is first introduced this potential market is empty because there is no
production capacity for the goods or services created by the innovation. The adjustment gap is
precisely the size of the potential market, and it can be defined as the difference between the
maximum possible demand and the actual demand at a given time:
t
i
tt
iD
i
DAG −=max,
(1.1)
where
Di
t
is the demand for the output of sector
i
at a given time and
Dt
i,max
is the
maximum expected demand at the same time. In other words,
Dt
i,max
is a potential demand,
which at the beginning of the life of a new product or service can be estimated with
considerable uncertainty. Nevertheless, it acts as a strong inducement for entrepreneurs to
create firms producing the new good or service. If
Dt
i,max
were to remain constant,
AGi
t
could be expected to have its maximum value at t = 0, that is at the origin of the sector, and to
decline gradually in the course of time. In the long run we expect the adjustment gap to close
and the corresponding market to become saturated. The concept of the adjustment gap
embodies the hypothesis of the eventual saturation of demand. However, even if the
adjustment gap eventually closes this does not mean that it will fall at all times. The
innovation that creates a given sector does not remain constant in the course of time, but it can
keep improving. So-called post-innovation improvements (Metcalfe, 1988; Gheorghiou et al.
1986) can both reduce the price of the innovation and improve its quality, thus expanding the
population of potential adopters. In our model
Dt
i,max
increases with the extent of the search
activities performed within the sector. Furthermore, consumers' demand
Di
t
is only gradually
created as they learn how the new goods and services can improve their utility. Thus, it is
even possible for
AGi
t
to increase during certain periods after the emergence of the sector.
TEVECON : Description of Model (no code)
3
Sectors
The definition of industrial sectors used in this model does not coincide with that commonly
used in statistical surveys. A sector is here defined as the collection of firms that produce a
differentiated product. The meaning of that definition can be better understood by reference to
a twin characteristic representation of products (Saviotti and Metcalfe 1984; Saviotti 1996) in
which one set of characteristics represents the internal structure of a product technology
(technical characteristics) and the other set represents the services performed for the users of
the product (Figure 1.1).
X
1Y1
X
2Y2
. .
. .
. .
X
nYm
Figure 1.1 Twin characteristics representation of products.
For what concerns the present model the twin characteristics representation is useful
because only service characteristics affect users choices. Thus it is only service characteristics
that affect directly demand and competition. In what follows we use only service
characteristics to represent industrial sectors. In general we can expect different sectors to
differ both for their technical and for their service characteristics. For example, cars and
photographic cameras differ both for their internal structure and for the services they perform.
However, there can be cases in which sectors differing for their technical characteristics have
some common service characteristics. For example, airplanes and trains have some common
service characteristics. In this case two different sectors provide outputs that are partly
substitutable and, as we will see later, they can be subject to inter-sector competition. A
representation of such sectors would have to take into account the internal characteristics of
firms, ranging from their strategy, organisation, financial aspects, competencies etc., and the
characteristics of their outputs, be they product or services. In what follows we concentrate on
products, although a generalisation of this framework to services can be developed (Gallouj
and Weinstein 1997). Also, in the present version of the model we will concentrate
exclusively on product space. Thus, a product model will be represented by a point in service
characteristics space. To the extent that the producers in a given industry produce
differentiated products, their product models will be represented by a distribution of points in
TEVECON : Description of Model (no code)
4
service characteristics space. Such distribution of differentiated product models, or product
population, is one of the possible representations of an industrial sector as defined in this
paper (Figure 1.2). The representation in Figure 1.2 is particularly simplified because it uses
only two service characteristics. This is done only to provide a graphic representation, which
it would be impossible for any number of characteristics greater than three. Of course, this
implies that the two sectors in Figure 1.2 offer common services and differ only for the values
of these common characteristics, a situation which is possible but not very general. In the
most general case, that of two sectors not sharing any service characteristics, we would need
at least four dimensions to represent their product populations. Figure 1.2 is used as an
illustration, but the model is not limited to product technologies offering common services.
The fact that in this version of the model we use only service characteristics to
represent product models, and thus industrial sectors, does not mean that we consider
technical characteristics irrelevant. The true nature of a radical innovation consists in
developing a new internal structure with novel technical characteristics, although the services
it provides may show continuity with existing services. For example, the advent of the jet
engine in aircraft created a wholly new set of technical characteristics to provide more
efficiently services common to previous aircraft engine types. In the present version of the
model we concentrate on service characteristics because an industrial sector needs to have
producers and consumers, service characteristics being the interface between the two. The
superiority of a set of technical characteristics over another can only be judged by its ability to
provide more efficiently services. This allows us to investigate some properties of our
artificial economic system, and in the present version we concentrate on these properties.
Both technical and service characteristics are dimensions of product technology.
Process technology is taken into account by means of improvements in productive efficiency
due to a combination of learning by doing and of learning by searching (See equation 1.6)
TEVECON : Description of Model (no code)
5
Y2
Y1
P1
P2
Figure 1.2 Representation of two product populations (P1 and P2), corresponding to two industrial
sectors, in service characteristics space. Y1 and Y2 could be size and speed for aircraft, or processing
speed and the maximum size of the files that can be processed for a computer.
A number of trends can contribute to the evolution of industrial sectors in the course
of time. For example, each population/sector can move away from the origin of the axes as
the level of characteristics supplied increases gradually. Furthermore, a population can
separate into two or more as the corresponding technology specialises. Finally, new
technologies can be created in wholly new dimensions of characteristics space, for example
supplying services that were previously not available.
Demand
In some previous versions of our model (Saviotti and Pyka 2004a, 2004b, 2004c), we had a
very simplified representation of demand. Essentially demand entered the model in two ways:
first, by means of the concept of adjustment gap (
AGi
t
), defined as equal to the difference
between the maximum and the actual demand at a given time; second, by means of the
assumption that all output produced in the economy was to be consumed. The second
assumption is equivalent to Say's law. Those assumptions were included in the model in order
to simplify it. Of course, they were very restrictive and limited unnecessarily the model. The
first explicit demand function, introduced in 2008 had the following demand form:
t
i
i
t
i
t
t
ip
YY
DΔ⋅
=
(1.2)
TEVECON : Description of Model (no code)
6
where
Yi
t
,
ΔYi
t
and
pi
t
are the average value of the services produced, the degree of
differentiation and the average price of the products of sector
i
respectively. In this section,
we describe the explorations of this demand function employed. In order to explain how these
experiments were carried out, we have to give the time dependence of
Yi
t
,
ΔYi
t
and
pi
t
(Equation 1.3, 1.4 and 1.5).
)SEkkexp(
Yt
i
t
i
1514
1
1
−+
=
(1.3)
)SEkkexp(
Yt
i
i
t
1716
1
1
−+
=Δ
(1.4)
)SEkkexp(pt
i
i
t
1918
1−+=
(1.5)
)]exp(1[ 54
0t
i
it
iDacckkSESE ⋅−−⋅+=
(1.6)
where
SEi
t
are the search activities carried out in sector
i
. In our model, the term search
activities is a generalized analogue of research and development (R&D) and indicates all the
activities which scan the external environment searching for replacements of or additions to
existing routines (Nelson and Winter 1982, pp. 14-15, 149, 155-157). In our model, search
activities
SEi
t
increase with accumulated demand
Dacci
t
, but at a decreasing rate. This time
path depends on the presence of limited technological opportunities in a specific industry, and
is determined by the sector specific constant k4i and by a starting value SE0. Equation (1.3)
and (1.4) show how the factors affecting demand depend on search activities.
k14 −k19
are
constants, to be considered as parameters affecting the time paths of
Yi
t
,
ΔYi
t
and
pi
t
.
Equation (1.3) and (1.4) have the form of logistic equations. They tell us that both the services
performed by the products of sector i, and their degree of differentiation rise with search
activities at a rate, which starts slowly, accelerates until reaching a maximum, and then falls
gradually. This assumption is not completely ad-hoc. The logistic form of the equation can be
obtained by assuming that (i)
Yi
t
has an upper boundary, and that (ii) the rate of growth of
Yi
t
depends on the product of its instant value times the difference between its upper boundary
and its instant value. In turn, these assumptions are equivalent to admitting that improvements
in the performance of a new technology can be very rapid and even accelerate in the initial
period of its life cycle, when learning effects, etc., can provide a source of increasing returns
to adoption, but that eventually decreasing returns to further improvements will be
encountered, leading to an upper boundary. The constants
k14
and
k16
give us the time when
TEVECON : Description of Model (no code)
7
the logistic curve starts growing, while the constants
k15
and
k17
give us the slope of the
central part of the curve, during which the rate of growth of either
Yi
t
or
ΔYi
t
reaches a
maximum. As varying
k14 −k17
, we can vary the rate of growth of
Yi
t
and
ΔYi
t
. Using these
forms for
Yi
t
and
ΔYi
t
we assume that both the services produced and the degree of
differentiation of the products of sector
i
will increase as a consequence of search activities.
The rate of growth of
Yi
t
and
ΔYi
t
will start slowly, will accelerate later; in the end it will
become slow due to the exhaustion of the possibilities inherent in the technology used to
modify
Yi
t
and
ΔYi
t
. The equation for
pi
t
has a different form because we expect
pi
t
to fall as
a result of search activities.
This demand equation contained the effect of price, as any demand equation has to do,
but also the effects of output quality and of differentiation. Written in the form of equation
(1.2) the risks to overstate demand and does not exploit all the possible links to innovation. In
(Saviotti and Pyka 2012, 2013, 2015), we introduced a demand equation containing terms,
which effect of disposable income and of preferences on demand (Equation 1.7). In this way
not only we provide a more complete representation of the demand function, but we also
created a co-evolutionary link between demand and innovation. In fact, we are convinced that
innovation would not have had any impact on economic development unless a demand and
markets had been created for the goods and services embodying the innovations (Saviotti and
Pyka 2012, 2013, 2015).
Di
t=kpref ,iDi
0DDisp,i
Yi⋅ ΔYi
pi
(1.7)
Investment, competencies and income distribution
The versions of TEVECON used in the papers published up to 2013 were based a
homogeneous population and did not give us the opportunity to explore the issues related to
the distribution of various properties in the population. Starting from 2014 we have
introduced two social classes, which differ for their level and quality of education. As a
consequence, the two social classes differ for their competencies, wages, income per capita,
disposable income and demand. We imagined two social classes that could be, for example,
blue and white collar workers or workers and managers, and called them L, for low, and H for
high. Thus, the L class would be constituted by blue-collar workers, while the H class would
be consisted by managers. The population share of the two classes can be expected to vary in
TEVECON : Description of Model (no code)
8
different historical periods. The equations representing the two social classes L and H are
described in Section 2.24
SECTION 2
This section concentrates mainly on equations and graphic representations, although it does
provide some information about the underlying concepts. A more complete description of
these concepts can be found in Section 1, which might have some overlaps with Section 2.
2.1) Dynamics of the number of firms in a population
This is the central equation in TEVECON. It describes the change in the net number of firms
in each sector
i
in the course of time. The change in the net number of firms is the result of
the processes of entry and exit into and out of the sector. The term k1FAitAGit describes the
rate of entry while the two terms
−ICi
t
and
−MAi
t
describe processes of exit. The variables
determining the rate of entry,
FAi
t
and
AGi
t
, are financial availability and adjustment gap
respectively. Their meaning is described immediately below. Figure 2.1 represents
graphically the change in the number of firms in different sectors. As it can be seen, the
number of firms rises at first, reaches a maximum and then falls to a very low value.
ΔNi
t=k1⋅FAi
t⋅AGi
t−ICi
t−MAi
t
(2.1)
where:
k1
= Parameter affected by a number of factors, including the costs of creating a firm, the
presence of entrepreneurs in the economic system etc.
FAi
t
= Financial availability in sector
i
(see below)
AGi
t
= Adjustment gap in sector
i
(see below)
TEVECON : Description of Model (no code)
9
Figure 2.1 Evolution of the number of firms in subsequent sectors (Vertical axis: the number of firms,
horizontal axis: time)
It is to notice that in Figure 2.1 each sector describes a lifecycle, with the number of
firms increasing rapidly at the beginning, reaching a maximum and then falling to a lower
level. The occurrence of an industry life cycle is not explicitly programmed in TEVECON.
The industry life cycle occurs result of the interaction of demand and competition. When the
initial temporary monopoly is gradually replaced by a growing intensity of competition and
the sector saturates the rate of entry falls below the rate of exit, the degrees of industrial
concentration increases. In the end the sector can become an oligopoly or a monopoly
depending on the parameters of the TEVECON model.
2.2) Financial availability FAi
t
Financial availability represents the amount of financial resources available for investments in
sector
i
. It is not just the amount of resources in the economic system. It reflects also the
knowledge required to estimate the economic development potential of new innovations. In
fact it is the fraction of the financial resources of the whole economic system which investors
are prepared to invest in sector
i
. Thus,
FAi
t
depends on the expectations of the market
potential of given innovations. We can expect growing financial availability to accelerate the
rate of entry of firms into a sector. This can easily be proved by varying the value of
FAi
t
in
different runs of the model (Equation 2.1). Henceforth each set of runs of the model in which
one or few variables are systematically changed will be called an experiment. However, the
comparison of different constant levels of financial availability will only tell us that an
economic system able to invest more in an emerging sector will have a higher rate of growth
of firms in the sector but it will not give us a realistic picture of the dynamics of investment in
emerging sectors. Thus, it is possible to assume that financial operators will observe the
-
20
40
60
80
100
135 69 103 137 171 205 239 273 307 341 375 409 443 477
TEVECON : Description of Model (no code)
10
behaviour of the economic system and spot the potential of emerging sectors. If they notice
that some aspects of an emerging sector, for example the rate of creation of new firms, grow
more rapidly than average for the whole economic system, they can invest more heavily in the
emerging than in the average, and typically more mature, sector in the expectation to enjoy
higher than average (supranormal) rates of profit. This kind of behaviour is represented by
equation (2.2):
)]
1
1
(1[
3∑
−
−⋅+⋅=
j
t
j
t
i
x
t
idt
dN
ndt
dN
kkFA
(2.2)
where:
k3
= The amount of financial resources available in the whole economic system
kx
= The optimism (or over optimism) of financial operators with respect to development
potential of sector
i
.
dN j
t
dt
= The rate of change in the number of firms in sector
i
∑
−j
t
j
dt
dN
n1
1
= The average rate of change in the number of firms in sectors
i≠j
Equation (2.2) is a form of replicator dynamics and it tells us that the investment in sector
i
(
FAi
t
) depends on the extent to which the rate of growth of the number of firms in sector
i
is
above that for the average in the rest of the economic system. However, for a given difference
between the rate of growth of the number of firms in sector
i
and in the rest of the economic
system the amount of
FAi
t
will depend on the two parameters
k3
and
kx
, where
k3
is the
amount of financial resources available in the whole economic system and
kx
is the optimism
(or over optimism) of financial operators with respect to development potential of sector
i
.
Equation (2.2) is not used in all the runs of TEVECON. In some runs it is possible to use
FAi
t
as a parameter the value of which is varied in different runs.
2.3) Adjustment Gap AGi
t
The term adjustment gap indicates the expected size of the market created by a pervasive
major innovation. The term gap indicates something to be compensated or filled. In fact, as
the innovation emerges there are neither a demand nor a production capacity for it. Potential
users and consumers do not know about its existence and properties and entrepreneurs have
TEVECON : Description of Model (no code)
11
not yet had the time to invest in new production facilities. As demand grows and production
facilities are built the gap is gradually closed giving rise to a saturated market. The gap may
never be completely closed if the output of the sector keeps changing in a qualitative way. An
example of this change would be today's cars compared to those of Henry Ford's era. In
today's cars there are many new internal structures and functionalities, supplying new
services, which were completely absent in much older cars. The implication of this is that
while a sector can saturate in volume terms it will not necessarily saturate in value terms
(Saviotti, Pyka, and Krafft 2007). Also, we cannot expect the size of the adjustment gap to fall
at all times after the emergence of a new sector. During the life cycle of the sector
innovations, the result of search activities (
SEi
t
, see later) have two effects: (i) they increase
efficiency, thus reducing costs and prices, (ii) they increase the services supplied by the
product (
Yi
t
), which we will consider a measure of product quality, and the degree of product
differentiation (
ΔYi
t
). As a consequence of both (i) and (ii), the population of potential
adopters of the output of sector
i
grows. Thus
AGi
t
can even grow in the intermediate phases
of the life cycle of the sector. Eventually, even if no complete saturation takes place, the size
of
AGi
t
will fall below its maximum. We can then distinguish in the life cycle of each sector
an early and more entrepreneurial period, in which there are high rates of
Ni
t
of profit, and a
more mature and more managerial period during production, which processes would become
relatively more routine work. In this sense,
AGi
t
can be defined as the difference between
maximum demand and instant demand (Equation 2.3). Figure 2.2 shows the dynamics of
different sectors in the system.
t
i
t
i
t
iDDAG −=max
(2.3)
Figure 2.2 Evolution of the adjustment gap of subsequent sectors. (Vertical axis: the adjustment gap
AGi
t
, horizontal axis: time)
-
0.5
1.0
1.5
2.0
135 69 103 137 171 205 239 273 307 341 375 409 443 477
TEVECON : Description of Model (no code)
12
2.4) Sectoral demand Di
t
Two types of demand equation have been used in subsequent versions of TEVECON
(Equation 2.4 and 2.5). In both of them demand depends on product price, on the services
supplied by the product, which measure product quality, and on product diversification. We
can expect demand to increase as pi (product price) falls and as
Yi
t
(services supplied by the
product) and
ΔYi
t
rise. Also, pi can be expected to fall due to the growing efficiency of
production processes and to rise due to growing product quality (services) or to growing
product differentiation.
Di
t=Di
0Yi⋅ ΔYi
pi
(2.4)
Di
t=kpref ,iDi
0DDisp,i
Yi⋅ ΔYi
pi
(2.5)
where :
Di
t
= Demand for good/service of sector
i
at time t
kpref ,i
= Parameter defining the preferences of consumers for good/service of sector
i
at time t
Di
0
= Demand for good/service of sector
i
at the time of its introduction
DDisp,i
= Disposable income which can be allocated to good/service in sector
i
at time t
Yi
= Aggregate measure of the characteristics/services supplied by good/service in sector
i
at
time t, measures product or output quality
ΔYi
t
= Output differentiation of good/service in sector
i
at time t
pi
t
= Price of good/service in sector
i
at time t
Equation (2.5) contains two new terms,
kpref ,i
and
DDisp,i
, which represent the preferences of
consumers for good/service
i
at time t, and the disposable income, which can be allocated to
the same good/service
i
at time t. The two give rise to two different time paths (Figure 2.3
and 2.4).
TEVECON : Description of Model (no code)
13
Figure 2.3 Evolution of the demand for the output of subsequent sectors, calculated using equation
(2.4) (Vertical axis: the demand for sectoral output, horizontal axis: time)
Figure 2.4 Evolution of the demand for the output of subsequent sectors, calculated using equation
(2.5) (Vertical axis: the demand for sectoral output, horizontal axis: time)
2.5) Search Activities SEi
t
Search activities are a very important component of TEVECON. They are a generalized
analogue of R&D. Search activities include all the activities, which scan the external
environment to look for alternatives to existing routines. In TEVECON search activities can
be fundamental or sectoral. Furthermore, we can expect search activities to be affected by
demand and by the level of human capital present in the economic system. In particular,
sectoral search activities can be expected to rise with the demand for the output of the same
sector (Equation 2.6). However, in a given country such search activities will be possible only
when the required level of human capital is available (Equation 2.8). For the moment only the
-
1
2
3
4
5
6
7
135 69 103 137 171 205 239 273 307 341 375 409 443 477
TEVECON : Description of Model (no code)
14
demand equation (2.8) has been used. Furthermore, this part describes only sectoral search
activities. Fundamental search activities are described later (see entry conditions and
investment in fundamental research).
“Demand pushed” search activities:
)]exp(1[)5.0( 54
0t
i
lt
iDacckkSESED ⋅−−⋅+−=
(2.6)
where:
5.0)1(10
4⋅−+= ik i
k4
i
= A constant for each sector and increments with 0.5 for later sectors
“Supply pushed” search activities:
t
iSEorg
t
iCShumankkSES ⋅⋅=
(2.7)
where:
CShumani
t=share_human ⋅share_ sec tor
i
t⋅Total Investmentt
t
i
t
iSEDSESceSEdifferen −=
(2.8)
NOTE: In the programme we do not use this at the moment, as in equation (2.9)
SEi
t
is set equal to
SEDi
t
.
t
i
t
iSEDSE =
(2.9)
Figure 2.5 Evolution of sectoral search activities
SEi
t
(Vertical axis: sectoral search activity,
horizontal axis: time)
-
2
4
6
8
10
12
14
135 69 103 137 171 205 239 273 307 341 375 409 443 477
TEVECON : Description of Model (no code)
15
2.6) Mergers and Acquisitions MAi
t
Mergers and acquisitions occur with a frequency, which depends positively on the number of
firms existing at a given time and on returns to adoption, and negatively on the adjustment
gap. In other words, the closer the economic system is to saturation the higher the probability
of mergers and acquisitions. It is to be observed that this term describes also the probability of
failure since it would be affected by the same factors in the same order. We could possibly
rename
MAi
t
.
t
i
t
i
t
i
t
i
t
iDSE
MC
NkMA
−
⋅⋅=−1
9
(2.10)
Figure 2.6 Sectoral evolutions of mergers, acquisitions and failures in the course of time (Vertical
axis: the number of firm changed by mergers, acquisitions and failures, horizontal axis: time)
2.7) Returns to Adoption MCi
t
This term describes all the forms of returns to adoption, including scale economies. It is now
present only in this equation.
0
MCMC t
i=
(2.11)
where:
1
0== constMC
2.8) Intensity of Competition ICi
t
This is very important part of TEVECON. Here the intensity of competition is the combined
result of intra-sector and inter sector competition. Intra sector competition is very similar to
the one, which is normally found in textbooks. Inter-sector competition occurs when different
sectors produce products supplying comparable services. In the present form the effect of
-4.0
-3.0
-2.0
-1.0
-
1.0
2.0
135 69 103 137 171 205 239 273 307 341 375 409 443 477
TEVECON : Description of Model (no code)
16
intra sector competition is represented
Ni
t
, the number of firms in sector
i
at time t, and the
intensity of inter sector competition is represented by
Ntotal
t
, the total number of firms in the
whole economic system. The constant
kIC
is a measure of the competitiveness of the
economic system, as determined, for example, by anti monopoly laws etc. The constant RII is
the ratio between the inter- and intra- sector competition. When RII = 0 there is only intra
sector competition and as RII grows inter sector competition grows with respect to intra sector
competition. This is an approximate form since we can expect the intensity of competition to
be affected also by the extent of product differentiation.
t
totalII
t
i
t
total
t
i
IC
t
iNRN
NN
kIC
⋅+
⋅
⋅=−
−
1
1
(2.12)
Figure 2.7 Sectoral intensity of competition. (Vertical axis: sectoral intensity of competition,
horizontal axis: time)
∑
=
i
t
i
t
total NN
(2.13)
Here a more advanced version would include the effect of product differentiation. The
above equation would then take the following form:
t
totalII
t
i
t
total
t
i
i
IC
t
iNRN
NN
Y
kIC
⋅+
⋅
Δ
⋅=−
−
1
1
1
(2.14)
Thus, the greater the extent of product differentiation, the lower the intensity of
competition. Product differentiation gives producers a local monopoly. This corresponds to
monopolistic competition.
-
1.0
2.0
3.0
4.0
5.0
6.0
135 69 103 137 171 205 239 273 307 341 375 409 443 477
TEVECON : Description of Model (no code)
17
2.9) Demand Accumulation
∑
=
t
t
i
t
iDDacc
(2.15)
2.10) Maximum Demand Dmaxi
t
Maximum demand plays an important role in TEVECON. The maximum demand for the
output of a sector
i
is defined as the maximum possible size of the market for
i
. The
described concept of adjustment gap above is defined as the difference
Dmax,i
t−Di
t
. Since at
time zero creation of the new market,
Di
t
, is equal to zero,
Dmax,i
t
represents the maximum
possible size of the market for
i
. We can expect for
Dmax,i
t
to depend, generally positively, on
search activities (
SEi
t
), since, through output quality and output differentiation (Equation 2.21
and 2.22), they affect demand. We can then transform instant demand (
Di
t
) into maximum
demand (
Dmax,i
t
) by means of a function, called
TIi
t
.
TIi
t
is a sigmoid function which
increases at variable rates with
SEi
t
.
)]([1
1
0
2122 SESEkkExp
TI t
i
t
i−−+
=
(2.16)
Figure 2.8
TIi
t
as a function of search activities (Vertical axis:
TIi
t
, horizontal axis: time)
t
i
t
i
t
iTI
D
D=max
(2.17)
-
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
135 69 103 137 171 205 239 273 307 341 375 409 443 477
TEVECON : Description of Model (no code)
18
Figure 2.9
Dmax,i
t
as a function of search activities (Vertical axis:
Dmax,i
t
, horizontal axis: time)
2.11) Condition for the emergence of new sectors
One the most specific features of TEVECON is the endogenously variable number of sectors.
The creation of a new sector is induced by the previous dynamics of the economic system.
This can happen in a number of ways. The first implementation of this principle is the
following: as a sector i becomes saturated and starts creating declining opportunities for
growth or profit entrepreneurs start searching for new opportunities by setting up a niche
which could later become a new sector. In this version the saturation occurs when the
adjustment gap stops falling. That happens when the slope of its rate of change becomes zero.
Possible alternatives are (i) when the rate of profit tends to zero or (ii) when the rate of growth
of output tends to zero. In addition to this component the timing of entry of a new sector is
determined by a stochastic component and by the effect of fundamental search activities SEF.
Fundamental search activities SEF tend to shorten the delay between the creation of sectors
i
and
i+1
and thus to accelerate the process of economic development. This is due to the fact
that each new sector is created by a radical and pervasive innovation and that this type of
innovations is expected to be created by fundamental search activities.
⎩
⎨
⎧>
=otherwise
holdEntryThrescounterforN
N
t
i
t
i
t
i
t
i0
(2.18)
)( SEFkholdEntryThres seft
t
i⋅−=
ϕ
(2.19)
where
[ ]
301;300∈
t
ϕ
, which means equally distributed random number between 300 and 301
(Note: no random effect!)
⎩
⎨
⎧<+
=
−
−−
−
otherwise
AGAGifcounter
counter
t
i
t
i
t
i
t
i0
11
11
1
(2.20)
-
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
135 69 103 137 171 205 239 273 307 341 375 409 443 477
TEVECON : Description of Model (no code)
19
2.13) Output quality and output differentiation
The quality of a product is here represented by the services it supplies to its users/consumers.
In turn, such services are measured by its service characteristics. This follows from the twin
characteristics representation of product technology, according to which a product can
represented by two sets of characteristics: technical characteristics, corresponding to its
internal structure, and service characteristics, corresponding to the services performed for its
users/consumers (P. P. Saviotti and Metcalfe 1984). This representation can itself be
considered an extension of Lancaster's characteristics approach (Lancaster 1966). In
TEVECON the output of a sector can be a material product or a service. In both cases
consumer or user demand is for the services supplied in an embodied or disembodied form
respectively. Hence, we can talk of output quality and differentiation.
Output quality, which is equal to Service Level Yi
t
The services
Yi
t
supplied by a given output in sector
i
, the differentiation and the price of the
same output, can be expected to vary in the course of time due the effect of search activities.
We expect
Yi
t
and
ΔYi
t
to rise according to a logistic equation, as seen in equation (2.21) and
(2.22), and
pi
t
to change according to equation (2.24). As far as
Yi
t
and
ΔYi
t
are concerned,
we expect that search activities can only lead to their growth, although this will occur at
different rates due to the effectiveness of search activities in different sectors. This differential
effectiveness is described in the model by the parameters
k14
and
k15
for services,
k16
and
k17
for product differentiation,
k18
and
k19
for price.
)](exp[1
1
0
1514
0
SESEkk
yY t
i
i
t
i−−+
+=
(2.21)
-
0.2
0.4
0.6
0.8
1.0
1.2
135 69 103 137 171 205 239 273 307 341 375 409 443 477
TEVECON : Description of Model (no code)
20
Figure 2.10 Sectoral evolution of output quality, represented by the level of services
Yi
t
supplied by
the output. (Vertical axis: output quality, horizontal axis: time)
Output differentiation ∆Yi
t
)]([1
1
0
1716
0
SESEkkExp
yY t
i
i
t
i−−+
+Δ=Δ
(2.22)
Figure 2.11 Sectoral evolution of output differentiation, represented by the variation
ΔYi
t
of the level
of services
Yi
t
supplied by the output. . (Vertical axis: output differentiation, horizontal axis: time)
2.14) Prices pi
t
Prices are now calculated as unit cost + mark up. In previous versions of TEVECON this was
not the case. Unit costs are determined by labour costs (labour * wages), physical capital costs
(capital * rate of interest), and by the effect of search activities on process efficiency, services
and product differentiation. The mark up is now fixed at 20% of unit costs but that can be
changed. In turn product prices reflect the influence of growing production efficiency and of
rising product quality
uci
t=Li
t⋅wi
t+Kpi
t⋅r
Qi
t⋅exp(k18 −k19 ⋅SEi
t)⋅exp(kyipi ⋅Yi
t+kdyipi ⋅ ΔYi
t)
(2.23)
where:
uci
t
= Unit costs in sector
i
at time t
Li
t
= Employment in sector
i
at time t
Kpi
t
= Investment in capital goods in sector
i
at time t
-
0.2
0.4
0.6
0.8
1.0
1.2
135 69 103 137 171 205 239 273 307 341 375 409 443 477
TEVECON : Description of Model (no code)
21
r
= Rate of interest
SEi
t
= Search activities in sector
i
at time t
Yi
t
= Aggregate measure of the characteristics/services supplied by good/service
i
at time t,
measures product or output quality
ΔYi
t
= Output differentiation of good/service
i
at time t
Qi
t
= Output of sector
i
at time t
The term ‘
exp(k18 −k19 ⋅SEi
t)
’ represents the efficiency enhancing effect of search activities.
The term ‘
exp(kyipi ⋅Yi
t+kdyipi ⋅ ΔYi
t)
’ represents the effect of search activities on output quality
and output differentiation
2.14.1) Mark-up pricing
t
i
t
iucp⋅+= 2.110
(2.24)
Figure 2.12 Change in sectoral unit costs over time
Figure 2.13 Change in sectoral prices over time
-
0.2
0.4
0.6
0.8
1.0
1.2
135 69 103 137 171 205 239 273 307 341 375 409 443 477
8.0
8.5
9.0
9.5
10.0
10.5
11.0
11.5
135 69 103 137 171 205 239 273 307 341 375 409 443 477
TEVECON : Description of Model (no code)
22
2.15) Sectoral output Qi
t
In the present version of TEVECON sectoral output is calculated as a function of human
capital, physical capital and search activities. The relationship between these variables and
Qi
t
is given by equation (2.25). Furthermore,
Qi
t
is also function of
Q0
, output at the time the
sector is created, of
γ
, the efficiency of production, and of the term
(1+
α
ci
t)
, which provides
a feedback loop limiting the differences between demand and supply. In essence this
expression is a production function, but it is not assumed to have the properties commonly
associated with a production function, such as constant elasticity of substitution etc.
Qi
t=Q0+
γ
⋅(1+
α
ci
t)⋅(1−exp(−k11 ⋅SEi
t−kcspq1⋅CSphysicali
t−k11 ⋅HCi
t)
(2.25)
Figure 2.14 Sectoral output over time
2.16) Investment, competencies and income distribution
The versions of TEVECON used in the papers published up 2013 contained a homogeneous
population and did not allow us to explore issues related to the distribution.
Investment originates from savings, which originate from income, which in turn originates
from output.
Outputt=Incomet
(2.26)
Total Investmentt=s⋅Incomet
(2.27)
where:
s
= Saving rate
-
0.5
1.0
1.5
2.0
135 69 103 137 171 205 239 273 307 341 375 409 443 477
TEVECON : Description of Model (no code)
23
Total investment is then distributed amongst capital goods, education and fundamental search
activities:
Total Investmentt=Kpt+EDt+SEFt
(2.28)
where:
Kpt
= Capital goods at time t
EDt
= Education at time t
SEFt
= Fundamental search activities at time t
2.16.1) Investment in Fundamental Search Activities (SEFt)
As in the case of sectoral search activities, the term fundamental search activities here
includes not only R&D but all non routine activities aimed at scanning the external
environment of firms, which they could use to look for alternatives to their present routines.
As opposed to sectoral search activities, which are specific to their sector, fundamental search
activities are general and fundamental. Their main utilization in TEVECON consists in
speeding up the emergence of new sectors by making easier to create the radical innovations,
which will give rise to the new sectors.
SEF
t=(R&D sharei
t
i
∑⋅Total Investmentt)
(2. 29)
In most of our runs up to date it is given a fixed value, for example:
SEFt=(R&D sharei
t
i
∑⋅Total Investmentt)
=sSEF⋅Total Investmentt=const⋅Total Investmentt
=0.2 ⋅Total Investmentt
(2.30)
Total investment can then be allocated to different sectors
Investment Sharei
t=pi
t⋅Qi
t
Incomet
(2.31)
Investmenti
t=Investment Sharei
t⋅Total Investmentt
(2.32)
where:
Qi
t
= Output of sector
i
TEVECON : Description of Model (no code)
24
Investment Sharei
t
= Investment share of sector
i
at time t
Investmenti
t
= Investment in sector
i
at time t
The saving rate,
s
, has so far been assumed fixed. All savings has been assumed to be
invested.
2.16.2) Physical Capital Stock
The stock of physical capital is the result of investment, which is obtained by first calculating
the share of total investment allocated to the sector and then by calculating the share of
physical capital within the sector.
Kpi
t=(1−
ρ
)⋅Kpi
t−1+sKp ⋅sQi
t⋅Total Investmentt
(2.33)
where:
sKp
= Share of physical capital in overall investment
Kpi
t
= Accumulated physical capital of sector
i
at time t
sQi
t
= Share of sector
i
in overall output
2.17) Quality of human capital
The quality of human capital is essentially created by education. Thus its level
hi
t
depends on
the share of investment allocated to education (
EDi
t
), and on the effectiveness of the
education system in creating human capital (
ked
).
In turn, the total amount of human capital
HCi
t
depends on the amount of unskilled labour
multiplied by the level of human capital.
t
ied
t
iEDkh ⋅=
(2.34)
t
i
t
i
t
ihlabourHC ⋅=
(2.35)
TEVECON : Description of Model (no code)
25
Figure 2.15 Quality of human capital over time
Figure 2.15 Quality of human capital over time (Plotting hh+hl)
Figure 2.16 Sectoral human capital
HCi
t
over time
2.18) Local equilibrium between demand and supply
This part of the model is added to make sure that demand does not differ very much from
supply. It calculates excess demand and it introduces a routine, which reduces excess demand.
-
0.5
1.0
1.5
2.0
135 69 103 137 171 205 239 273 307 341 375 409 443 477
CS_ ed
-
100
200
300
400
500
135 69 103 137 171 205 239 273 307 341 375 409 443 477
TEVECON : Description of Model (no code)
26
It acts in similar to way to a system of stocks except that what is 'stocked' and then reduced is
excess demand. It would be possible to start calculating excess supply and then to reduce it in
the same way.
t
i
t
i
t
i
t
iD
QD
EXD −
=
(2.36)
Figure 2.17
EXDi
t
over time
2
)EXD(t
i
t
i=
α
(2.37)
Figure 2.18
α
i
t
over time
The maximum values of ait are restricted to 0.1 and -0.1 to slow down the adjustment
processes.
∑
=
t
t
i
t
ci
αα
(2.38)
-1.5
-1.0
-0.5
-
0.5
1.0
135 69 103 137 171 205 239 273 307 341 375 409 443 477
-0.2
-0.1
-0.1
-
0.1
0.1
0.2
135 69 103 137 171 205 239 273 307 341 375 409 443 477
TEVECON : Description of Model (no code)
27
Figure 2.19
α
ci
t
over time
2.10) Macro Income
∑
=
⋅=
n
i
t
i
t
i
tQpIncome
1
(2.39)
Figure 2.20 Income over time
2.20) Population
The population of TEVECON's economic system is expected to increase or to fall depending
on whether food production is greater than or lower than the survival quantity (Equation
2.40).
⎥
⎦
⎤
⎢
⎣
⎡−
⋅−⋅=
FoMin
FoMin
pop
t
Q
FoodQ
ED
k
PopPop 0
01
(2.40)
where:
Popt
= Population at time t;
QFoMin
= Minimum quantity of food required for survival;
Food
= Food production at time t
-10
-
10
20
30
40
50
135 69 103 137 171 205 239 273 307 341 375 409 443 477
-
10
20
30
40
50
60
70
80
135 69 103 137 171 205 239 273 307 341 375 409 443 477
TEVECON : Description of Model (no code)
28
kpop
= A parameter which determines the effect of food production on the rate of population
growth
ED0
= Investment in education at time zero
2.21) Employment
Sectoral employment is calculated by the number of firms and by output by assuming that
labour per unit of output increases with increasing firm size. This implies that the labour
productivity of larger firms is higher than the labour productivity of smaller firms. This is
effectively a sectoral demand for labour.
Labour
i
t=k12 ⋅Ni
t−1
Qi
t
(2.41)
LabourD
t=Labour
i
t
i
∑
(2.42)
Aggregate employment is the sum of all sectoral employment levels at a given time
Figure 2.21 Sectoral employment over time
Figure 2.22 Aggregate employment over time
-
100
200
300
400
500
135 69 103 137 171 205 239 273 307 341 375 409 443 477
-
100
200
300
400
500
600
700
800
900
135 69 103 137 171 205 239 273 307 341 375 409 443 477
aggregate employment
TEVECON : Description of Model (no code)
29
2.22) Unemployment
LabourS
t=fpop ⋅Populationt
(2.43)
Labour
S
t
= Labour supply at time t
fpop
= Working share of the whole population
Populationt
= Total population at time t
Unemploymentt=LabourD
t−LabourS
t
(2.44)
Figure 2.23 Unemployment over time
2.23) Wages
t
i
t
i
t
i
wagesi
t
ilabour
PQ
kwwages ⋅
⋅+= 0
(2.45)
TEVECON : Description of Model (no code)
30
Figure 2.24 Evolution of sectoral wages (Vertical axis: sectoral wages, horizontal axis: time)
2.24) Education, the distribution of competencies, income and others
The versions of TEVECON used in the papers published up to 2013 were based a
homogeneous population and did not give us the opportunity to explore the issues related to
the distribution of various properties in the population. Starting from 2014 we have
introduced two social classes, which differ for their level and quality of education. As a
consequence, the two social classes differ for their competencies, wages, income per capita,
disposable income and demand. We imagined two social classes that could be, for example,
blue and white collar workers or workers and managers, and called them L, for low, and H for
high. Thus, the L class would be constituted by blue-collar workers and the H class by
managers. The population share of the two classes can be expected to vary in different
historical periods.
Education is a component of the total investment in the economic system (as seen in
Equation 2.28) and its share of total investment can be varied. Once the education share of the
total investment carried out in the economic system has been decided, the education budget
can be allocated in different ways to the two classes L and H in terms of the quantity and
quality of education they receive. The distribution of education that follows from these
decisions leads to distribution of competencies, which in TEVECON is represented by a
distribution of the quality of human capital. In turn, since the quality of human capital affects
the quantity of human capital, the distribution of education affects output, wages and growth.
Furthermore, the distribution of education leads to a dynamics in which the population share
of each class varies in the course of time.
TEVECON : Description of Model (no code)
31
In our experiments we started by defining the initial population share of each social
class, L (Low) and H (High) (Equation 2.46a and 2.46b), then the sectoral education
expenditure allocated to each social class (Equation 2.47a and 2.47b), then the relative quality
of education each class would receive (Equation 2.48a and 2.48b).
2.24.1) Population share of the two social classes:
PopL=sPopL ⋅Pop
(2.46a)
PopH=sPopH ⋅Pop
(2.46b)
where,
1=+ PopHPopL ss
2.24.2) Education expenditures share:
EDiL
t=sEDiL
⋅EDi
t
(2.47a)
EDiH
t=sEDiH
⋅EDi
t
(2.47b)
where,
1=+ EDi HEDiL ss
Share of sectoral education investment is going to each social class (Equation 2.47a and
2.47b).
2.24.3) Quality of human capital hi :
hiL
t=kt
EDiL
⋅EDt
iL
(2.48a)
ht
iH =kt
EDiH
⋅EDt
iH
(2.48b)
Impact of sectoral investment in education (
EDt
iL
or
EDt
iH
) and of education quality (
kt
EDiL
or
kt
EDiH
) on the quality of human capital (
hiL
t
or
ht
iH
) are described in equation (2.48a) and
(2.48b)
where:
sPopL
and
sPopH
= Population shares of the L and H classes
sEDiL
and
sEDiH
= Sectoral education shares of the L and H classes
kt
EDiL
and
kt
EDiH
= Education quality of the L and H classes*
hiL
t
and
ht
iH
= Quality of human capital of the L and H classes
(*In general we expect
kEDiH ≥kEDiL
, but this could be the object of experiments)
TEVECON : Description of Model (no code)
32
2.24.4) Labour:
We assume that the sectoral demand for labour in each class can be
LiL
t=sPopL ⋅Li
t
(2.49a)
LiH
t=sPopH ⋅Li
t
(2.49b)
2.24.5) Quantity of Human capital at the sectoral level:
Hi
t=(sPopL ⋅hiL
t+sPopH ⋅hiH
t)Li
t
(2.50)
Hi is one of the factors in the sectoral production function
2.24.6) Wages:
)(
)()(
iLiH
wiHiH LL
iqip
kw +
=
(2.51a)
iHiL
ii
wiLiL LL
Qp
kw +
=
(2.51b)
Equation (2.51) represents wages for the two social classes L and H. The parameter
kwiL
and
kwiH
convert labour productivities into wages.
We can expect
kwiL
and
kwiH
to be related to the quality of human capital in the two
cases. We could start with
kwiH=hiH
and
kwiL=hiH
or we could use:
iH
iL
wiHwiL h
h
kk =
(2.52)
2.24.7) Dynamics of the population share of the two classes
We can calculate the changes in the shares of education expenditure of the L and H classes in
the course of time:
)1(
0EDiL
t
EDlLEDi L
tsss Δ+=
(2.53a)
)1(
0EdiH
t
EDiHEDi H
tsss Δ+=
(2.53b)
We can expect
Δst
EDiL
and
Δst
EDiH
to be affected by (i) income per capita, (ii) search intensity
(SEi
Qi
)
,
Yi
,
ΔYi
,
AGi
etc. Since
st
EDiL
and
st
EDiH
are not independent:
1=+ t
EDiH
t
EDiL ss
(2.54)
1)1()1( 00 =Δ++Δ+t
EDiHEDi H
t
EDiLEDil ssss
(2.55)
TEVECON : Description of Model (no code)
33
t
EDiH
EDiL
EDiH
t
EDiL s
s
s
sΔ−=Δ0
0
(2.56)
But, how do
Δst
EDiL
and
Δst
EDiH
depend on
hi
? Over a given period we assume that:
EDiH
EDiL
EDiH
EDiL
h
h
s
s
Δ
Δ
=
Δ
Δ
(2.57)
This dynamics could change the shares of educational expenditures of the two classes.
The population shares of the two classes can change for given levels of investment in
education because with higher investment a larger share of the population can be educated.
The rate of change of the two populations depends on how much education increases the
quality of human capital (Equation 2.57).
2.24.8) Relationship between output quality and hi:
Given that:
iquali
tYkEDED i+= 0
(2.58)
and
iEDiEDkh =
(2.59)
then:
iqual
ED
i
ED
iYk
k
h
k
h+=
0
(2.60)
iqualEDii Ykkhh =−0
(2.61)
TEVECON : Description of Model (no code)
34
Constants: meaning and values:
k1
3
weight for entry terms
k3
1
weight for capital
k5
0.01
weight determining the pace of technological progress
kIC
0.1
RII
10
k9
0.01
weight for the M&A term
k11
0.0000051
k12
1
weight in the employment term
k14
1
k15
0.25
k16
1
constant in the Y and ∆Y equation
k17
0.25
weight determining the pace of product differentiation
k18
1
k19
0.1
k21
0.25
k22
1
g
500
weight in the output equation
korg
1
kSE
1
r
0.01
depreciation rate
ksef
100
kwages
1
share_physical
0.4
share_humanl
0.4
share_rd
0.2
ms
0.25
marginal saving rate
TEVECON : Description of Model (no code)
35
Initial Values
D0
100
p0
10
SE0
1
Y0
0.2
DY0
0.2
Q0
1
MC0
1
TEVECON : Description of Model (no code)
36
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