Pareto Salary

If the square root of people produce half of the value, how many times higher than the average salary should the salary of the top people be?

number of people productivity of top people average productivity ratio
10 15.81% 10.000% 1.58x
100 7.91% 1.000% 7.91x
1000 5.27% 0.100% 52.71x
10000 3.95% 0.010% 395.28x
100000 3.04% 0.001% 3043.55x

Example Calculation For 10000 People

people productivity average
10000.00 100.00% 0.01%
100.00 50.00% 0.50%
10.00 25.00% 2.50%
3.16 12.50% 3.95%

Code

import math

def run(number, percent):
  # print '| %9.2f | %6.2f%% | %6.2f%% |' % (number, percent, percent / number)
  nxt = math.sqrt(number)
  if 2 * nxt > number:
    return percent / number
  return run(nxt, percent / 2.)

for exp in range(5):
  number = math.pow(10, exp + 1)
  top = run(number, 100.)
  avg = 100. / number
  print '| %6.0f | %5.2f%% | %6.3f%% | %7.2fx |' % (number, top, avg, top / avg)