The exact mathematical form of the Pareto principle

The exact mathematical form of the empirical Pareto Principle is derived using the optimum power law which is based on information theory. It is shown that the 80-20 Rule is approximately 70-20 for populations below 400, which means that 20% of the individuals have 70% of the resources. Around the population of 100,000 it is nearly 80% but as the population goes into billions, the top 20% get to have nearly 84% of the resources increasing the disparity. This implies that more dense populations have greater inequality than less dense ones which is an unexpected result.