

Concepts of thermodynamics in Economic Systems I: Lagrange principle and Boltzmann Distribution of Wealth Jürgen Mimkes Physics Department, University of Paderborn, Germany
Abstract:
In many particle systems of N elements (atoms, people, goods) and k
categories (energy level, income class, price level) the most probable
distribution is given by the Lagrange principle with constraints,
The Carnot Process of Economic Growth and Wealth Distribution Jürgen Mimkes Physics Department, University of Paderborn, Germany
Abstract:
Economic growth is a differential process of capital (K) and labor (L)
and may be calculated by the non exact differential form δg( K, L).
The closed integral will be non zero and leads to economic growth. The
integral may be split into two parts, production (Y) and consumption (C),
both will depend on the production process. According to the laws of calculus
the non exact differential δg may by transformed into an exact form
by an integrating factor (T): δg = T δS. The new function S
is called entropy. Depending on the economic system (market, country) T
is a mean value of capital, a mean price level or a standard of living.
J. R. Iglesias^{*}, S. Risau Gusman^{*} and M. F. Laguna^{#} ^{*}Instituto de Fisica, Universidade Federal do Rio Grande do Sul, C.P. 15051, 91501970 Porto Alegre RS, Brazil ^{#}Centro Atomico Bariloche, Instituto Balseiro and CONICET, 8400 San Carlos de Bariloche, Argentina Abstract: Different models of capital exchange among economic agents have been recently proposed trying to explain the emergence of Pareto's power law distribution of wealth. Most of these models consider the existence of risk aversion and also a probability that the poorer agent be somehow favored in each exchange. Here we add the hypothesis that the agent's connectivity is not only strongly related to its wealth but also to its success. So, starting from agents placed on a random lattice (i.e. with a gaussian distribution of links), an agent with success in its economic transactions will receive the expected monetary reward, but it will also increase its connectivity, at the expense of other agents (so that the total connectivity remains constant). When the system arrives to a stationary state, it is observed that the wealth distribution has been modified by the dynamics of the lattice, getting closer to a power law for some values of the parameters of the model. As expected, the lattice itself is different from the random initial one. The Gini coefficients are calculated and they show that the reconnection of the lattice induces a kind of "protective screening" of less favored agents, resulting in a distribution of wealth less unequal than on a static network for some values of the parameters. Talk. Geoff Willis^{*} and Jürgen Mimkes^{#} ^{*}Risk Reduction Ltd., Yorkshire, United Kingdom ^{#}Physics Department, University of Paderborn, Germany
Abstract:
Two sets of high quality income data are analysed in detail, one set from the UK, one from the USA. It is firstly demonstrated that both a lognormal distribution and a Boltzmann distribution can give very accurate fits to both these data sets. The absence of a power tail in the US data set is then discussed. Taken in conjunction with detailed evidence from the UK and Japanese income data, a strong case is made for the mathematically separate treatment of waged and unwaged income. The authors present a case for preferring the use of the Boltzmann distribution over the lognormal function, this leads to a brief review of the work of a number of researchers, which shows that
a coherent theory for the distribution of all income can be postulated.
Geoff Willis Risk Reduction Ltd., Yorkshire, United Kingdom
Abstract:
The paper starts with the assumption that income and wealth distributions are formed from exponential / Boltzmann distributions with a power decaying tail.
Juan C. Ferrero Centro Láser de Ciencias Moleculares and INFIQC, Facultad de Ciencias Químicas, Universidad Nacional de Córdoba, 5000 Córoba Argentina Abstract: The individual distribution of money for various countries follows a Boltzmann distribution except at high values, where the experimental probability densities are systematically larger than the fitted values. This discrepancy can be settled by the use of nonextensive statistics, as developed by Tsallis, which conserves the Boltzmann shape at low values of money but follows a Pareto's power law in the tail, indicating fractal behaviour. In some cases, the distribution can be described by a single equilibrium function but in others two components appear. The evolution of an arbitrary initial distribution to the equilibrium, two components distribution, is explained as a consequence of the different state degeneracy associated with each of them. The social consequences, within a country and at global level are analyzed. Juan C. Ferrero Centro Láser de Ciencias Moleculares and INFIQC, Facultad de Ciencias Químicas, Universidad Nacional de Córdoba, 5000 Córoba Argentina
Abstract:
Bimodal (or in general, polymodal) Boltzmann distributions are
indicative of
the presence of different ensembles of economic agents within a given
population, which are at equilibrium. Examples of bimodal distributions
far for equilibrium are not easy to find, because a sudden change in the
economical situation is required to produce it. One clear example of this
behaviour is the individual income distribution of Argentina. The crisis
at the end of 2001 resulted in a strong and fast perturbation, which in
the period of 4 months produced a devaluation of the local currency by a
factor of 3. The resulting bimodal distributions are near Gaussian,
indicating a nonequilibrium situation. The evolution through years
20022004 is analyzed.
A generalization, using rate equations for a simple three level system
provides further insight on the temporal evolution of the distribution of
money to equilibrium.
Ning Ding, Ning Xi and Yougui Wang^{*} Department of Systems Science, School of Management, Beijing Normal University, Beijing, 100875, People's Republic of China ^{*}ygwang@bnu.edu.cn
Abstract:
Mobility like distribution is also an important aspect of the study on
income and wealth. To find out the mechanism of the income and wealth
distribution, a series of models have been constructed, among which money
transfer models attract much attention. In this presentation, we choose
four transfer models as typical ones to demonstrate the mobilities by
recording the agents' rank time series and by observing the volatility
of them. Like the shape of distribution, the mobility is also determined
by the trading rule in these transfer models. To compare the mobility
quantitatively, an index raised by economists, ``the per capita aggregate
change in logincome'', is employed to measure the value of reranking
degree, and we find that the mobility decreases as the saving rate increases
in one model. A stratification phenomenon is observed in other one model
and the resulting mobility is quite small. It is worth noting that even
though different models have the same distribution, their degrees of
mobility may be quite different. These findings suggest that the
characteristics of mobility should be checked when evaluating this
kind of models.
Wataru Souma^{*} and Makato Nirei^{#} ^{*}ATR Network Informatics Laboratories, Kyoto 6190288, Japan ^{#}Department of Economics, Utah State University, Logan, UT 84322, USA
Abstract:
This paper analyzes empirical personal income distributions
and
proposes a simple stochastic model to explain it. Using the personal
tax returns data
in the U.S. and Japan, we clarify the middle income range follows an
exponential
distribution and the top 1 percent follows an power law distribution.
We then propose a minimal twofactor model that reproduce these
characteristics.
Our model of personal income consists of asset accumulation process and
a wage process.
The asset accumulation process is multiplicative due to the stationary
random asset returns.
The wage process is assumed additive, reflecting the productivity
heterogeneity. We show
that this simple process can successfully reproduce the empirical
distribution of income.
In particular, the model can reproduce the particular transition of the
distribution shape
from the middle part which decays exponentially to the tail part with
decays in power.
This model also allows us to derive the tail exponent of the
distribution analytically.
Yoshi Fujiwara ATR Network Informatics Laboratories, Kyoto 6190288, Japan
Abstract:
By employing exhaustive lists of personal income and firms in Japan,
and also large firms in European countries, we show that the
uppertail of the distribution of income and firm size has powerlaw
(ParetoZipf law), and that in this region their growth rate is
independent of the personal income or firm size (Gibrat's law of
proportionate effect). In addition, detailed balance holds in the
powerlaw region; the empirical probability for an individual (or
firm) to change its income (or size) from a value to another is
statistically the same as that for its reverse process in the
ensemble. We prove that ParetoZipf law follows from Gibrat's law
under the condition of detailed balance. We also show that the
distribution of growth rate possesses a nontrivial relation between
the positive side of the distribution and the negative side, through
the value of Pareto index, as is confirmed empirically. Furthermore,
we also show that these properties break down in the non powerlaw
region of distribution, and can possibly do so temporally according to
drastic change in financial or real economy.
Thomas Lux Department of Economics, University of Kiel, Olshausenstr. 40, 24118 Kiel, Germany.
Abstract:
This paper revisits the seminal KarekenWallace model of exchange rate
formation in a twocountry overlapping generations world. Following along
the lines of Arifovic [Journal of Political Economy, 104 (1996) 510541]
and Lux and Schornstein [Journal of Mathematical Economies, in press] we
investigate a dynamic version of the model in which agents decision rules
are updated using genetic algorithms. Our main interest is in whether the
equilibrium dynamics resulting from this learning process helps to explain
the main stylized facts of freefloating exchange rates (unit roots in
levels together with fat tails in returns and volatility clustering).
Time series analyses of simulated data indicate that for particular
parameterizations, the characteristics of the exchange rate dynamics are,
in fact, very similar to those of empirical data. However, appearance or
not of realistic time series characteristics depends crucially on the
number of agents (not more than about 1000). With a larger population, this
collective learning dynamics looses its realistic appearance and instead
exhibits regular periodic oscillations of the agents choice variables. In
the present paper, we investigate two extensions of the model with an
emphasis on whether the fading away of realistic time series features for
larger populations can be overcome in a setting with additional elements of
heterogeneity among agents. In particular we allow for (i) heterogeneity of
wealth by imposing a realistic distribution of resources rather than assuming
identical endowments of agents, (ii) subgroup dynamics of the genetic
algorithm learning process (inspired by Darwin's continent cycle theory).
While the stratification of wealth seems to have a surprisingly small effect
on the dynamics, the introduction of a structured population of parallel
genetic algorithms appears to amount to an effective decrease of the
population (compared to the homogeneous case) and produces realistic time
series properties for larger wealth numbers of agents.
Mishael Milakovic and Carolina Castraldi Department of Economics, [Monetary Economics and International Finance] University of Kiel, Olshausenstr. 40, 24118 Kiel, Germany.
Abstract:
We examine several named subsets of the wealthiest individuals in the US
and the UK that are compiled by Forbes Magazine and the Sunday Times. Since
we are dealing with named subsets it is possible to calculate the returns
that wealth portfolios achieve over time. The data support conventional
wisdom of a wealth distribution with power lawdistributed right tail,
and they allow us to calibrate a statistical equilibrium model of wealth
distribution. The model accounts for the power law tail distribution and
is also consistent with the observed asymmetric Laplace distribution of
portfolio returns. Moreover, with information on the distribution of
portfolio returns, the model provides an indicator for how often changes
in the composition of the wealthiest portfolios occuran indicator we
call turnover activity. We also calculate a simple mobility measure
from the subsets and look at trends in equality, mobility and turnover activity.
F. Clementi^{*,+}and M. Gallegati^{#,+} ^{*}Department of Public Economics, University of Rome La Sapienza, Via del Castro Laurenziano 9, I 00161 Rome, Italy. Email address: fabio.clementi@uniroma1.it. ^{#}Department of Economics, Universit`a Politecnica delle Marche, Piazzale Martelli 8, I 62100 Ancona, Italy. Email address: gallegati@dea.unian.it. ^{+}S.I.E.C., Universita Politecnica delle Marche, Piazzale Martelli 8, I 62100 Ancona, Italy. Web address: http://www.dea.unian.it/wehia/.
Abstract:
We analyze four sets of income data: the US Panel Study of Income Dynamics
(PSID), the British Household Panel Survey (BHPS), the German SocioEconomic
Panel (GSOEP), and the Italian Survey on Household Income and Wealth (SHIW).
It is firstly demonstrated that a two parameter lognormal distribution can
give very accurate fits to the lowmedium income range (more than 90% of the
population), whereas the high income range (less than 10% of the population)
is well fitted by a Pareto or powerlaw function. This mixture of two
qualitatively different distributions seems stable over the years covered
by our data sets, although the indexes specifying them fluctuate over time.
We quantify these fluctuations by establishing some links with the country
specific business cycle phases, and show how the separation between the two
regimes of the income distributions may be due to different income dynamics.
In particular, we find that for the top percentiles of the distributions
capital income rather than labour earnings accounts for a vaste share of
the total income, so that its contribution to the latter may be responsible
for the observed powerlaw behaviour in the tail. Secondly, to identify
the contribution of the individual factors and to assess their relative
importance to the overall inequality, we investigate income inequality
using a decomposition analysis by income sources. Our results suggest that
capital income makes by far the most significant contribution to overall
inequality, confirming in this way its role in determining the Pareto
powerlaw tail.
Anirban Chakraborti^{*}, Rui Carvalho, Bikas K. Chakrabarti, Giulia Iori, Kimmo Kaski, Marco Patriarca and Srutarshi Pradhan ^{*}Department of Physics, Brookhaven National Laboratory, New York, USA.
Abstract:
We study a statistical model consisting of N economic agents in a closed
economy which interact with each other by exchanging money, according to a
given microscopic random law, depending on a parameter λ which
controls the saving propensity of the agents. We focus on the equilibrium or
stationary distribution of the money exchanged and verify through numerical
fitting of the simulation data that the final form of the equilibrium
distribution is that of a standard Gamma distribution. We also study
variations of this model by introducing effects of commodity trading,
formation of trade partners, etc.
Robin Marris Department of Economics, London University
Abstract:
Personal distributions of income and wealth are subject to Static and
Dynamic theories.
Victor M. Yakovenko and A. Christian Silva Department of Physics, University of Maryland, College Park, MD 207424111, USA
Abstract:
Personal income distribution in the USA has a welldefined twoclass
structure. The majority of population (9799%) belongs to the lower
class characterized by the exponential BoltzmannGibbs ("thermal")
distribution, whereas the upper class (13% of population) has a Pareto
powerlaw ("superthermal") distribution. By analyzing income data from
the US tax agency (Internal Revenue Service) for 19832001 [1], we show
that the "thermal" part of the distribution is stationary in time, save
for a gradual increase of the income temperature (the average income in
nominal dollars). On the other hand, the "superthermal" tail is
nonstationary, swelling and shrinking with the course of the stock
market. We discuss the concept of equilibrium inequality in a society,
based on the principle of maximal entropy, and quantitatively show that
it applies to the majority of population.
Victor M. Yakovenko Department of Physics, University of Maryland, College Park, MD 207424111, USA
Abstract:
We review foundations of statistical mechanics of money formulated in
Ref. [1]. On the basis of analogy between conservation of energy in
physics and money in economics, we argue that the equilibrium
probability distribution of money in a closed economic system should
follow the exponential BoltzmannGibbs law. We demonstrate how the
BoltzmannGibbs distribution emerges in computer simulations of economic
models. We also discuss the role of debt, and models with broken
timereversal symmetry, for which the BoltzmannGibbs law does not hold.
We consider a thermal machine, in which the difference of money
temperatures between different countries causes steady flow of money
(trade deficit) and allows an intermediary to extract monetary profit
from the nonequilibrium condition. We discuss relation with the
kinetic Boltzmann and diffusion FokkerPlanck equations and illustrate
how a combination of additive and multiplicative random processes can
generate the "thermal" and "superthermal" classes empirically observed
in income distribution in the USA and other countries.
Przemyslaw Repetowicz, Stefan Hutzler and Peter Richmond Department of Physics, Trinity College Dublin 2, Ireland
Abstract:
The distribution of income or wealth can be shown via numerous examples to
have remained broadly unchanged over time for a range of different societies.
We review various approaches to modelling these distributions of income in
recent years. We then focus on the model of interacting agents proposed and
studied numerically by Chatterjee and colleagues (2003). This model allows
agents to both save and exchange wealth at random. Closed equations for the
wealth distribution are developed using a mean field approximation. We show
that when all agents have the same fixed savings propensity, subject to
certain well defined approximations defined in the text, these equations
yield the conjecture proposed by Patriarca, Chakraborti and Kaski (2003) for
the form of the stationary income distribution. If the savings propensity for
the equations is chosen according to some random distribution we show further
that the wealth distribution for large values of wealth displays a Pareto
like power law tail, ie P(m)~m^{1+ν}. However the value of ν for
the model is exactly unity. Exact numerical simulations for the model
illustrate how, as the savings distribution function narrows to zero, the
wealth distribution changes from a Pareto form to an exponential function.
Intermediate regions of wealth may be approximately described by a power law
with ν > 1. But, the tail exponent ν never reaches values of 1.6 1.7
that characterize empirical wealth data. This conclusion is not changed if
three body agent exchange processes are allowed. We discuss a number of
modifications, such as the inclusion of agent memory and redistribution of
income that can lead to more realistic values of the Pareto exponent.
F. Clementi^{*,+}and M. Gallegati^{#,+} ^{*}Department of Public Economics, University of Rome La Sapienza, Via del Castro Laurenziano 9, I 00161 Rome, Italy. Email address: fabio.clementi@uniroma1.it. ^{#}Department of Economics, Universit`a Politecnica delle Marche, Piazzale Martelli 8, I 62100 Ancona, Italy. Email address: gallegati@dea.unian.it. ^{+}S.I.E.C., Universita Politecnica delle Marche, Piazzale Martelli 8, I 62100 Ancona, Italy. Web address: http://www.dea.unian.it/wehia/.
Abstract:
We investigate the shape of the Italian personal income distribution using
microdata from the Survey on Household Income and Wealth, made publicly
available by the Bank of Italy for the years 19772002. We find that the
upper tail of the distribution is consistent with a Paretopower law type
distribution, while the rest follows a twoparameter lognormal distribution.
The results of our analysis show a shift of the distribution and a change
of the indexes specifying it over time. As regards the first issue, we test
the hypothesis that the evolution of both gross domestic product and
personal income is governed by similar mechanisms, pointing to the existence
of correlation between these quantities. The fluctuations of the shape of
income distribution are instead quantified by establishing some links with
the business cycle phases experienced by the Italian economy over the years
covered by our dataset.
Sitabhra Sinha The Institute of Mathematical Sciences (IMSc), CIT Campus, Taramani, Chennai600113, India
Abstract:
It is known that asset exchange models with symmetric
interaction between agents show either a Gibbs distribution or a
condensation of the entire wealth in the hands of a single agent,
depending upon the rules of exchange. In this talk we will explore the
effects of introducing asymmetry in the interaction between agents with
different amounts of wealth. These could be implemented in several ways:
e.g., (1) in the net amount of wealth that is transferred from one agent
to another during an exchange interaction, or (2) the probability of
gaining vs. losing a net amount of wealth from an exchange interaction.
We show that, in general, the introduction of asymmetry leads to power
laws. Distributing the asymmetry parameter randomly over the entire
population of agents results in a wealth distribution very similar to
that empirically observed in various societies, with the tail having a
Paretolike power law behavior, while the lowwealth region has an
exponential nature.
Sitabhra Sinha The Institute of Mathematical Sciences (IMSc), CIT Campus, Taramani, Chennai600113, India
Abstract:
The distribution of gross earnings of movies released each year
show a distribution that is Gaussian for the most part but having a
powerlaw tail with exponent 3. While this offers interesting parallels
with income distributions of individuals, it is also clear that it cannot
be explained by simple asset exchange models, as movies do not interact
with each other directly. In fact, movies (because of the large quantity
of data available on their earnings) provide the best entrypoint
for studying the dynamics of how "a hit is born" and the resulting
distribution of popularity (of products or ideas). In this talk we will
explore various interesting features of movie income distribution, and
present a networkbased model for explaining the same.
Kimmo Kaski^{1}, Marco Patriarca^{1,3}, Anirban Chakraborti^{2} and Guido Germano^{3} ^{1}Laboratory of Computational Engineering, Helsinki University of Technology, P.O. Box 9203, 02015 HUT, Finland ^{2}Department of Physics, Brookhaven National Laboratory, Upton, New York 11973, USA ^{3}Physikalische Chemie PhilippsUniversität Marburg 35032, Marburg
Abstract:
Some analogies between kinetic models of gases and statistical models of
closed economy markets are reviewed. In such models, usually consisting of
N agents interacting with each other by exchanging money according to a
given microscopic random law, the average money plays the role of temperature.
Generalized models with a saving propensity in the trades between agents are
considered. In these models the analogy with the gaskinetic model is
confirmed by the equilibrium distribution being given by a gammadistribution,
which represents just the general MaxwellBoltzmann kinetic energy distribution
in a gas in D dimensions, where D, the effective dimension of the gas, is
related to the effective dimension of the space. We also consider more general
models with individual saving propensity and study the static and dynamic
correlation between money and saving propensity. The results are analyzed in
the light of recent studies of these models based on a Boltzmann equation
or master equation approach.
Sudhakar Yarlagadda Theoretical Condensed Matter Physics Division and Center for Applied Mathematics and Computational Science, Saha Institute of Nuclear Physics, Calcutta, India Abstract: We develop a stochastic model where the poorer end of the society engage in twoparty trading while the richer end perform trade with gross entities. Using our model we are able to capture some of the essential features of wealth distribution in societies: the BoltzmannGibbs distribution at the lower end and the Paretolike power law tails at the richer end. A reasonable scenario to connect the two ends of the wealth spectrum will be presented. Also, an analytic approach to obtain different power law exponents will be given. Furthermore, a link with the models in macroeconomics is also attempted. Abhirup Sarkar Indian Statistical Institute, Calcutta Abstract: The purpose of the paper is to look at the welfare effects of trade in agricultural goods in a lessdeveloped country where the agricultural market is controlled by a handful of large farmers. It is shown that the success of trade reform depends upon the distribution of output between large and small farmers and the success of land reform leading to redistribution from the large to the poor depends on trade reform. In other words, if undertaken in isolation, each reform might lead to a fall in welfare, but if jointly undertaken, they will lead to an increase in welfare. Thus the two reforms are complementary. Arnab Chatterjee Theoretical Condensed Matter Physics Division and Center for Applied Mathematics and Computational Science, Saha Institute of Nuclear Physics, 1/AF, Bidhannagar, Kolkata 700 064, India.
Abstract:
We numerically simulated the idealgas models of trading markets, where each
agent is identified with a gas molecule and each trading as an elastic or
moneyconserving twobody collision. Unlike in the ideal gas, we introduce (quenched) saving propensity of the agents, distributed widely between the agents
(0 ≤ λ ≤ 1). The system remarkably selforganizes to a critical
Pareto distribution of money P(m) ~ m^{(ν + 1)} with ν ≃ 1.
We analyse the robustness (universality) of the distribution in the model.
We also argue that although the fractional saving ingredient is a bit
unnatural one in the context of gas models, our model is the simplest so far,
showing selforganized criticality, and combines two centuryold
distributions: Gibbs (1901) and Pareto (1897) distributions.
Bikas K Chakrabarti Theoretical Condensed Matter Physics Division and Center for Applied Mathematics and Computational Science, Saha Institute of Nuclear Physics, 1/AF, Bidhannagar, Kolkata 700 064, India.
Abstract:
We analyze an ideal gas like model of a trading market with quenched random
saving factors for its agents and show that the steady state income (m)
distribution P(m) in the model has a power law tail with Pareto index ν
exactly equal to unity, confirming the earlier numerical studies on this
model. The analysis starts with the development of a master equation for the
time development of P(m). Precise solutions are then obtained in some special
cases.
Short presentations: Prashant Gade Centre for Modeling and Simulation, University of Pune, India Abstract: We attempt to investigate the problem of wealth distribution from the viewpoint of asset exchange. A simple asset exchange model called Yardsale model gives wealth condensation asymptotically. We show that if few members in population choose different rules for asset exchange, we are able to reproduce a power law tail. We also study a nonlinear variant of Yardsale model in this context. In another problem, we study a population which exchanges assets by Yardsale rule alone. However, if extreme events like disasters, revolution, bancruptcy or taxation (essentially anything that will not allow wealth condensation as a stable steady state) are introduced, the asymptotic distribution under such conditions also has a power law tail. Anita Mehta S N Bose National Centre for Basic Sciences, Kolkata, India
Abstract:
Our model describes wealth aggregation amongst conglomerates. Interacting
conglomerates compete for growth as agents
in this 'winnertakesall' model; for finite assemblies, the largest
conglomerate always wins. In meanfield, our model
exhibits glassy dynamics, with two wellseparated time scales, corresponding
to individual and collective behaviour; the survival probability of a
conglomerate
eventually falls off according to a universal law ln t^{1/2}.
In finite
dimensions, this glassiness is enhanced: the dynamics manifests both
ageing and metastability. Pattern formation is manifested in each
metastable state: some conglomerates survive forever, and can be vastly
rich, provided each has a sphere of influence totally isolated from the others.
Indrani Bose and Subhasis Banerjee Department of Physics, Bose Institute, 93/1, A. P. C. Road, Kolkata700009, India.
Abstract:
We propose a stochastic model of evolution of income in a society of
economic agents. In the model, an economic agent (may be an individual or a
group), can be in two states: inactive and active. Transitions between the
states occur at random time intervals with activation and deactivation rate
constants k_{a} and k_{d} respectively. In the inactive state,
addition to an agents income occurs at the rate b_{w}. In the active
state, there is an additional rate, j_{w}, for the increase in income,
i.e., the total rate at which income increases is
b_{w} + j_{w}. In any state, active or inactive, income
diminishes at a rate proportional to the current income, the
proportionality constant γ_{ω} is the rate constant
for income decay. In the stochastic model, the only stochasticity is
associated with the random
transitions between the inactive and active states of an agent. Let P(X, t)
be the probability density function describing income distribution with X
representing income. We write down an equation describing the time evolution
of P(X, t). In the steady state, the density function has the form of a beta
distribution. Income distributions for the poor, middle and rich classes of
society are further obtained separately. In economic literature, beta
distribution and its generalizations, namely, the generalized beta
distribution functions have been proposed to describe the income distributions
of different economic societies. Our stochastic model provides a simple
basis for the appearance of betatype distributions.
Dipti Prakas Pal^{*} and Hridis Kumar Pal^{#} ^{*}Department of Economics, University of Kalyani, Kalyani, Nadia, West Bengal 741235, India. Email address: diptiprakas@yahoo.co.in ^{#}Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400076. India. Email address: hridispal@iitb.ac.in
Abstract:
In every economic system a set of agents, called economic agents, participate
in the process of an operation just as a set of particles (e.g, a collection
of gas molecules forming a box of gas) join together to form a physical
system. The physical system is described by a set of parameters which limit
its operation. For example, a gaseous system may be described by the size
of the box in which the gas moves. The length, breadth and height (i.e,
volume) fix the boundary and hence the parameters. So also the production
system of an economy may be described by the types of activities (services,
industry, agriculture etc.) in which economic agents (like gaseous particles)
take part. An economic agent (a person, say) may have access to one or all
the activities and acquire the capabilities (energy) to enter into the market.
The incomecapability hence differs from persons to person in the system.
To put it otherwise the total incomecapability of the economic system at a
time point is distributed among the agents (persons) depending upon their
actual participation in the diverse processes of production (different types
of activities are the parameters).
Udayan K Basu Future Business School, Kolkata.
Abstract:
Even after liberalization of financial markets and a consequential shift
in the role of commercial banks, extending working capital facilities to
industry and trade continues to be a major activity for the banking sector
in India. Working capital loans are granted in India normally in the form
of cash credit. Under this facility a borrower can avail of any amount of
credit not exceeding the sanctioned limit and pays interest based on daily
actual balances outstanding in the loan account. While some fluctuation in
level of utilization based on actual requirement is only to be expected, the
actual level of fluctuation often is much beyond what is projected by
borrowing companies at the time of submission of loan proposals. This creates
a serious problem of fund management for banks and the solution lies in
ensuring that borrowers take the task of forecasting their requirements
seriously.
The Tandon Committee, set up by the central bank of the country under the
chairmanship of Mr. P. L. Tandon for going into various aspects of followup
of bank credit, examined, inter alia, this issue and recommended that working
capital loans should be bifurcated into a fixed demand loan component and a
fluctuating cash credit component carrying differential rates of interest.
The bifurcation should be worked out based on projected fund requirement in
such a way that any departure from target results in payment of penalty by
borrower in the form of additional interest. In other words, the process of
bifurcation should ensure a minimum value for the overall annual interest
burden for a borrower in case it adheres strictly to its projections.
The problem is thus basically one of optimization.
Debasis Bagchi Bengal Engineering and Science University, Shibpur, Howrah 711 103, India.
Abstract:
We examine whether powerlaw distribution emerges in Indian capital market
similar to the wealth distribution of individuals in an economy and how the
exponent of powerlaw behaves at various high wealth levels as well as how
the relative growth and decline of firms over time affects the distribution.
Using a database of 500 companies having highest market capitalization in
Indian capital market, we observe that the powerlaw distribution emerges at
the top 10% wealth level of the firms. As we go down on the ranks, the
powerlaw becomes less conspicuous, which is consistent with other research
findings. The value of the exponent is observed to compare well with respect
to wealth distribution of the individuals in the economy. The behaviour of
exponent in respect of high growth and declining firms is also investigated.
We observe that the value of exponent in respect of high growth firms does
not change over time, but the value reduces during the same period in the
case of firms showing negative growth. The ttest shows that as the rank
difference is high and statistically significant for the declining firms as
against the growing firms, it has expectedly caused the exponent to change
its value.
K. Bhattacharya^{1}, G. Mukherjee^{1,2} and S. S. Manna^{1} ^{1}Satyendra Nath Bose National Centre for Basic Sciences BlockJD, SectorIII, Salt Lake, Kolkata700098, India ^{2}Bidhan Chandra College, Asansol 713304, Dt. Burdwan, West Bengal, India
Abstract:
A group of $N$ traders trade by the method of pairwise conservative
money
reshuffling. In a trade, two traders $i$ and $j$ $(1 \le i,j \le N, i \ne
j)$
having moneys $m_i$ and $m_j$ are selected with probabilities depending on
their
individual wealths like, $\pi_i \propto m_i^{\alpha}$ where $\alpha$ is a
preassigned $m$ independent constant parameter. On the board both the
traders
put all their monies and just reshuffle their total money $m_i+m_j$ by
randomly
partitioning with uniform probability. In the stationary state the money
distribution is observed to follow a Pareto distribution with a power law
tail: $P(m) \sim m^{(1+\nu)}$. Our numerical results show that the Pareto
exponent
is continuously tunable and $\nu = \alpha1$ for all values of $\alpha > 0$.
Poster presentations: Ning Ding, Ning Xi and Yougui Wang Department of Systems Science, School of Management, Beijing Normal University Beijing, 100875, People's Republic of China
Abstract:
To explore the mechanism behind the distribution, a series of transfer
models are constructed basing on the analogies between money transfer
in business and energy transfer in molecule collision among which the
model with uniform saving rate draws much attention. Many efforts are put
into to find out the exact mathematic presentation of the static
distribution. However, investigating the static distribution only cannot
provide the whole picture of the dynamic mechanism behind the distribution.
For this aim, some researchers observed dynamics of the models: the money
circulation and mobility. If the distribution can be take as the cross
section of the system, the circulation and the mobility are the lengthways
sections which are helpful for us to expose mechanism of distribution.
And investigating the two dynamic characteristics is also meaningful to
economics research. Monetary circulation is the dynamics about how the
money moves in the economy. Based on the dynamics, the monetary velocity,
an important macroeconomic variable could be discussed at the microlevel.
While mobility is the dynamics about how the people move in the economy. It
is an indispensable supplement to distribution in the study on inequality.
Chitro Majumdar Department of Economics, University of Kiel, WilhelmSeeligPlatz 1 Olshausenstr. 40 D21118 Kiel
Abstract:
Since the Normal distribution is symmetric, stationary Arma Gaussian models
are not adequate for data exhibiting strong asymmetry. Many time series
encountered in practice are nonGaussian. This paper illustrates for a first
order auto regressive and first order moving average model with
nonconsecutively observed or missing data, the closed from the exact
likelihood function obtained, and the exact maximum likelihood estimation for
a stationary Arma(1, 1) model with incomplete data asymmerty with zeromean
process:
A. Sarkar and P. Barat Variable Energy Cyclotron Centre, 1/AF Bidhan Nagar, Kolkata700 064, India Abstract: We have carried out extensive studies on the daily close price index of the Bombay Stock Exchange (BSE) for the period of 1997 to 2004. To reveal the exact scaling behavior of the BSE price index we made use of four newly developed robust methods of scaling analysis namely (i) Finite Variance Scaling Analysis (ii) Diffusion Entropy Analysis (iii) Detrended Fluctuation Analysis and (iv) Hurst RescaledRange Analysis. We have also performed recurrence analysis on the BSE price indices. Our analysis clearly revealed the statistical independence i.e. the absence of scaling in the BSE price index. Soumen Roy and Somendra M. Bhattacharjee Institute of Physics, Bhubaneswar 751005 Abstract: Recent renormalization group results predict nonselfaveraging behaviour at criticality for relevant randomness. Contrary to this expectation, strong selfaveraging behaviour is found in the critical region of a quenched Ising model on an ensemble of smallworld networks, despite the relevance of the random bonds at the pure critical point.Single realisation finitesize data of various physical quantities show as good a data collapse(finite size scaling) as the average. Kamalika BasuHajra Department of Physics, University of Calcutta, 92 A P C Road, Kolkata 700009. Abstract: We consider a growing network in which an incoming node gets attached to the $i^{th}$ existing node with the probability $\Pi_i \propto K(k_i)T(\tau)$, where $K(k_i) \sim {k_i}^{\beta}$ and $T(\tau) \sim{\tau}^{\alpha}$, $k_{i}$ being the degree of the $i^{th}$ node and $\tau$ its present age. We find the phase diagram in the ${{\alpha}{\beta}}$ plane. While the network shows scale free property only along a curve, small world property exists over a large region in the phase diagram. The degree distribution also shows interesting features in different parts of the phase diagram. We also discuss a real world network, viz, the citation network, where the age of the nodes plays an important role in deciding the attachment probability of the incoming nodes. We observe here that very old papers are seldom cited, while recent papers are cited with greater frequency. We find out the distribution $T(t)$ of $t$, the time gap between the published and the cited paper. For different sets of data, we find a universal behaviour: $T(t) \sim t^{0.9}$ for $t \leq t_c$ and $T(t) \sim t^{2}$ for $t>t_c$ where $t_c \sim O(10)$. We then analyse the results of the model system in light of the results obtained for the real network. Srutarshi Pradhan Department of Physics NTNU, Trondheim 7491 Norway Abstract: We point out some major drawbacks in random trading market models and propose a realistic modification which overcomes such drawbacks through `sensible trading'. We apply such trading policy in different situations: (a) Agents with zero saving factor (b) with constant saving factor and (c) with random saving factor. In all the cases the richer agents seem to follow power law in terms of their wealth (money) distribution and this is consistent with Pareto's observation. 