Author presents a model of the distribution of wealth within a market society that: 1) can be calibrated to display the basic "stylized facts" (mixed exponential and Pareto distribution of wealth; Gini coefficient); 2) demonstrates the effectiveness of relatively modest changes in tax and transfer policies in reducing the degree of inequality characterizing the society.
This note introduces how to create scenarios by using the knowledge that has been generated by the participants on the driving forces. Besides, it goes into detail on how these could evolve in the future.
This document was used by Robin Bourgeois, Senior Foresight Advisor, GFAR Secretariat for the "Grassroots Foresight initiative - Training of Resource persons
Participatory Prospective Analysis –Scenario Building." This workshop was held on February 1-7, 2015 in Quezon City, The Philippines.
Check out "Empowering local organisations through foresight" by Robin Bourgeois at: http://bit.ly/17GoTt4
The author finds that using the ratio of a fast moving average to that of a slower one as an indicator to buy or sell individual stocks outperforms both traditional measures of price momentum (recent rate of change in security price) as well as the proximity of the stock price to its 52 week high.
This note introduces how to create scenarios by using the knowledge that has been generated by the participants on the driving forces. Besides, it goes into detail on how these could evolve in the future.
This document was used by Robin Bourgeois, Senior Foresight Advisor, GFAR Secretariat for the "Grassroots Foresight initiative - Training of Resource persons
Participatory Prospective Analysis –Scenario Building." This workshop was held on February 1-7, 2015 in Quezon City, The Philippines.
Check out "Empowering local organisations through foresight" by Robin Bourgeois at: http://bit.ly/17GoTt4
The author finds that using the ratio of a fast moving average to that of a slower one as an indicator to buy or sell individual stocks outperforms both traditional measures of price momentum (recent rate of change in security price) as well as the proximity of the stock price to its 52 week high.
Strumsky lobo (2011) does patenting intensity beget qualityivan weinel
This paper addresses the following research question: Is the quality of patents issued in a given metropolitan area related to the per capita rate of patent authorship (patenting intensity / productivity)? The authors conclude that there may be a small positive response of patent quality (avg. number of citations received per patent granted) to increases in patenting productivity. Highly productive inventors do not necessarily generate high quality patents.
커빙의 Django, Celery, Azure Cloud, SNS 연동, 컨텐츠 수집 기술을 한눈에 볼 수 있도록 소개한 자료 입니다.
커빙을 처음 개발하면서 많은 어려움이 있었고,
또 많은 분들의 도움으로 좋은 결과를 얻을 수 있었습니다.
조금 더 깊은 내용을 다뤘으면 하는 아쉬움이 있지만,
다른 분들에게 조금이나마 도움이 되었으면 좋겠네요!
A Course in Public EconomicsResources for InstructorsJo.docxransayo
A Course in Public Economics:
Resources for Instructors
John Leach
August 2002
Course Design
Overview
Areviewof thecontents andmethodologyofeachchapter follows. Thenumber in themiddle
column is an estimate of the chapters difÞculty, on a 1�5 scale with 1 being the easiest. For
this purpose, I have imagined the students to be in their third or fourth year, with one or two
terms of Varian-style intermediate microeconomics, and with a grasp of basic calculus but
little exposure to statistics.
1: Introduction 1 Discusses the two fundamental theorems of welfare economics.
Informally states the requirements of the Þrst theorem, and de-
scribes themarket failures that arisewhen these requirementsare
not satisÞed: public goods, externalities, imperfect competition.
Introduces theconceptofasymmetric information, anddiscusses
its relevance to the Þrst theorem. Argues that asymmetric infor-
mation precludes the government from transferring income in a
lump sum fashion, so that the requirements of the second theo-
rem are also unlikely to be satisÞed. This chapter are entirely
verbal.
2: The Exchange
Economy
2 Introduces theconceptofParetooptimalityand illustrates itwith
a simple example. Develops the Edgeworth box, and uses it
to discuss Pareto optimality and competitive equilibrium within
the context of an exchange economy with two people and two
goods. Demonstrates the two theorems for this economy. The
arguments are verbal and graphical.
3: An Algebraic
Exchange
Economy
2 Constructs an algebraic version of the two person, two good ex-
change economy. Describes Pareto optimal allocations as so-
lutions to an under-determined equation system and presents a
Cobb-Douglas example. Describes competitive equilibrium as
the solution to an equation system and presents a Cobb-Douglas
example. Demonstrates the two theorems by comparing the two
equation systems.
4 Course Design
4: The Production
Economy
3 Develops a two person, two good economy in which the people
areendowedwith twofactorsofproductionand theownershipof
Þrms, but not with consumer goods. Describes a Pareto optimal
allocation as one satisfying three efÞciency conditions, and dis-
cusses eachefÞciencycondition. Shows that aParetooptimal al-
location can be represented as a solution to anunder-determined
equation system. Describes competitive equilibrium, and shows
that it can also be thought of as the solution to an equation sys-
tem. Presents an example of competitive equilibrium involving
simple functional forms. Demonstrates theÞrst theorembycom-
paring the equation systems.
5: Consumer
and Producer
Surplus
2 Shows that the increase in total cost when output rises can be
measured by an area under the marginal cost curve. Presents a
more general rule of the relationship between margins and to-
tals. Introduces consumer and producer surplus, and uses the
general rule to measure them. Argues that a system of free mar-
kets maximizes surplus, and that interventions cause a loss o.
Cascade process and Pareto rule: application to runoff data of two Mexican ri...IJERA Editor
This paper has two objectives: the first is to show that the annual runoff of rivers such as Conchos and Nazas (Mexico), follow the Pareto rule of 80:20 when classes are ordered from largest to less, and can be compared with cascade processes. The second objective is to show that cascade process produce the core which gives rise to fractional integral and therefore to differential equations of fractional order. Finally, we conclude that the Pareto rule is a first approach to saturation described by the complementary characteristic function, and runoff data provide the order of the temporal derivative. Therefore, cascade processes are manifested ubiquitously in nature, and show us a way to evolve towards the imbalanced and become in distribution mechanisms that turn into a transition that destroys old and build new correlations.
Abstract— Land subsidence caused by groundwater overdraft has been a severe problem in most developing economies, such as Taiwan. Groundwater is a renewable resource that can be depleted by overdraft, and it is also a common resource which incites overdraft. To alleviate the overdraft problem, we set up a decentralized game-theoretical common resource utilization model. In this model, we examine the self-enforcing factors and the condition of getting a cooperative outcome hence we might be able to alleviate the overdraft problem.
A brief study on the measures of income distribution for both analytic and quantitative purposes in terms of size distribution and functional distribution.
The study includes discussion on following concepts-
Lorenz Curve
Gini Coefficient
Absolute Poverty
Foster Greer Thorbecke Measure
model of a protected currency area for developing countriesSehrGlobal
It is the description of a complementary currency with the attribute of a never changing value, settled by a never changing quantity of this complementary currency. It leads to the possibility of monetary scaling based on this absolute value and allows the introduction of mathematically determined exchange rates. Also Trading imbalances can be considered in the mathematically determination of exchange rates.
It is the model of a global reference complementary currency, abbreviating named ANNA, with the task to be a currency and exchange rate system for central banks.
It should be seen as a system of voluntary participation and leads to a currency area, if more than one country will participate to the system. The architecture of the monetary system implies minimum a second complementary currency as an intermediary foreign exchange currency. This monetary design will lead to a protection of the currency area, because:
1) It is a global system and independent from national interests. The monetary policy in ANNA will be less complex due to the absence of additional money supply and interest rates.
2) The intermediary foreign exchange currency leads to balancing effects between the systems of ANNA and FOREX
3) Monetary policy of single national inside currencies remains completely in self determination of the countries.
4) The exchange rates of inside currencies are always conclusive to each other, due to the mathematically determination. It prevents from speculative trading of currencies.
5) The never changing value of ANNA is a long term consideration of debts. It allows also the introduction of independent interest free national currencies. Both aspects together can be seen as a tool to interrupt the helix of debts.
The system succeeds if mutual benefits can be obtained for the FOREX and the participating countries. Heavily indebted poor countries could fulfill these requirements.
Strumsky lobo (2011) does patenting intensity beget qualityivan weinel
This paper addresses the following research question: Is the quality of patents issued in a given metropolitan area related to the per capita rate of patent authorship (patenting intensity / productivity)? The authors conclude that there may be a small positive response of patent quality (avg. number of citations received per patent granted) to increases in patenting productivity. Highly productive inventors do not necessarily generate high quality patents.
커빙의 Django, Celery, Azure Cloud, SNS 연동, 컨텐츠 수집 기술을 한눈에 볼 수 있도록 소개한 자료 입니다.
커빙을 처음 개발하면서 많은 어려움이 있었고,
또 많은 분들의 도움으로 좋은 결과를 얻을 수 있었습니다.
조금 더 깊은 내용을 다뤘으면 하는 아쉬움이 있지만,
다른 분들에게 조금이나마 도움이 되었으면 좋겠네요!
A Course in Public EconomicsResources for InstructorsJo.docxransayo
A Course in Public Economics:
Resources for Instructors
John Leach
August 2002
Course Design
Overview
Areviewof thecontents andmethodologyofeachchapter follows. Thenumber in themiddle
column is an estimate of the chapters difÞculty, on a 1�5 scale with 1 being the easiest. For
this purpose, I have imagined the students to be in their third or fourth year, with one or two
terms of Varian-style intermediate microeconomics, and with a grasp of basic calculus but
little exposure to statistics.
1: Introduction 1 Discusses the two fundamental theorems of welfare economics.
Informally states the requirements of the Þrst theorem, and de-
scribes themarket failures that arisewhen these requirementsare
not satisÞed: public goods, externalities, imperfect competition.
Introduces theconceptofasymmetric information, anddiscusses
its relevance to the Þrst theorem. Argues that asymmetric infor-
mation precludes the government from transferring income in a
lump sum fashion, so that the requirements of the second theo-
rem are also unlikely to be satisÞed. This chapter are entirely
verbal.
2: The Exchange
Economy
2 Introduces theconceptofParetooptimalityand illustrates itwith
a simple example. Develops the Edgeworth box, and uses it
to discuss Pareto optimality and competitive equilibrium within
the context of an exchange economy with two people and two
goods. Demonstrates the two theorems for this economy. The
arguments are verbal and graphical.
3: An Algebraic
Exchange
Economy
2 Constructs an algebraic version of the two person, two good ex-
change economy. Describes Pareto optimal allocations as so-
lutions to an under-determined equation system and presents a
Cobb-Douglas example. Describes competitive equilibrium as
the solution to an equation system and presents a Cobb-Douglas
example. Demonstrates the two theorems by comparing the two
equation systems.
4 Course Design
4: The Production
Economy
3 Develops a two person, two good economy in which the people
areendowedwith twofactorsofproductionand theownershipof
Þrms, but not with consumer goods. Describes a Pareto optimal
allocation as one satisfying three efÞciency conditions, and dis-
cusses eachefÞciencycondition. Shows that aParetooptimal al-
location can be represented as a solution to anunder-determined
equation system. Describes competitive equilibrium, and shows
that it can also be thought of as the solution to an equation sys-
tem. Presents an example of competitive equilibrium involving
simple functional forms. Demonstrates theÞrst theorembycom-
paring the equation systems.
5: Consumer
and Producer
Surplus
2 Shows that the increase in total cost when output rises can be
measured by an area under the marginal cost curve. Presents a
more general rule of the relationship between margins and to-
tals. Introduces consumer and producer surplus, and uses the
general rule to measure them. Argues that a system of free mar-
kets maximizes surplus, and that interventions cause a loss o.
Cascade process and Pareto rule: application to runoff data of two Mexican ri...IJERA Editor
This paper has two objectives: the first is to show that the annual runoff of rivers such as Conchos and Nazas (Mexico), follow the Pareto rule of 80:20 when classes are ordered from largest to less, and can be compared with cascade processes. The second objective is to show that cascade process produce the core which gives rise to fractional integral and therefore to differential equations of fractional order. Finally, we conclude that the Pareto rule is a first approach to saturation described by the complementary characteristic function, and runoff data provide the order of the temporal derivative. Therefore, cascade processes are manifested ubiquitously in nature, and show us a way to evolve towards the imbalanced and become in distribution mechanisms that turn into a transition that destroys old and build new correlations.
Abstract— Land subsidence caused by groundwater overdraft has been a severe problem in most developing economies, such as Taiwan. Groundwater is a renewable resource that can be depleted by overdraft, and it is also a common resource which incites overdraft. To alleviate the overdraft problem, we set up a decentralized game-theoretical common resource utilization model. In this model, we examine the self-enforcing factors and the condition of getting a cooperative outcome hence we might be able to alleviate the overdraft problem.
A brief study on the measures of income distribution for both analytic and quantitative purposes in terms of size distribution and functional distribution.
The study includes discussion on following concepts-
Lorenz Curve
Gini Coefficient
Absolute Poverty
Foster Greer Thorbecke Measure
model of a protected currency area for developing countriesSehrGlobal
It is the description of a complementary currency with the attribute of a never changing value, settled by a never changing quantity of this complementary currency. It leads to the possibility of monetary scaling based on this absolute value and allows the introduction of mathematically determined exchange rates. Also Trading imbalances can be considered in the mathematically determination of exchange rates.
It is the model of a global reference complementary currency, abbreviating named ANNA, with the task to be a currency and exchange rate system for central banks.
It should be seen as a system of voluntary participation and leads to a currency area, if more than one country will participate to the system. The architecture of the monetary system implies minimum a second complementary currency as an intermediary foreign exchange currency. This monetary design will lead to a protection of the currency area, because:
1) It is a global system and independent from national interests. The monetary policy in ANNA will be less complex due to the absence of additional money supply and interest rates.
2) The intermediary foreign exchange currency leads to balancing effects between the systems of ANNA and FOREX
3) Monetary policy of single national inside currencies remains completely in self determination of the countries.
4) The exchange rates of inside currencies are always conclusive to each other, due to the mathematically determination. It prevents from speculative trading of currencies.
5) The never changing value of ANNA is a long term consideration of debts. It allows also the introduction of independent interest free national currencies. Both aspects together can be seen as a tool to interrupt the helix of debts.
The system succeeds if mutual benefits can be obtained for the FOREX and the participating countries. Heavily indebted poor countries could fulfill these requirements.
how to swap pi coins to foreign currency withdrawable.DOT TECH
As of my last update, Pi is still in the testing phase and is not tradable on any exchanges.
However, Pi Network has announced plans to launch its Testnet and Mainnet in the future, which may include listing Pi on exchanges.
The current method for selling pi coins involves exchanging them with a pi vendor who purchases pi coins for investment reasons.
If you want to sell your pi coins, reach out to a pi vendor and sell them to anyone looking to sell pi coins from any country around the globe.
Below is the contact information for my personal pi vendor.
Telegram: @Pi_vendor_247
USDA Loans in California: A Comprehensive Overview.pptxmarketing367770
USDA Loans in California: A Comprehensive Overview
If you're dreaming of owning a home in California's rural or suburban areas, a USDA loan might be the perfect solution. The U.S. Department of Agriculture (USDA) offers these loans to help low-to-moderate-income individuals and families achieve homeownership.
Key Features of USDA Loans:
Zero Down Payment: USDA loans require no down payment, making homeownership more accessible.
Competitive Interest Rates: These loans often come with lower interest rates compared to conventional loans.
Flexible Credit Requirements: USDA loans have more lenient credit score requirements, helping those with less-than-perfect credit.
Guaranteed Loan Program: The USDA guarantees a portion of the loan, reducing risk for lenders and expanding borrowing options.
Eligibility Criteria:
Location: The property must be located in a USDA-designated rural or suburban area. Many areas in California qualify.
Income Limits: Applicants must meet income guidelines, which vary by region and household size.
Primary Residence: The home must be used as the borrower's primary residence.
Application Process:
Find a USDA-Approved Lender: Not all lenders offer USDA loans, so it's essential to choose one approved by the USDA.
Pre-Qualification: Determine your eligibility and the amount you can borrow.
Property Search: Look for properties in eligible rural or suburban areas.
Loan Application: Submit your application, including financial and personal information.
Processing and Approval: The lender and USDA will review your application. If approved, you can proceed to closing.
USDA loans are an excellent option for those looking to buy a home in California's rural and suburban areas. With no down payment and flexible requirements, these loans make homeownership more attainable for many families. Explore your eligibility today and take the first step toward owning your dream home.
Lecture slide titled Fraud Risk Mitigation, Webinar Lecture Delivered at the Society for West African Internal Audit Practitioners (SWAIAP) on Wednesday, November 8, 2023.
The European Unemployment Puzzle: implications from population agingGRAPE
We study the link between the evolving age structure of the working population and unemployment. We build a large new Keynesian OLG model with a realistic age structure, labor market frictions, sticky prices, and aggregate shocks. Once calibrated to the European economy, we quantify the extent to which demographic changes over the last three decades have contributed to the decline of the unemployment rate. Our findings yield important implications for the future evolution of unemployment given the anticipated further aging of the working population in Europe. We also quantify the implications for optimal monetary policy: lowering inflation volatility becomes less costly in terms of GDP and unemployment volatility, which hints that optimal monetary policy may be more hawkish in an aging society. Finally, our results also propose a partial reversal of the European-US unemployment puzzle due to the fact that the share of young workers is expected to remain robust in the US.
Turin Startup Ecosystem 2024 - Ricerca sulle Startup e il Sistema dell'Innov...Quotidiano Piemontese
Turin Startup Ecosystem 2024
Una ricerca de il Club degli Investitori, in collaborazione con ToTeM Torino Tech Map e con il supporto della ESCP Business School e di Growth Capital
Currently pi network is not tradable on binance or any other exchange because we are still in the enclosed mainnet.
Right now the only way to sell pi coins is by trading with a verified merchant.
What is a pi merchant?
A pi merchant is someone verified by pi network team and allowed to barter pi coins for goods and services.
Since pi network is not doing any pre-sale The only way exchanges like binance/huobi or crypto whales can get pi is by buying from miners. And a merchant stands in between the exchanges and the miners.
I will leave the telegram contact of my personal pi merchant. I and my friends has traded more than 6000pi coins successfully
Tele-gram
@Pi_vendor_247
how can i use my minded pi coins I need some funds.DOT TECH
If you are interested in selling your pi coins, i have a verified pi merchant, who buys pi coins and resell them to exchanges looking forward to hold till mainnet launch.
Because the core team has announced that pi network will not be doing any pre-sale. The only way exchanges like huobi, bitmart and hotbit can get pi is by buying from miners.
Now a merchant stands in between these exchanges and the miners. As a link to make transactions smooth. Because right now in the enclosed mainnet you can't sell pi coins your self. You need the help of a merchant,
i will leave the telegram contact of my personal pi merchant below. 👇 I and my friends has traded more than 3000pi coins with him successfully.
@Pi_vendor_247
how can I sell pi coins after successfully completing KYCDOT TECH
Pi coins is not launched yet in any exchange 💱 this means it's not swappable, the current pi displaying on coin market cap is the iou version of pi. And you can learn all about that on my previous post.
RIGHT NOW THE ONLY WAY you can sell pi coins is through verified pi merchants. A pi merchant is someone who buys pi coins and resell them to exchanges and crypto whales. Looking forward to hold massive quantities of pi coins before the mainnet launch.
This is because pi network is not doing any pre-sale or ico offerings, the only way to get my coins is from buying from miners. So a merchant facilitates the transactions between the miners and these exchanges holding pi.
I and my friends has sold more than 6000 pi coins successfully with this method. I will be happy to share the contact of my personal pi merchant. The one i trade with, if you have your own merchant you can trade with them. For those who are new.
Message: @Pi_vendor_247 on telegram.
I wouldn't advise you selling all percentage of the pi coins. Leave at least a before so its a win win during open mainnet. Have a nice day pioneers ♥️
#kyc #mainnet #picoins #pi #sellpi #piwallet
#pinetwork
What website can I sell pi coins securely.DOT TECH
Currently there are no website or exchange that allow buying or selling of pi coins..
But you can still easily sell pi coins, by reselling it to exchanges/crypto whales interested in holding thousands of pi coins before the mainnet launch.
Who is a pi merchant?
A pi merchant is someone who buys pi coins from miners and resell to these crypto whales and holders of pi..
This is because pi network is not doing any pre-sale. The only way exchanges can get pi is by buying from miners and pi merchants stands in between the miners and the exchanges.
How can I sell my pi coins?
Selling pi coins is really easy, but first you need to migrate to mainnet wallet before you can do that. I will leave the telegram contact of my personal pi merchant to trade with.
Tele-gram.
@Pi_vendor_247
where can I find a legit pi merchant onlineDOT TECH
Yes. This is very easy what you need is a recommendation from someone who has successfully traded pi coins before with a merchant.
Who is a pi merchant?
A pi merchant is someone who buys pi network coins and resell them to Investors looking forward to hold thousands of pi coins before the open mainnet.
I will leave the telegram contact of my personal pi merchant to trade with
@Pi_vendor_247
What price will pi network be listed on exchangesDOT TECH
The rate at which pi will be listed is practically unknown. But due to speculations surrounding it the predicted rate is tends to be from 30$ — 50$.
So if you are interested in selling your pi network coins at a high rate tho. Or you can't wait till the mainnet launch in 2026. You can easily trade your pi coins with a merchant.
A merchant is someone who buys pi coins from miners and resell them to Investors looking forward to hold massive quantities till mainnet launch.
I will leave the telegram contact of my personal pi vendor to trade with.
@Pi_vendor_247
how to sell pi coins effectively (from 50 - 100k pi)DOT TECH
Anywhere in the world, including Africa, America, and Europe, you can sell Pi Network Coins online and receive cash through online payment options.
Pi has not yet been launched on any exchange because we are currently using the confined Mainnet. The planned launch date for Pi is June 28, 2026.
Reselling to investors who want to hold until the mainnet launch in 2026 is currently the sole way to sell.
Consequently, right now. All you need to do is select the right pi network provider.
Who is a pi merchant?
An individual who buys coins from miners on the pi network and resells them to investors hoping to hang onto them until the mainnet is launched is known as a pi merchant.
debuts.
I'll provide you the Telegram username
@Pi_vendor_247
how to sell pi coins effectively (from 50 - 100k pi)
Simple regs rdc ineq
1. arXiv:1007.0461v2[physics.soc-ph]13Jul2010
How simple regulations can greatly reduce inequality
J. R. Iglesias1
1
Programa de P´os-Gradua¸c˜ao em Economia and Instituto de F´ısica,
Universidade Federal do Rio Grande do Sul, 91501-970 Porto Alegre, Brazil
(Dated: July 14, 2010)
Many models of market dynamics make use of the idea of wealth exchanges among economic
agents. A simple analogy compares the wealth in a society with the energy in a physical system,
and the trade between agents to the energy exchange between molecules during collisions. However,
while in physical systems the equipartition of energy is valid, in most exchange models for economic
markets the system converges to a very unequal “condensed” state, where one or a few agents
concentrate all the wealth of the society and the wide majority of agents shares zero or a very tiny
fraction of the wealth. Here we present an exchange model where the goal is not only to avoid
condensation but also to reduce the inequality; to carry out this objective the choice of interacting
agents is not at random, but follows an extremal dynamics regulated by the wealth of the agent.
The wealth of the agent with the minimum capital is changed at random and the difference between
the ancient and the new wealth of this poorest agent is taken from other agents, so establishing a
regulatory tool for wealth redistribution. We compare different redistribution processes and conclude
that a drastic reduction of the inequality can be obtained with very simple regulations.
PACS numbers: 89.65.s, 89.65.Gh, 05.20.y, 05.65.+b
I. INTRODUCTION
Empirical studies focusing the income distribution of workers, companies and countries were first presented more
than a century ago by Italian economist Vilfredo Pareto. He observed, in his book “Cours d’Economie Politique” [1],
that the distribution of income does not follow a Gaussian distribution but a power law. That means that the
asymptotic behavior of the distribution function is not exponential (as it should be for a Gaussian distribution) but
follows a power function that decreases, for big values of the wealth, as w−α
, being α > 1 the exponent of the
power law. Non-gaussian distributions are denominated Levy distributions [2], thus this power law distribution is
nowadays known as Pareto-Levy Distribution. Then, Pareto asserted that in different countries and times the income
distribution follows a power law behavior, i.e. the cumulative probability P(w) that an agents have an income which
is at higher or equal to w is given by P(w) ∝ w−α
[1]. The exponent α is named Pareto index. The value of this
exponent changes with geography and time, but a typical values are close to 3/2. The bigger the value of the Pareto
exponent the higher the inequality in a society.
However, recent data indicate that, even though Pareto distribution provides a good fit in the the high income
range, it does not agree with the observed data over the middle and low income ranges. For instance, data from
Japan [3, 4], Italy [5], India [6], the United States of America and the United Kingdom [7–9] are fitted by a log-normal
or Gaussian distribution with the maximum located at the middle income region plus a power law for the high income
strata. This kind of behavior is also observed in the wage distribution in Brazil. We have represented on Fig. 1 the
number of families as a function of the annual income and it is clear that for low and middle salaries the distribution
follows an almost Gaussian law, while for high salaries the curve clearly departs from the exponential and may be
described, in spite of the high noise, as a power law distribution. The Pareto exponent for this distribution is 2.7.
If we consider that the results in Fig. 1 are not cumulative, The integration of the curve will deliver the cumulative
distribution and the high income region will show a exponent 1.7 very near Pareto’s value of 3/2.
One way of justifying in a qualitative way the two regimes: Gaussian + power law, is by considering that in the low
and middle income classes the process of wealth accumulation is additive, causing a Gaussian-like distribution, while
in the high income range, wealth grows in a multiplicative way (interests or other mechanism of multiplying assets),
generating the observed power law tail [4].
Another verification of Pareto-Levy’s law is shown on Fig. 2, where the accumulated Gross Domestic Product of
the 100 richest cities in Brazil [11] is plotted as a function of the ranking. The county of S˜ao Paulo concentrates the
biggest fraction of the total Brazilian domestic product, around 12%, followed by Rio de Janeiro, Bras´ılia and Belo
Horizonte. All in all the first 100 counties in the ranking concentrate almost 60% of the Brazilian GDP. The log-log
plot used on Fig. 2 makes the power law explicit , as a power function becomes a straight line when plotted in double
logarithmic scale (while exponentials, or Gaussians, look as parabolas, for example the low – middle income region
in Fig. 1). This power law is valid for the richest counties. However, as there are more than 5500 in Brazil, the vast
majority (not included in the graphic) shares the other 40% of the GDP, so, it is certain that the distribution deviates
form the power low and becomes a Gaussian distribution for the big majority of cities and towns.
2. 2
103
104
105
102
103
104
105
106
Numberoffamilies
Income
Brazil, income data 2004
Power law, exponent -2.7
Gaussian
FIG. 1: Number of families per salary class (in Brazilian Real, annual value). Data collected from IBGE, PNAD 2004 [10]
1 10 100
10
20
30
40
50
60
ParticipationintheGDP(%)
Ranking
SP
RJ
BSB BH
FIG. 2: Cumulative participation in the GDP of the 100 richest counties in Brazil. The red line is an interpolation with a linear
law, indicating, in the double logarithmic scale, that the distribution follows a power law. Data extracted from IBGE [11]
3. 3
Power laws are not rare in nature, so it is not surprising that the wealth distribution follows a power law. The energy
liberated in earthquakes, the size of avalanches, the size of cities, the frequency of all these phenomena are described
by power laws [12]. The quiz with the income and wealth distribution is not the power law, but how this distribution
is generated through the dynamics of the agents interacting. On the other hand, a Pareto-Levy distribution is more
unequal than a Gaussian: when the distribution follows a power law there are more affluent agents than in the case of
a Gaussian distribution, but also more poor agents. And when the Pareto exponent increases the middle class tends
to disappear.
In order to try to describe the processes that generate a given profile for the wealth distribution, in recent years
diverse exchange models have been widely applied to describe wealth and/or income distributions in social systems.
Different mathematical models of capital exchange among economic agents have been proposed trying to explain these
empirical data (For a review see ref. [13]). Most of these models consider an ensemble of interacting economic agents
that exchange a fixed or random amount of a quantity called “wealth”. This wealth represents the agents welfare.
The exact choice of this quantity is not straightforward, but one can think that it stands for the exchange of a given
amount of money against some service or commodity. Within these models the amount of exchanged wealth when
two agents interact corresponds to some economic “energy” that may be randomly exchanged. If this exchanged
amount corresponds to a random fraction of one of the interacting agents wealth, the resulting wealth distribution is
– unsurprisingly – a Gibbs exponential distribution [7].
Aiming at obtaining distributions with power law tails, several methods have been proposed. Numerical
procedures[13, 16–19, 21], as well as some analytical calculations [22, 23], indicate that one frequent result of that
kind of models is condensation, i.e. concentration of all available wealth in just one or a few agents. This result
corresponds to a kind of equipartition of poverty: all agents (except for a set of zero measure) possess zero wealth
while few ones concentrate all the resources. In any case, an almost ordered state is obtained, and this is a state of
equilibrium, since agents with zero wealth cannot participate in further exchanges. The Gini coefficient [29] of this
state is equal to 1, indicating perfect inequality [13]. Several methods have been proposed to avoid this situation, for
instance, exchange rules where the poorer are favored [6, 13, 21, 23, 24] but in all circumstances the final state is one
with high inequality, i.e. very near condensation.
The exchange rules that produce condensation consider that, when two agents interact, the exchanged amount
∆w is proportional to the wealth of one of the participants or to both [22]. One particular example is ∆w =
min{(1 − β)w′
; (1 − β)w′′
}, where w′
and w′′
are the wealth of the two interacting agents, and β is the capital fraction
that the agents risk during an exchange [13, 21, 23]. It is worth noting that even approaching a condensed state,
in the intermediate stages the wealth distribution goes through a series of power law distributions where the Pareto
exponent increases as a function of time [23]. As real societies are not in a condensed state (since such a state would
represent the “thermal death” of the economy), some kind of regulation must be present to guarantee that resources
in the power law tail are re-injected back in the region of Gaussian distribution.
A few years ago we presented an alternative model for wealth distribution, the Conservative Exchange Market
Model (CEMM), inspired by the ideas of John Rawls [26] and Amartya Sen [27] and also on the Bak-Sneppen model
for extinction of species [28]. The main point of the model is that some kind of action should be taken to change the
state of the poorest agent in the society. The idea of a society that take measures in order to improve the situation
of the most impoverished is compatible with the propositions of John Rawls, in his book “A Theory of Justice” [26],
directed towards an inventive way of securing equality of opportunity as one of the basic principles of justice. He
asserts that no redistribution of resources within a state can occur unless it benefits the least well-off: and this should
be the only way to prevent the stronger (or richer) from overpowering the weaker (or poorer). The practical way to
carry out this proposition in a simulation was adapted from the Bak-Sneppen model of Self-Organized Criticality
applied to the extinction of biological species [28]. In this model the less fitted species disappears and is replaced by
new one with different fitness, and the appearance of this new species affects the environment changing the fitness
of the neighboring species. In 2003 we developed a similar model where the fitness is substituted by the assets of
a particular agent, and the model is now conservative, the difference between the new and the old wealth is taken
from (if positive) or given to (if negative) the assets of the neighbors of the poorest agent [14, 15]. The distribution
obtained follows an exponential law as a function of the square of wealth and a poverty line with finite wealth is also
obtained, i.e. the poorer agents do not have zero wealth (as it happens in the most exchange models). Also, the
Gini coefficient obtained is relatively low and compares well with the values of the Gini coefficient of some European
countries as Denmark or Sweden [15]. This suggest a path to decrease inequality in real societies [15].
Here we revisit this model including regulatory mechanisms in order to further diminish inequality. We will verify
that proportional taxes have a important effect on redistribution, while “uniform” taxes, like consumption taxes,
exhibit a lesser effect. But in both situations the impact on the poverty line and the Gini coefficient is really
impressive.
In the next section we present a very short review of the original model: the Conservative Exchange Market Model
(CEMM) and its main conclusions. Then, we introduce regulatory tools in the model in order to compare with the
4. 4
previous results: Two kind of regulatory mechanisms will be discussed and the obtained results will be compared.
Finally, in the last section we present our conclusions.
II. THE CONSERVATIVE EXCHANGE MARKET MODEL - CEMM
The Conservative Exchange Market Model (CEMM) [14] is a simple macroeconomic model that consists of a one-
dimensional lattice with N sites and periodic boundary conditions. That means that each site represents an economic
agent (individuals, industries or countries) linked to two neighbors. Periodic boundary conditions denote that the
lattice closes on itself like a ring, being the last site in the chain neighbor of the first one. To each agent it is assigned
some wealth-parameter that represents its welfare, like the GDP for countries or accumulated wealth for individuals.
One chooses an arbitrary initial configuration where the wealth is a number between 0 and 100 distributed randomly
and uniformly among agents. The dynamics of the system is supported on the idea that some measure should be taken
to modify the situation of the poorest agent. In this context, this process is simulated by an extreme dynamics [28]:
at each time step, the poorest agent, i.e., the one with the minimum wealth, will perform (or be the subject of) some
action trying to improve its economic state. Since the outcome of any such measure is uncertain, the minimum suffers
a random change in its wealth, ∆w [14, 15]. In the first version of the model it is assume that whatever wealth is
gained (or lost) by the poorest agent it will be at the expenses of its neighbors and that ∆w will be equally deducted
from (or credited to) its two nearest neighbors on the lattice, making the total wealth constant. Numerical simulations
on this model showed that, after a relatively long transient, the system arrives at a self-organized critical state with a
stationary wealth distribution (Fig. 1 of Ref. 14) in which almost all agents are above a certain threshold or poverty
line.
Another possibility is to subtract ∆w from two agents picked at random. This situation has also been considered [15,
20], it is the annealed or mean field version of the model, and corresponds to a situation in which the agents with
which the exchange takes place are chosen at random and not based on geographical proximity.
In the nearest-neighbor version of the model, one founds a minimum wealth or poverty line that is ηT ≈ 40% of
the maximum initial wealth and above this threshold the distribution of the wealth of the agents is an exponential
P(w) ≈ exp(−w2
/2σ2
), with σ = 22.8 [20]. The obtained Gini coefficient, G [29], is very low, of the order of G = 0.1.
In the mean-field case the model exhibits a lower threshold, ηT ≈ 20%, and, beyond it, also an exponential distribution
with a higher value of σ ≈ 56.7 [20] and of the Gini coefficient G ≈ 0.25.
In the present article we would like to discuss a similar model still using extremal dynamics, but making some
changes in the way the wealth is redistributed. In the original CEMM model [14, 15] the quantity of money of the
agent with the minimum wealth is changed to an arbitrary value between the limits {0, 100} and the difference between
the new and the old wealth, ∆w, is taken from the neighbors in the local version of the model or from agents picked
at random in the mean-field version.
Now, we will include regulations on the form of taxes, and we will consider two scenarios: 1) Uniform taxes and 2)
Proportional taxes.
III. CEMM WITH UNIFORM TAXES
Let us first consider the situation where the amount attributed to the poorest agent is equally collected from the
full population. In this way each of the agents (including the agent of minimum wealth) will contribute to improve the
situation of the less favored ones. This kind of redistribution simulates a tax that is the same for every agent. Taxes
on consumption, like TVA in Europe, ICM in Brazil, IVA in Argentine, etc., are of this type, every agent contributes
the same amount independent of his available resources. The obtained wealth distribution in this case of uniform
and global taxes, is of the same type as in the original model [14] but now the poverty line is lower than in the local
case (≈ 25% of the maximum wealth) and higher that in the mean-field case. Also, the Gini coefficient is in between
G ≈ 0.2. Finally the wealth distribution is almost linear and it is represented in Fig. 3, where we show the results
for a number of agents N = 104
and 107
time-steps (we have verified that in this limit the system has attained the
state of self-organize criticality and there are no more changes neither in the poverty line nor in the Gini coefficient).
So, a system with uniform taxes exhibit less inequality than the previous mean-field model, but higher than the local
model.
5. 5
20 40 60 80 100
0
200
400
600
Agents
Wealth
Gini=0.2
FIG. 3: Plot of the wealth distribution for N = 10000 agents considering that taxes are uniformly distributed among all agents.
The poverty line is ηT = 25
0 2000 4000 6000 8000 10000
20
40
60
80
100
Wealth
Agents
Poverty Line
FIG. 4: Plot of the wealth of each agent in a system with 10000 agents with local proportional taxes. “Islands” of poverty and
affluence are observed, but the poverty line is high, of the order of 40
IV. CEMM WITH PROPORTIONAL TAXES
Let us now assume a more equitable way to apply taxes: proportional taxes, equivalent to the taxes on income
or on fortune. Here we will assume a linear proportionality, but it is very easy to modify the model to consider
progressive or regressive taxation. As this case has not been previously studied we will consider both the local and
global scenarios.
A. Local taxes
The dynamics here is very similar to the original CEMM. In the original model if the agent with minimum wealth
changes his fortune by a quantity ∆w, this capital (positive or negative) is equally subtracted from his neighbors.
Each one of them have a deduction ∆w/p where p is the number of neighbors considered[21]. We will consider now
that the deduction is not equally performed but proportional to the wealth of the neighbor. We define a factor
6. 6
30 40 50 60 70 80 90 100
0
200
400
600
800
1000
1200
1400
1600
Agents
Wealth
Gini=0.1
FIG. 5: Histogram of the wealth distribution with local proportional taxes. There is a strong middle class and the distribution
is exponential, as if refs. 14, 21
λ = ∆w/Knn where Knn is the total capital of the p neighbors. Each neighbor will suffer a subtraction (if ∆w > 0)
or addition (if ∆w < 0) on his wealth equal to λwi. That means that if the i-agent is one of the neighbors his wealth
at time (t + 1) will be
wi(t + 1) = (1 − λ)wi(t), (1)
i.e., his wealth will be reduced if ∆w > 0 or will increase if ∆w < 0. It is straightforward to verify that with this
condition the total wealth is conserved.
In Fig. 4 we have represented the wealth of the agents in a scale from 0 to 100. We have again considered 104
agents and p = 4 neighbors. Because the transfer of wealth is local, some “geographical” segregation appears in the
wealth distribution. This is clear in Fig. 4 where it is possible to see that the poverty line is relatively higher than
in the previous situation, of the order of 40, but also that there are geographical differences: on the left one observes
a “burst” of poor agents below the poverty line, but it is also possible to see that there are wealthy and middle
class regions in the plot, indicating that the dynamics induces regional differences. Certainly this kind of behavior
should be visible in a more emphatic way if one consider a complex lattice instead of the very simple one-dimensional
model that we describe here. In any case, the Gini coefficient is very low, of the order of G = 0.1, as for the local
model previously studied [20]. Therefore, even if the results are encouraging they are not very different from the
original CEMM where the difference received by the poorest agent were equally shared (and not proportional) by the
neighbors. Also, the wealth distribution is exponential, as in ref. [21] and it is represent5ed in Fig. 5: there is a peak
in the number of agents just above the poverty line, and then the number of agents decreases exponentially as the
wealth increases.
It is when one examines the application of global taxes that differences appear, as well in the poverty line and the
Gini coefficient than in the type of distribution.
B. Global taxes
Let us now consider that the amount ∆w received by (or deduced from) the poorest agent is subtracted from (or
added to) all the agents (including the recipient) but in proportion to their wealth. Equation (1) is still valid but now
λ = ∆w/Ktot, being Ktot the wealth of the full society.
Globalization has its shortcomings when compared to local models but still the results are impressive. The poverty
line is a little lower than in the local case, 32 compared to 40 and the Gini coefficient higher, of the order of G = 0.16.
We have represented on Fig. 6 the wealth of each agent and we can verify that the distribution is more homogeneous
7. 7
0 2000 4000 6000 8000 10000
20
30
40
50
60
70
80
90
100
Poverty Line
Wealth
Agents
FIG. 6: Plot of the wealth of each agent in a system with 10000 agents, for the case of global proportional taxes. The distribution
is uniform, without islands, and the poverty line is of the order of 32
from a geographical point of view. However, if one examines the wealth distribution, plotted on Fig. 7, the figure
suggest a power law distribution, even if we do not have enough statistics, particularly for the tail of affluent agents,
to determine the value of the exponent. In any case the distribution is not exponential and this is an expected when a
multiplicative redistribution is considered. Finally if we compare the distributions for local taxes (Fig. 5) and global
taxes (Fig. 7) it evident that the number of poor agents is lower and the number of middle class agents is higher in
the situation with global taxes, while the poverty line is higher in the case of local taxes.
Then when proportional taxes are applied to the full population, each agent contributes with a very small amount,
but we obtain a society where there are no zero-wealth agents, neither geographical disparities, as it can be observed
in Fig. 6. Also, the wealth distribution is a power law, then the number of affluent agents is bigger than in the case
of an exponential distribution, nevertheless the Gini coefficient is still very low, as it is shown on Fig. 7.
V. DISCUSSION AND CONCLUSION
Inequalities are related to social and economic phenomena and its origin is a subject of much debate. The fraction of
rich and poor people in a country depends on the inequalities of the income distribution but also on the remuneration
of labor, profits, taxes, etc. The model here presented is certainly a very simplified one; for example, taxes do
not play just a redistributive objective, but also are used by governments to assure the infrastructure needed to
economic development. Nonetheless, in spite on its simplicity the present model describes a very strong redistributive
mechanism, that coincides with some public policies, like the “bolsa-familia” (family fellowship, allocate to very poor
family groups) in Brazil, or the small loans to jobless people in order to develop their own business. Even in the global
case, and with taxes proportional to the possessions of each agent, the contribution of each one of them is very small
but results in a low Gini coefficient, even lower than the one observed in the most egalitarian countries, like Denmark
or Japan (where the Gini coefficient is of the order of G = 0.25). Finally, the poverty line is much higher that the one
obtained with purely exchange models.
We remark also that the local version of the model generates a wealth distribution with a very low Gini index, so
very close to an full equitable society, but with geographical differences. In the global case, the Gini coefficient is a
little higher , but from a geographical point of view the distribution is more uniform, so maybe this is a point in favor
of globalization. And coming back to the inspiration of this work, it is interesting that the minimum dynamics favors
wealth redistribution when acting on the poorest agents, in the same sense defined by Rawls [26]. It seems that this
kind of dynamics, when applied to markets, is a road to ensure to the poorest agent a chance to improve his situation.
We conclude that the model, in spite of its simplicity, is able to reproduce some properties of modern economies,
particularly the wealth distribution of welfare societies, and it indicates a way to improve the situation of extreme
inequality in some countries with very high Gini indexes.
8. 8
40 60 80 100
0
200
400
600
800
1000
Agents
Wealth
Gini= 0.16
FIG. 7: Histogram of the wealth distribution in the case of global proportional taxes. There is still a strong middle class and
the distribution looks like a power law
Acknowledgements
We acknowledge fruitful discussions with G. Abramson, S. Gon¸calves, F. Laguna, S. Souza, R. Don´angelo and J.L.
Vega. We acknowledge financial support from Brazilian agencies CNPq and CAPES.
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