This paper, "The Price and Cost of Bitcoin" by Marthinsen and Gordon, addresses a critical puzzle in cryptocurrency economics: the relationship between Bitcoin's market price and its production (mining) cost. While a popular narrative suggests mining cost acts as a price floor, empirical econometric studies (e.g., Kristofek, 2020; Fantazzini & Kolodin, 2020) show the opposite—mining costs follow price changes. This research aims to provide the missing economic theory to explain this observed causality, moving beyond correlation to establish a logical chain of causation from price to cost.
Traditional monetary models like the Quantity Theory of Money (QTM) or Purchasing Power Parity (PPP) are largely ineffective for Bitcoin analysis. This is because Bitcoin currently functions poorly as a widespread unit of account or medium of exchange (Baur et al., 2018). Most goods and services are priced in fiat currencies, with Bitcoin acting more as a speculative asset than a currency for daily transactions.
A prevalent but largely unsubstantiated belief posits that the cost of Bitcoin creation (mining) provides a fundamental support level for its price. The logic is that if the price falls below the cost of production, mining becomes unprofitable, miners would cease operations, and the security of the Bitcoin network (maintaining the public ledger) would be threatened (Garcia et al., 2014). A related belief is that price must rise with increasing production costs.
Recent econometric analyses have debunked the cost-floor theory, demonstrating that changes in mining costs are lagged responses to changes in Bitcoin's price. However, these statistical models, while identifying the correlation direction, fail to explain the why—the underlying economic mechanism driving this behavior. This paper seeks to fill that explanatory gap.
The core argument is that Bitcoin's price is determined in a global, speculative market by factors like investor sentiment, regulatory news, macroeconomic trends, and adoption narratives—largely independent of current mining costs. A rising price increases the revenue potential for miners, creating an incentive for them to invest in more and better hardware (increasing hash rate) to compete for block rewards. This investment drives up the marginal cost of mining (primarily electricity and hardware), causing costs to follow price.
Framework: A simplified causal model can be represented as a directed acyclic graph (DAG):
External Shock (e.g., positive regulatory news) → ↑ Bitcoin Market Price → ↑ Expected Mining Profitability → ↑ New Miner Entry & Investment in ASICs → ↑ Total Network Hash Rate → ↑ Mining Difficulty (protocol adjustment) → ↑ Marginal Cost of Production (Electricity + Depreciation).
Case Example (2020-2021 Bull Run): Bitcoin's price surged from ~$5,000 in March 2020 to over $60,000 by March 2021. This price increase preceded a massive influx of mining investment. Companies like Marathon Digital and Riot Blockchain ordered billions of dollars worth of new mining rigs. The global Bitcoin network hash rate and mining difficulty soared to all-time highs months after the price rally began, demonstrating the lagged response of mining costs (capex and opex) to price signals.
The relationship can be formalized. A miner's profit ($\pi$) per unit time is:
$\pi = \frac{R}{D \cdot H} \cdot H_m \cdot P - C_e \cdot H_m - C_h$
Where:
$R$ = Block reward (BTC)
$D$ = Network Difficulty
$H$ = Total Network Hash Rate
$H_m$ = Miner's Hash Rate
$P$ = Bitcoin Price (USD/BTC)
$C_e$ = Cost of Energy per unit of Hash Rate
$C_h$ = Fixed Hardware Costs (amortized)
In competitive equilibrium, expected profit tends to zero. Setting $\pi = 0$ and solving for the breakeven price $P_{be}$ shows its dependence on network conditions ($D, H$) which are themselves functions of past prices:
$P_{be} = \frac{D \cdot H}{R} \cdot (C_e + \frac{C_h}{H_m})$
Since $D$ and $H$ adjust upwards in response to a higher $P$ with a lag (due to hardware procurement and delivery times), $P_{be}$ is a function of lagged $P$, not a determinant of current $P$.
Core Insight:
Marthinsen and Gordon deliver a crucial, if belated, correction to a pervasive market myth. The "cost-as-floor" theory is not just empirically wrong; it's conceptually backwards. Bitcoin mining is a derivative industry whose economics are dictated by the asset's market price, not the other way around. Treating mining cost as a fundamental valuation metric is akin to valuing Tesla by the cost of its factory electricity—it confuses an operational input with the driver of speculative demand.
Logical Flow:
The paper's logic is sound and aligns with basic microeconomics: price signals drive resource allocation. A higher Bitcoin price increases the marginal revenue product of hash power, attracting capital and labor (in this case, ASICs and electricity) until the marginal cost of production rises to meet the new equilibrium. The 14-day difficulty adjustment is the key protocol mechanism that translates price-driven hash rate increases into higher sustained costs.
Strengths & Flaws:
Strengths: The paper successfully provides the missing theoretical link for prior econometric findings. Its strength lies in applying classical production theory to a novel digital asset. It effectively debunks a dangerous heuristic used by some investors.
Flaws: The analysis, while correct on direction, is somewhat simplistic. It underplays the potential for a weak long-run equilibrium relationship. In a scenario of prolonged price depression, the attrition of miners could reduce network hash rate and difficulty, lowering the marginal cost for survivors, potentially creating a loose lower bound. Furthermore, it doesn't fully integrate the role of transaction fees, which may become a more significant part of miner revenue post-halving, potentially altering the dynamics.
Actionable Insights:
This paper's conclusion is supported by broader research in asset pricing. As noted in the seminal work on speculative bubbles by Brunnermeier & Oehmke (2013), asset prices in markets with heterogeneous beliefs and leverage can become decoupled from any fundamental "cost" for extended periods. Bitcoin, with its fixed supply and purely speculative demand drivers, is a prime example of this phenomenon.