Multiplicative Growth and Inequality

This is a NetLogo simulation of multiplicative vs. additive growth and the impact on equality of wealth. You will explore the intrinsic effects why "the rich get richer" and the benefits of cooperation induced by a form of wealth tax.

To simply run this model click:
https://netlogoweb.org/web?https://dl.dropboxusercontent.com/s/u3d9vih6b0rw4va/Multiplicative%20Growth%20and%20Inequality.nlogo?dl=0
To start press "setup" and then "go".

To download this model and run with locally installed NetLogo:
https://dl.dropboxusercontent.com/s/u3d9vih6b0rw4va/Multiplicative%20Growth%20and%20Inequality.nlogo?dl=1
(recommended for best performance)

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

• Try different values for multiplicative growth "mult-mean", "mult-sdev" and additive growth "add-mean", "add-sdev",
• 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)
• Compare the wealth-distribution for no additive growth (set both "heads-add", "tails-add" to 0.0) to other values of additive growth (eg. 0.5, 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?

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.

Rich get Richer vs. Wealth Tax

"The rich get richer" - you can hear it everywhere today. But why? Playing with this NetLogo model you will learn and understand the intrinsic workings of multiplicative growth and a possible remedy.
We abstract economic transactions by simulating a bilateral coin game played pairwise by a set of turtles sitting on a green 2d-world. Each pair throws a coin and the winner gets a fraction of the looser's wealth, multiplied by arbitrary factors - modelling typical business life.

The vertical position reflects their actual wealth, the horizontal position the turtle’s unique who number. Currently playing pairs are pictured by a link.
Lorenz Curve, Gini Coefficient and a histogram show the actual distribution of wealth.

To simply run this model click:
https://netlogoweb.org/web?https://dl.dropboxusercontent.com/s/n6hfa3qgzbb4di8/Rich%20get%20Richer%20vs%20Wealth%20Tax.nlogo?dl=0
To start press "setup" and then "go".

To download this model and run with locally installed NetLogo:
NetLogo:https://dl.dropboxusercontent.com/s/n6hfa3qgzbb4di8/Rich%20get%20Richer%20vs%20Wealth%20Tax.nlogo?dl=1
(recommended for best performance)

WHAT IS IT?

We abstract economic transactions by simulating a bilateral coin game played pairwise by a set of turtles sitting on a blue 2d-world. The vertical position reflects their actual wealth, the horizontal position the turtle's unique who number. Currently playing pairs are pictured by a link. Lorenz Curve, Gini Coefficient and a histogram show the actual distribution of wealth. You can explore the effects of cumulative growth obscured by the misleading ergodic hypothesis in traditional economics and the benefits of cooperation induced by a form of wealth-tax.

HOW IT WORKS

• A fraction "select-ratio" of turtles throw a coin pairwise at each tick, the bet is a fraction "transfer-ratio" of the minimum of the wealth of both turtles.
• For the looser the bet is multiplied by "loose-mult" and then subtracted from his wealth. For the winner the bet is multiplied by "win-mult" and then added to his wealth.
• After all pairs have thrown their coins and their wealth was transferred, some redistribution in the form of a wealth-tax may be applied: If "tax-factor" is > 0 and 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 thru risk-sharing between players.

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 receives the equal "init-wealth" wealth. If you switch "random-init-wealth?" to "on" each turtle receives a random wealth between 1 and "init-wealth".
• Set the fraction of the minimum wealth of both turtles "leverage" to bet and the fraction of all turtles to play in one tick "selection-ratio".
• Set the multiplicative factors "loose-mult", "win-mult" (default: 1.0) to be applied to the transfer of the bet.
• Optional set a "tax-factor", "tax-limit", and "redist-all?"
• If you want bancrupt turtles to die, set "turtles-die?" to on.
• To initialize the simulation "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 black world area. Each turtle will go up or down vertically dependent of its current wealth after each tick.
• Each pair of turtles (link) engaged in throwing a coin is connected by a line.
• 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 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

• Try different values for multiplicative growth ("loose-mult", "win-mult"),
• Compare the wealth-distribution for no multiplicative growth (set both "loose-mult", "win-mult" to 1.0) to other values of multiplicative growth (eg. 0.6, 1.5)
• Try different "tax-factor"s and "tax-limits", switch "redist-all?" on/off.
• What effects can you see in the histogram, Gini Plot and Lorenz Curve?

RELATED MODELS

http://ccl.northwestern.edu/netlogo/models/WealthDistribution

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.

Idea influenced by Ole Peters, LML, see: https://ergodicityeconomics.files.wordpress.com/2018/06/ergodicity_economics.pdf

Throwing Coins - Inequality and Tax

Simulation of a multiplicative coin game in NetLogo

Based on the paper “Ergodicity Economics”, published 2018 by Ole Peters and Alexander Adamou @ London Mathematical Laboratory:

“We toss a coin, and if it comes up heads we increase your monetary wealth by 50%; if it comes up tails we reduce your wealth by 40%. We’re not only doing this once, we will do it many times. Would you submit your wealth to the dynamic our game will impose on it?”,
see:
https://ergodicityeconomics.files.wordpress.com/2018/06/ergodicity_economics.pdf

Our turtles assume they will get rich playing this game. They are presented in their blue 2d-world as yellow circles. Their vertical position reflects their actual wealth, the horizontal position is their unique “who” number.

You will experience their fate mislead by a wrong ergodic hypothesis for multiplicative growth - like most traditional economists. 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 their wealth.This is a NetLogo model simulating a coin game based on multiplicative growth.

To simply run this model click:
https://netlogoweb.org/web?https://dl.dropboxusercontent.com/s/brtpecs53p216fp/Throwing%20Coins%20-%20Inequality%20and%20Tax.nlogo?dl=0
To start press "setup" and then "go".

To download this model and run with locally installed NetLogo:https://dl.dropboxusercontent.com/s/brtpecs53p216fp/Throwing%20Coins%20-%20Inequality%20and%20Tax.nlogo?dl=1
(recommended for best performance)

HOW IT WORKS

All turtles play the coin game. Each of them throws a coin at each tick: If heads are shown, individual wealth is multiplied by "mult-heads" and "add-heads" is added. If tails are shown, individual wealth is multiplied by "mult-tails" and "add-tails" is added. After all turtles have thrown their coins and their wealth was adopted, some redistribution in the form of a wealth-tax may be applied: If "tax-factor" is > 0 and 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 sharing the risk between players.

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 receives the equal "init-wealth" wealth; if you switch "random-init-wealth?" to "on" each turtle receives a random wealth between 1 and "init-wealth".
• Set the fraction of actual wealth to bet by "leverage" (default: 1.0).
• Set the multiplicative factors "mult-heads", "mult-tails" (defaults: 0.6, 1.5) with which your bet will be multiplied in case of win / loss.
• Set the additive values "add-heads", "add-tails" (defaults: 0.0, 0.0) which will be added to your bet in case of win / loss.
• 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 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

• Try different values for multiplicative growth ("heads-mult", "tails-mult") and additive growth ("add-heads", "add-tails"),
• Compare the wealth-distribution for no multiplicative growth (set both "heads-mult", "tails-mult" to 1.0) to other values of multiplicative growth (eg. 0.6, 1.5)
• Compare the wealth-distribution for no additive growth (set both "heads-add", "tails-add" to 0.0) to other values of additive growth (eg. -0.2, 0.3)
• 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?

RELATED MODELS

http://ccl.northwestern.edu/netlogo/models/WealthDistribution

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.

Multiplicative Growth and Unequal Distribution of Wealth

Each process of multiplicative growth has the intrinsic property that wealth is accumulated by a very small group of "happy" players; they don't have to execute any power or tricky capitalist strategies.

We show this intrinsic property by a simple speadsheet simulation of multiplicative growth as a game: 50 players play 50 rounds.

To see a running example just click here.

Each player starts with equal wealth = 1 in round 0, his wealth in the next round is computed as newWealth = oldWealth * randomFactor;
randomFactor is a normally distributed random variable with mean = 1.05 and standard deviation = 0.2 . You may change mean and sdev in the green fields.

So in this simple spreadsheet growth is simulated by the formula
   newWealth = oldWealth * NORMINV(RANDOM();mean;sdev)

Recalculation for another set of randomFactors will start every minute.

Look at the Wealth Distribution Histogram and find out how many players are in the class with lowest wealth compared to the class with highest wealth.

Wealth tax and Heritage tax are profound measures for compensation and redistribution against growing inequality of wealth. See what happens if you apply a moderate wealth tax:

Simulation with wealth tax in Google Spreadsheets
(click link for direct view)

Simulation without wealth tax in Google Spreadsheets
(click link for direct view)

Simulation in Excel for download
(click link, then choose download button upper right corner)

Simulation in LibreOffice Calc ods for download
(click link, then choose download button upper right corner)

For a detailed discussion see:
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

and my paper in German:
Vorteile von Vermögenssteuern spielerisch erklärt