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## NetLogo User Community Models

# Multiplicative Growth and Inequality.nlogo

Author: Rupert Nagler, Jan 2020, nagler@idi.co.at

## WHAT IS IT?

Simulation of multiplicative vs additive growth and the impact on equality of wealth.

Our turtles assume they have all the same chance to get wealthy doing business. They are represented in their blue 2d-world as yellow circles. Their vertical position reflects their actual wealth while their horizontal position reflects their unique "who" number.

You will experience the difference between additive growth (as generated by labour income vs. consumption) and multiplicative growth (as generated by investments, interests, shares). Multiplicative growth will automaticly lead to an uneven distribution of wealth, while a **wrong ergodic hypothesis** will make you think - like most traditional economists - that everybody has equal chances in multiplicative economic growth.

You can explore the intrinsic effects why **"the rich get richer"** and the benefits of **cooperation** induced by a form of wealth tax. Lorenz Curve, Gini Coefficient and a histogram show the current distribution of the current wealth of each turtle.

## HOW IT WORKS

All turtles play by the same rules; nobody cheats or has more influence or better connections. In each round a percentage "leverage" of the current wealth of each turtle is multiplied by a normally distributed random variable with mean "mult-mean" and standard deviation "mult-sdev". Added to the wealth is another normally distributed random variable with mean "add-mean" and standard deviation "addd-sdev".

After the wealth of all turtles has been adopted, some redistribution in the form of a wealth tax may be applied: If "tax-factor" is > 0 and current wealth is > "tax-limit" a wealth tax (wealth * tax-factor) is subtracted. Then the collected wealth tax is redistributed evenly to all turtles or to the poor turtles below tax-limit, depending on the switch "redist-all?".
So you can simulate the effects of cooperation between players through risk-sharing.

## HOW TO USE IT

* Use the sliders to control the number of turtles "num-turtles" and the initial wealth "init-wealth".
* If you switch "random-init-wealth?" to "off" each turtle starts with equal "init-wealth" wealth; if you switch "random-init-wealth?" to "on" each turtle starts with a random wealth between 1 and "init-wealth".
* Set the fraction of current wealth to multiply in each round "leverage" (default: 1.0).
* Set the multiplicative parameters "mult-mean", "mult-sdev" (defaults: 1.05, 0.3) for the generation of the random normally distributed variable, by which the fraction of current wealth will be multiplied.
* Set the additive parameters "add-mean", "add-sdev" (defaults: 0.0, 0.0) for the generation of the random normally distributed variable, which will be added to current wealth.
* Optional set "tax-factor", "tax-limit", and "redist-all?"
* If you want bancrupt turtles to die, set "turtles-die?" to on.
* To setup the simulation, press "setup".
* To play one round press "go-1", to play as long as you wish, press "go".

## THINGS TO NOTICE

* You see all turtles sitting on the blue world area. Each turtle will go up or down vertically dependent of its current wealth after each tick.
* In the wealth-plot you see min, max, mean and median of the turtles wealth on a log10 scale.
* In the wealth-distribution histogramm you see the number of turtles in different classes of wealth.
* In monitor "richest 1% own wealth%" you see the actual % of total wealth owned by the richest 1% of turtles
* In the Lorenz Plot you see the actual shape of the Lorenz Curve.
* In the Gini Plot you see the value of the Gini Coefficient over time.

## THINGS TO TRY

* Compare the wealth-distribution for no multiplicative growth (set "mean-mult" to 1.0 and "sdev-mult" to 0.0) to other values of multiplicative growth (eg. 1.01, 0.2)
* Try different "tax-factor"s and "tax-limit"s, switch "redist-all?" on/off.
* What changes can you see in the histogram, Gini Plot and Lorenz Curve?

## EXTENDING THE MODEL

* better visualization ideas?
* turtles get children and die of age
* implement inheritance tax

## NETLOGO FEATURES

* plotting on a log scale,
* using turtle world to show turtle ranking by position,
* histogram with varying upper and lower bounds,

## RELATED MODELS

## CREDITS & REFERENCES

Credit: computation of Lorenz Curve and Gini index copied from:
NetLogo Wealth Distribution model. Wilensky, U. (1998). http://ccl.northwestern.edu/netlogo/models/WealthDistribution.
Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

Wikipedia: Distribution of wealth, retrieved 12/2019
https://en.wikipedia.org/wiki/Distribution_of_wealth

Wikipedia: Lorenz Curve, retrieved 12/2019
https://en.wikipedia.org/wiki/Lorenz_curve

Wikipedia: Gini Coefficient, retrieved 12/2019
https://en.wikipedia.org/wiki/Gini_coefficient

Wikipedia: Ergodic process, retrieved 12/2019
https://en.wikipedia.org/wiki/Ergodic_process

Ergodicity Economics, Ole Peters and Alexander Adamou, 2018
https://ergodicityeconomics.files.wordpress.com/2018/06/ergodicity_economics.pdf

Entrepreneurs, Chance, and the Deterministic Concentration of Wealth, Joseph E. Fargione u.a., 2011
https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0020728&type=printable

https://arxiv.org/pdf/1506.03414.pdf

Capital and Ideology, Thomas Piketty, 2019
http://piketty.pse.ens.fr/files/Piketty2020SlidesLongVersion.pdf

Farmers Fable: Simulation benefits of cooperation, retrieved 12/2019
https://www.farmersfable.org/

Gier, Marc Elsberg, novel, blanvalet 2019
https://gier-das-buch.de/gier.php