A Currency Distribution that Encourages Stable Prices

Summary: Frink is creating a currency whose distribution is designed to grow at the correct rate relative to the number of users to encourage a stable value. Our distribution has been verified by studying multiple cryptocurrencies as well as government currencies. Increases and Decreases in usage per user will likely still increase/decrease the price of the currency. Frink does not promise stable price, especially early on, but it is designed to stabilize faster.

It's graphs like these that scare investors. Particularly everyday potential users and businesses.

Price stability is a major issue in the world of cryptocurrency which prevents major adoption. Cryptocurrencies provide many major advantages, low transaction fees alone should heavily encourage adoption by businesses. But businesses are already taking enough risks, why would they want to take the risk that the money they are accepting will lose more value than they make in profit? And most customers don’t feel safe moving their money over to such a currency that could have half of it’s value disappear practically overnight.


The problem is that almost all cryptocurrencies are designed with a fixed supply growth based on time, which unfortunately is awful for price stability. This is a problem because no one can predict how many users will be using the currency even just a year from now. And as time has proven, no one will ever be able to predict it with high accuracy! Want proof that a fixed total supply is awful? There are roughly 100 countries in the world with a population smaller than Bitcoin’s user base. Yet many of them with populations far smaller, have very stable prices for their currency. A perfect example of this is the Iceland Krona, used by 270,000 adults, yet it’s biggest price swing over any one year period has been roughly 50% and that was a large one. Bitcoin, however, has extreme volatility despite having a much larger user base and having had 10 years to stabilize. The primary factor causing this difference is that Bitcoin’s supply is fixed, while the currencies of these small countries are flexible and able to dynamically adapt to changing economic situations. Almost all other cryptocurrencies have adopted this model from Bitcoin and have the same inherent flaw.


The current most popular solution is to create a centralized token backed by a more stable currency, such as Tether, which is backed by USD. Yet much controversy over whether Tether has been honest with their reserves is a perfect example of why such a token cannot be centralized. Bernie Madoff is a perfect example of why such a system cannot be trusted, Tether has been accused of similar scamminess. The next most popular solution is to over-collateralize the token requiring far more money to be used to create a ‘stable’ token than the token is worth, typically more than 50%. If the underlying currency crashes by more than a smaller number such as 25%, then all those stable coins are taken out of circulation and the person who bought them has now lost the entire investment spent on buying them. Meaning he still risks losing the money spent buying the ‘stable currency’, but can’t profit if the value increases, which is a bad deal for the user. And if the token becomes reasonably popular, then it kills itself because the currency has inflated the money supply of the government currency it’s based off of, therefore causing itself to lose value. So at the end of the day, neither of these is great solution.


Frink takes a different approach. Frink first pays users to sign up, then on an ongoing basis pays those who most contribute to the currency by mining for Frinks or referring new users.


By varying the supply of the currency with the number of users, Frink essentially removes the changes in price that come from changes in number of users, which is the largest source of price instability. However, changes in spending habits of the average user will still be reflected in the price. The spending habits of the average user should stabilize much faster than in other cryptocurrencies.


Frink does not guarantee stable prices, increased usage of the currency should increase the price. Decreased usage will decrease the price.


Quantity Theory of Money

Before we get too ahead of ourselves let’s dive into the economics a little bit to explain the price stability and above all why current cryptocurrencies are unfortunately inherently designed for price instability, making them bad currencies.


A famous economic formula that can be applied to any currency is the Quantity Theory of Money, here is the “Fisher Version”:


P = MV/T


P = Average Price of Purchases (Example: Price of USD in terms of Frinks)

M = Money Supply (Total number of units of currency)

V = Velocity of Money (Number of times an average unit of currency changes hands)

T = Total Number of Purchases


New users bring with them changes to the velocity of money and number of purchases. This show us that having a fixed money supply but changing number of users like current cryptocurrencies is inherently unstable in terms of price. The money supply must be able to expand or contract to accommodate these users. And cryptocurrencies have shown that clearly they have not balanced this equation well. This can not be easily done without being able to directly measure the number of users.


The currency must grow or shrink fairly slowly to avoid big downward crashes in price, which scares users. If the price of the currency increases too quickly, then people rush in and buy more leading to bubbles, which ultimately crash. If the price moves too quickly download, then people tend to panic dump, forming the opposite of a bubble, resulting in extreme volatility. Current cryptocurrencies are proof of this and particularly susceptible due to rigid distribution rules.


At the end of the day, this means that for true price stability, someone must be able to tweak one of the variable in this equation. The only one that can be easily changed is the money supply by expanding or contracting it. And this must also be done in a fully decentralized manner.


Frink Stabilizes Faster as the Network Grows


Before we get too ahead of ourselves let’s dive into the economics a little bit to explain the price stability and above all why current cryptocurrencies are unfortunately inherently designed for price instability.


The biggest factors that affect the price of a currency are:

  • Money Supply (aka number of Frinks)

  • Number of Users

  • The equivalent of a Per Capita GDP for all users of a given currency

No one can directly control the GDP of the currency, however by linking the money supply to the number of users, Frink can grow the money supply at the proper rate relative to the number of users to encourage price stability. Speculation over how the GDP may change will always factor into the price of any currency and cannot directly be controlled or accounted for. The GDP of our average user should change fairly slowly over time.


Because the price of any free floating cryptocurrency in its early stages will always fluctuate, just like the price of any commodity, Frink is not designed for a fixed value but rather is simply designed to grow it’s money supply at a rate that encourages eventual but relatively fast price stability. Ultimately the free market will still determine the fair price.


Frink’s solution, is to expand the money supply along with the number of users. This should encourage price stability to be achieved faster as the network grows, after allowing Frink to go through a price finding period. This should achieve improved price stability though the Per Capita GDP of the users will likely change over time, which will be reflected in the price of the currency.


If this does not prove stable enough, Frink has a backup plan, this is to use a machine learning algorithm, to dynamically tweak the amount paid to the miners. Frink will evaluate the necessity to do this based upon Frink’s price stability after we reach 5 million users.


Neither of this solutions works nearly as well for the average cryptocurrency unless it has knowledge of the number of users using it, which is Frink’s speciality.


How Much Does a New User Expand the Market Cap?


Odlyzko’s Law suggests that in general the average value that an individual user brings to a network is log(n), where n is the number of users. Therefore since the total value of the network is the sum of the average values of every individual user, the total value of the network is n*log(n). Research has tied this number to the value of the Bitcoin and Ethereum networks indicating that this relationship holds for cryptocurrencies and can be used to describe the relationship between number of users and their market cap. We will further investigate real world proof of this relationship shortly.


Therefore, everytime a new user joins the network, the increase in the value of the market cap of the currency is n*log(n)-(n-1)*log(n-1). If we want to achieve price stability, we should add that much money to the money supply by paying it to the users. We pay part of this to the new user, part of this is paid to the miners.


Additional Dynamic Price Targeting


Frink is also investigating and researching the idea of turning on dynamic price targeting after 5 million users. This will not force the price of the currency to move in one direction or another but rather merely encourage further price stability. Note that we don't care about our price relative to government currencies but rather our price relative to the prices of goods, such as precious metals.


The easiest way to do this is by expanding or shrinking the money supply. Expanding the money supply is easy, print a little more money and pay the miners! Shrinking is a little trickier since no one wants their money to be removed from circulation.


Methods that Frink can use to shrink the money supply:

  • Decrease and burn some of the amount being paid to miners (ideal)

  • Enable/Increase and Burn Transaction fees

  • Change the minimum account balance required to mine

  • Increase interest on money that is in savings accounts

  • On death or prolonged inactivity, charge a death tax at the time of executing a will

  • Slowly drain money from inactive accounts

Note some of these methods may be illegal due to security laws and will be fully vetted before implementation. Miners of course have to approve all changes.


The issue of course is that for Frink to remain a truly decentralized currency, this must be done in a decentralized way. Therefore for this reason as well as for increased accuracy, if Frink’s miners and Frink decide improved price stability is needed, Frink will add a machine learning algorithm that is able to process the data far faster and more accurately that humans could. More than half the network must vote for this, or the feature is not enabled.


The machine learning algorithm will be able to expand or contract the money supply and monitor current users, current miners, current transactions, and practically any other variable you could imagine to nudge the currency towards continued long term stability. Machine learning today is perfect for this kind of application. For the sake of maintaining privacy, only those who opt-in to free transactions in exchange for sharing a little bit more information about themselves and tying transactions to their IDs will have their data used within these calculations.


Real World Evidence

As shown in the graph below, there is clear evidence and much research that shows that the growth rate of the Bitcoin’s Market Cap is correlated with n*log(n). Similar research has been done for other cryptocurrencies, particularly Ethereum.

This graph shows strong evidence Odlyzko’s Law applies to Bitcoin

This graph shows the Bitcoin marketcap compared to Odlyzko’s prediction of the market cap as a function of transactions per day showing a very strong correlation between the two.


However, it is important to look for evidence of this within large government currencies as well to be sure this relationship truly holds and isn’t somehow special to cryptocurrencies, since we need this to be robust when we reach that size. Here are the results of our research. Note that users are only the population 15 years or older and M2 and GDP are expressed as their value in USD.

When we further analyze this, we find the correlation coefficient between log(M2/(n * log(n))) and the log(GDP) of 0.96. For those not familiar with correlations, the closer a correlation coefficient is to 1 then the stronger the correlation. The reason for using the log function is because correlation coefficient looks for a linear relationship and log straightens these enough to achieve it. This indicates, as expected, that there is an extremely strong correlation between the two and confirms that n*log(n) is a good number of tokens to grow the money supply alongside the number of users. We also tested Metcalfe’s law: n^2 and Sarnoff's Law: n


Metcalfe’s Law was somewhat close with a correlation coefficient of 0.88, Sarnoff’s Law was also relatively close at a correlation of 0.77. Therefore Odlyzko’s Law was chosen as experimentally it shows the closest correlation to current cryptocurrencies as well as making the most intuitive sense.


Clearly there is some noise still largely due to factors that I have not accounted for that affect currency prices such as predicted GDP growth, inflation rate, interest, government debt, political issues, etc. These will be factored into the price of Frinks as well. But with increased number of users, these too should stabilize for the Frink economy. These factors will not be eliminated but will be minimized and become noise level as new users join the currency and the GDP per capita stabilizes as new users join the currency.


Additionally, these factors can be accurately measured and it should be possible to dynamically compensate for them in a decentralized manner to create a very stable currency. In the meantime, please be aware that we are not promising stability of the currency, do not plan on it!


Summary of Frink’s Distribution and Price Stability


Bitcoin and other cryptocurrencies have proven that nobody knows how to value the currency early on. So be warned, it will take time for the market to find the correct price.


However, this distribution should improve the stability, particularly because after the first bubble or two, it becomes very obvious when the currency is in a bubble when the price graph looks like the below graph. Additionally, it prevents investors from speculating on how the price will change based on the number of future users, which encourages actual user usage.


Additional, as we’ve shown the per capita GDP is strongly linked to the price of the currency, the higher the per capita GDP, the higher the price. This will add some volatility to the mix but the difference in per capita GDP between currencies varies by much less and slower than the number of users. Additionally, being able to accurately know what this number is will allow it to be more obvious what the current price is.

Note this graph does not account for changes in usage or how seriously investors are taking cryptocurrencies in general these days compared to early days

The above graph shows the market cap of Bitcoin compared to the predicted market cap using Odlyzko’s Law. This was calculated by dividing the real Bitcoin market cap by the one predicted by Odlyzko’s Law based on the number of addresses used within the last 24 hours. While there is room for disagreement on what exactly the correct price it, what becomes immediately obvious is where the bubbles are. Knowing this and having a currency designed to create a similar price chart should lead the market to be aware anytime it’s in a bubble and the market should automatically avoid those big bubbles.


If bubbles are prevented, then speculators are more likely to avoid trying to buy to get rich quick when they know it it obvious to all that it’s overvalued and we should be left with users who actually want to use it as a currency.

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