Little Miss Shiny
Not quite. The stock market crash that played a major role in causing the Great Depression happened because people were speculating with money they didn't actually have.
^ This
The stock market crash was due to people taking out loans with the assumption that they would be able to get their money back in the future with no uncertainty. When the market crashed, millions of people had no money and were in debt. With no money, they stopped buying stuff... which meant that industries which provided that stuff went out of business, people employed in those industries no longer had jobs or money, and then they went into debt...
Rather, we will be seeing what's happened in other online communities before. Increasing prices will drive away existing users, and new users will not stick around because the high prices on everything make it impossible for them to purchase anything. The community will get older, the population less and less. Gaia Online will be forced to cater more and more to the few people who spend money on the site, which means prices (both in Gold and Cash) will continue to go up until the spenders finally stop spending money. At that point, the site will be mostly dead - large lack of users, no more financial incentive for Gaia to maintain or update the site.
Typically, what happens in that the server gets a "reboot" in the form of everyone starting off again with no gold and no items, to eliminate the inflation. And then it runs through the same cycle again.