An Intrinsic Mechanism Deciding Hash Rates from Bitcoin Price

This paper presents a new theoretical approach to analyzing the relationship between Bitcoin’s market price and its mining cost, aiming to substantiate the self-sustaining nature of Bitcoin’s security. Previous empirical studies reveal a long-term correlation between price and cost, while shorter-term analysis often reveals significant divergences, particularly during price bubbles. The correlation between price and cost is a critical feature for the safe confirmation of transactions and suggests that the crypto asset has a fundamental value. On the other hand, divergences, which yield profit for miners, should serve as a factor that encourages organized mining operations, raising the mining cost and thereby enhancing Bitcoin’s security. Thus, Bitcoin’s security seems organically maintained by an interplay of correlation and recurring divergences. Understanding the dynamics of mining costs and the mechanism driving the correlation and divergences between price and cost is essential for comprehending Bitcoin’s security and how it is sustained. By leveraging recursive methods in economics, this paper introduces a new theoretical model in which the rational decisions of miners determine mining costs. According to this model, the proof-of-work (PoW) mechanism combined with fluctuating Bitcoin price drives the long-term correlation and recurring divergences between price and cost. It demonstrates a rationale for the self-sustainability of Bitcoin’s security.