This isn't as clear as I want it to be. Sorry.
Mr Ponzi issues a financial asset. Assume that the demand to hold that asset grows at the same rate as GDP. If people are willing to hold that asset at a rate of return less than the growth rate of GDP, Mr Ponzi can run a sustainable Ponzi scheme. He can issue new assets to pay the interest on the existing assets, and still issue a few more to provide some income for himself. Another name for a sustainable Ponzi scheme is a rational bubble.
Consider paper currency. Bank of Canada notes, for example. The Bank of Canada promises that this asset will earn a rate of return, in real terms, equal to minus 2% on average. That is below the expected growth rate of the economy. It is a sustainable Ponzi scheme, and a profitable one for the Bank of Canada. It is a rational bubble.
"Does the economy need a bubble?" is the wrong question. We know it needs a bubble. The empirical evidence is right there in our pockets. The only question is: how big a bubble does it need? Or, what does it depend on?
People willingly hold paper currency, even at a very low rate of return, because it is more liquid than other assets, which need to pay a higher rate of return.
We can imagine an economy in which the only liquid asset is paper currency, and all other assets are much less liquid, and in which paper currency is the only Ponzi asset, and all other assets pay a rate of return greater than the growth rate of GDP. If the issuer of that paper currency promises a real rate of return of minus 2%, and people choose to hold (say) 5% of their annual income in paper currency, then that economy needs a bubble equal to 5% of GDP.
Now suppose the issuer of that paper currency promises a 0% real rate of return instead. (The Bank of Canada targets 0% inflation instead of 2% inflation). And suppose people now want to hold (say) 10% of their annual income in paper currency. Then that economy needs a bubble equal to 10% of GDP.
Let's keep going. What would happen if the issuer of paper currency promised a rate of return equal to the growth rate of GDP? (The Bank of Canada targets zero growth in nominal GDP, so the inflation rate is minus the growth rate in real GDP.) Suppose people now want to hold (say) 123% of their annual income in paper currency. Then that economy needs a bubble equal to 123% of GDP. That is the exact borderline between paper currency being a bubble asset and not a bubble asset. The Bank of Canada issues an amount of paper currency equal to 123% of GDP, then issues no more ever again (assuming the demand for currency is proportional to GDP).
Now suppose there were some exogenous change in the demand for currency, that caused it suddenly to double, as a percentage of people's annual incomes. The economy would need a bubble twice as big as before. And if the issuer of paper currency didn't satisfy that need for a bubble twice as big, the price level would have to halve to satisfy it. And if the price level couldn't halve instantly (because prices are sticky) there would be a recession, because of the excess demand for currency, which serves as the medium of exchange.
But currency is not the only liquid asset. Some assets are more liquid than others. Some may be liquid enough that people will hold them even if they expect a rate of return that is permanently below the growth rate of the economy. Any such asset can be used for a sustainable Ponzi scheme (a rational bubble).
Let us imagine an economy with a spectrum of Mr Ponzi's. And let's line up all the Mr Ponzi's in order of how liquid their liabilities are.
The first Mr Ponzi (the Bank of Canada) can issue the most liquid liabilities. The second Mr Ponzi (the Government of Canada?) can issue the second most liquid liabilities. And so on down the line of Mr Ponzi's.
If he wants to, the first Mr Ponzi can drive all the other Mr Ponzi's out of business. He simply needs to promise a rate of return just slightly below the growth rate of the economy. Since all the other Mr Ponzi's, who issue less liquid liabilities, would need to pay a rate of return above his if they wanted people to buy their liabilities, they wouldn't be able to run a sustainable business.
Suppose the first Mr Ponzi doesn't do that. He then leaves room for the second Mr Ponzi. And if the second Mr Ponzi wants to, he can drive all the other Mr Ponzi's out of business. Suppose the second Mr Ponzi doesn't want to do that. He then leaves room for the third Mr Ponzi. And so on.
You can think of this post as a continuation of my post on Turgot's land beating Samuelson's money.
Samuelson said you could have an economy which needed a bubble, because the rate of interest is below the growth rate of the economy. People would want to hold what Samuelson called "money" (but which might better be called "government bonds") purely as a way of saving, even if they knew it was a pure Ponzi asset.
Stefan Homburg said that Samuelson was wrong, because land would be just as good a savings vehicle as Samuelson's "money", since land too lasts forever, and land is even better, because land pays rent, because land is productive.
But if land is less liquid than Samuelson's "money", the economy might still need a bubble. We know that land is less liquid than currency, and we know that the economy needs a bubble, because people are willing to hold currency even though its rate of return is below the growth rate.
But what Finance tries to do is convert less liquid assets into more liquid assets. For a while, Finance succeeded in making land (in particular, the land on which houses are built) into a more liquid asset. If Finance succeeded in making land as liquid as currency, the economy would not need a bubble. If Finance succeeded in making land nearly as liquid as currency, the economy would only need a small bubble. But if Finance suddenly fails, and land becomes less liquid, the economy suddenly needs a much bigger bubble.