Does anyone know the formula for how large the manufacturing sector of a population will be, or where it is documented?
Agricultural is 5% * (colony cost + 1).
Service is 100% * the fourth root of the colony population (in billions), but no higher than 70%, and also no higher than whatever is left after the agricultural sector is manned.
Manufacturing is 100% minus the other two, but no lower than 0% (obviously).
Source: My own observations and reverse engineering. I've never seen a non-conforming case.
Note that these formulas lead to unintuitive situations in which adding more population to a colony can reduce the number of manufacturing workers available.
The higher the colony cost, the less population needed to reach this inflection point.
After the inflection point, adding more population will continue to reduce the number of manufacturing workers.
For colonies with colony cost >= 5.0, the number of manufacturing workers will continue decreasing as population is added past the inflection point, eventually dropping to zero.
For colonies for which ~1.7 <= colony cost < 5.0, the number of manufacturing workers will decrease as population is added past the inflection point, until the service sector maxes at 70% at ~240M pop. After that point, adding more pop will add more manufacturing workers at a constant rate (of 25% - colony cost * 5%).
For colonies with colony cost < ~1.7, there is no inflection point. Adding more population always adds more manufacturing workers, albeit at a decreasing rate of return until the service sector maxes at 70% at ~240M pop, and a constant rate thereafter (of 25% - colony cost * 5%).
Some examples:
Col Cost | | Population (M) | | Manu. Workers (M) | |
6.0 | | 60 | | 9.3 |
6.0 | | 70 | | 9.49 |
6.0 | | 80 | | 9.45 |
6.0 | | 179 | | 0 |
Col Cost | | Population (M) | | Manu. Workers (M) | |
5.0 | | 90 | | 13.7 |
5.0 | | 100 | | 13.8 |
5.0 | | 110 | | 13.7 |
5.0 | | 240.1 | | 0 |
Col Cost | | Population (M) | | Manu. Workers (M) | |
4.0 | | 90 | | 19.37 |
4.0 | | 100 | | 19.44 |
4.0 | | 110 | | 19.36 |
4.0 | | 240.1 | | 12.01 |
4.0 | | 387.1 | | 19.36 |
Col Cost | | Population (M) | | Manu. Workers (M) | |
3.0 | | 160 | | 26.81 |
3.0 | | 170 | | 26.84 |
3.0 | | 180 | | 26.76 |
3.0 | | 240.1 | | 24.01 |
3.0 | | 268.4 | | 26.84 |
Col Cost | | Population (M) | | Manu. Workers (M) | |
2.0 | | 200 | | 36.25 |
2.0 | | 210 | | 36.34 |
2.0 | | 220 | | 36.33 |
2.0 | | 240.1 | | 36.02 |
2.0 | | 242.25 | | 36.34 |