When you use R = P*N-I, you are still following the static view point, which is not true. The actual game is dynamic.
Remember we build settlers?
First we invest 100 production and hope we can get it back in some turns, the quickly the better; but after we settle it to build city we naturally maximize our food output. Why? Because we choose to invest again.
Supposing we have a tile A with 3 production output (plain hill with forest) and a tile B with 3 food output (non-irrigated corn), the action we move the citizen from tile A to tile B is just a second investment: the input is the growth requirement(22), and return will happen from the 8th turn when the city grows to lv2 . If the 2nd citizen works on a grassland forest(tile C), the return is 1, so the ROI(based on my definition) is 22.
But before the return is greater than investment 22 turns later, now you have to make another decision here: to let the second people work on tile A or tile C? new investment comes.
When you invest in every turn, actually you are accumulating the invest/return result. This is why the integral calculus has to be used. |