Exercises: Bitcoin's Economic Model

Conceptual Exercises

Exercise 10.1: Supply Schedule Calculation

Calculate the total number of Bitcoin that will have been mined by the end of the 7th halving epoch (approximately 2036). Show your work using the geometric series formula. What percentage of the total 21 million supply does this represent?

Hint: Use the formula Supply(n) = 21,000,000 x (1 - 0.5^n), where n is the number of completed halving epochs.

Exercise 10.2: The Lost Coins Debate

Estimates suggest 3-4 million BTC are permanently lost. Write a 300-word analysis addressing the following: - Does the loss of coins make Bitcoin more or less suitable as a monetary system? - How do lost coins affect the store-of-value thesis versus the medium-of-exchange thesis differently? - Compare this to physical gold lost at sea, in shipwrecks, or in ancient buried hoards that will never be recovered. Does the comparison change your analysis?

Exercise 10.3: Stock-to-Flow Critical Analysis

PlanB's stock-to-flow model predicts that Bitcoin's price should increase as its S2F ratio increases with each halving. Identify three methodological problems with using this model for investment decisions. For each problem, explain: - What the specific issue is - Why it matters for the model's reliability - How a defender of the model might respond to the criticism

Exercise 10.4: The Digital Gold Comparison

Create a weighted scoring matrix comparing gold and Bitcoin as stores of value. Choose 8 properties you consider most important for a store of value, assign each a weight (totaling 100%), and score both gold and Bitcoin on each property (1-10 scale). Explain your weighting choices. What does your analysis reveal about your own assumptions?

Exercise 10.5: The Intrinsic Value Debate

The bear case argues that Bitcoin has "no intrinsic value." The bull case argues that no money has intrinsic value — value is always socially constructed. - Define "intrinsic value" precisely. Is there a widely agreed-upon definition? - Does the U.S. dollar have intrinsic value? Why or why not? - Does gold? (Consider: what would gold be worth if no one used it as money or jewelry — only industrial applications?) - Does the concept of intrinsic value even apply to monetary instruments? Defend your position.

Quantitative Exercises

Exercise 10.6: Halving Impact Analysis

Using the historical data provided in the chapter: 1. Calculate the average percentage price increase 12 months after each of the four halvings. 2. Calculate the median percentage price increase. 3. If you excluded the first halving (extremely small market, potentially not representative), how do the average and median change? 4. What is the trend in post-halving returns across the four events? If this trend continued linearly, what would the model predict for the 12-month return after the 5th halving (approximately 2028)? 5. Why should you be cautious about this linear extrapolation?

Exercise 10.7: Volatility Comparison

Using the annualized volatility figures from Section 10.8: 1. Calculate the average annualized volatility for Bitcoin over the period 2020-2025. 2. If the S&P 500's average annualized volatility over the same period was approximately 18%, how many times more volatile has Bitcoin been? 3. Using the rough rule of thumb that a 1-standard-deviation move occurs about 68% of the time, what range of annual returns would you expect for Bitcoin with 40% annualized volatility? (Assume a mean annual return of 50%.) 4. What would a 2-standard-deviation negative year look like? Has Bitcoin experienced returns worse than this?

Exercise 10.8: Wealth Concentration Analysis

The chapter mentions that the top 2% of Bitcoin addresses hold approximately 95% of all Bitcoin. 1. Calculate the Gini coefficient for a simplified distribution where 2% of holders own 95% and 98% of holders own 5%. (You may use the simplified formula for a two-group population.) 2. Compare this to the global wealth Gini coefficient (approximately 0.88) and the U.S. wealth Gini coefficient (approximately 0.85). What does the comparison suggest? 3. Why might using address-level data overstate concentration? (Hint: think about exchanges and multi-address wallets.) 4. Why might it understate concentration? (Hint: think about individuals with multiple addresses.)

Exercise 10.9: Mining Economics After Halving

A Bitcoin miner operates 1,000 Bitmain S21 machines, each producing approximately 200 TH/s and consuming 3,500 watts. Assume the total network hash rate is 700 EH/s, the block reward is 3.125 BTC, and Bitcoin's price is $85,000. 1. Calculate the miner's share of the total network hash rate. 2. Estimate the daily Bitcoin revenue (assuming 144 blocks per day). 3. Calculate the daily electricity cost at $0.05/kWh. 4. Calculate the daily profit or loss. 5. At what Bitcoin price does this operation break even (ignoring other costs like cooling, rent, and personnel)? 6. How would these numbers change after the next halving (block reward = 1.5625 BTC)?

Applied Exercises

Exercise 10.10: Building a Bitcoin Investment Thesis

You have been asked to write a 500-word investment memo for a university endowment considering a 2% allocation to Bitcoin. The endowment committee includes both Bitcoin enthusiasts and skeptics. Your memo must: - Present the bull and bear cases with equal weight - Identify the three most important risk factors - Recommend for or against the allocation with a clear rationale - Acknowledge what could prove your recommendation wrong

Exercise 10.11: Evaluating the El Salvador Experiment

Research the current status of El Salvador's Bitcoin adoption (as of your reading date). Write a 400-word assessment addressing: - What measurable economic outcomes has the experiment produced? - Has Bitcoin adoption for everyday transactions increased, decreased, or plateaued? - What lessons does the experiment offer for other countries considering similar moves? - What would you need to observe over the next 5 years to consider the experiment a success or failure?

Exercise 10.12: Stock-to-Flow Model Implementation

Using the stock_to_flow.py script provided in this chapter's code directory (or writing your own): 1. Calculate Bitcoin's S2F ratio at each halving date. 2. Plot the S2F ratio against Bitcoin's price at each halving (use log-log scale). 3. Fit a linear regression to the log-log data. 4. Use your model to predict the price at the next halving. What is the 95% confidence interval? 5. Plot the model's historical predictions against actual prices. Where did the model perform well? Where did it fail?

Exercise 10.13: Adoption Metrics Dashboard

Using the adoption_metrics.py script or your own code: 1. Plot at least three adoption metrics (active addresses, hash rate, transaction volume) over time. 2. Calculate the correlation between each metric and Bitcoin's price. 3. Which metric has the strongest correlation with price? Does correlation imply causation in this case? 4. Identify a period where adoption metrics and price diverged significantly. What might explain the divergence?

Discussion Questions

Exercise 10.14: The Monetary Philosophy Question

Bitcoin maximalists argue that Bitcoin's fixed supply makes it "sound money" — money that cannot be debased by political decisions. Keynesian economists argue that the ability to adjust money supply is essential for managing economic cycles. Research both positions and write a 300-word response to the following prompt: "Is the inability to adjust money supply a feature or a bug?"

Exercise 10.15: The ETF Paradox

The approval of spot Bitcoin ETFs was celebrated by Bitcoin advocates as institutional validation. However, Bitcoin was designed to be a peer-to-peer system that does not require trusted intermediaries. ETF holders do not hold Bitcoin — they hold shares in a fund that holds Bitcoin on their behalf, with a custodian (usually Coinbase) managing the private keys. - Does ETF-based Bitcoin ownership undermine Bitcoin's core value proposition? - Is there a difference between "adoption of Bitcoin" and "adoption of Bitcoin exposure"? - Could the concentration of Bitcoin in ETF custodians create a new form of the centralization risk that Bitcoin was designed to eliminate?

Exercise 10.16: The Volatility Horizon

The chapter shows that Bitcoin's volatility is declining but remains far above traditional stores of value. Consider the following thought experiment: at what level of annualized volatility would you personally consider an asset a suitable "store of value"? Is there a specific threshold, or does it depend on the time horizon? How does your answer change if you are a 25-year-old saving for retirement versus a 65-year-old retiree depending on your savings for living expenses?