I am trying to figure out a way of estimating price increases over time in cryptocurrency sytems with deflationary economics. As some of you might be aware, some cryptoassets include deflationary economics, or 'tokenomics' as they are sometimes referred to in those circles. The way deflation is achieved over time is often by adding transaction fees that charge a certain percentage of the total value moved and 'destroying' all or some of the cryptoasset units taxed. Due to the constantly reducing supply of units, holders see their value increase even though their wallet amount remains unchanged, because individual units increase in price over time. That said, it is not immediately clear to me how to calculate how long one would have to hold in order for the increased value emerging from deflation to counterbalance the value they lost from taxation.
As an example, in a basic system with no deflation or inflation, and no transaction fees, if one were to purchase USD 1000 worth of a cryptoasset, and if we assume the asset would see a 5% annual growth in price, then after 10 years of holding, the person's wallet would be worth USD 1648.72, a growth of 64.87%.
Now, if we consider a cryptoasset that charges a 10% fee on each transaction, out of which 9% is destroyed, things get a little complicated. If one bought USD 1000 worth of that cryptoasset, they would instantly lose 10% of their holdings at the buy-in, and another 10% 10 years later when liquidating. Assuming that at the time of purchase the cryptoasset has a marketcap of USD 1 000 000 000, and a total amount of 900 000 000 units in existence, then a unit is USD 1.1111111111 and USD 1000 would buy them 900 units. However, in actuality they will only have 729 units because the wallet will be taxed at a rate of 10% twice, at buy-in and liquidation.
Now, assuming that the average daily trading volume is, say, USD 1 000 000; and that the average yearly price growth is still 5% (not including the value added by destroying units), how could I calculate the value one would end up with considering 9% of that USD 1 000 000 traded daily are permanently destroyed? What impact would the constant deflation have on the price over time (assuming the constant 5% growth, not counting the deflation), and how long would it take for the increase in price due to deflation to overtake the loss of value one experienced as a result of the tax? I'm unfortunately not good enough to figure this out by myself and would really appreciate some help figuring it out.
Also, please let me know if you have any tag suggestions that could improve my chances of finding an answer to this. Since I am not that knowledgeable of mathematics, I do not know if there are any other tags that would be relevant to my question.
Thank you all so much in advance.
Regards,
vector81