Halving Fallacy

Bitcoin consensus-rules produce a predictable rate of monetary inflation. This rate is reduced by half every four years at a point called the halving. There are several step functions in Bitcoin. The halving occurs every 210,000 strong blocks, the difficulty adjustment every 2,016 strong blocks and chain reorganization approximately every 10 minutes. The numeric values that control these intervals are arbitrary yet the discontinuity is necessary due to the discrete intervals required for proof of work.

There is a theory that the halving subsidy creates a financial cliff for miners that may lead to a perpetual stall. The theory is based on the confluence of two step functions (halving and difficulty), causing the period of another (reorganization) to expand dramatically. The theory assumes that the difficulty adjustment resets average miner economic profit to zero, allowing only the top 50% of miners to survive over time, eventually reducing mining to just a few miners. In other words the difficulty adjustment is considered a pooling pressure.

However there is no reason to believe that the adjustment reduces any miner's profit to zero. The consequence of the assumption is not that there will be few miners, but that there will be none, due to the difficulty adjustment alone.

Consider the case of no price change. In this case there is no reason to expect a change in total hash rate. In this case there are no adjustments to difficulty, and we can conclude that the average mine generates the market return on capital (not zero!). Below market return on capital reduces hash rate and above market increases it, as capital chases returns. Addition of hash power decreases profits, discouraging hash power, and reduction of hash power increases profits, encouraging hash power. In other words, in the absence of price changes we conclude that any number of independent miners can compete indefinitely (modulo actual pooling pressures). The case where price is increasing or decreasing is no different.