Microsoft Word - Role of diversity and tolerance in economic development.docxWitold Kwasnicki Institute of Economic Sciences
Wroclaw University, Poland e-mail: kwasnicki@prawo.uni.wroc.pl http://kwasnicki.prawo.uni.wroc.pl/
Abstract
In the first part of the paper a description of evolutionary model of industry development
is presented. This part is followed by simulation study focused on investigation of the role
of diversity and heterogeneity of firms’ behaviour on tempo and modes of industrial
development, particularly related to rate of technological development (innovativeness).
References to R.A. Fisher’s theorem of natural selection is presented. Simulation results
suggests that it is possible to generalize Fisher’s observation. Speeding up economic
growth due to higher variety is observed not only in a case of evolutionary process
approaching the equilibrium but also due to higher variety caused by tolerant
environment in the long run, thanks to more frequent emergence of gradual and radical
innovations. Those innovations cause emergence of new equilibria toward whom the
process is continuously approaching.
theorem, growth rate, innovation
The presented paper is a continuation of our earlier work on ‘Diversity and Development:
Tempo and Mode of Evolutionary Processes' (Kwasnicka, Kwasnicki, 1986). The main
conclusion of investigating a general model of evolutionary processes presented in that paper
was that “the main source of improvements (innovations) is the neighborhood, not, as is
commonly believed, the best elements. The existence of the neighborhood diminishes the
average quality of the population; that is, it causes a worsening of system performance. …
the existence of diversity is of essential importance for long range system development seems
to be intuitively acceptable, but we see strong need of solid verification of this hypothesis.”
Ronald Aylmer Fisher (1930) in his famous book The Genetical Theory of Natural
Selection stated his “fundamental theorem of natural selection” in the form: “The rate of
increase in fitness of any organism at any time is equal to its genetic variance in fitness at that
time.” The Fisher’s theorem has been widely discussed either by biologists as well as by
researchers of other disciplines. In the context of evolutionary economics the theorem was
interestingly analysed by J.S. Metcalfe (1994). Metcalfe distinguishes what he calls “Fisher's
principle from various forms of his fundamental theorem of natural selection”. In opinion of
Stan Metcalfe “the principle is general and states that, in the context of a population of diverse
behaviours across which selection is taking place in a constant environment, the rate of
change of mean behaviour is a function of the degree of variety in behaviour across the
population. … When these behaviours are one dimensional, the principle becomes the
fundamental theorem of natural selection, that the rate of improvement of mean behaviour is
proportional to the variance in behaviour in the population.”
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It is worth to mention that eleven years later R.A. Fisher presented his theorem in much
more clearly form, namely: “The rate of increase in the average fitness of a population is
equal to the genetic variance of fitness of that population” (Fisher, 1941).
What we present in that paper is only partially related to the problem stated by R.A. Fisher.
As we will show variety is really very important for long term evolutionary development, but
there is essential difference between our proposition and Fisher’s finding. While Fisher based
his consideration on the given and finite set of genotypes (solutions) we are asking to what
extend emergence of new solutions (genotypes), i.e. innovations-novelties, is influenced
(accelerated or slowed down) by variety (diversity) controlled by selective environment, i.e.
selective environments with different levels of tolerance, i.e., different levels of acceptance of
deviant solutions within current population of solutions (genotypes, population).
In the first part of the paper we use the evolutionary model of industry development to
extend the former findings. After short presentation of the evolutionary model a simulation
study focused on investigation of the role of diversity, tolerance and heterogeneity of firms’
behaviour on tempo and modes of industrial development, particularly related to rate of
technological development (innovativeness), is presented.
Evolutionary modelling in economy
In very short way we can say that main features of evolutionary models are following:
• „Dynamics first”; far from equilibrium analysis;
• Development seen in historical perspective; macro-characteristics based on micro-
behaviours;
• Search for novelties (innovation), hereditary information;
• Selection leads to differential growth;
• Spontaneity of development.
Almost all evolutionary models worked out in the last decades within a sphere of economic
analysis are dynamical ones and are focused on far-from-equilibrium analysis. Other crucial
features of evolutionary process are not present in many models. The features which seem to
be crucial to call a model an evolutionary one are: diversity and heterogeneity of economic
agents (firms) and their behaviour, search for innovation based on a concept of hereditary
information (knowledge), and selection process which leads to diversified rate of growth and
spontaneity of development. Interesting question in relation to economic evolutionary models
is presence of decision making procedures. In many models that procedure is not present in
many others it has more or less complicated form.
In the following parts of this paper we will outline an evolutionary model and we will
present a selection of current simulation results of that model. 1 The model describes the
behaviour of a number of competing firms producing functionally equivalent products. The
decisions of a firm relating to investment, price, profit, etc. are based on the firm’s evaluation
of behaviour of other, competing firms, and the expected response of the market. The firm’s
1 Further reading on that model can be found at: http://kwasnicki.prawo.uni.wroc.pl/?page_id=387
For the first time the model has been presented in (Kwasnicki, Kwasnicka, 1992). Detailed description of the
model can be found my book (Kwasnicki, 1996), which can be read on
http://books.google.pl/books?id=di8lJFzNTk0C&printsec=frontcover&source=gbs_navlinks_s#v=onepage&q&f
=false or to be downloaded from: http://kwasnicki.prawo.uni.wroc.pl/todownload/KI&E.pdf
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knowledge of the market and knowledge of the future behaviour of competitors is limited and
uncertain. Firms’ decisions can thus only be suboptimal. The decisions are taken
simultaneously and independently by all firms at the beginning of each period (e.g. once a
year or a quarter). After the decisions are made the firms undertake production and put the
products on the market. The products are evaluated by the market, and the quantities of
different firms’ products sold in the market depend on the relative prices, the relative value of
products’ characteristics and the level of saturation of the market. In the long run, a preference
for better products, i.e. those with a lower price and better characteristics, prevails.
Each firm tries to improve its position in the industry and in the market by introducing
innovations in order to minimize the unit costs of production, maximize the productivity of
capital, and maximize the competitiveness of its products on the market. The general structure
of the model is presented in Figure 1.
The product’s price depends on the current technology of the firm, on market structure and
on the assumed level of production to be sold on the market. The two arrows between Price
and Production indicate that the price is established in an interactive way to fulfil the firms
objectives (i.e., to keep relatively high profits in the near future and to assure further
development in the long run). Modernization of products through innovation and/or initiating
new products by applying radical innovation depends on the investment capacity of the firm.
Thus, in managing innovation, each firm takes into account all economic constraints, as they
emerge during the firm’s development. It thus frequently occurs that to economic constraints
prevent a prosperous invention from being put into practice.
One of the distinguished features of the model is the coupling of technological
development and economic processes. Current investment capacity is taken into account by
each firm in the decision making process. Success of each firm in the search for innovation
R&D fundsProduction and
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depends not only on R&D funds spent by each firm to search for innovation, but also on the
extent to which firms make private knowledge public. Making the private knowledge of a
firm public can in some cases speed up industrial development, but also diminishes a firm’s
incentives to spend more funds on R&D projects. We may therefore expect only a certain part
of private knowledge to be made public.
Firms’ investment capacity depends on firms’ savings and available credits, and also,
indirectly, on the firm’s debt. Production and investment decisions are based on the firm’s
expectations on future behaviour of its competitors, market structure, expected profit and the
past trend of the firm’s market share. Current technical and economic characteristics of
products offered for sale and the technology used to manufacture the products are taken into
account in the price setting decisions, investment and production. Due to inevitable
discrepancies between a firm’s expectation and real behaviour of the market, the firm’s
production offered for sale on the market is different from market demand (it can be either
smaller or larger than demand).
We distinguish invention (i.e. a novelty being considered to be introduced into practice)
and innovation (an invention introduced into the production process). There are two ways in
which firms search for inventions: autonomous, in-house research, and imitation of
competitors. Public knowledge allows not only for imitation of competitors, but may also
concern the research process (the arrow from public knowledge to autonomous research
indicates this influence). From all inventions only a small fraction is selected to actually be
used. Innovation may modernize current production but can also initiate new, radical way of
production, i.e. by introducing essentially new technology. In general, each innovation may
reduce unit costs, increase the productivity of capital, and improve product performance.
However, it frequently happens that improvement of one factor is accompanied by
deterioration of the two other. Firms therefore face the problem of balancing positive and
negative factors of each invention. An invention will only become an innovation if the
positive factors prevail.
In the model each firm may simultaneously produce products with different prices and
different values of the characteristics, i.e., the firm may be a multi-unit operation. Different
units of the same firm manufacture products by employing different sets of routines.
Multi-unit firms exist because of searching activity. New technical or organizational solutions
(i.e. a new set of routines) may be much better than the actual ones but immediate full
modernization of production is not possible because of investment constraints on the firm. In
such situations the firm continues production using the old routines and tries to open a new
unit where production applying the new set of routines is started on a smaller scale.
Subsequently, old production techniques may be slowly phased out.
Simulation of industry development is done in discrete time in four steps:
1. Search for innovation (i.e., search for new sets of routines which potentially may
replace the old set currently employed by a firm).
2. Firms’ decision making process (calculation and comparison of investment,
production, net income, profit, and some other characteristics of development which
may be attained by employing the old and the new sets of routines. Decisions of each
firm on: (a) continuation of production by employing old routines or modernizing
production, and (b) opening (or not) of new units).
3. Entry of new firms.
4. Selling process (market evaluation of the offered pool of products; calculation of
firms’ characteristics: production sold, shares in global production and global sales,
total profits, profit rates, research funds, etc).
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The search for innovation
The creative process is evolutionary by nature, and as such its description should be based
on a proper understanding of the hereditary information (see Kwasnicki, 1996, Chapter 2).
According to the tradition established by Schumpeter, and Nelson and Winter (1982), we use
the term ‘routine’ to name the basic unit of the hereditary information of a firm. The set of
routines applied by the firm is one of the basic characteristics describing it. In order to
improve its position in the industry and in the market, each firm searches for new routines and
new combinations of routines to reduce the unit costs of production, increase the productivity
of capital, and improve the competitiveness of its products in the market. Nelson and Winter
(1982, p. 14) define routines as ‘regular and predictable behavioural patterns of firms’ and
include in this term such characteristics as ‘technical routines for producing things ...
procedures of hiring and firing, ordering new inventory, stepping up production of items in
high demand, policies regarding investment, research and development, advertising, business
strategies about product diversification and overseas investment’. A large part of research
activity is also governed by routines. ‘Routines govern choices as well as describe methods,
and reflect the facts of management practice and organizational sociology as well as those of
technology’ (Winter, 1984).
Productivity of capital, unit costs of production, and characteristics of products
manufactured by a firm depend on the routines employed by the firm (examples of the
product characteristics are reliability, convenience, lifetime, safety of use, cost of use, quality
and aesthetic value). The search activities of firms ‘involve the manipulation and
recombination of the actual technological and organizational ideas and skills associated with a
particular economic context’ (Winter, 1984), while the market decisions depend on the
product characteristics and prices. We may speak about the existence of two spaces: the space
of routines and the space of product characteristics.
We assume that at time t a firm is characterized by a set of routines actually employed by
the firm. There are two types of routines: active, that is, routines employed by this firm in its
everyday practice, and latent, that is, routines which are stored by a firm but not actually
applied. Latent routines may be included in the active set of routines at a future time. The set
of routines is divided into separate subsets, called segments, consisting of similar routines
employed by the firm in different domains of the firm’s activity. Examples are segments
relating to productive activity, managerial and organizational activity, marketing, and so on.
In each segment, either active or latent routines may exist. The set of routines employed by a
firm may evolve. There are four basic mechanisms for generating new sets of routines,
namely: mutation, recombination, transition and transposition.
The probability of discovering a new routine (mutation) depends on the research funds
allocated by the firm for autonomous research, that is, in-house development. It is assumed
that routines mutate independently of each other. The scope of mutation also depends on
funds allocated for in-house development.
The firm may also allocate some funds for gaining knowledge from other competing firms
and try to imitate some routines employed by competitors (recombination). It is assumed that
recombination may occur only between segments, not between individual routines, that is, a
firm may gain knowledge about the whole domain of activity of another firm, for example, by
licensing. A single routine may be transmitted (transition, see Figure 2) with some probability
from firm to firm. It is assumed that after transition a routine belongs to the subset of latent
routines. At any time a random transposition of a latent routine to the subset of active routines
may occur (Figure 3). It is assumed that the probabilities of transition of a routine from one
firm to another and the probabilities of transposition of a routine (from a latent to an active
routine) are independent of R&D funds, and have the same constant value for all routines.
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In general, the probability of transposition of a routine for any firm is rather small. But
randomly, from time to time, the value of this probability may abruptly increase and very
active processes of search for a new combination of routines are observed. This phenomenon
is called recrudescence. Recrudescence is viewed as an intrinsic ability of a firm’s research
staff to search for original, radical innovations by employing daring, sometimes apparently
insane, ideas. This ability is connected mainly with the personalities of the researchers and
random factors play an essential role in the search for innovations by recrudescence, so the
probability of recrudescence is not related to R&D funds allocated by a firm to ‘normal’
research. It is assumed that recrudescence is more probable in small firms than in large ones
which spend huge quantities on R&D, although it is possible to assume that the probability of
recrudescence does not depend on firm size.
As a rule, mutation, recombination and transposition on a normal level (that is, with low
probabilities in long periods) are responsible for small improvements and, during the short
periods of recrudescence, for the emergence of radical innovations.
Firm’s decisions
It seems that one of the crucial problems of contemporary economics is to understand the
process of decision-making. Herbert Simon states that ‘the dynamics of the economic system
depends critically on just how economic agents go about making their decisions, and no way
Active Latent
r r r r r L L L L L1 2 k i n ... ... ...
1 2 ... ... ... ... ... ... ...
ki u
1st firm
r r r r r L L L L L1 2 k i n ... ... ...
1 2 ... ... ... ... ... ...
ki p
2nd firm
Active Latent
r r r r r L L L L L1 2 k i n ... ... ...
1 2 ... ... ... ... ... ... ...
ki u
7
has been found for discovering how they do this that avoids direct inquiry and observations of
the process’ (Simon, 1986, p. 38).
The background of the decision making procedure adopted in the model is presented in
detail in Kwasnicki (1996). It is assumed that each firm predicts future development of the
market (in terms of future average price and future average product competitiveness), and on
the basis of its expectations on future market development and expected decisions of its
competitors, each firm decides on price of its products, investment and quantity of production
which it expects to sell on the market. Current investment capability and the possibility of
borrowing are also considered by each firm.
The decision making procedure allows to model diversified situations faced by different
firms, for example, the power of a small firm to influence the average price is much smaller
than that of a large firm. So, small firms are, in general, ‘price takers’ in the sense that they
assume that the future average price will be very close to the trend value, while large firms
generally play the role of ‘price leaders’ or ‘price makers’.
Price, production and investment are set by a firm in such a way that some objective
function is maximized. Contrary to the neoclassical assumption it is not a maximization in the
strict sense. The estimation of values of the objective function is not perfect and is made for
the next year only. In other words, it is not a global, once and for all, optimization, but rather
an iterative process with different adjustments taking place from year to year.
Different price-setting procedures (based on different objective functions and the markup
rules) have been scrutinized, the results of which are presented in Kwasnicki and Kwasnicka
(1992), and Kwasnicki (1996). In many simulation experiments, firms were allowed to select
different price setting procedures. The results of these experiments suggest that firms applying
the objective O1 function (presented below) dominate on the market and in the long run
supersede all others. This objective function has the following form:
O t F t
( ) ( ) ( )
( )
( )
( ) ,+ = −
+ +
QS ti
(1)
where Fi is the magnitude coefficient (with values between 0 and 1), Qi the supply of firm
i, 'i the expected income of firm i at t +1 (defined by equation (2), below), QS is the global
production of the industry in year t and ' the global net income of all firms in year t. '(t) and
QS(t) play the role of constants in equation and ensure that the values of both terms in this
equation are of the same order.
The expected income of firm i ('i) and the expected profit of this firm (Ai) are defined as
Γi i
sQ t p t V v Q t= − −( )( ( ) ( ( )) )η (2)
Π Γi i iK t= − −( )( )ρ δ (3)
where V is unit production costs, v(Q) is the factor of unit production cost as a function of
the scale of production (economies of scale), 0 is the constant production cost, Ki(t) the
capital needed to obtain the output Q(t), D the normal rate of return and * the physical capital
depreciation rate (amortization).
The function O1 expresses short- and long-term thinking of firms during the
decision-making process (the first and second terms in equation (1), respectively). Plausible
values for the parameters are a4 = 1 and a5 = 5, implying that the long run is much more
important for survival and that firms apply a flexible strategy, i.e., the relative importance of
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short- and long-term components changes in the course of firm’s development (the long-term
one is much more important for small firms than for the big ones).
The decision-making procedure presented above, with the search for the ‘optimal’
price-setting procedure based on the objective function concept constructs a formal scheme
for finding the proper value of the price and expected production to be sold on the market.
Naturally this scheme is only an approximation of what is done by real decision-makers.
They, of course, do not make such calculations and formal optimization from year to year,
they rather think in the routine mode: ‘My decisions should provide for the future prospects of
the firm and also should allow income (or profit) to be maintained at some relatively high
level’. Decisions on the future level of production and the future product price depend on the
actual investment capabilities of the firm.
Entry
In each period (t, t + 1) a number of firms try to enter the market. Each entrant enters the
market with assumed capital equal to InitCapital and with the initial price of its products
equal to the predicted average price. The larger the concentration of the industry, the greater
the number of potential entrants (that is, firms trying to enter the market). The value of
InitCapital is selected in such a way that the initial share of an entrant is not larger than 0.5%.
In general, any firm may enter the market and if a firm’s characteristics are unsatisfactory,
then it is quickly eliminated (superseded) from the market. But because of the limited capacity
of computer memory for simulations, a threshold for potential entrants is assumed. It is
assumed that a firm enters the market only if the estimated value of objective O1 of that firm
is greater than an estimated average value of the objective O1 in the industry. It may be
expected that a similar (rational) threshold exists in real industrial processes.
Products competitiveness on the market
The productivity of capital, variable costs of production and product characteristics are the
functions of routines employed by a firm (see Figure 4). Each routine has multiple, pleiotropic
effects, that is, may affect many characteristics of products, as well as productivity, and the
variable costs of production. Similarly, the productivity of capital, unit costs of production
and each characteristic of the product can be function of a number of routines (polygeneity).
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We assume that the transformation of the set of routines into the set of product
characteristics is described by m functions Fd ,
,,...,3,2,1),( mdrFz dd == (4)
where zd is the value of characteristic d, m the number of product characteristics, and r the
set of routines. It is assumed also that the productivity of capital A(r) and the unit cost of
production V(r) are also functions of firm’s routines, where these functions are not firm
specific and have the same form for all firms.
An attractiveness of the product on the market depends on the values of the product
characteristics and its price. The competitiveness of products with characteristics z and price p
is equal to
( ) , ( , ,...., ),= =α 1 2 (5)
where q(z) is the technical competitiveness, z a vector of product characteristics, and "
price elasticity.
In the presence of innovation, technical competitiveness varies according to the
modification of routines made by each firm, or because of introducing essentially new
routines. Technical competitiveness is an explicit function of product characteristics. As
explained above, each routine does not influence the product’s performance directly, but only
indirectly through the influence on its characteristics. We assume the existence of a function q
r r r r r L L L L L1 2 k i n ... ... ...
1 2 ... ... ... ... ... ... ...
ki u
z z z z1 2 i m... ... ...
q(z)p
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enabling calculation of technical competitiveness of products manufactured by different firms.
We say that q describes the adaptive landscape in the space of product characteristics. In
general, this function depends also on some external factors, varies in time, and is the result of
co-evolution of many related industries. The shape of the adaptive landscape is dynamic, with
many adaptive peaks of varying altitudes. In the course of time some adaptive peaks lose their
relative importance, others become higher.
Due to the on-going search process, at any moment each firm may find a number of
alternative sets of routines. Let us denote by r the set of routines actually applied by a firm
and by r * an alternative set of routines. Each firm evaluates all potential sets of routines r
* as
well as the old routines r by applying the decision-making procedure outlined in the former
section. For each alternative set of routines the price, production, investment (including the
modernization investment), and value of objective function are calculated. The decision of
firm i on modernization (i.e., replacing the r routines by r * routines) depends on the expected
value of the firm’s objective function and its investment capability. Modernization is
undertaken if the maximum value of the objective function from all considered alternative sets
of routines r * is greater than the value of the objective function possible by continuing the
actually applied routines r, and if the investment capability of the firm permits such
modernization. If the investment capability does not allow modernization, then the firm:
1. continues production employing the ‘old’ routines r, and
2. tries to open a new small unit where routines r * are employed; production is started
with an assumed value of capital equal to InitCapital.
To modernize production, extra investment is necessary. This ‘modernization investment’
depends on the discrepancy between the ‘old’ routines r and the ‘new’ routines r * . For
simplicity, it is assumed that modernization investment IM is a non-decreasing function of
distance between the old routines r actually applied by a firm and the new set of routines r * .
All products manufactured by the entrants and the firms existing in the previous period are
put on the market and all other decisions are left to buyers; these decisions primarily depend
on the relative values of competitiveness of all products offered, but quantities of products of
each firm offered for sale are also taken into account. It is assumed that global demand Q d (t)
for products potentially sold on a market is equal to an amount of money – M(t) – which the
market is inclined to spend on buying products offered for sale by the firms divided by the
average price, p(t), of the products offered by these firms,
Q t M t
M t N t p te( ) exp( )( ( )) ,= γ β (7)
where N is a parameter characterizing the initial market size, ( the growth rate of the
market,
and $ the (average) price elasticity. The average price of all products offered for sale on
the market is equal to
=
(8)
where Q s (t) is global supply and is equal to
11
(9)
Global production sold on the market is equal to the smaller value of demand Q d (t)
and supply Q s (t),
QS t Q t Q td s( ) min{ ( ), ( )}.= (10)
The selection equation describing competition among firms (products) in the market
has the following form (fi is the market share of products manufactured by firm i):
f t f t c t
c ti i
( ) = −1 (11)
where c(t) is the average competitiveness of products offered for sale,
c t f t c te
i i i
( ) ( ) ( ).= −∑ 1 (12)
This means that the share (fi) of firm i in global output increases if the competitiveness of
its products is higher than the average of all products present on the market, and decreases if
the competitiveness is lower than the average. The rate of change is proportional to the
difference between the competitiveness of products of firm i and average competitiveness.
Finally, the quantity of products potentially sold by firm i (i.e., the demand for products of
firm i) is equal to
Q t QS t f ti
d
i( ) ( ) ( ).= (13)
The above equations are valid if the production offered by the firms exactly fits the
demand of the market. This is a very rare situation and therefore these equations have to be
adjusted to states of discrepancy between global demand and global production, and
discrepancy between the demand for products of a specific firm and the production offered by
this firm. The details of this adjustment process are presented in Kwasnicki (1996). Equation
describes the market demand for products of firm i offered at a price pi(t) and with
competitiveness ci(t). In general, however, the supply of firm i is different from the specific
demand for its products. The realization of the demand for products of firm i does not depend
only on these two values of demand and supply, but on the whole pool of products offered for
sale on the market. The alignment of supply and demand of all firms present on the market is
an adaptive process performed in a highly iterative and interactive mode between sellers and
buyers. In our model, we simulate the iterative alignment of supply and demand in a
two-stage process in which a part of the demand is fulfilled in the first stage, and the rest of
the demand is, if possible, fulfilled in the second stage. If there is no global oversupply of
production, then in the first stage of the supply–demand alignment process all demand for
production of specific firms, wherever possible, is fulfilled, but there is still the shortfall in
production of firms which underestimated demand for their products. This part of demand is
fulfilled in the second stage of the supply–demand alignment process. At this stage, the
products of the firms which produce more than the specific demand are sold to replace the
shortfall in production by the firms which underestimated the demand for their products.
The supply–demand alignment process is slightly different if a global oversupply of
production occurs. It seems reasonable to assume that in such a case the production of each
firm sold on the market is divided into (1) the production bought as the outcome of the
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competitive process (as described by equations 15 and 17), and (2) the production bought as
the outcome of a non-competitive process. The latter part of production does not depend
directly on product competitiveness but primarily depends on the volume of production
offered for sale, i.e., random factors play a much more important role in the choice of relevant
products to be bought within this part of the production. In general, the division of production
of each firm into these two parts depends on the value of global oversupply. The higher
oversupply, the larger is the part of production of each firm which is sold on the basis of
non-competitive preferences.
Usually global oversupply, if it occurs, is small, so the major part of production is
distributed under the influence of competitive mechanisms and only a small part is distributed
as a result of non-competitive distribution. But to clarify the necessity of distinguishing the
two proposed stages of the selling–buying process let us consider the following, albeit
artificial, situation. Except for one firm, the production of all other firms exactly meets the
demand for their products. The a-typical firm produces much more than the demand for its
products. It could be assumed that the production sold by all firms is exactly equal to the
specific demands for their products, which is equivalent to the assumption that the volume of
overproduction of the a-typical firm does not influence the behaviour of the market. In an
extreme case, we may imagine that the volume of production of the a-typical firm is infinite
and the rest of the firms continue to produce exactly what is demanded. Does this mean that
the excessive production would go unnoticed by the buyers and that they would remain loyal
to firms producing exactly what is demanded? It seems a more adequate description requires
the incorporation of the assumption that the future distribution of products sold on the market
depends on the level of overproduction of all firms, and particularly the level of
overproduction of the a-typical firm. And it seems that in the case of the overproduction of
one firm its share in the global production sold will increase at the expense of all firms
producing exactly what is demanded. In the extreme case, when overproduction of the a-
typical firm tends to infinity, the only products sold on the market belong to that firm, and the
shares of all other firms will be zero. But it does not mean that producing more than is
demanded is an advantageous strategy for the firm and that it is an effective weapon to
eliminate the competitors. In fact, the bulk of overproduction is not sold on the market and is
lost by the firm. In effect the a-typical firm’s profit is much smaller than expected, or even
may be negative. After some time the firm’s development stop and in the end it will be
eliminated from the market.
Tolerance and adaptive landscape
Dictionary definition of tolerance relates, among others, to allowable of deviation from a
standard and the range of variation permitted in maintaining a specified size (e.g. length), in
relation to social behaviour it refers to the ability to accept, experience, or survive something
harmful or unpleasant. In the context of evolutionary processes we may say that the selective
environment can be more or less tolerant, in the sense that more tolerant selective
environment allows for coexistence less advanced (less competitive) elements, i.e. at any time
beside the best element (best solution, best product, best technology, etc.) there exist
numerous less advanced elements. We model the more or less tolerant environment by
selection of different technical competiveness functions q(z) – see eq. 5. In general we can
made our simulation assuming high dimensional technical characteristic space z, but to
visualize the simulation results (concurrently not losing the generality of our conclusions and
findings) we propose to make simulations for two dimensional space of technical
characteristics z1 and z2. The adaptive landscape q(z1, z2) will have only two peaks, just to
show to what extend the more or less tolerant environment will affect speed of climbing the
13
adaptive hill and the possibility of finding a radical innovation on the higher adaptive peak.
Therefore we propose the following shape of the adaptive landscape:
=
+
(14)
The altitude of the lower adaptive peak h1 is equal to 1.0 and the altitude of the higher peak
is twice of the lower one (i.e. h2=2.0); slope is equal to 0.004, the coordinates of the first and
the second peaks are equal to , =(15, 20) and , =(35, 40), respectively. The
parameter tolerance is a positive number, the higher the value of the parameter the more
tolerant is the selective environment. The shapes of the adoptive landscape (and the contour
maps) for different values of the tolerance are presented in Figure 5. As we see, the less
tolerant selective environment the more narrow ridges of the two hills (peaks) are. The cross
section of the two peaks along the ridges is exactly the same for the landscapes described by
the equation (14); this cross section is presented in the Figure 6. We see (Figures 5 and 6) that
there is a rather deep adaptive valley between the two peaks.
tolerance=0.05 tolerance=0.05
10
20
30
40
50
60
10
20
30
40
50
60
10
20
30
40
50
60
14
tolerance=2.0
tolerance=0.2
tolerance=5.0
tolerance=5.0
Fig. 5. The shapes and the map of the adaptive landscapes for different values of the tolerance
parameter
Fig. 6. The cross section of the two peaks along the ridge
0 10
20 30
40 50
10
20
30
40
50
60
10
20
30
40
50
60
10
20
30
40
50
60
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
15
We have made numerous simulation experiments for the same initial conditions and for
different values of the tolerance parameter. In all experiments the simulation runs have started
form a single firm (‘a founder of the industry’) manufacturing products with technical
characteristics (5, 10); so we see that the initial ‘distance’ to the lower adaptive peak is equal
to (10, 10) and the higher peak equal to (30, 30). All the time new firms can enter the market,
and all incumbent firms search for inventions and introduce innovations just to improve the
technological performance of the products, diminished the cost of production, and increase
the productivity of capital. We can expect that due to evolutionary mechanism of searching
for innovations we will observe evolution toward the lower peak, and after reaching it firms
will try to find inventions allowing to jump from the lower adaptive peak to the higher one.
As our former works show (e.g. Kwasnicki, 1996, Kwasnicka, Kwasnicki, 2005) it is highly
improbable that firms will reach the higher peak ‘walking’ along the valley (i.e., lowering the
technical competiveness of the manufactured products). Usually due to the search for
inventions through mutations, imitations and recrudescence, a new better products placed on
the slope of the higher peak is founded, and since that moment we are observing the ‘march’
of the firms toward the higher peak and superseding of the products with characteristics close
to the lower peak (we will see the illustration of that process in the later part of that paper).
The question we would like to explore is how the tolerance affect the tempo (speed) of
evolution? In all simulation experiment in the first phase we observe the evolution of the
industry (a population of the firms) toward the lower peak (from their initial state of
technological characteristics (5, 10)). In most simulation the lower peak is reached after 60
years of evolution. At that year search for new (radical) invention placed on the higher peak is
initiated, mainly due to the operation of the recrudescence mechanism, but also due to the
recombination (imitation) process. In each of the simulation run we observe the moments of
reaching specific states (namely the average technological competitiveness at three years 20,
40, and 60) along the ridge of the of the lower peak (namely along the path between initial
state (5, 10) and the top of the hill (15, 20). Next we observe the period from the year 60 to
the moment of finding invention placed on the higher adaptive hill. The summery of the
results are presented in Tables 1 and 2, and in Figure 7. We have selected 11 values of the
tolerance parameter (ranging from 0.01 up to 100), and for each value we have made 10
simulation experiments. The average values of the technical competitiveness and maximum
values of the technical competitiveness (frontiers of the research) at mentioned three years
(20, 40, and 60) are presented in Table 1 and in Figure 7. We see that there is strong
relationship between the tolerance and the sped of evolution, namely more tolerant selective
environment (i.e. the adaptive landscape with higher value of the tolerance parameter) the
quicker is the evolution toward the lower peak. It is caused mainly due to higher diversity of
products (innovations) manufactured by the firms (see e.g. Figures 13 to 16) for more tolerant
selective environment. Thanks to the higher diversity it eager to find better solutions
(invention) due to imitation (recombination) as well as due to autonomous research of the
firms (mutation). For low values of the tolerance parameter (0.01, 0.02) evolution is very slow
and almost stop at the halfway to the lower peak in the first 60 years of evolution.
16
Fig. 7. Technical competitiveness reached at different time for different tolerance level (upper
graph), and the evolution toward the first (lower) peak (lower graph) - average values of
technical competitiveness out of ten runs
Table 1. The average values of the technical competitiveness for different time Tolerance/ time 0.01 0.02 0.05 0.1 0.2 0.5 1 2 5 10 100
at 20 0.279 0.359 0.402 0.403 0.406 0.408 0.414 0.444 0.497 0.479 0.489
at 40 0.394 0.568 0.698 0.792 0.797 0.799 0.879 0.829 0.796 0.836 0.883
at 60 0.529 0.728 0.922 0.933 0.960 0.951 0.959 0.958 0.909 0.892 0.933
max at 20 0.306 0.413 0.447 0.460 0.461 0.465 0.499 0.545 0.605 0.590 0.557
max at 40 0.428 0.623 0.779 0.893 0.899 0.878 0.947 0.929 0.899 0.925 0.968
max at 60 0.580 0.783 0.976 0.981 0.998 0.996 0.999 0.999 0.994 0.996 0.999
10 -2
10 -1
10 0
10 1
10 2
0 10 20 30 40 50 60 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
time
17
Table 2. Waiting times for jumping to higher peak in the adaptive landscape Tolerance
0.01 0.02 0.05 0.1 0.2 0.5 1 2 5 10 100.0
run1 ? 80 ? 125 76 40 52 9 44 13 16
run2 ? ? 35 44 29 9 6 70 20 17 38
run3 34 ? ? 40 9 25 16 18 2 4 8
run4 117 68 ? 43 22 48 53 9 22 11 36
run5 ? 87 ? 118 ? 51 15 10 3 3 7
run6 ? ? ? ? 38 61 56 49 3 4 2
run7 ? ? 20 10 125 35 4 43 21 12 30
run8 ? ? ? 131 ? 8 50 31 22 22 9
run9 ? 136 130 48 29 12 37 10 9 11 10
run10 80 ? 114 94 125 7 10 4 37 12 5
Avarage - - - - - 29.6 29.9 25.3 18.3 10.9 16.1
St. dev. - - - - - 20.1 21.6 22.1 14.4 6.0 13.4
Fig. 8. The average waiting time for radical innovation emergence (and its standard
deviation) for different values of the tolerance parameter
Much higher influence of the tolerance is observed in the second phase of the evolution,
namely search for the radical invention placed on the higher adaptive hill. The waiting times
for emergence of the radical innovation placed on the higher peaks for all simulation runs are
presented in Table 2 and Figure 8. Due to the limitation of the simulation software we are able
to make simulation runs for maximum 200 years. It turns out that for numerous runs for low
tolerance selective environment the 140 years (i.e. the period after the year 60) is not enough
to find radical innovation. All that unsuccessful runs are marked by question marks (?) in the
Table 2. Naturally for that runs it was not possible to calculate the average waiting time, but
in general it is clearly visible that the greater the tolerance of the selective environment the
quicker the radical innovation emerges. Two phenomena play here important role, namely (1)
the more intolerant selective environment is, the smaller is the area with the high values of
technical competitiveness of the radical innovation placed on the second adaptive peak, and
(2) for higher tolerance, the average competiveness is smaller than the potential maximal
competitiveness (due to higher diversity) and the selective environment eagerly ‘accept’
radical innovation (placed on the second peak) with lower technical competitiveness (see the
replication equation (11)). Scrutiny of the results presented in Table 2 and Figure 8 allows to
notice the high variety of the waiting time for the same value of the tolerance parameter and
observed in different simulation runs, e.g., for the tolerance equal to 0.5 the shortest waiting
10 0
10 1
10 2
18
time is 7 years and the longest is 61 years, the average waiting time is equal to 29.6 years and
the standard deviation is equal to 20.1.
Fig. 9. Trajectories of development for 10 simulation runs (Tolerance=0.2)
In Figures 9 to 11 the trajectories of development (defined by the average values of both
technical characteristics , for all years from zero to 200) are presented for three
selected values of the tolerance parameter (namely relatively low tolerance, medium tolerance
and relatively high tolerance). It is seen that for low tolerance the diversity of trajectories is
small (all ten trajectories are very close to each other), and the higher the tolerance the more
diversified trajectories are. The trajectories show, mentioned earlier, the two phases of
industry evolution, namely the climbing of the population of firms from the initial state (5, 10)
to the lower peak, and next jump from the lower to the higher peak (over the valley).
0 10
20 30
40 50
10
20
30
40
50
60
19
Fig. 10. Trajectories of development for 10 simulation runs (Tolerance=1.0)
0 10
20 30
40 50
10
20
30
40
50
60
20
Fig. 11. Trajectories of development for 10 simulation runs (Tolerance=5.0)
Just to illustrate the second phase of the industry evolution (jumping from lower to higher
adaptive peak) in the next few Figures we present the industry states for specific years. In
Figure 12 the industry state in the simulation experiment for medium tolerance level
(Tolerance=1.0, the 10 th
simulation run) just in a year of emergence of the radical innovation
(in the 62 year). This radical innovation is marked by red star on the higher peak. All other
firms (products) ale still placed on the lower peak. It is worth to notice that that innovation
differs radically from all other products in terms of the technical characteristics , but
the technical competitiveness is lower that the competitiveness of all other incumbent
products (firms). I has been accepted due to its advantages in terms of the cost of production
and the efficiency of applied capital (relatively low cost of production and high productivity
of capital). In the following years (63 to 66) the initial innovation has been developed and the
evolution toward the higher peak has been initiated (see two first maps for t=64 and t=66 in
Figure 13) but it occurred that the other firms has made parallel improvement of the
incumbent products and that radical innovation has been superseded form the market. In the
67 year there was no innovation placed on the higher peak (see the third map in Figure 13, for
t=67). But the search process of all firms has been going on, and after three year another
0 10
20 30
40 50
10
20
30
40
50
60
21
radical innovation emerged in the higher peak (see the fourth map in Figure 13). This was
successful innovation and in the next years the new firms imitated and improved that
innovation so more and more firms manufactured products placed on the higher peak, closer
and closet the to the maximum of the hill (see the next maps in Figure 13 for t= 85, 100, and
130, respectively). As we see after 60 years from the initial radical innovation, in the year
130, the hole industry is placed on the higher peak.
Fig. 12. Emergence of the first radical innovation in the 62 year for run 10, Tolerance=1.0)
0 10
20 30
40 50
10
20
30
40
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60
22
10
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40
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60
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23
10
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60
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60
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24
t=130
Fig. 13. Sequence of innovation for run 10 (Tolerance=1.0), for selected years
Just to show difference in the mood of evolution for less tolerant selective environment
(tolerance=0.2) and more tolerant environment (tolerance=5.0) the series of the maps
illustrating of emergence of radical innovation and subsequent substitution process (moving
of the industry form the lower to higher peak) are presented in Figures 14 and 15,
respectively. One general observation is that for low tolerance the diversity of firms (seen
e.g. in terms of the size of the ‘cloud’ of firms) is much lower than in the former experiment
(tolerance=1.0) and fore higher tolerance the diversity is much higher.
t=89
10
20
30
40
50
60
0
10
20
30
40
50
60
10
20
30
40
50
60
10
20
30
40
50
60
10
20
30
40
50
60
26
Fig. 14. Sequence of innovation for run 1 (Tolerance= 0.2), for selected years
In the last Figure 16 we present the states of emergence of radical innovation for all other
simulation experiment for the tolerance parameter equal to 5.0. Comparing the states of
emergence of radical innovation for all 10 simulation runs (presented in Figure 15 (the first
run) and Figure 16 (all other nine runs) we clearly see high diversity of these radical
innovation, e.g. they are emerging in different, far distanced places of the adaptive landscape.
t=104
10
20
30
40
50
60
10
20
30
40
50
60
27
t=119
t=134
t=164
Fig. 15. Sequence of innovation for run 1 (Tolerance=5,0), for selected years
0 10 20 30 40 50 60 0
10
20
30
40
50
60
10
20
30
40
50
60
10
20
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60
28
10
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29
10
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40
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60
10
20
30
40
50
60
10
20
30
40
50
60
30
t=69, run 9
t=92, run 10
Fig. 16. Emergence of radical innovation in runs 2 to 10 (Tolerance=5.0)
0 10 20 30 40 50 60 0
10
20
30
40
50
60
10
20
30
40
50
60
10
20
30
40
50
60
31
Conclusions
The simulation results of the model of industrial development indicate that highly tolerant
selective environment foster higher diversity and temporal lowering of the average
competiveness of incumbent products, but this temporary, local deterioration of the evolution
is compensated by much quicker long term development. Therefore the high tolerance ought
to be advantageous for general, long term evolution.
The obtained simulation results suggest that Joseph A. Schumpeter (1942, p. 83) was
perfectly right expressing the opinion that: "A system ... that at every point in time fully
utilizes its possibilities to its best advantage may yet in the long run be inferior to a system
that does so at no given point in time, because the latter's failure to do so may be a condition
for a level or speed of long-run performance."
Very similar opinions has been expressed by many other researches. Let’s mention only a
few of them. John Stuart Mill in his book On Liberty (1859, chapter II, ‘On individuality, as
one of the elements of wellbeing’) writes that: “What has made the European family of
nations an improving, instead of a stationary portion of mankind? Not any superior excellence
in them, which when it exists, exists as the effect, not as the cause; but their remarkable
diversity of character and culture. Individuals, classes, nations, have been extremely unlike
one another: they have struck out a great variety of paths, each leading to something valuable;
and although at every period those who travelled in different paths have been intolerant of one
another, and each would have thought it an excellent thing if all the rest could have been
compelled to travel his road, their attempts to thwart each other's development have rarely had
any permanent success, and each has in time endured to receive the good which the others
have offered. Europe is, in my judgment, wholly indebted to this plurality of paths for its
progressive and many-sided development. But it already begins to possess this benefit in a
considerably less degree.”
In our modern time, Richard Florida, the author of The Rise of the Creative Class,
postulates that for quick but harmonious creative development of a society ought to be
focused on three T’s, namely Technology, Talent, and Tolerance. As he writes in The flights
of the creative class “This brings me to the third T, tolerance. While economists have long
recognized technology and talent as key drivers of economic growth, they tend to think of
them in the same way they think of more conventional factors of production, like raw
materials. That is, they think of them as constituting a stock.” (p. 38). In opinion of Florida
tolerance and diversity clearly matter to high-technology concentration and growth. Diversity
is a powerful force in the development of any system. It is important choices of the new
workforce, whose members want to work for firms and live in societies that express their
openness and tolerance. The leading factor in choosing a place to live and work is, in opinion
of Richard Florida, diversity. This three t’s are closely interrelated: tolerance attracts talent;
talent attracts technology-driven growth.
Richard Florida and Gary Gates write in Technology and Tolerance: Diversity and High
Tech Growth: "What sets high-technology centers such as San Francisco, Boston, and New
York apart from other metropolitan areas? Why have some cities—many home to some of the
nation's most prestigious university research centers and college graduates—been unable to
attract talented technology workers? Our theory is that a city's diversity—its level of tolerance
for a wide range of people—is key to its success in attracting talented people. Diverse,
inclusive communities that welcome unconventional people—gays, immigrants, artists, and
free-thinking 'bohemians'—are ideal for nurturing the creativity and innovation that
characterize the knowledge economy… Gays predict not only the concentration of high-tech
industry, but also its growth …"
32
Paolo Saviotti in his book on Technological evolution, variety, and the economy ( E. Elgar,
1996 ) give a lot of evidences that diversity, variety are important factors for proper
technological development.
R.A. Fisher was perfectly right writing that: “The rate of increase in the average fitness of
a population is equal to the genetic variance of fitness of that population” (Fisher, 1941) but
we think that it is possible to generalize this observation. Speeding up economic growth due
to higher variety is observed not only in a case of evolutionary process approaching the
equilibrium but also due to higher variety caused by tolerant environment in the long run,
thanks to more frequent emergence of gradual and radical innovations. Those innovations
cause emergence of new equilibria toward whom the process is continuously approaching.
References
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