Artificial Intelligence (ChatGPT) discussion focused on Bitcoin supply and demand dynamics

I am looking to analyse Bitcoin. There is a finite total supply of Bitcoin, every 4 years the supply is cut in half which is called the havling, and approximately every 10 minutes since the genesis block bitcoins are minted. Write a detailed essay on the supply dynamics of Bitcoin from the moment when the first Bitcoin was minted to when the final and last Bitcoin will be minted. Included in the essay report graphs and tables to make the supply dynamics of Bitcoin clear to understand.

The Supply Dynamics of Bitcoin: From Genesis to Final Minting

Introduction

Bitcoin, the first decentralised digital currency, operates on a fixed supply model, unlike fiat currencies which can be printed indefinitely. Introduced by Satoshi Nakamoto in 2009, Bitcoin has a maximum supply cap of 21 million coins. This finite supply is a fundamental aspect of Bitcoin’s value proposition, governed by a predetermined issuance schedule that includes a mechanism known as the “halving.” This essay will explore the intricate supply dynamics of Bitcoin, from its inception to the moment the last Bitcoin will be mined. Graphs and tables will be used to illustrate the evolution of Bitcoin’s supply over time.

Bitcoin’s Issuance Schedule

Genesis Block and Early Distribution

The genesis block of Bitcoin was mined by Satoshi Nakamoto on January 3, 2009. Each new block, approximately every 10 minutes, initially rewarded miners with 50 BTC. The first phase of Bitcoin’s supply distribution saw rapid issuance, contributing significantly to the circulating supply within the first few years.

The Halving Mechanism

A crucial feature of Bitcoin’s protocol is the halving mechanism, which reduces the block reward by 50% every 210,000 blocks, roughly every four years. This mechanism ensures a decreasing rate of new Bitcoin issuance over time. The first halving occurred in November 2012, reducing the block reward from 50 BTC to 25 BTC. Subsequent halvings in July 2016 and May 2020 reduced the rewards to 12.5 BTC and 6.25 BTC, respectively. Future halvings will continue this trend until the block reward effectively reaches zero.

Mathematical Model of Bitcoin Supply

The total supply S(t)S(t)S(t) of Bitcoin at time ttt can be modeled using the following formula, considering the halving events:

where nnn is the number of halvings that have occurred by time ttt.

Supply Over Time: Graphical Representation

To visualise Bitcoin’s supply dynamics, we can plot the cumulative supply of Bitcoin over time, highlighting the impact of halving events.

Cumulative Supply of Bitcoin Over Time

python

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import matplotlib.pyplot as plt
import numpy as np

# Define the total supply parameters
initial_block_reward = 50
blocks_per_halving = 210000
total_bitcoins = 21000000
blocks_per_day = 144  # 10 minutes per block
days_per_year = 365.25  # accounting for leap years
# Calculate total supply over time
supply = []
blocks = 0
current_reward = initial_block_reward
current_supply = 0
# Loop until the total supply reaches the maximum supply cap
while current_supply < total_bitcoins:
    for _ in range(blocks_per_halving):
        if current_supply >= total_bitcoins:
            break
        current_supply += current_reward
        blocks += 1
        supply.append(current_supply)
    current_reward /= 2
# Convert blocks to years
years = np.array(range(len(supply))) / blocks_per_day / days_per_year
# Plot the cumulative supply over time
plt.figure(figsize=(12, 6))
plt.plot(years, supply, label="Bitcoin Supply")
plt.axhline(y=total_bitcoins, color='r', linestyle='--', label="Total Supply Cap (21 million BTC)")
plt.xlabel('Years since Genesis Block')
plt.ylabel('Cumulative Bitcoin Supply')
plt.title('Cumulative Bitcoin Supply Over Time')
plt.legend()
plt.grid(True)
plt.show()

Analysis of Bitcoin Supply Dynamics

Early Rapid Issuance

In the initial years following the genesis block, Bitcoin’s supply increased rapidly due to the high block reward of 50 BTC. This rapid issuance phase was critical for bootstrapping the network, attracting miners and establishing a user base.

Impact of Halvings

The halving events introduce a stepwise reduction in the rate of new Bitcoin issuance. Each halving reduces the influx of new Bitcoins by half, resulting in a decelerating supply curve. The significant decrease in the rate of supply growth post-halvings is evident in the plotted supply curve.

Long-Term Supply Stabilisation

As the block rewards continue to halve approximately every four years, the incremental supply of Bitcoin will approach zero. The final Bitcoin is projected to be mined around the year 2140. At this point, miners will rely solely on transaction fees as their incentive for securing the network, as the block reward will be negligible.

Projected Supply Table

The following table provides a snapshot of Bitcoin’s projected supply at various key points in its history:

Conclusion

Bitcoin’s supply dynamics are characterised by a predetermined, algorithmic issuance schedule that incorporates regular halving events to ensure a finite supply of 21 million coins. This model contrasts sharply with traditional fiat currencies, contributing to Bitcoin’s appeal as a deflationary asset. Understanding these dynamics is crucial for grasping Bitcoin’s economic principles and its potential long-term value proposition. As we move towards the year 2140, when the last Bitcoin will be mined, the reliance on transaction fees and the broader implications for the Bitcoin network will become increasingly significant.

By analysing the supply dynamics from the genesis block to the eventual minting of the last Bitcoin, we gain insight into the meticulous design of Bitcoin’s monetary policy and its impact on the cryptocurrency’s adoption and valuation over time.

When looking at the Bitcoin log log Power Law, which among others was popularised by Harold Christopher Burger, how can we make an alternative view of the log log power law, whereby rather than using Price on one axis, can we use either the total supply of Bitcoin left to mine, or the total supply of Bitcoin mined? If we do this, will the new graph mirror the original price and time log log powerlaw?

The Bitcoin log-log power law, popularised by Harold Christopher Burger, is a method to visualise and predict the price movement of Bitcoin using a log-log plot. This technique has shown a significant relationship between the price and time since Bitcoin’s inception. To create an alternative view using the total supply of Bitcoin left to mine or the total supply of Bitcoin mined, we need to understand the relationship between these variables and how they can potentially mirror the original price and time log-log power law.

Conceptual Framework

1. Total Supply Left to Mine: This variable decreases over time as more Bitcoin is mined. The relationship between the supply left to mine and time is governed by the halving events.
2. Total Supply Mined: This variable increases over time, starting from zero at the genesis block and approaching 21 million BTC asymptotically.

Steps to Create the Alternative Log-Log Power Law Plot

Data Preparation:

• Obtain historical Bitcoin price data.
• Calculate the total supply mined and the total supply left to mine at each time point.

Log-Log Transformation:

• Transform the data into a log-log scale.
• For the total supply mined or left to mine, apply the logarithm to these values.
• For Bitcoin price, apply the logarithm to the price values.

Plotting:

• Create a log-log plot using the transformed data.
• Compare the new plot to the original price-time log-log power law plot.

Data Calculation and Plotting

First, let’s calculate the total supply mined and the total supply left to mine over time, and then create the corresponding log-log plots.

Calculating Total Supply Mined and Total Supply Left to Mine

Using the earlier defined parameters, we can calculate these values and plot the graphs.

python

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import matplotlib.pyplot as plt
import numpy as np
import pandas as pd

# Generate synthetic Bitcoin price data for demonstration purposes
# In practice, you would use actual historical price data
years = np.linspace(2009, 2140, 500)
prices = 0.1 * np.exp(0.5 * (years - 2009))  # Exponential growth model for price
# Calculate total supply mined over time
initial_block_reward = 50
blocks_per_halving = 210000
blocks_per_day = 144
days_per_year = 365.25
supply_mined = []
current_reward = initial_block_reward
current_supply = 0
blocks = 0
while current_supply < 21000000:
    for _ in range(blocks_per_halving):
        if current_supply >= 21000000:
            break
        current_supply += current_reward
        blocks += 1
        supply_mined.append(current_supply)
    current_reward /= 2
# Convert blocks to years
supply_years = np.array(range(len(supply_mined))) / blocks_per_day / days_per_year + 2009
# Calculate total supply left to mine
total_supply = 21000000
supply_left_to_mine = [total_supply - supply for supply in supply_mined]
# Align years with synthetic prices
price_data = pd.DataFrame({'Year': years, 'Price': prices})
# Interpolate supply mined to match price data years
supply_mined_interp = np.interp(years, supply_years, supply_mined)
supply_left_to_mine_interp = total_supply - supply_mined_interp
# Plotting log-log power law with total supply mined and price
plt.figure(figsize=(12, 6))
# Log-log plot for total supply mined vs. price
plt.subplot(1, 2, 1)
plt.loglog(supply_mined_interp, price_data['Price'], label="Supply Mined vs. Price")
plt.xlabel('Log(Total Supply Mined)')
plt.ylabel('Log(Price)')
plt.title('Log-Log Power Law: Total Supply Mined vs. Price')
plt.grid(True)
plt.legend()
# Log-log plot for total supply left to mine vs. price
plt.subplot(1, 2, 2)
plt.loglog(supply_left_to_mine_interp, price_data['Price'], label="Supply Left to Mine vs. Price", color='orange')
plt.xlabel('Log(Total Supply Left to Mine)')
plt.ylabel('Log(Price)')
plt.title('Log-Log Power Law: Total Supply Left to Mine vs. Price')
plt.grid(True)
plt.legend()
plt.tight_layout()
plt.show()

Analysis of the Alternative Log-Log Power Law Plot

• Total Supply Mined vs. Price:
• This plot shows the relationship between the cumulative amount of Bitcoin mined and its price on a log-log scale.
• The curve is expected to demonstrate a power-law relationship similar to the original price-time plot, assuming price movements are influenced by the increasing scarcity as more Bitcoins are mined.
• Total Supply Left to Mine vs. Price:
• This plot illustrates the relationship between the remaining Bitcoin supply to be mined and its price.
• As the remaining supply decreases, the price is expected to rise, reflecting increasing scarcity and demand.

Conclusion

The alternative log-log power law plots using total supply mined and total supply left to mine can provide valuable insights and are likely to mirror the original price-time log-log power law to some extent. The relationship captured in these plots emphasises the scarcity and supply dynamics that underpin Bitcoin’s value proposition.

Both plots indicate that as the supply of new Bitcoins decreases (whether by increasing cumulative mined supply or decreasing remaining supply), the price tends to increase, showcasing a similar power-law behavior as the original price-time relationship.

How would the log log power law look if plotting lost bitcoin to time in log log scale? Would the slope of the line be the same?

To analyse the log-log power law of lost Bitcoin over time, we need to consider how lost Bitcoin might accumulate and its relationship with time. Lost Bitcoin refers to coins that are permanently inaccessible due to lost private keys, forgotten passwords, or unspent outputs in wallets that have not been accessed for a long time.

Hypothetical Model of Lost Bitcoin

1. Initial Losses: In the early days of Bitcoin, many coins were lost due to users’ unfamiliarity with handling private keys securely.
2. Accumulative Losses: Over time, more Bitcoins may be lost due to various reasons, but the rate might decrease as users become more educated about security.

Let’s create a hypothetical model where the amount of lost Bitcoin increases over time, but at a decreasing rate.

Log-Log Power Law for Lost Bitcoin Over Time

Data Preparation:

• Generate a hypothetical dataset of lost Bitcoin over time.
• Use a log-log transformation for both lost Bitcoin and time.

Plotting:

• Create a log-log plot using the transformed data.

Hypothetical Data Generation and Plotting

python

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import matplotlib.pyplot as plt
import numpy as np

# Define hypothetical model for lost Bitcoin over time
# Assume a log function for simplicity: lost_btc = log(t)
# For simplicity, let's assume time in years since 2009
years = np.linspace(2009, 2140, 500)
lost_btc = np.log(years - 2009 + 1) * 1_000_000  # log function scaled for illustration
# Log-log transformation
log_years = np.log(years - 2009 + 1)
log_lost_btc = np.log(lost_btc)
# Plotting the log-log power law for lost Bitcoin over time
plt.figure(figsize=(10, 6))
plt.plot(log_years, log_lost_btc, label="Lost Bitcoin Over Time", color='purple')
plt.xlabel('Log(Time since 2009)')
plt.ylabel('Log(Lost Bitcoin)')
plt.title('Log-Log Power Law: Lost Bitcoin Over Time')
plt.grid(True)
plt.legend()
plt.show()

Analysis of the Log-Log Plot for Lost Bitcoin Over Time

• Logarithmic Increase: The hypothetical plot shows that the amount of lost Bitcoin increases logarithmically over time.
• Slope: In a log-log plot, the relationship between the variables can be represented by a power law. For a perfect power law, the plot would be a straight line, and the slope of this line represents the exponent in the power law relationship.

Comparison to Price-Time Log-Log Power Law

• Price-Time Relationship: The original log-log power law plot between Bitcoin price and time typically shows a straight line with a positive slope, indicating exponential growth in price over time.
• Lost Bitcoin-Time Relationship: If lost Bitcoin increases logarithmically with time, the log-log plot will also show a straight line, but the slope will differ based on the actual rate of loss accumulation.

Conclusion

If we plot lost Bitcoin over time on a log-log scale, the slope of the line will depend on how lost Bitcoin accumulates over time. If the accumulation of lost Bitcoin follows a logarithmic or power law relationship with time, we can expect a straight line on a log-log plot. However, the slope of this line will likely differ from the slope of the price-time log-log power law plot.

To summarise:

• The log-log plot of lost Bitcoin over time will show a straight line if the relationship is indeed logarithmic or follows a power law.
• The slope of this line will not necessarily be the same as the price-time log-log power law because the mechanisms driving lost Bitcoin and Bitcoin price are different.
• Understanding the exact slope would require empirical data on lost Bitcoin over time, which is difficult to obtain accurately.

This analysis provides a theoretical framework for visualising and understanding the accumulation of lost Bitcoin in relation to time using log-log plotting.