In the AoT economy, gold is continually generated. An infinite amount of gold can be gotten from farming. If gold was just put back into the market, in order to keep up with the amount of money in circulation, you would eventually be paying millions to get a sword.
When you make a purchase from the store, or pay off something, the money is taken out of circulation.
Also, cops can get a small amount of cash in the form of wages. When a criminal pays fines, the fine is divided up between all cops online, and they can collet it.