In short, yes!
Presumably wealth would be shared equally across the entire population of the area. Well doing so would lead to a surge in demand for all kinds of goods. Makes sense right? If you suddenly had a million dollars you’d almost immediately make some purchases. Maybe it’s something you need like a better car or a new computer, or just something you want like a bigger TV… but you’d definitely buy something pretty quick.
The real problem with that is demand for products is not spread out over time but is rather one big sudden blip on the charts. Demand for goods will outstrip supply, leading to prices rising. Prices rise to capture more profits from that increased demand or to recoup the seller’s own increased expenses. It’s just the way of our world… and presumably Tolkien’s world as well. After all, why would the dwarves hoard gold if it had no value in a Tolkien economic system.
But, it is a fantasy book.
And it’s Tolkien’s fantasy book. Considering that industrialization is part of the bad guys modus operandi, inflation my not occur as expected.
Inflation could be worse because the good guys use artisans with lower production capacities, leading to scarcer goods, or it could be better because the good guys citizens are perfectly willing to wait in line for their artisan made goods. There’s potential for multiple outcomes.
Ultimately, if the sheer amount of wealth in the lonely mountain were to be shared equally inflation would surely occur. It ends up being a question of how much inflation occurs.