Abstract

Bitcoin, the first and largest cryptocurrency, has shown remarkable growth in adoption and market capitalization since its inception. As its supply is finite and demand continues to rise due to its unique properties, Bitcoin has the potential to become the dominant asset in the global economy. Bitcoin's fixed supply will absorb market share from all other products/assets on average, causing them to lose value over time due to their higher rates of inflating supply, and less desirable traits for storing wealth.

This paper discusses the effects this process may impose on the global economy, potential benefits, problems that could arise, and possible solutions. It explores the concept of Bitcoin as a store of value becoming a financial black hole, inevitably graduating to its ultimate form; a decentralized and deflationary globally adopted currency - The Bitcoin Singularity.

The Bitcoin Economy - Age of Prosperity

Inevitable widespread adoption of Bitcoin will lead to a future of abundance and prosperity for consumers by transforming the inflationary economies of today into a long-term global deflationary economy. As the supply of goods, services, and other assets continue to increase, their prices will decrease relative to Bitcoin's fixed supply, increasing the total market share of Bitcoin over time.

As Bitcoin's market share grows, its price denominated in all other assets will also increase, further amplifying the attention it receives due to its unique properties creating a self-reinforcing cycle. This process naturally incentivizes consumers to save rather than spend. The shift in consumer behavior will lead to heightened competition among businesses as they strive to create the most beneficial and productive products that remain in demand from a consumer-first perspective.

Bitcoin Economy - Original image by OpenAI's DALL-E 2

This heightened competition ensures that only the best products survive in markets, compounding benefits for consumers and promoting true economic growth. In this economy, even governments will have to prioritize their efforts around the interest of consumers in order to earn and retain Bitcoin, if they wish to maintain their power for any significant duration. Adoption of Bitcoin may create a more equitable and efficient global economy, benefiting all participants.

Mathematical Analysis - Supply

( Feel free to skip this section if you are more interested in the story than the supporting equations. )

"Market Capitalization, or market cap for short, is a measurement of the total value of a given asset. It is calculated using formula (M=PS) where (M)arket cap equals the (P)rice of a single unit of the asset multiplied by the total (S)upply of units in circulation. (P)rice can be solved by rearranging the formula as such; P=M/S."

I will be Analyzing the mathematics behind how Bitcoin's black-hole effect works through use of the market capitalization formula, and intuitive reproducible examples. The goal of this analysis is to explore how Bitcoin's value is affected by changes in the supply of other assets.

This analysis compares Bitcoin (BTC) to a hypothetical index containing the average value of all assets in existence excluding Bitcoin, using a controlled test environment where demand for both remains stagnant (not growing). This allows us to observe supply-based effects without any additional factors.

The proposed index is similar in concept to Index Funds in the stock market, the (DXY) U.S Dollar Index, or the measure of Bitcoin Dominance over the index of other cryptocurrencies. Bitcoin is denominated by the index. (BTC / Index of All Assets)

To facilitate familiarity and understanding, I have chosen to display the units of value in dollars ($), even though dollars (USD) would be included within the index.

Bitcoin Variables:

• bP = $47,619.04 ^{-BTC price}
• bM = $1T ^{-BTC market cap}
• bS = 21M ^{-BTC supply}

bM / bS = bP = $1T / 21M = $47,619.04 ^{-Calculated BTC price: $47,619.04}

Index Variables:

• P = $100 ^{-Index price}
• M = $100T ^{-Index market cap}
• S = 1T ^{-Index supply}

M / S = P = $100T / 1T = $100 ^{-Calculated index price: $100}

bP / P = (BTC/Index denominated value) = $47,619.04 / $100 = $476.1904

Simulation:

"Let's apply this math to observe what happens when (S)upply of the index increases from 1T to 2T"

M / New S = New P = $100T / 2T = $50 ^{-Calculated new index price: $50}

bP / New P = (new denominated value) = $47,619.04 / $50 = $952.3808

"The price of the index has dropped by a factor of 2 from $100 to $50, and Bitcoin's index-denominated value has increased by the same factor of 2 from $467.19 to $952.38 respectively (rounded)."

$952.3808 / $476.1904 = 2 ^{-Proof BTC value went up by a factor of 2}

($1T / 21M = $47,619.04) * 2 = $95,238.08 ^{-Calculated new BTC price: $95,238.08}

$95,238.08 * 21M = $2T ^{-Calculated new BTC market cap: $2T}

"The supply increase of the index results in an increase in Bitcoin price and market cap of equal factor."

Analysis conclusion:

As we can see, Bitcoin's fixed supply ensures its price and market cap are directly corelated with the supply-based performance of other assets, as demonstrated by the simulation. The increase in the index supply from 1T to 2T resulted in a decrease in the index price from $100 to $50, and an increase in Bitcoin's price from $47,619.04 to $95,238.10, and market cap from $1T to $2T. This shows that as the supply of other assets increase, Bitcoin's value reacts positively and proportionately.

Interestingly, Bitcoin's fixed supply can be seen as a similar constraint as the total (M)oney supply variable when applying the MV=PQ Quantity Theory of Money formula, where the (V)elocity of money, and (Q)uantity of goods and services remain constant. While this formula is structured differently, the underlying message is similar to the market cap formula in that Bitcoin's fixed supply has a direct impact on its growth in market share as the supply of other assets inflate.

It's important to note that demand for bitcoin must remain neutral or positive for this to work, and cannot decline at a rate which would counter these effects. However, this is not much to ask compared to most or all other assets in the world which do not come with this supply-side advantage.

Potential Concerns & Resolutions

This section will cover some of the commonly suggested concerns surrounding the idea of the Bitcoin Singularity, and the deflationary economy that would result.

Concern 1:

• Deflationary pressures in the economy may lead to reduced spending and consumption, resulting in hoarding and potential economic slowdown.

Possible resolutions:

1. In a deflationary economy, consumers may only spend on necessary and beneficial products, leading to a more efficient allocation of resources and potentially increasing true economic growth. The assumption that high velocity of money is important may not hold in a long-term deflationary economy given the lack of supporting historical data on the subject.
2. In a deflationary economy, the value of money increases over time, which provides a natural incentive for individuals to save and invest. This can lead to increased capital formation over time, which in turn can stimulate economic growth in favor of the consumer.
3. The development of payment channels and incentivizing spending through rewards or loyalty programs may increase the circulation of Bitcoin. However, the focus should be on promoting spending on productive and valuable goods/services rather than arbitrary spending.

Concern 2:

• The concentration of wealth among early adopters and miners may lead to unequal distribution of resources and power in society.

Possible resolutions:

1. Over time, this issue can naturally be addressed through death & inheritance, spending on necessities and luxuries, and loss of private keys. These factors will inevitably result in the gradual redistribution of wealth, ensuring a more equitable distribution for all in the long term
2. This issue is not unique to deflationary economies, as inflationary currencies also suffer from this problem. Therefore, it is important to recognize that this issue is a common challenge across different types of economies and should be addressed accordingly.
3. It is important to acknowledge that early adopters and miners are entitled to the rewards for taking on the early risk associated with Bitcoin. Thus, it is not necessary to force them to lose their wealth faster due to inflationary pressures that exist in traditional economies.

Concern 3:

• The decentralized nature of Bitcoin may lead to regulatory challenges and potential conflicts with governments and financial institutions.

Possible resolutions:

1. Governments and financial institutions would be forced to collaborate with consumers to stay relevant in a Bitcoin dominant economy. As they can no longer print meaningful value, they would have to offer services in alignment with consumers' interests which are capable of earning Bitcoin according to supply and demand. Failure in this may lead to replacement by an entity more suitable for the role, forcing transparency and democratic collaboration.
2. One likely outcome could also be the development of decentralized governance mechanisms enabling decision-making and dispute resolution in a transparent and democratic manner. This can help ensure that the interests of all stakeholders are represented and society is able to self-regulate in a way that is fair and equitable.

Concern 4:

• If only the most necessary and productive businesses and products can compete in this economy, there may be less jobs, how will consumers earn bitcoin to survive?

Possible resolutions:

1. With the constantly lowering prices of goods and services, consumers would be able to purchase more with the same amount of Bitcoin over time. This could lead to a higher standard of living for consumers as they can afford to purchase more goods and services.
2. Consumers could earn Bitcoin through various means, such as selling goods or services, mining, or participating in Bitcoin-related activities which generate yield. Additionally, Bitcoin mining could be integrated into heating systems for homes, and excess computing resources could be utilized during idle time or while playing video games, creating new opportunities for consumers to generate value and earn Bitcoin to both survive and thrive.

Although this paper does not cover all the potential issues and respective solutions, it has provided a compelling case that potential concerns have relevant potential solutions. Further discussions on this topic will be highly appreciated. It will be interesting to observe how events unfold over time and whether they favor or contradict the presented ideas.

Conclusion

Bitcoin's unique properties, including its finite supply, decentralized & secure nature, and ability to transfer value without intermediaries, have led to its rapid adoption and growth in value. This paper has explored the potential effects of Bitcoin's continued growth on the global economy, including the creation of a deflationary economy that could benefit consumers and promote true economic growth.

The mathematical analysis presented in this paper demonstrates how Bitcoin's fixed supply leads to an increase in its price and market cap as the supply of other assets increases, providing further evidence for its potential to become the dominant asset in the global economy.

While there are potential problems that could arise with the widespread adoption of Bitcoin, such as regulatory challenges and reduced consumer spending, this paper argues that the benefits of a deflationary Bitcoin economy outweigh the potential costs.

In conclusion, demand for Bitcoin's unique properties and its fixed supply have the potential to transform the global economy, creating a more equitable and efficient system that benefits all participants. Its continued growth and adoption will be an important area of research and exploration in the coming years.