Math problem: When would the freicoin money supply converge?

[jtimon]

@Holy-Fire
I don't understand why you call it inflationary if the monetary base is constant. The point is to charge hoarding to make transactions cheaper. I must admit that I cannot think of a demurrage rate/units generated per block that is not arbitrary.

Because what matters is the amount of money you store relative to the total money in existence. This varies in the same way whether new money is generated or your own money decays.

But with a fixed monetary base, there is not likely to be price inflation. If the growth (which leads to price deflation) equals the demurrage, the purchasing power of your money would remain constant. If the demurrage were less than the growth, your purchasing power would increase with time.

The same will happen if the growth equals the inflation. Hence, demurrage is equivalent to inflating the block reward.

Yes. the block reward is increased.
I don't understand the first sentence. What will happen if growth equals inflation? I assume you're talking about monetary inflation.
The purchasing power will stay the same if growth equals monetary inflation?
With a stable monetary supply, growth leads to price deflation, not to price inflation.
I don't get it. Am I missing something?

[Meni Rosenfeld]

The purchasing power will stay the same if growth equals monetary inflation?

This.
You're making this more complicated than it is. All I said is that erasing 3% of all existing coins each year is equivalent, in real terms, to increasing the block reward by 3% each year.

[jtimon]

The purchasing power will stay the same if growth equals monetary inflation?

This.
You're making this more complicated than it is. All I said is that erasing 3% of all existing coins each year is equivalent, in real terms, to increasing the block reward by 3% each year.

The block reward is nominally constant, but proportionally to the total supply is in fact decreasing as the total supply increases. Once the maximum supply is out there, the proportion of the total annual reward compared to the total supply is constant and equal to the demurrage rate. If each year we erase 3% of the supply, the total annual reward will be equal to 3% of the total supply, forever.
I still don't understand what you mean or I disagree.

[Meni Rosenfeld]

The block reward is nominally constant, but proportionally to the total supply is in fact decreasing as the total supply increases. Once the maximum supply is out there, the proportion of the total annual reward compared to the total supply is constant and equal to the demurrage rate. If each year we erase 3% of the supply, the total annual reward will be equal to 3% of the total supply, forever.

That's correct. With 3% demurrage and constant block reward, the total annual reward is equal to 3% of the total supply. With no demurrage and 3% yearly increase in block reward, the total annual reward is equal to 3% of the total supply. Hence, the two are equivalent.

[jtimon]

The block reward is nominally constant, but proportionally to the total supply is in fact decreasing as the total supply increases. Once the maximum supply is out there, the proportion of the total annual reward compared to the total supply is constant and equal to the demurrage rate. If each year we erase 3% of the supply, the total annual reward will be equal to 3% of the total supply, forever.

That's correct. With 3% demurrage and constant block reward, the total annual reward is equal to 3% of the total supply. With no demurrage and 3% yearly increase in block reward, the total annual reward is equal to 3% of the total supply. Hence, the two are equivalent.

Thank you, I finally understood it. Sorry for taking so long.
I though you we're meaning that the reward would increase in real terms with demurrage.
You mean that for achieving the same reward without destroying money, it would be just necessary to increase the nominal reward by the same percentage.
The main difference is that you would have an exponential monetary inflation if you increase the nominal reward each year.
Most people in this forum (including me) won't accept an exponential growth of the monetary base easily.

[cunicula]

By the way, what do you think about those freicoins?
Feel free to criticize them. Nobody seem to like demurrage here.

Demurrage is equivalent to simply increasing the block reward by the same percentage each year. I don't feel strongly about this either way, but I think that since we can't divine what the future growth rate of the economy will be, it's better to make the currency non-inflative rather than setting an arbitrary inflation rate.

+1

Demurrage = inflation wearing a new hat

[cunicula]

The block reward is nominally constant, but proportionally to the total supply is in fact decreasing as the total supply increases. Once the maximum supply is out there, the proportion of the total annual reward compared to the total supply is constant and equal to the demurrage rate. If each year we erase 3% of the supply, the total annual reward will be equal to 3% of the total supply, forever.

That's correct. With 3% demurrage and constant block reward, the total annual reward is equal to 3% of the total supply. With no demurrage and 3% yearly increase in block reward, the total annual reward is equal to 3% of the total supply. Hence, the two are equivalent.

Thank you, I finally understood it. Sorry for taking so long.
I though you we're meaning that the reward would increase in real terms with demurrage.
You mean that for achieving the same reward without destroying money, it would be just necessary to increase the nominal reward by the same percentage.
The main difference is that you would have an exponential monetary inflation if you increase the nominal reward each year.
Most people in this forum (including me) won't accept an exponential growth of the monetary base easily.

Okay, do I have this right? Most people on the forum won't accept exponential growth in the monetary base. However, people may accept a system (demurrage) which is mathematically equivalent to exponential growth in the monetary base. This is so asinine it just might work.  

[jtimon]

Okay, do I have this right? Most people on the forum won't accept exponential growth in the monetary base. However, people may accept a system (demurrage) which is mathematically equivalent to exponential growth in the monetary base. This is so asinine it just might work.  

The two systems aren't mathematically equivalent. The only thing they have in common is the decrease in purchasing power for the money holders. Differences:

1) Inflation changes prices and that's unconvenient for business calculations. The nominal unit has to decrease its value forever. Inflation warranties that there won't be stable prices. On the other hand, with demurrage (like in bitcoin) the price inflation/deflation depends on growth. In bitcoin it also depends on hoarders, in freicoin you don't expect many of them.

2) Inflation increases the gross interest on lending while demurrage decreases it. To eliminate the liquidity premium/basic interest was the aim of the free money inventor and that can't be done through inflation (gross interest = basic interest + inflation premium + risk premium).

[cunicula]

Ok there are these nominal differences. Do they matter for economic decision making in some way?

[jtimon]

Ok there are these nominal differences. Do they matter for economic decision making in some way?

Yes.
Demurrage fights the basic interest and allow capital yields to drop to zero like profits do by competition.
Of course, there would be innovations that would allow capital yields (if they deserve that name in that context) to rise temporally in some sectors, but new capital of those types would be produced again until the profits go to zero. With money-capital, the other capitals can't drop below the basic interest by competition, because money won't allow its production if they're not going to yield the same or more than what money can yield from the wares.

On the other hand, inflation (if predictable and not based on monetizing cheap debt) only rises the gross interest by rising its inflation premium component, leaving basic interest/liquidity premium intact.
If inflation is based on monetizing cheap debt, inflation is much worse because it alters the financial market letting some investors (usually governments) borrow cheaper outside the market and lenders with demand for their money artificially reduced.

government or central bank printing != block chain currency with exponentially growing monetary base (expocoin) != block chain currency with demurrage (freicoin).

Demurrage also promotes long term thinking.

[cunicula]

My position is that banks are capable of using calculators and factoring in money supply growth when calculating interest rates. Meaning that none of your proposed advantages matter. I agree that they exist howevever, so I don't think there is anything left to argue about.

[jtimon]

My position is that banks are capable of using calculators and factoring in money supply growth when calculating interest rates.

Yes. Expocoin distorts the unit of value in a way that bank's computers can easily ignore.
That's why expocoin would have an inflation premium and freicoin won't.
Freicoin would drive down real interest (basic interest/liquidity premium + risk premium) and expocoin won't.
Expocoin just increases nominal (gross) interest, freicoin decreases basic interest.

Meaning that none of your proposed advantages matter. I agree that they exist howevever, so I don't think there is anything left to argue about.

But are they advantages or they don't matter?
I think if they're advantages, they matter.