The Price and Cost of Bitcoin: Unraveling the Causal Chain

1. Introduction & Overview

This paper, "The Price and Cost of Bitcoin" by Marthinsen and Gordon, addresses a critical gap in cryptocurrency research. While numerous studies attempt to explain or predict Bitcoin's price volatility, few have rigorously examined the relationship between its price and the cost of mining. The prevailing, yet largely unsubstantiated, belief has been that mining costs act as a fundamental price floor. This research employs economic theory to debunk this notion and explain the observed econometric reality: mining costs follow price movements, not precede them.

2. Literature Review

2.1 Economic Factors and Bitcoin's Price

Traditional monetary models like the Quantity Theory of Money (QTM) or Purchasing Power Parity (PPP) are ill-suited for Bitcoin analysis. As Baur et al. (2018) note, Bitcoin is not yet a widespread unit of account or medium of exchange. Most goods and services are priced in fiat currencies, with Bitcoin acting as a settlement layer at the spot exchange rate, making conventional price index creation impossible.

2.2 The Cost-as-Price-Floor Hypothesis

A popular hypothesis, suggested by Garcia et al. (2014), posits that the cost of creating a Bitcoin (via mining) establishes a support level. The logic is that if the price falls below production cost, mining becomes unprofitable, jeopardizing the security of the blockchain ledger. Related work by Meynkhard (2019) and Hayes (2019) has used mining costs to forecast prices.

2.3 Econometric Challenges

Recent econometric analyses by Kristofek (2020) and Fantazzini & Kolodin (2020) have challenged this view. Their findings indicate a reversal of the presumed causality: changes in mining costs lag changes in Bitcoin's price. However, these studies stop at identifying the correlation without providing a theoretical economic explanation for why this lag occurs—a gap this paper aims to fill.

3. Core Insight: Analyst's Perspective

4. The Causal Chain: Price to Cost

4.1 Theoretical Framework

The core of the paper's contribution is modeling the causal chain. It posits that Bitcoin's price is primarily determined by speculative demand and market sentiment—factors largely external to the mining ecosystem. A positive price shock increases the expected revenue for miners. This acts as a signal, incentivizing:

1. Entry of New Miners: Attracted by perceived profitability.
2. Investment in More/Efficient Hardware: Increasing the network's total computational power (hash rate).
3. Adjustment of Mining Difficulty: The Bitcoin protocol automatically adjusts the difficulty of the cryptographic puzzle to maintain a ~10-minute block time. A higher hash rate leads to a higher difficulty.

The increased difficulty and competition for blocks raise the marginal cost of producing a new Bitcoin. Thus, the price increase sets off a sequence of events that ultimately raises the cost of production.

4.2 Mathematical Formulation

The relationship can be conceptualized through a simplified model. Let $P_t$ be the Bitcoin price at time $t$, and $C_t$ be the average mining cost. The hash rate $H_t$ is a function of expected profitability, which is driven by price.

$H_t = f(E[P_{t+1}], \text{Energy Cost})$

Difficulty $D_t$ adjusts based on $H_t$:

$D_{t+1} = D_t \cdot \frac{ \text{Target Block Time} }{ \text{Actual Block Time} } \approx g(H_t)$

The cost $C_t$ is then a function of the energy required to solve a block at difficulty $D_t$ with hardware efficiency $\eta$ and energy price $E$:

$C_t \approx \frac{ D_t \cdot \text{Energy per Hash} \cdot E }{ \eta \cdot \text{Bitcoin Block Reward} }$

Since $D_t$ is driven by $H_t$, which is driven by $P_t$, we get the causal chain: $P_t \rightarrow H_t \rightarrow D_t \rightarrow C_t$. This formalizes why $C_t$ lags $P_t$.

5. Experimental Results & Data Analysis

While the full empirical analysis is in the original paper, the implied results align with prior econometric studies. A Granger causality test on time-series data of Bitcoin price and a composite mining cost index (incorporating hardware costs, energy prices, and hash rate) would likely show:

• No Granger Causality from Cost to Price: Rejecting the hypothesis that cost predicts price.
• Significant Granger Causality from Price to Cost: Confirming that past prices help predict future mining costs.

Chart Description (Conceptual): A dual-axis chart over a 5-year period. The primary axis (left) shows Bitcoin's USD price, exhibiting high volatility with major peaks and troughs. The secondary axis (right) shows a mining cost index. Visually, the cost curve closely follows the price curve but with a noticeable lag of several weeks to months, especially after major price movements. Shaded regions highlight periods where price clearly led cost increases (e.g., post-2020 halving rally).

6. Analysis Framework: A Practical Case

Case: Evaluating a Mining Investment Post-Price Rally

Scenario: Bitcoin price surges 50% in one month. A fund considers investing in a new mining operation.

Framework Application:

1. Demand Signal: Analyze the cause of the price rally (e.g., institutional adoption news, macro hedge). Is it sustainable?
2. Lag Assessment: Recognize that the current "high profitability" is a snapshot. Use the causal model: $\text{Price} \uparrow \rightarrow \text{New Miners Enter} \rightarrow \text{Hash Rate} \uparrow \rightarrow \text{Difficulty} \uparrow \rightarrow \text{Future Cost} \uparrow \rightarrow \text{Future Margin} \downarrow$.
3. Decision Matrix: Project the time lag for hash rate/difficulty adjustment (historically 1-3 months). Model future costs based on projected hash rate growth. The investment thesis should not be based on current margins but on projected margins after the industry adjusts.

This framework prevents the common pitfall of overestimating long-term returns by using lagging cost data.

7. Future Applications & Research Directions

• Predictive Models: Incorporate this causal understanding into new forecasting models. Instead of using cost to predict price, use price and sentiment indicators to predict future hash rate and mining difficulty, which are crucial for network security analysis.
• ESG & Policy Analysis: Understand that Bitcoin's energy consumption is a function of its price. Policies aiming to reduce carbon footprint must consider the demand-side (price drivers) as much as the supply-side (energy source).
• Mining Stock Valuation: Apply the framework to value publicly traded mining companies. Their future earnings are not simply "price minus cost" but are dependent on their ability to outpace difficulty increases and manage CapEx cycles triggered by price movements.
• Cross-Asset Analysis: Extend the model to other Proof-of-Work cryptocurrencies and compare the elasticity and lag structure of their price-to-cost relationships.

8. References

1. Marthinsen, J. E., & Gordon, S. R. (2022). The Price and Cost of Bitcoin. Quarterly Review of Economics and Finance. DOI: 10.1016/j.qref.2022.04.003
2. Baur, D. G., Hong, K., & Lee, A. D. (2018). Bitcoin: Medium of exchange or speculative assets? Journal of International Financial Markets, Institutions and Money, 54, 177-189.
3. Hayes, A. S. (2019). Bitcoin price and its marginal cost of production: support for a fundamental value. Applied Economics Letters, 26(7), 554-560.
4. Fantazzini, D., & Kolodin, N. (2020). Does the hashrate affect the Bitcoin price? Journal of Risk and Financial Management, 13(11), 263.
5. Kristofek, M. (2020). Bitcoin, mining and energy consumption. Digital Assets Lab.
6. CoinShares Research. (2023, January). The Bitcoin Mining Network. Retrieved from https://coinshares.com
7. Isola et al. (2017). Image-to-Image Translation with Conditional Adversarial Networks (CycleGAN). IEEE Conference on Computer Vision and Pattern Recognition (CVPR). [External reference example for methodological rigor].