Troop

When I first began my discussion, I mentioned that there are two aspects to consider when we talk about the number of officer in each rank. So far, I have outlined the macroscopic view with regard to the structure of an army for a country. The problem, however, would look very much different when we see it from a microscopic point of view.

I mean when you consider the strategy of each individual troop.

The difference in perspective is simple. Although continual expansion is not a valid strategy to maintain a healthy staff ratio when you consider the entire army, it is a workable method when applied microscopically. In other words, for each individual troop, there is no reason to encourage resignation of Generals or Majors. To the head of a troop, the team should grow. There are always reasons to improve and increase the scope of work provided, aren't there?

But, how could every individual troop expand but the size of the army as a whole remains static?

PS. In a certain universe with a different set of laws for physics, this mathematical paradox does exisit. There, you can have the GDP growth rate of a country lower than the rates of each and every of its province.