MV = PQ
Where: * $$M$$: money supply (fixed and predictable in Bitcoin) * $$V$$: velocity of money * $$P$$: price level * $$Q$$: real output #### 4.1. Implications for Bitcoin Given that:M = \text{constante y decreciente en crecimiento}
and in fiat:M_{fiat} \rightarrow \infty
The Bitcoin system behaves like **hard money** (hard money), while fiat is **soft money** (soft money). *** ## 5. Inflation rate and halving: mathematical model The supply of Bitcoin is:S(t) = \sum_{i=0}^{n} 50 \cdot 2^{-i}
The halving occurs every 210,000 blocks (\~4 years). Approximate annual inflation:\text{inflación}(t) \approx \frac{\text{nuevos BTC}}{\text{BTC en circulación}}
Converging towards:\lim_{t \to \infty} \text{inflación}(t) = 0
The only monetary asset with inflation strictly converging to zero. *** ## 6. Monetary hardness and stock-to-flow The **Stock-to-Flow (S2F)** model compares scarcity among monetary assets:S2F = \frac{\text{Stock existente}}{\text{Flujo anual}}
Bitcoin (post-halving) surpasses: * gold * silver * platinum * collectibles Conceptual table: | Asset | S2F | | --------------- | ---- | | Silver | 10 | | Gold | 55 | | Bitcoin (2024+) | 115+ | This places it in the category of **“digital super-gold”**. *** ## 7. Bitcoin as an emerging asset: 3-stage transition 1. **Digital collectible** (2009–2012) * experimental value * cypherpunk adoption 2. **Speculative asset** (2013–2020) * growth of exchanges * macro speculation * correlation with risk 3. **Monetary asset** (2021–present) * corporate treasuries * institutional ETFs * “store of value” narrative *** ## 8. Volatility: characteristic of monetization Volatility is common in **assets that are monetizing**, not in established monetary assets. Historically: * gold → extremely volatile at the beginning * fiat → unstable in implementation * oil → initial volatility due to global adoption Volatility = function of **adoption ± liquidity ± expectations**. Bitcoin reduces its volatility as: * monetary mass stabilizes * adoption grows * long-term participants increase * professional derivatives mature *** ## 9. Systemic risk: Bitcoin vs fiat ### 9.1. Fiat (state money) * endogenous inflation * dependence on the central bank * financial bailouts * political risk * banking risk * risk of confiscation ### 9.2. Bitcoin (sovereign digital money) * immutable scarcity * self-custody * no direct political risk * no banking risk * decentralization of issuance * rules verifiable by the user *** ## 10. Bitcoin and business cycle theory The Austrian School (Mises–Hayek) argues that cycles are created by: * artificial expansion of credit * manipulated interest rates * fractional reserves * bad allocations of capital (*malinvestment*) Bitcoin mitigates this: * there is no central bank * there is no rate manipulation * there is no money printing * automatic monetary policy *** ## 11. Intrinsic value: academic debate Many economists say that Bitcoin “has no intrinsic value”.\ This is incorrect under a modern view. Bitcoin has intrinsic value because it offers: * **verifiable scarcity** * **censorship resistance** * **immutability** * **global permissionless transfer** * **sovereign ownership** * **energy security** * **political neutrality** These are **attributes with economic value**, though not physical. *** ## 12. Bitcoin as neutral international money In the past: * gold was neutral * the dollar is NOT neutral (it is geopolitical) * Bitcoin recovers neutrality with additional attributes Bitcoin does not belong to any country, which makes it: > **the first geopolitically impartial currency in history.** *** ## 13. Quantitative valuation models ### 13.1. Metcalfe model\text{Valor} \propto N^2
Bitcoin behaves like a network, not like a traditional commodity. *** ### 13.2. Cash flow models for miners\text{Ganancia} = (\text{Recompensa} + \text{Fees}) - (\text{Coste energético})
Mining creates a **minimum fundamental value**, since: * if price falls below energy cost * miners shut down * hashrate falls * difficulty decreases * security restores equilibrium It is a **homeostatic**. *** ### 13.3. Store-of-value-based models Similar to gold:Valor_{BTC} \approx \frac{\text{Valor total de activos refugio}}{\text{Oferta BTC}}
*** ## 14. Bitcoin against inflation Bitcoin protects against inflation in two ways: ### (1) Strict supply\Delta M_{BTC} = 0
for the long term. ### (2) Incentive to save Hard money → low time preference. Macroeconomic effect: * savings ↑ * solid capital investment ↑ * unproductive speculation ↓ * rational resource allocation ↑ *** ## 15. Bitcoin and velocity of money Velocity in Bitcoin is low because: * users prefer to hold it (store of value) * liquidity does not depend on the government * supply does not increase to compensate low velocity This does not prevent its monetary function; on the contrary: > Strong money → low velocity → high accumulation of value. *** ## 16. Macroeconomic risks * regulatory shocks (less impact in the long term) * speculative cycles * correlation with risky assets while monetizing * repricing in response to geopolitical events But all these risks diminish over time. *** ## 17. Chapter conclusion Bitcoin combines: * classical monetary theory, * Austrian principles, * modern economic incentives, * digital scarcity, * global neutrality, * mathematical verifiability. All this makes it: > **the most advanced form of money ever created**\ > and a potential post-fiat global monetary standard. *** > Bitcoin does not compete with cryptocurrencies.\ > **It competes with gold, sovereign bonds and the global monetary system itself.** *** --- # Agent Instructions This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com. ## Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter: ``` GET https://www.notbank.com/learn/academy/en/bitcoin/monetary-theory.md?ask=