Also, for Difficult levels it could be also;

Easy = 10,000 - (Provincial Income x 0.5)
Normal = 8,000 - (Provincial Income x 1.0)
Hard = 6,000 - (Provincial Income x 1.5)
Expert = 4,000 - (Provincial Income x 2.0)

Note: this may put some in negative territory, and the factions will need to hold of building until they get into positive.

PS: I may do a calculation later, if someone is interested. I will use the region guide (excluding initial trade income)