Mechanics for wealth

I am pondering running a Cthulhu game.  There are two salient facts:  (a) CoC has an awesome setting and awful rules, and (b) I'm currently most familiar with the PbtA engine.  The Mythos World hack seems pretty straightforward: rename the stats, steal some moves from Apocalypse World and Dungeon World, figure out what to do with Sanity and Magic, copy the list of skills.  I'm not saying I've got it quite all figured out yet, but I think I've already got something I could run better than I could run by-the-book CoC. The thing I *don't* have is a decent system for money and wealth. 

I know I *don't* want everyone to have to know exactly how many dollars they have in their wallet, or in their bank account, or trust fund, or what their annual income is.  And since the broke private investigator and the dilletante heiress are both standard CoC characters, I know I need a system that's approximately equally easy to use for both.

I'm pretty sure that means the wealth rating has to be logarithmic.  (Just abstracting to "1-barter" or "1-profit" doesn't solve anything if one character feels lucky to have 1 or 2, while another has an allowance of thousands.)  For items below your current wealth rating, you can just acquire them without worrying about it.  Items above your current wealth are unavailable, or at least require extraordinary effort.  Items *at* your current wealth might require a roll, where one of the possible outcomes is that you exhaust your funds and have to reduce your wealth level.

It seems like this is likely to be a common issue across any games set in approximately modern worlds, from steampunk to space opera.  I don't want to go re-inventing it if someone else has already written it, but I'm far from familiar with the full range of hacks out there.  Can anyone direct me to a working system?

You might take a look at The Hood, which iirc has something like a log scale for wealth. Wealth is important, anyhow, and it's in a contemporary setting:
http://rpg.drivethrustuff.com/product/128165/The-Hood

As an aside, have you looked at Tremulus? It might save you some work.

You might want to consider using a normal AW barter system as the base and then some other moves to handle the outliers of wealth.  For example:

Perhaps a character who you want to be constantly poor either has a move that lets them spend barter for some effect to keep the money flowing away from them, or has custom gigs (like the Operator) where the benefit is in intangibles (like clues, +forward, insight, or whatever) and the catastrophe is -barter or debt collectors catching up with them or something else that makes money flow away from them.

And perhaps a rich dilettante only has a normal amount of barter, but has a move to get goods and services without paying barter for them. Similar to the Chopper telling his gang to turn out their pockets, or perhaps even the ability to use the standard barter moves but with +hot instead of +barter spent.  Call the move "Well Connected Trust Fund" or the like.

I don't have any mechanics for wealth in my game Fourth World aside from a kind of "You are rich enough to need a move for it" move:

? Luxurious Riches Abundant
Your coffers are bottomless and you live your life in impossible opulence. When you make it known that you want something, and it can be bought, roll+Glorious. On a 10+, it will be delivered as fast as is possible. On a 7-9, it will be delivered, and Destiny picks one:
• There will be a delay - long enough for you to miss an important opportunity.
• It will be faulty, deficient, or cursed.
• It will carry a price not payable in coin - something important to you will be despoiled.

You might use something similar to the mechanic I'm using for my Mouse Guard hack.

Instead of having money, characters have an attribute called Resources that they have to select at CharGen and upgrade by levelling. Resources is a summary of your character's wealth, favors and contacts, professional skills, and haggling ability. A character with high resources might be "poor" but an excellent haggler, whereas a character with low resources might be "rich" but without any concept of the value of money.

Then use a move like this:

STRIKE A BARGAIN
When you haggle or offer payment for something for sale, roll +RES. On a 10+ choose one cost. On a 7–9, choose one cost and the GM chooses one cost.
   Tense negotiations and hard haggling wear you out, take the Strapped (RES) debility.
   The mouse you deal with needs a concrete assurance of your trustworthiness.
   The mouse you deal with demands a concession suiting their interests.
   You can’t get quite what you need, describe a close but imperfect alternative.
   It will take days/weeks/months.

This way nobody needs to know how much money they have at the moment, only their vague ability to scrape an offer together. The consequences for failure can be a temporary debility (because they spent all their liquid funds), a permanent reduction of the Resources attribute (for extreme cases, when they permanently traded away something of irreplaceable value), or the seller refusing to part with something at any price they can offer.

Limitations to this:
Technically, a player with a Resources of 8 has a chance, however slim, of buying just about anything. You can control this by making clear what is and isn't for sale. You can have sellers refuse to deal with people of "obviously minimal means", or otherwise make their life hard.

Another option to control this is to set a minimum Resources Required rating for different things, so that players with Resources of less than 10, for example, couldn't even attempt to buy a gun. Or a player with Resources less than 13 couldn't attempt to buy a house.