Bitcoin’s money supply is set so that it halves roughly every four years, until it reaches 21 million coins in circulation (Nakamoto, 2008).
The
increase in the money supply halves, not the money supply itself.
More importantly, your assertion that value of a bitcoin is more volatile because of the fixed money supply is flawed. The flaw is the conflation of "supply" in "supply and demand" and "money supply". The meanings of the word "supply" in these two concepts are very different. The quantities of bitcoins available to meet demand (the "supply") comes from holders of bitcoins. You cannot claim that supply is fixed just because the money supply is fixed.
As the quantity in the supply curve approaches the money supply limit, we can assume that the price and slope approach infinity, and near that point the supply is inelastic and the price is very volatile as you claim. However, note that increased hoarding of bitcoins (or simply holding) raises the supply curve and moves the intersection with the demand curve away from the money supply limit and towards higher elasticity and decreased volatility.
Thank you for your response; I really appreciate someone is actually reacting to what I wrote. You are absolutely right about the
increase in the money supply, I'm not sure how that mistake slipped into the paper.
I don't understand your distinction between money supply and supply (to meet demand). There will be 21 million Bitcoins in the future, and unless fractional reserve banking is adopted that will also be the money supply. (Fractional reserve banking is likely to be adopted only in a limited form, due to Bitcoin's inherent volatility and illiquidity.) I don't see how Bitcoin's supply curve might be raised by the increased hoarding of Bitcoins. If you mean the amount of Bitcoins offered on exchanges, then if Bitcoin is hoarded, its price will rise, encouraging some of its holders to sell it and profit on the trade. But there will still be the same amount of Bitcoins among its users. Because the price must rise to accommodate the increased demand (no new Bitcoins can be created), it makes Bitcoin's price unstable, hence volatile, not ideal for money.