; Throwing Coins - Inequality and Tax.nlogo; Rupert Nagler Jan 2020 globals [ gini-index-reserve ; actual Gini % lorenz-points ; list of Lorenz points coins ; number of thrown coins tails ; number of tails - results ] turtles-own [ wealth ; actual wealth of turtle tax ; actual amount of wealth tax turtle has payed ] to setup clear-all ask patches [set pcolor 104] setup-turtles set coins 0 set tails 0 update-lorenz-and-gini reset-ticks end to setup-turtles create-turtles num-turtles [ set heading 0 set color yellow set shape "circle" ifelse random-init-wealth? [; random distributuion set wealth random-float init-wealth ][; equal distribution set wealth init-wealth ] set tax 0 ; place turtle on plain according id(own) on x-axsis and wealth on y-axsis setxy (who / num-turtles * 100) wealth ] end to go playing taxing move-turtles if not any? turtles [stop] update-lorenz-and-gini tick end to playing ; each turtle throws coin ask turtles [ ; leverage is the fraction of wealth to bet set wealth win (wealth * leverage) + wealth * (1 - leverage); compute new wealth on thrown coin ] end to-report win [stake] ; function to compute new wealth according to coin throw with multiplicative and additive win let m mult-heads ; initialise with win factors let a add-heads set coins coins + 1 if one-of list false true [ ; throw coin, in case loose change to loose factors set m mult-tails set a add-tails set tails tails + 1 ] report (stake * m) + a end to taxing if tax-factor > 0 [ ; do we have to compute taxes? let notax-turtles [self] of no-turtles ; empty unsorted list of turtles let sumtax 0 ask turtles [ ; pay wealth tax ifelse wealth > tax-limit [ ; is there a tax to pay? set tax wealth * tax-factor set wealth wealth - tax ; turtle pays tax set sumtax sumtax + tax ; add to total tax collected ] [ set tax 0 set notax-turtles lput self notax-turtles ; add to list of notax-turtles ] ] let count-notax-turtles length notax-turtles ; number of notax-turtles ifelse redist-all? or (count-notax-turtles <= 0) [ ; do we have to redistribute to all turtles? let mtax (sumtax / count turtles) ; divide total tax between all turtles ask turtles [ ; redistribute tax to all turtles set wealth wealth + mtax ; redistribute ] ] [; divide total tax between all no-tax-turtles let mtax (sumtax / count-notax-turtles) ask turtle-set notax-turtles [ ; changes list into agentset set wealth wealth + mtax ; redistribute ] ] ] end to move-turtles ; according to new wealth ask turtles [ if turtles-die? [ ; should bancrupt turtles die? if wealth < 1.0E-10 [die] ] set ycor (wealth + min [wealth] of turtles) / max [wealth] of turtles * 100 ] end to update-lorenz-and-gini ; recompute value of gini-index-reserve and the points in lorenz-points for the Lorenz and Gini-Index plots let sorted-wealths sort [wealth] of turtles let total-wealth sum sorted-wealths let wealth-sum-so-far 0 let index 0 let c-turtles count turtles set gini-index-reserve 0 set lorenz-points [] ; now actually plot the Lorenz curve -- along the way, we also calculate the Gini index repeat c-turtles [ 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 / c-turtles) - (wealth-sum-so-far / total-wealth) ] end @#$#@#$#@ GRAPHICS-WINDOW 370 10 883 524 -1 -1 5.0 1 10 1 1 1 0 1 1 1 0 100 0 100 1 1 1 ticks 30.0 BUTTON 180 10 235 43 NIL setup NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 240 10 295 43 go go T 1 T OBSERVER NIL NIL NIL NIL 0 SLIDER 180 95 352 128 mult-heads mult-heads 0.1 10.0 1.5 0.1 1 NIL HORIZONTAL SLIDER 0 95 172 128 mult-tails mult-tails 0.1 10.0 0.6 0.1 1 NIL HORIZONTAL MONITOR 880 480 1075 525 min-wealth min [wealth] of turtles 17 1 11 MONITOR 880 10 1080 55 max-wealth max [wealth] of turtles 17 1 11 SLIDER 180 135 352 168 add-heads add-heads -1 1 0.0 0.1 1 NIL HORIZONTAL SLIDER 0 135 172 168 add-tails add-tails -1 1 0.0 0.1 1 NIL HORIZONTAL PLOT 0 275 370 570 Plot min max mean and median wealth time log 10 wealth 0.0 10.0 0.0 10.0 true true "" "" PENS "min" 1.0 0 -13840069 true "" "let aw min [wealth] of turtles\nifelse (aw > 1.0E-12)\n [plot-pen-down plot log aw 10]\n [plot-pen-up plot 0]" "max" 1.0 0 -2674135 true "" "let aw max [wealth] of turtles\nifelse (aw > 1.0E-12)\n [plot-pen-down plot log aw 10]\n [plot-pen-up plot 0]" "mean" 1.0 0 -4079321 true "" "let aw mean [wealth] of turtles\nifelse (aw > 1.0E-12)\n [plot-pen-down plot log aw 10]\n [plot-pen-up plot 0]" "med" 1.0 0 -11033397 true "" "let aw median [wealth] of turtles\nifelse (aw > 1.0E-12)\n [plot-pen-down plot log aw 10]\n [plot-pen-up plot 0]" PLOT 1145 10 1495 570 Histogram wealth distribution wealth per bin # turtles in bin 0.0 100.0 0.0 1000.0 false false "set-plot-pen-mode 1\nset-plot-y-range 0 num-turtles\nset-histogram-num-bars 20\n" "set-plot-x-range (round (min [wealth] of turtles)) (round (max [wealth] of turtles + 1))\nset-plot-y-range 0 count turtles\nset-histogram-num-bars 20" PENS "live-turtles" 1.0 1 -16777216 true "" "histogram [wealth] of turtles" MONITOR 0 225 170 270 mean-wealth mean [wealth] of turtles 2 1 11 SLIDER 970 525 1142 558 tax-factor tax-factor 0 1 0.0 0.1 1 NIL HORIZONTAL MONITOR 700 530 840 575 mean-tax mean [tax] of turtles 3 1 11 SLIDER 970 560 1142 593 tax-limit tax-limit 0 1000 500.0 100 1 NIL HORIZONTAL BUTTON 295 10 350 43 go 1 go NIL 1 T OBSERVER NIL NIL NIL NIL 0 SLIDER 0 10 172 43 num-turtles num-turtles 100 3000 1000.0 100 1 NIL HORIZONTAL MONITOR 595 530 685 575 turtles alive count turtles 17 1 11 MONITOR 500 530 593 575 turtles dead num-turtles - count turtles 17 1 11 SWITCH 375 530 498 563 turtles-die? turtles-die? 0 1 -1000 MONITOR 0 175 75 220 # coins coins 17 1 11 MONITOR 75 175 175 220 coins/tails tails / coins 17 1 11 PLOT 890 60 1140 225 Lorenz Curve % Population % total Wealth 0.0 100.0 0.0 100.0 false false "" "" PENS "Lorenz" 1.0 0 -2674135 true "" "plot-pen-reset\nset-plot-pen-interval 100 / count turtles\nplot 0\nforeach lorenz-points plot" "pen-1" 100.0 0 -7500403 true "plot 0 plot 100" "" PLOT 890 235 1140 470 Gini-Index v. Time Time Gini 0.0 50.0 0.0 1.0 true false "" "" PENS "default" 1.0 0 -5298144 true "" "plot (gini-index-reserve / count turtles) / 0.5" SWITCH 0 50 170 83 random-init-wealth? random-init-wealth? 1 1 -1000 SLIDER 180 50 350 83 init-wealth init-wealth 1 100 1.0 1 1 NIL HORIZONTAL SWITCH 845 530 962 563 redist-all? redist-all? 0 1 -1000 SLIDER 180 180 352 213 leverage leverage 0.1 5.0 1.0 0.1 1 NIL HORIZONTAL MONITOR 180 225 350 270 median wealth median [wealth] of turtles 17 1 11 @#$#@#$#@ # Throwing Coins - Inequality and Tax.nlogo Author: Rupert Nagler, Jan 2020, nagler@idi.co.at ## WHAT IS IT? Simulation of a coin game based on multiplicative growth. 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. ## 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? ## 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 on varying upper and lower bounds, ## RELATED MODELS http://ccl.northwestern.edu/netlogo/models/WealthDistribution http://ccl.northwestern.edu/netlogo/models/Sugarscape3WealthDistribution ## CREDITS & REFERENCES credit: computation of lorenz curve and gini index copied from: NetLogo models WealthDistribution in-depth readings: 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 An evolutionary advantage of cooperation, Ole Peters and Alexander Adamou, 2018 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 ## COPYRIGHT Copyright 2020 Rupert Nagler. All rights reserved. Permission to use, modify or redistribute this model is hereby granted, provided that both of the following requirements are followed: * this copyright notice is included. * this model will not be redistributed for profit without permission from Rupert Nagler. 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