globals
[
max-grain ; maximum amount any patch can hold
gini-index-reserve
lorenz-points
collection
total-wealth1
Tax_Rate
a ; a binary variable to indicate when the Middle Class will side with the Lower Class
b ; a binary variable to indicate when the Middle Class will side with the Upper Class
p ; a proportion of the "wealth" held by the Upper Class (and Middle Class if b = 1)
rho ; a proportion of the population of the Lower Class (and Middle Class if a =1)
countopp1
countopp2
countrev1
countrev2
ETick ; Elapsed Time or Ticks
RichTick ; Elapsed Time or Ticks under Current Rich Control
PoorTick ; Elapsed Time or Ticks under Current Poor Control
RichAct ; a binary variable set to 1 when the Rich have successfully Oppressed.
PoorAct ; a binary variable set to 1 when the Poor have successfully Revolted.
]
patches-own
[
grain-here ; the current amount of grain on this patch
max-grain-here ; the maximum amount of grain this patch can hold
]
turtles-own
[
age ; how old a turtle is
wealth ; the amount of grain a turtle has
life-expectancy ; maximum age that a turtle can reach
metabolism ; how much grain a turtle eats each time
vision ; how many patches ahead a turtle can see
Preferred_Tax_Rate ; the preferred tax rate for each turtle
Resentment ; the resentment for each turtle due to distance from tax rate to preferred tax rate
]
;;;
;;; SETUP AND HELPERS
;;;
to setup
clear-all
;; set global variables to appropriate values
set max-grain 50
;; call other procedures to set up various parts of the world
setup-patches
setup-turtles
update-lorenz-and-gini
set countopp2 0 ; counter for number of times Oppress routine is used
set countrev2 0 ; counter for number of times Revolt routine is used
set ETick 0
set RichTick 0
set PoorTick 0
reset-ticks
end
;; set up the initial amounts of grain each patch has
to setup-patches
;; give some patches the highest amount of grain possible --
;; these patches are the "best land"
ask patches
[ set max-grain-here 0
if (random-float 100.0) <= percent-best-land
[ set max-grain-here max-grain
set grain-here max-grain-here ] ]
;; spread that grain around the window a little and put a little back
;; into the patches that are the "best land" found above
repeat 5
[ ask patches with [max-grain-here != 0]
[ set grain-here max-grain-here ]
diffuse grain-here 0.25 ]
repeat 10
[ diffuse grain-here 0.25 ] ;; spread the grain around some more
ask patches
[ set grain-here floor grain-here ;; round grain levels to whole numbers
set max-grain-here grain-here ;; initial grain level is also maximum
recolor-patch ]
end
to recolor-patch ;; patch procedure -- use color to indicate grain level
set pcolor scale-color yellow grain-here 0 max-grain
end
;; set up the initial values for the turtle variables
to setup-turtles
set-default-shape turtles "person"
crt num-people
[ move-to one-of patches ;; put turtles on patch centers
set size 1.5 ;; easier to see
set-initial-turtle-vars
set age random life-expectancy ]
recolor-turtles
set Tax_Rate mean [Preferred_Tax_Rate] of turtles ;;Let the initial Tax Rate be set by the average Preferred Tax Rate of the turtles.
end
to set-initial-turtle-vars
set age 0
face one-of neighbors4
set life-expectancy life-expectancy-min +
random (life-expectancy-max - life-expectancy-min + 1)
set metabolism 1 + random metabolism-max
set wealth metabolism + random 50
set vision 1 + random max-vision
end
;; Set the class of the turtles -- if a turtle has less than a third
;; the wealth of the richest turtle, color it red. If between one
;; and two thirds, color it yellow. If over two thirds, color it blue.
to recolor-turtles
let max-wealth max [wealth] of turtles
ask turtles
[ ifelse (wealth <= max-wealth / 3)
[ set color red ]
[ ifelse (wealth <= (max-wealth * 2 / 3))
[ set color yellow ]
[ set color blue ] ] ]
;; once the turtles have been partitioned among their classes, set their preferred marginal tax rate. Upper
;; classes prefer lower marginal tax rates and Lower classes prefer higher marginal tax rates.
ask turtles
[ifelse (color = blue)
[set Preferred_Tax_Rate Upper_Tax_RateMin + random-float (Upper_Tax_RateMax - Upper_Tax_RateMin)]
[ifelse (color = yellow)
[set Preferred_Tax_Rate Mid_Tax_RateMin + random-float (Mid_Tax_RateMax - Mid_Tax_RateMin)]
[set Preferred_Tax_Rate Lower_Tax_RateMin + random-float (Lower_Tax_RateMax - Lower_Tax_RateMin)] ] ]
end
;;;
;;; GO AND HELPERS
;;;
to go
ask turtles
[ turn-towards-grain ] ;; choose direction holding most grain within the turtle's vision
harvest
ask turtles
[ move-eat-age-die ]
recolor-turtles
;; grow grain every grain-growth-interval clock ticks
if ticks mod grain-growth-interval = 0
[ ask patches [ grow-grain ] ]
;; If the Tax Rate goes over 90%, set the Tax Rate = 90%.
;; If the Tax Rate is under 90%, increase (or decrease) the Tax Rate by an exponential factor for consectutive Ticks under Lower (or Upper) control.
if (Tax_Rate > 0.9)
[set Tax_Rate 0.9]
if (Tax_Rate < 0.9)
[set Tax_Rate Tax_Rate * ((1.48 - exp (-0.75 * PoorTick)) * PoorAct + (.5 + exp (-0.75 * RichTick)) * RichAct)]
set ETick ETick + 1
update-lorenz-and-gini
tick
end
;; determine the direction which is most profitable for each turtle in
;; the surrounding patches within the turtles' vision
to turn-towards-grain ;; turtle procedure
set heading 0
let best-direction 0
let best-amount grain-ahead
set heading 90
if (grain-ahead > best-amount)
[ set best-direction 90
set best-amount grain-ahead ]
set heading 180
if (grain-ahead > best-amount)
[ set best-direction 180
set best-amount grain-ahead ]
set heading 270
if (grain-ahead > best-amount)
[ set best-direction 270
set best-amount grain-ahead ]
set heading best-direction
end
to-report grain-ahead ;; turtle procedure
let total 0
let how-far 1
repeat vision
[ set total total + [grain-here] of patch-ahead how-far
set how-far how-far + 1 ]
report total
end
to grow-grain ;; patch procedure
;; if a patch does not have it's maximum amount of grain, add
;; num-grain-grown to its grain amount
if (grain-here < max-grain-here)
[ set grain-here grain-here + num-grain-grown
;; if the new amount of grain on a patch is over its maximum
;; capacity, set it to its maximum
if (grain-here > max-grain-here)
[ set grain-here max-grain-here ]
recolor-patch ]
end
;; each turtle harvests the grain on its patch. if there are multiple
;; turtles on a patch, divide the grain evenly among the turtles
to harvest
; have turtles harvest before any turtle sets the patch to 0
ask turtles
[ set wealth floor (wealth + (grain-here / (count turtles-here))) ]
;; now that the grain has been harvested, have the turtles make the
;; patches which they are on have no grain
ask turtles
[ set grain-here 0
recolor-patch ]
;; Now that the turtles have "wealth", the Tax Rate can be set.
;; First, calculate the amount of "resentment" for each turtle. If the mean "resentment" of the turtles within a class is greater than that class's threshold,
;; then have that class either Oppress (if Upper Class) or Revolt (if Lower Class). If the mean "resentment" of the turtles in the Middle Class exceeds their
;; threshold, then the Middle Class will either side with the Upper Class if their average Preferred Tax Rate is less than the actual Tax Rate
;; or side with the Lower Class if their average Preferred Tax Rate is greater than the actual Tax Rate.
set a 0
set b 0
ask turtles
[set Resentment (Preferred_Tax_Rate - Tax_Rate) ^ 2]
if ((mean [Resentment] of turtles with [color = yellow] > Mid_Resentment_Thresh) AND (mean [Preferred_Tax_Rate] of turtles with [color = yellow] > Tax_Rate))
[Side_Poor]
if ((mean [Resentment] of turtles with [color = yellow] > Mid_Resentment_Thresh) AND (mean [Preferred_Tax_Rate] of turtles with [color = yellow] < Tax_Rate))
[Side_Rich]
if (mean [Resentment] of turtles with [color = blue] > Upper_Resentment_Thresh)
[Oppress]
if (mean [Resentment] of turtles with [color = red] > Lower_Resentment_Thresh)
[Revolt]
set countopp2 countopp2 + countopp1
set countrev2 countrev2 + countrev1
set RichTick (RichTick + 1) * RichAct
set PoorTick (PoorTick + 1) * PoorAct
end
to move-eat-age-die ;; turtle procedure
fd 1
;; consume some grain according to metabolism
set wealth (wealth - metabolism)
;; grow older
set age (age + 1)
;; Now that the Tax Rate has been set, the redistribution of the wealth can begin.
;; First, find the total wealth of the Upper Classes. If the wealth of any turtle is greater than 40% of the total wealth of the Upper Classes,
;; then tax the wealth above that amount at the Tax Rate.
set total-wealth1 sum [ wealth] of turtles with [color = blue] / count turtles with [color = blue]
if (wealth > 0.4 * total-wealth1)
[ set wealth wealth - Tax_Rate * (wealth - 0.4 * total-wealth1)
set collection Tax_Rate * (wealth - 0.4 * total-wealth1)]
;; The wealth that is taxed is collected and distributed to the Lower and Middle Classes
if (wealth < 0.4 * total-wealth1)
[ set wealth wealth + collection / (count turtles with [color = red] + count turtles with [color = yellow]) ]
;; check for death conditions: if you have no grain or
;; you're older than the life expectancy or if some random factor
;; holds, then you "die" and are "reborn" (in fact, your variables
;; are just reset to new random values)
if (wealth < 0) or (age >= life-expectancy)
[ set-initial-turtle-vars ]
end
to Side_Poor
set a 1
end
to Side_Rich
set b 1
end
to Oppress
set p (sum [wealth] of turtles with [color = blue] + b * sum [wealth] of turtles with [color = yellow])/ sum [wealth] of turtles
if (random-float 1 < 1 - p)
[set Tax_Rate mean [Preferred_Tax_Rate] of turtles with [color = blue]
set countopp1 1
set RichAct 1
set PoorAct 0]
end
to Revolt
set rho (count turtles with [color = red] + a * count turtles with [color = yellow])/ count turtles
if (random-float 1 < 1 - rho)
[set Tax_Rate mean [Preferred_Tax_Rate] of turtles with [color = red]
set countrev1 1
set PoorAct 1
set RichAct 0]
end
;; this procedure recomputes the value of gini-index-reserve
;; and the points in lorenz-points for the Lorenz and Gini-Index plots
to update-lorenz-and-gini
let sorted-wealths sort [wealth] of turtles
let total-wealth sum sorted-wealths
let wealth-sum-so-far 0
let index 0
set gini-index-reserve 0
set lorenz-points []
;; now actually plot the Lorenz curve -- along the way, we also
;; calculate the Gini index.
;; (see the Info tab for a description of the curve and measure)
repeat num-people [
set wealth-sum-so-far (wealth-sum-so-far + item index sorted-wealths)
set lorenz-points lput ((wealth-sum-so-far / total-wealth) * 100) lorenz-points
set index (index + 1)
set gini-index-reserve
gini-index-reserve +
(index / num-people) -
(wealth-sum-so-far / total-wealth)
]
end
; Copyright 1998 Uri Wilensky.
; See Info tab for full copyright and license.
@#$#@#$#@
GRAPHICS-WINDOW
537
47
1236
767
25
25
13.51
1
10
1
1
1
0
1
1
1
-25
25
-25
25
1
1
1
ticks
30.0
BUTTON
8
256
84
289
setup
setup
NIL
1
T
OBSERVER
NIL
NIL
NIL
NIL
1
BUTTON
105
256
175
289
go
go
T
1
T
OBSERVER
NIL
NIL
NIL
NIL
1
SLIDER
8
72
176
105
max-vision
max-vision
1
15
5
1
1
NIL
HORIZONTAL
SLIDER
8
301
176
334
grain-growth-interval
grain-growth-interval
1
10
4
1
1
NIL
HORIZONTAL
SLIDER
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106
176
139
metabolism-max
metabolism-max
1
25
15
1
1
NIL
HORIZONTAL
SLIDER
8
38
176
71
num-people
num-people
2
1000
367
1
1
NIL
HORIZONTAL
SLIDER
8
208
176
241
percent-best-land
percent-best-land
5
25
20
1
1
%
HORIZONTAL
SLIDER
8
174
176
207
life-expectancy-max
life-expectancy-max
1
100
83
1
1
NIL
HORIZONTAL
PLOT
1
426
253
606
Class Plot
Time
Turtles
0.0
50.0
0.0
250.0
true
true
"set-plot-y-range 0 num-people" ""
PENS
"low" 1.0 0 -2674135 true "" "plot count turtles with [color = red]"
"mid" 1.0 0 -1184463 true "" "plot count turtles with [color = yellow]"
"up" 1.0 0 -13345367 true "" "plot count turtles with [color = blue]"
SLIDER
8
335
176
368
num-grain-grown
num-grain-grown
1
10
4
1
1
NIL
HORIZONTAL
SLIDER
8
140
176
173
life-expectancy-min
life-expectancy-min
1
100
1
1
1
NIL
HORIZONTAL
PLOT
262
429
474
609
Class Histogram
Classes
Turtles
0.0
3.0
0.0
250.0
false
false
"set-plot-y-range 0 num-people" ""
PENS
"default" 1.0 1 -2674135 true "" "plot-pen-reset\nset-plot-pen-color red\nplot count turtles with [color = red]\nset-plot-pen-color yellow\nplot count turtles with [color = yellow]\nset-plot-pen-color blue\nplot count turtles with [color = blue]"
PLOT
197
223
431
423
Lorenz Curve
Pop %
Wealth %
0.0
100.0
0.0
100.0
false
true
"" ""
PENS
"lorenz" 1.0 0 -2674135 true "" "plot-pen-reset\nset-plot-pen-interval 100 / num-people\nplot 0\nforeach lorenz-points plot"
"equal" 100.0 0 -16777216 true "plot 0\nplot 100" ""
PLOT
197
37
431
217
Gini-Index v. Time
Time
Gini
0.0
50.0
0.0
1.0
true
false
"" ""
PENS
"default" 1.0 0 -13345367 true "" "plot (gini-index-reserve / num-people) / 0.5"
PLOT
11
624
211
774
Taxes
Time
Taxes
0.0
10.0
0.0
10.0
true
false
"" ""
PENS
"default" 1.0 0 -16777216 true "" "plot collection"
PLOT
223
620
423
770
Average Wealth of Upper Classes
Time
Wealth
0.0
10.0
0.0
10.0
true
true
"" ""
PENS
"Upper" 1.0 0 -13345367 true "" "plot total-wealth1"
"Middle" 1.0 0 -1184463 true "" "plot sum [ wealth] of turtles with [color = yellow] / count turtles with [color = yellow]"
"Lower" 1.0 0 -2674135 true "" "plot sum [ wealth] of turtles with [color = red] / count turtles with [color = red]"
SLIDER
449
54
482
204
Upper_Tax_RateMin
Upper_Tax_RateMin
0
1
0.04
.01
1
NIL
VERTICAL
SLIDER
491
51
524
205
Upper_Tax_RateMax
Upper_Tax_RateMax
0
1
0.07
.01
1
NIL
VERTICAL
SLIDER
450
215
483
365
Mid_Tax_RateMin
Mid_Tax_RateMin
0
1
0.3
.01
1
NIL
VERTICAL
SLIDER
494
215
527
367
Mid_Tax_RateMax
Mid_Tax_RateMax
0
1
0.5
.01
1
NIL
VERTICAL
SLIDER
449
370
482
520
Lower_Tax_RateMin
Lower_Tax_RateMin
0
1
0.32
.01
1
NIL
VERTICAL
SLIDER
494
371
527
521
Lower_Tax_RateMax
Lower_Tax_RateMax
0
1
0.61
.01
1
NIL
VERTICAL
PLOT
6
783
211
940
TaxRate_Time
Time
Tax Rate
0.0
10.0
0.0
1.0
true
false
"" ""
PENS
"default" 1.0 0 -16777216 true "" "plot Tax_Rate"
SLIDER
235
801
268
993
Upper_Resentment_Thresh
Upper_Resentment_Thresh
0
0.2
0.096
0.002
1
NIL
VERTICAL
SLIDER
294
801
327
980
Mid_Resentment_Thresh
Mid_Resentment_Thresh
0
0.5
0.25
0.005
1
NIL
VERTICAL
SLIDER
356
805
389
997
Lower_Resentment_Thresh
Lower_Resentment_Thresh
0
0.2
0.036
0.002
1
NIL
VERTICAL
@#$#@#$#@
## WHAT IS IT?
This model simulates the distribution of wealth. "The rich get richer and the poor get poorer" is a familiar saying that expresses inequity in the distribution of wealth. In this simulation, we see Pareto's law, in which there are a large number of "poor" or red people, fewer "middle class" or green people, and many fewer "rich" or blue people.
## HOW IT WORKS
This model is adapted from Epstein & Axtell's "Sugarscape" model. It uses grain instead of sugar. Each patch has an amount of grain and a grain capacity (the amount of grain it can grow). People collect grain from the patches, and eat the grain to survive. How much grain each person accumulates is his or her wealth.
The model begins with a roughly equal wealth distribution. The people then wander around the landscape gathering as much grain as they can. Each person attempts to move in the direction where the most grain lies. Each time tick, each person eats a certain amount of grain. This amount is called their metabolism. People also have a life expectancy. When their lifespan runs out, or they run out of grain, they die and produce a single offspring. The offspring has a random metabolism and a random amount of grain, ranging from the poorest person's amount of grain to the richest person's amount of grain. (There is no inheritance of wealth.)
To observe the equity (or the inequity) of the distribution of wealth, a graphical tool called the Lorenz curve is utilized. We rank the population by their wealth and then plot the percentage of the population that owns each percentage of the wealth (e.g. 30% of the wealth is owned by 50% of the population). Hence the ranges on both axes are from 0% to 100%.
Another way to understand the Lorenz curve is to imagine that there are 100 dollars of wealth available in a society of 100 people. Each individual is 1% of the population and each dollar is 1% of the wealth. Rank the individuals in order of their wealth from greatest to least: the poorest individual would have the lowest ranking of 1 and so forth. Then plot the proportion of the rank of an individual on the y-axis and the portion of wealth owned by this particular individual and all the individuals with lower rankings on the x-axis. For example, individual Y with a ranking of 20 (20th poorest in society) would have a percentage ranking of 20% in a society of 100 people (or 100 rankings) --- this is the point on the y-axis. The corresponding plot on the x-axis is the proportion of the wealth that this individual with ranking 20 owns along with the wealth owned by the all the individuals with lower rankings (from rankings 1 to 19). A straight line with a 45 degree incline at the origin (or slope of 1) is a Lorenz curve that represents perfect equality --- everyone holds an equal part of the available wealth. On the other hand, should only one family or one individual hold all of the wealth in the population (i.e. perfect inequity), then the Lorenz curve will be a backwards "L" where 100% of the wealth is owned by the last percentage proportion of the population. In practice, the Lorenz curve actually falls somewhere between the straight 45 degree line and the backwards "L".
For a numerical measurement of the inequity in the distribution of wealth, the Gini index (or Gini coefficient) is derived from the Lorenz curve. To calculate the Gini index, find the area between the 45 degree line of perfect equality and the Lorenz curve. Divide this quantity by the total area under the 45 degree line of perfect equality (this number is always 0.5 --- the area of 45-45-90 triangle with sides of length 1). If the Lorenz curve is the 45 degree line then the Gini index would be 0; there is no area between the Lorenz curve and the 45 degree line. If, however, the Lorenz curve is a backwards "L", then the Gini-Index would be 1 --- the area between the Lorenz curve and the 45 degree line is 0.5; this quantity divided by 0.5 is 1. Hence, equality in the distribution of wealth is measured on a scale of 0 to 1 --- more inequity as one travels up the scale. Another way to understand (and equivalently compute) the Gini index, without reference to the Lorenz curve, is to think of it as the mean difference in wealth between all possible pairs of people in the population, expressed as a proportion of the average wealth (see Deltas, 2003 for more).
## HOW TO USE IT
The PERCENT-BEST-LAND slider determines the initial density of patches that are seeded with the maximum amount of grain. This maximum is adjustable via the MAX-GRAIN variable in the SETUP procedure in the procedures window. The GRAIN-GROWTH-INTERVAL slider determines how often grain grows. The NUM-GRAIN-GROWN slider sets how much grain is grown each time GRAIN-GROWTH-INTERVAL allows grain to be grown.
The NUM-PEOPLE slider determines the initial number of people. LIFE-EXPECTANCY-MIN is the shortest number of ticks that a person can possibly live. LIFE-EXPECTANCY-MAX is the longest number of ticks that a person can possibly live. The METABOLISM-MAX slider sets the highest possible amount of grain that a person could eat per clock tick. The MAX-VISION slider is the furthest possible distance that any person could see.
GO starts the simulation. The TIME ELAPSED monitor shows the total number of clock ticks since the last setup. The CLASS PLOT shows a line plot of the number of people in each class over time. The CLASS HISTOGRAM shows the same information in the form of a histogram. The LORENZ CURVE plot shows the Lorenz curve of the population at a particular time as well as the 45 degree line of equality. The GINI-INDEX V. TIME plot shows the Gini index at the time that the Lorenz curve is drawn. The LORENZ CURVE and the GINI-INDEX V. TIME plots are updated every 5 passes through the GO procedure.
## THINGS TO NOTICE
Notice the distribution of wealth. Are the classes equal?
This model usually demonstrates Pareto's Law, in which most of the people are poor, fewer are middle class, and very few are rich. Why does this happen?
Do poor families seem to stay poor? What about the rich and the middle class people?
Watch the CLASS PLOT to see how long it takes for the classes to reach stable values.
As time passes, does the distribution get more equalized or more skewed? (Hint: observe the Gini index plot.)
Try to find resources from the U.S. Government Census Bureau for the U.S.'s Gini coefficient. Are the Gini coefficients that you calculate from the model comparable to those of the Census Bureau? Why or why not?
Is there a trend in the plotting of the Gini index with respect to time? Does the plot oscillate? Or does it stabilize to a certain number?
## THINGS TO TRY
Are there any settings that do not result in a demonstration of Pareto's Law?
Play with the NUM-GRAIN-GROWN slider, and see how this affects the distribution of wealth.
How much does the LIFE-EXPECTANCY-MAX matter?
Change the value of the MAX-GRAIN variable (in the `setup` procedure in the Code tab). Do outcomes differ?
Experiment with the PERCENT-BEST-LAND and NUM-PEOPLE sliders. How do these affect the outcome of the distribution of wealth?
Try having all the people start in one location. See what happens.
Try setting everyone's initial wealth as being equal. Does the initial endowment of an individual still arrive at an unequal distribution in wealth? Is it less so when setting random initial wealth for each individual?
Try setting all the individual's wealth and vision to being equal. Do you still arrive at an unequal distribution of wealth? Is it more equal in the measure of the Gini index than with random endowments of vision?
## EXTENDING THE MODEL
Have each newborn inherit a percentage of the wealth of its parent.
Add a switch or slider which has the patches grow back all or a percentage of their grain capacity, rather than just one unit of grain.
Allow the grain to give an advantage or disadvantage to its carrier, such as every time some grain is eaten or harvested, pollution is created.
Would this model be the same if the wealth were randomly distributed (as opposed to a gradient)? Try different landscapes, making SETUP buttons for each new landscape.
Try allowing metabolism or vision or another characteristic to be inherited. Will we see any sort of evolution? Will the "fittest" survive?
Try adding in seasons into the model. That is to say have the grain grow better in a section of the landscape during certain times and worse at others.
How could you change the model to achieve wealth equality?
The way the procedures are set up now, one person will sometimes follow another. You can see this by setting the number of people relatively low, such as 50 or 100, and having a long life expectancy. Why does this phenomenon happen? Try adding code to prevent this from occurring. (Hint: When and how do people check to see which direction they should move in?)
## NETLOGO FEATURES
Examine how the landscape of color is created --- note the use of the `scale-color` reporter. Each patch is given a value, and `scale-color` reports a color for each patch that is scaled according to its value.
Note the use of lists in drawing the Lorenz Curve and computing the Gini index.
## CREDITS AND REFERENCES
This model is based on a model described in Epstein, J. & Axtell R. (1996). Growing Artificial Societies: Social Science from the Bottom Up. Washington, DC: Brookings Institution Press.
For an explanation of Pareto's Law, see http://www.xrefer.com/entry/445978.
For more on the calculation of the Gini index see:
* Deltas, George (2003). The Small-Sample Bias of the Gini Coefficient: Results and Implications for Empirical Research. The Review of Economics and Statistics, February 2003, 85(1): 226-234.
In particular, note that if one is calculating the Gini index of a sample for the purpose of estimating the value for a larger population, a small correction factor to the method used here may be needed for small samples.
## HOW TO CITE
If you mention this model in a publication, we ask that you include these citations for the model itself and for the NetLogo software:
* Wilensky, U. (1998). NetLogo Wealth Distribution model. http://ccl.northwestern.edu/netlogo/models/WealthDistribution. Center for Connected Learning and Computer-Based Modeling, Northwestern Institute on Complex Systems, Northwestern University, Evanston, IL.
* Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern Institute on Complex Systems, Northwestern University, Evanston, IL.
## COPYRIGHT AND LICENSE
Copyright 1998 Uri Wilensky.
![CC BY-NC-SA 3.0](http://i.creativecommons.org/l/by-nc-sa/3.0/88x31.png)
This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.
Commercial licenses are also available. To inquire about commercial licenses, please contact Uri Wilensky at uri@northwestern.edu.
This model was created as part of the project: CONNECTED MATHEMATICS: MAKING SENSE OF COMPLEX PHENOMENA THROUGH BUILDING OBJECT-BASED PARALLEL MODELS (OBPML). The project gratefully acknowledges the support of the National Science Foundation (Applications of Advanced Technologies Program) -- grant numbers RED #9552950 and REC #9632612.
This model was converted to NetLogo as part of the projects: PARTICIPATORY SIMULATIONS: NETWORK-BASED DESIGN FOR SYSTEMS LEARNING IN CLASSROOMS and/or INTEGRATED SIMULATION AND MODELING ENVIRONMENT. The project gratefully acknowledges the support of the National Science Foundation (REPP & ROLE programs) -- grant numbers REC #9814682 and REC-0126227. Converted from StarLogoT to NetLogo, 2001.
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