How can the economy of the Pokémon world even keep itself stable when domestic cats can just produce money out of thin air? The coins that Pay Day creates have real value. You pick them up in the game and you use them as regular money. I can’t be the only one who would, upon manifesting myself in the Pokémon world, quickly set up a Meowth farm and made them use Pay Day all day. Preferably somewhere close to the Pokémon center for that delicious free PP refillment.
Simple answer: it can’t. If any trainer with a Meowth can access an unlimited supply of money, then money can’t have a stable value. It doesn’t make sense.
If it doesn’t make sense, then we have misunderstood something or made a bad assumption (…or the worldbuilding is just fragile enough that we’ve broken it, but let’s make that our explanation of last resort). Either they can’t actually produce money out of thin air, or the coins don’t actually have value, or perhaps their capacity to produce money is not unlimited and has already been “priced into” the economic systems of regions where they are native.
I would actually like to think the second option is what’s going on: that the coins are like Harry Potter’s “leprechaun gold,” conjured magical material that simply ceases to exist after a few hours. If I were in charge of Pokémon’s worldbuilding, that’s the answer I’d give. Shopkeepers are going to be pretty upset about that, though, and the games don’t stop us from spending “Meowth gold” or holding onto it indefinitely. We probably can’t make this work easily given what we actually have.
So maybe they can’t produce money out of thin air. There’s a lot of support for this, honestly – Meowth’s Pokédex entries reference, over and over, the fact that it likes to collect round or shiny things, especially coins, and spends its down time prowling the streets looking for loose change. It has the Pickup ability for exactly this reason (you can also compare Pay Day in the TCG, which invariably allows the user to draw a card – Meowth just fetches stuff for you). Most of the stuff Meowth hurls at its opponent when using Pay Day is probably useless junk it’s picked up somewhere, but some of it is real coins, and that’s what you pick up off the ground at the end. If there is magic to it, maybe it’s that Meowth’s charm can store a large number of shiny things, like a sort of “purse of holding.”
And then there’s the third and perhaps most surprising possibility: no-one even cares.
The amount of money you get out of Pay Day is pretty small – five times the user’s level, for a maximum of 500 per use. Bear in mind that the currency in the Pokémon games is presumably equivalent to the Japanese Yen, whose value tends to hover just below that of one US cent. If exhausting Pay Day’s 20 PP and returning to a Pokémon Centre represents a full day’s work, which doesn’t seem to me like an outlandish assumption, then a Persian trained by a top-notch Pokémon master is producing just under $100 a day. For a day’s work in a modern industrialised society like Japan, where the minimum hourly wage is about ¥900, and a good job pays more like ¥2000 an hour, that’s… surprisingly meh, especially considering you need to be a highly skilled trainer to command a Pokémon of that level. Like, you can support yourself and your Pokémon on that, absolutely, but it doesn’t seem like you’ve found a massive exploit that breaks the system, more like you’ve found a job where you work and get money. It gets better if you can max out Pay Day’s PP at 32, but not you’re still not talking about crazy, dramatic levels of wealth here. Maybe you have multiple Persian, and maybe you can go through this whole routine with three or four of them every day, but you do have to get them to level 100 to see returns like this, which is a lot of work in itself. If everyone did that, then you’d have problems because the government wouldn’t be able to maintain the artificial scarcity of currency, but the relatively limited scale of what you can produce, even as an extremely powerful trainer, is probably why Game Freak never seriously thought about it or bothered putting explicit limits on it.