That limit is the marginal point where the expenditure equals the net asset value gain resultant from it, such as real estate prices. How can you know this limit? You can’t, but the bond market can guess at it.
Let’s say that you have a nice picket fence suburb with no police department and lots of robberies. You float a bond for your first police officer (not that this will help, but, run with it…). People buy it for nearly the risk-free rate. Why? Because they know that they will get paid back by the next bond, which will also get funded. Now the cop floats a bond for a Lamborghini. The demand is much lower, and the interest is unsustainable, so it doesn’t get funded.
Now here’s where it goes wrong. The mayor sees that nobody wants to pay for the Lambo, and solves the problem by packaging it up with everything else. This works for the first Lambo, but they want 10 Lambos, so the bond interest rate is unsustainable.
So what now? Taxes. They put a bunch of taxes on the residents, and then tell the investors that the Lambo bond will now get paid by tax revenues, which they have ultimate authority over. Now the calculus is different. The value of the expenditures is almost irrelevant. The only thing that matters is the marginal point where an additional dollar in tax reduces the net asset value by the inverse of the tax rate (e.g. $1 in tax revenue at 1% => $100 value destroyed). Notice we’re no longer talking about increasing values by large multiples, but destroying value by large multiples.
Now the Lambo bond goes out supported by tax revenues. The casual observer might note that the people of the town are now paying the bond holders for their right to exist on the land that they ‘own’. The major innovation from feudalism is that now the peasants actually pay for the land up-front too, and they pay for any improvements on it, and then higher rent for the improved property.
But that’s only an illusion of sustainability created by forceful extraction of resources. It’s like a strip-mining operation on middle class wealth. Profits are great until the resource runs out. So what is the solution there? Growth. Bring in more people to extract resources from. This is a requirement of the extractive funding model.
Market forces create sustainable economies. Any use of force distorts away from sustainability, toward finite extraction, and extractive models require expansion.