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### Lorenz curve

BehaviourComposer: ignore everything before this.

Draws a Lorenz curve that visualises the distribution of wealth. It also computes the Gini coefficient which measures the inequality of the distribution. Note that this requires a graphing area (default name is "Wealth Distribution" ). It can be specified using Empty Lorenz curve.

Begin micro-behaviour:

Begin description:

Draw Lorenz curve and update Gini coefficient.

End description

Draw Lorenz curve

Begin NetLogo code:

```substitute-text-area-for population-expression all-individuals
substitute-text-area-for wealth-expression my-wealth
substitute-text-area-for pen-color-expression round time mod 145
substitute-text-area-for lorenz-plot-name Wealth Distribution
let population population-expression
let wealth-attribute "wealth-expression"
let population-count count population
if population-count > 2 [
set-current-plot "lorenz-plot-name"
auto-plot-off
; draw the perfectly equitable distribution first
set-plot-pen-color 0
set-plot-x-range 0 100
set-plot-y-range 0 100
plot-pen-up
plotxy 0 0
plot-pen-down
plotxy 100 100
plotxy 0 0
set-plot-pen-color pen-color-expression
let individuals-by-wealth
sort-on [runresult wealth-attribute] population
let total-wealth sum [runresult wealth-attribute] of population
if total-wealth = 0 [stop]
let one-percent-of-the-population population-count / 100
let percent-of-population 0
let gini-coefficient 0
while [percent-of-population < 100]
[let agents-in-percent-of-population
sublist individuals-by-wealth
0 round (percent-of-population * one-percent-of-the-population)
let wealth-of-percent-of-population 0
forEach agents-in-percent-of-population
[set wealth-of-percent-of-population
wealth-of-percent-of-population + [runresult wealth-attribute] of ?]
let percent-of-wealth wealth-of-percent-of-population * 100 / total-wealth
set gini-coefficient gini-coefficient +
percent-of-population - percent-of-wealth
plotxy percent-of-population
percent-of-wealth
set percent-of-population percent-of-population + 1]
set my-gini-coefficient gini-coefficient / 5050]
```

End NetLogo code

## Variants

You can specify the population by editing the first text area. The second text area specifies what attribute of individuals is used comparisons. The third text area specifies the color of the plotting pen.

## How this works

After drawing the black diagonal line representing the equitable distribution it then picks a new pen colour and draws the Lorenz curve. It does this by sorting all the individuals by wealth and computing what percentage of the total that each percentile of the poorer individuals posses. While doing this it also computes the Gini coefficient by approximating it by summing the 100 rectangles between the Lorenz curve and the equitable distribution and dividing that by the area under the diagonal line (which is the sum of 1, 2, 3, ..., 98, 99, 100 or 5050).

## Related micro-behaviours

This needs an Empty Lorenz curve to specify an area where the curve is drawn.

## History

Draw Lorenz curve was rewritten by Ken Kahn on 27 January 2012

BehaviourComposer: ignore everything after this.