There's nothing boring about Tax!

Well the title might be a bit misleading, but I'll let you be the judge of that. A close friend and I were in the pub last week discussing the benefits of a tax system which, instead of being tiered, would be characterised by a continuous curve. My friend being an Economist, and me a Physicist, and both of us slightly tipsy thought that we might be able to change the world with our new theory - so I went home that night and wrote a small program using FlashMath to try and quantify some of our ideas. The program essentially integrated over a Cauchy-Schwartz curve and compared collected tax with that of the standard tiered system. I had planned on expanding on this by optimising the curve using measures such as utility (an economic measure of happiness of a population) but for now here is the source code:

package org.experimentalized
{
 package
{
 import flash.display.MovieClip;
 import com.experimentalized.math.quadrature.SimpsonsQuadrature;

 public class Tax extends MovieClip
 {
  private var gamma:Number = 7000;
  private var x0:Number = 22000;
  private var population:Number = 65000000;
  
  private var gamma2:Number = 12000;
  private var x1:Number = 30000;
  private var beta:Number = 0.52;
  
  public function Tax()
  {   
   trace(calculate_total_teired_tax_collected(1000000));
   trace(calculate_total_new_tax_collected(1000000));
  }
  
  public function calculate_total_new_tax_collected(Limit:Number):Number
  {
   var S:SimpsonsQuadrature = new SimpsonsQuadrature(new_tax_proportion,0,Limit,100);
   return S.integrate();
  }
  
  public function new_tax_proportion(X:Number):Number
  {
   return population*calculate_new_tax_collected(X)*evaluate_income_percentile(X);
  }
  
  public function calculate_new_tax_collected(income:Number):Number
  {
   var S:SimpsonsQuadrature = new SimpsonsQuadrature(lorenzian_cdf,0,income+0.001,100);
   return S.integrate();
  }
  
  public function lorenzian_cdf(X:Number):Number
  {
   return (1/Math.PI)*Math.atan((X-x1)/gamma2)*beta + beta/2;
  }
  
  public function calculate_total_teired_tax_collected(Limit:Number):Number
  {
   var S:SimpsonsQuadrature = new SimpsonsQuadrature(teired_tax_proportion,0,Limit,100);
   return S.integrate();
  }
   
  public function teired_tax_proportion(X:Number):Number
  {
   return population*calculate_teired_tax_collected(X)*evaluate_income_percentile(X);
  }
  
  public function calculate_teired_tax_collected(income:Number):Number
  {
   var taxable:Number = income - 7475;
   if(income>100000) taxable = income;
   
   var basic_rate:Number = taxable;
   if(basic_rate>35000) basic_rate = 35000;
   
   taxable = taxable - basic_rate;
   
   var higher_rate:Number = taxable;
   if(higher_rate>115000) higher_rate = 115000;
   
   taxable = taxable - higher_rate;
   
   var additional_rate:Number = taxable;   
   
   if(basic_rate<0) basic_rate = 0;
   if(higher_rate<0) higher_rate = 0;
   if(additional_rate<0) additional_rate = 0;
   
   return basic_rate * 0.2 + higher_rate * 0.4 + additional_rate * 0.5;
  }
    
  public function evaluate_income_percentile(X:Number):Number
  {
   //Model as lorenzian
   return (1/Math.PI)*(gamma/((X-x0)*(X-x0) + gamma*gamma))   
  }
 }
}

It isn't commented in the slightest but see what you can make out of it!