I’m not an Autarch either, but I am a medieval history buff if that helps and I’ve been trying to help my GM sort out some similar questions.
Historically speaking (mostly for flavor and possible RP opportunities), most wealth doesn’t take the form of coins, it takes the form of agricultural products (also ore, stone, and timber) and licensing rights (e.g. granting someone the right to collect the tolls for a given bridge). While coins have the advantage of lasting forever, they have the disadvantage of taking up quite a bit of space and being easy to steal (darn adventurers). Peasants aren’t really wealthy enough to have many coins, really and so they pay their taxes in grain, livestock, and goods. When commoners do pay with coins, they pay with copper pieces, not gold pieces. If you think about it this way, 10,000 gp in value of coins would typically be denominated in 500,000 - 1,000,000 small pieces of copper and silver (a problem that lower-level adventurers are acutely aware of). That being said, the most valuable things a lord owns are probably their land, peasants, castle, weapons, horses, and armour (actually in about that order), meaning that a noble’s net worth isn’t easily translated into cash either. What you do see, however, throughout the middle ages, is that nobles don’t have too much difficulty acquiring loans using their lands and future revenues as collateral. If Baron Willhelm owns 3,000,000 gp worth of land with an income of 20,000 gp/month and needs 500,000 gp now. Of course unlike now, the rates of interest (and usury) would be very high. 50-70% wouldn’t be unheard of. As you get into the renaissance period, the banks themselves have become large enough to start ruling lands and manipulating wars in their favor (e.g. the Fuggers supporting Emperor Maximilian I and the De Medici family in general). This could be an interesting plot to include in a campaign.
ACKS simplifies the accounting of wealth that is due to coins (or gems) and wealth that is made out of barter-able goods into “gold pieces,” which for all purposes is really an abstract measure of money rather than physical gold coins. This works quite well, as a medieval economy works largely on the barter system (unless you’re a noble), so commoners aren’t generally too bothered about being payed in grain rather than silver. Mercenaries might want their pay to be a bit more metallic, but converting grain to coins isn’t that difficult for a nobleman to do. Furthermore, the supply costs for a campaign are going to mainly reflect a need for agricultural products rather than boxes of gold and silver being transported in wagons, so this method works out.
The amount a barony could spend depends mainly on how much they’ve saved up for the campaign. However, rather than this reflecting the baron amassing a large pile of shiny metal bits, it would instead reflect him building up a stockpile of arms and armor, training men to fight, building siege weapons and wagons, stockpiling flour (which keeps for quite a while, actually), increasing their herds of livestock (animals are butchered where they are eaten, not in advance), etc.
To answer your question more directly, Domains at War: Campaigns provides the details of supplying an army on campaign. Add supply cost to the units’ wages to see the monthly cost of taking a given unit on campaign. Subtract this from whatever money the baron has. Size and duration will matter, as will any necessary construction (e.g. siege equipment/vallations/contravallations). I don’t imagine that a lowly baron would be going on much of a campaign by themselves. Costs add up quite quickly, and a baron simply can’t support a large enough force to be very effective against enemy fortifications. With that in mind, barons seem to be well-suited to raids against their neighbors, but for those I wouldn’t bother calculating the supply cost. It doesn’t really cost extra to use your mercenaries to attack the baron just down the road. Calculating exactly how many resources a baron has for such a campaign would seem easy for PCs (since they should know how much cash they have + their monthly income), but is a lot trickier for NPCs. I’d say the amount they’d save up depends entirely on the NPC’s disposition. Are they war-like? Have they been planning this for years? Does the baron typically squander his money on booze and women? Horses? Fancy Clothing?
