Some assets are more liquid than others (they have lower transactions costs of buying and selling). More liquid assets will have a lower desired rate of return than less liquid assets (that means people will be willing to own them even if they expect to earn a lower rate of return than less liquid assets).
Money (the good that is used as a medium of exchange) will be more liquid than other assets. (If some other asset were more liquid than money, people would switch to using that other asset as a medium of exchange instead of the existing money, and that other asset would become the new money).
Money will therefore have a lower desired rate of return (strictly, a desired rate of return that is not higher) than other assets.
A chain letter that is always growing faster than the economy will eventually burst. It would burst immediately, if people didn't think there would be a greater fool coming along who also thinks he can get in and out before it bursts. It is "unstable". A chain letter that always grows more slowly than the economy can exist forever. It is "stable". If the desired rate of return on a chain letter is above the growth rate of the economy, the chain letter would have to grow faster than the economy to get people to participate, and so it is unstable. If the desired rate of return on a chain letter is below the growth rate of the economy, it is [or can be] stable.
Chain letters, ponzi schemes, and bubbles, are all the same thing.
The more liquid an asset, and thus the lower the desired rate of return on that asset, the more likely it is that desired rate of return will be below the growth rate of the economy.
Demand curves, for stuff that doesn't have very close substitutes, usually slope down. If the "stuff" is something like apples, that means the price people are willing to pay (the "desired price", or Marshallian "demand price") is negatively related to the quantity bought. If the "stuff" is an asset, that means the desired rate of return is negatively positively related to the quantity held. [Because the demand price of the asset is negatively related to the desired rate of return, and two negatives make a positive.]
Some assets do not have very close substitutes, and have downward-sloping demand curves. Cars are one example. Money (the medium of exchange) is another. People will want to hold some cars even if the rate of return on holding cars is very low. People will want to hold some money even if the rate of return on holding money is very low. The rate of return on holding money got extremely low in Zimbabwe, before people stopped using that money altogether. It went very very negative.
It is perfectly possible for the desired rate of return on holding money to be below the growth rate of the economy. It nearly always is below the growth rate. That means is it perfectly possible for money to be a chain letter that is stable.
A stable chain letter has two equilibria: one in which it continues forever; and a second in which it bursts immediately. If people always expect it will continue forever, it will continue forever. If people expect it will burst immediately, it will burst immediately. Even a "stable" chain letter isn't totally stable.
In the basement of the Bank of Canada there is a large collection of baskets of consumer goods. The Bank of Canada promises that it will redeem its monetary liabilities on demand for those CPI baskets. It promises that the redemption price will rise at 2% per year, so that the actual rate of return on holding Bank of Canada currency will be minus 2% per year in real terms. It has enough CPI baskets in the basement that it can honour that promise even if all currency were brought in for redemption. Bank of Canada currency therefore trades at a price equal to its fundamental value, that fundamental value is falling at 2% per year, and in equilibrium the desired rate of return is also equal to the actual rate of return of negative 2%. (Purely as a convenience, the Bank of Canada also offers people the choice of redeeming their currency in bonds instead, where the market price of the bonds is the same as the promised price of the CPI baskets. And everybody takes them up on that offer, since CPI baskets are hard to carry around.)
I made up some stuff in that above paragraph. But would anyone ever know, if they hadn't looked inside the Bank of Canada's basement? And even if they did look inside the Bank of Canada's basement, and found it was full of bonds rather than CPI baskets, would they care?
[Update: "Observational equivalence", those are the words I was looking for!]