Here's the formula for computing yearly production income in a settlement:
Production_income = factor(pop) * p(goods) * (PE + 1%) + officials + manufactory
- factor(pop) is the population scale factor, a logarithmic function of the settlement's population
- p(goods) is the base price of the goods found in the province
- PE is the country's production efficiency (percentage)
- officials: tax collector +1d; governor +1d
- manufactory: 6d if a manufactory is present, or 12d if the type of goods in the provinces is of the right type.
The population scale factor ranges from 0.1 to 2.0 depending on population; for a colonial city it is 1.0. The base price of goods is 5, 10, or 15 ducats, depending on the province's goods. Production efficiency is largely based on infrastructure technology, but is also affected by domestic policy and goods manufactories.