VERY interesting read... thank you for that. I like this part : "
currencies do not have an intrinsic fair value. They get their value because
humans use them as a tool to be able to trade every good or service with every other human being. " I am quite interested to hear your
opinion on Crypto currencies with no coin cap, like Ethereum and how that would influence it's value. { I say it is crucial to have a coin cap, like
we have with Bitcoin }
Thank you @Kprawn Smiley I think that one is a key phrase.
With regard to currencies whose supply does not converge to a limit, I am going to show you two interesting solutions for the TDSTM. I have to say in advance that, because of my newbie account in bitcointalk, the images I post show only as a link. Therefore, I will not post formulas as images, but in text format. Let the first case be the one of a currency with a linear supply function such as this one, which starts with an initial supply of 0 units:
S = r*(t-ts) => dS/dt = r
If you integrate the equation for the total discounted supply:
M = r*(t-ts )+ r/i
The result for the total discounted supply has two parts. The first one represents the money in circulation (M0) and, as you can see only gets bigger and bigger with time. The other one is the part that accounts for the money not yet created, and it is a constant term. As time goes by, the second constant term becomes negligible when compared to the first term; which means that with time, the money in circulation becomes the heavy part compared to the money yet to be printed.
Let the second case be the one of a currency with an exponential supply function such as this one, which starts with an initial supply of 1 unit:
S = exp(r*t) => dS/dt = r*exp(r*t)
If you integrate the equation for the total discounted supply, you get two solutions:
M = exp(r*t)*(1 + r/(i-r)), r
M = inf, r>=i
The first solution is similar to the one I showed you for the linear supply function, but with the difference that M0 is exponential and the constant term is a bit different. As you can see, the first solution originates when the inflation rate (r) is smaller than the natural interest rate (not the manipulated interest rate, manipulated by the central banks). The second solution is the one that shows up in hyperinflation scenarios. When the government/central bank prints money at a sustained rate (r) higher than the natural interest rate, the total discounted supply get enormous.
In both cases, as opposing to limited supply currencies, M increases with time. Now if you plugged this M in the CFV model, you would see the effect in price. As you've read in my article, prices are relative, so I you were to use CFV, you'd need to compare two currencies. Depending on the properties of the currencies you chose, you would get a different fair value along time curve (ceteris paribus, of course).
I hope I've been able to answer your question.
Regards,
pablompa