Revenue from printing bonds is like revenue from printing currency, if r<g for bonds. But there's a limit to how much revenue the government can sustainably earn by doing them.

In our familiar world, where r<g for currency, currency isn't really a government "liability" in the normal sense of the word. Having a positive currency/GDP ratio, and keeping it constant over time as the economy grows, is instead a source of revenue for the government. It's like the government owning an asset, not owing a liability. The government-owned central bank is a profit-centre for the government. Printing currency is a profitable business. We even have a special name for those profits: "seigniorage".

But if you think about the currency in your pocket, there's nothing weird about it at all. It's all very familiar. If r<g, financing government deficits by selling bonds is just like financing government deficits by printing currency. Because currency pays the owner 0% nominal interest (and minus 2% real interest if the central bank targets 2% inflation), which is less than the growth rate of the economy. So r<g for currency.

In a weird world, where r<g, government bonds aren't really a government "liability" in the normal sense of the word. Having a positive debt/GDP ratio, and keeping it constant over time as the economy grows, is instead a source of revenue for the government. It's like the government owning an asset, not owing a liability.

A world where the interest rate on government bonds is (permanently) less than the growth rate of GDP ("r<g") is a weird world. The government can run a Ponzi scheme, where it borrows (sells more bonds) to pay for the interest on the existing bonds, so the stocks of bonds grows at the rate of interest. But since r<g, the economy is growing faster than the stock of bonds, so the debt/GDP ratio is falling over time. So unlike the real Mr Ponzi's scheme, it's sustainable. The government would actually need to borrow more than is needed to pay the interest on the bonds, if it wanted to keep the debt/GDP ratio constant over time.

All economics students are familiar with the idea that printing money is a source of government revenue. But slightly more advanced students also know there is a limit to how much revenue, in real terms (adjusted for inflation), the government can sustainably get by printing money (and Zimbabwe is what happens when the government tries to go past that sustainable limit). Because the faster the government prints money and spends it, the higher the rate of inflation. And the higher the rate of inflation the more negative the real rate of interest on money (the higher the opportunity cost of holding money), and the quicker people will get rid of money they earn, and so the smaller their money/income ratio.

Here's some simple math to illustrate: let Mdot be the amount of money printed per year. Let NGDP be nominal GDP. So Mdot/NGDP is the government's revenue from printing money as a fraction of NGDP. Multiply and divide by the stock of money M, and this equation becomes:

Government revenue from printing money as fraction of NGDP = (Mdot/M)x(M/NGDP) = growth rate of money x (money/NGDP) ratio.

Money demand curves slope down. The higher the money growth rate, the higher the inflation rate, and the smaller is M/NGDP. The money growth rate that maximises government revenue (as a fraction of NGDP) is where the elasticity of the demand curve is exactly one, just like for any revenue-maximising monopolist.

The same idea should apply to government bonds. Government bonds are not as special as currency, but they are still special. They are (usually) safer and more liquid than other assets, so it is no surprise if they pay a lower rate of interest than other assets. And that interest rate differential is the opportunity cost of holding government bonds instead of other assets, and the demand curve for government bonds should slope down as a function of that interest rate differential, just like the demand curve for money slopes down. The only difference is that government money (currency) pays 0% nominal interest, while government bonds (normally) pay a positive nominal rate of interest. But if that nominal rate of interest is less than the growth rate of NGDP, the principle is the same.

If r<g for government bonds, then issuing bonds and printing currency are both sources of government revenue. But there's a limit to how much revenue the government can collect from those sources. A higher Bond/NGDP ratio requires a higher rate of interest paid on bonds to persuade people to hold a higher ratio. There is some Bond/GDP ratio (and associated rate of interest on bonds) that maximises sustainable government revenue from printing bonds. And if the Bond/GDP ratio gets too high, then the bond rate of interest rises to equal or exceed the growth rate of the economy, and that source of government revenue disappears.

I think this math is right (don't trust me):

Sustainable government revenue from printing bonds, as a fraction of NGDP = (g-r)(B/NGDP) where B is the stock of bonds

A higher debt/NGDP ratio means a higher r, so a lower (g-r), so there are two offsetting effects. Sustainable government revenue is maximised where the bond demand curve has an elasticity of one.

The only difference between the bond formula and the money formula is that the nominal rate of interest on money is assumed to be 0%. And if we assume that the growth rate of NGDP equals the money growth rate (which it must be if the M/NGDP ratio is constant over time), the two formulas become equivalent.

Think of the government like a price-discriminating monopolist, that sells two financial instruments (currency and bonds), paying different rates of interest, making a profit on each. (Of course, it's really a lot more than just two, given the whole term-structure.)

[The other important difference between government money and government bonds is that the first is unit of account and medium of exchange and the second isn't. But that doesn't affect the point in this post about their similarity as sources of government revenue when r<g.]

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