# Interpretation of the most popular asset valuation model in the encryption circle EoE: MV=PQ

The trading equation (EoE) derived by John Stuart Mill is the most popular valuation model in the current encryption circle. This equation is an identity:

MV=PQ

among them,

M = Money Supply, which is the average number of currencies in circulation for a certain period of time;

V=Velocity of Money, which is the average number of turnovers per unit of currency in a certain period of time, that is, the velocity of money circulation;

P = Price, the weighted average price of the final goods and services in economic activity;

Q = Economic Quantity, the number of transactions in final goods and services (also known as real GDP).

PQ represents the nominal gross domestic product of society, that is, the total value of goods and services produced. According to this model, many people believe that the transaction rate of cryptocurrencies will lead to a decline in value. And we have reached a very different conclusion in the following analysis: According to the MV=PQ model, at a given cryptocurrency supply and price level, the higher the transaction rate means the higher the encrypted network GDP. The cryptocurrency has the potential to add value.

However, the establishment of the current cryptocurrency valuation model is still in the exploratory stage. Because the EoE model is derived from the traditional monetary theory, there are natural defects in the currency denomination in the encrypted network, and the conclusions drawn on this basis may deviate from the actual situation.

## Interpretation of EoE

MV is an effective purchasing power. For example, I used \$1 to buy an ice cream. The ice-selling person used this one dollar to buy a French fries, so the "\$1" here produced a value of \$2 (a total of two dollars). The transaction), which generated a purchasing power of \$2. Where M=1 and V=2. The quantity theory of money uses EoE to link GDP to money supply. It is based on the following assumptions:

1. Assume that Q is exogenous (not dependent on money supply) and that it does not change much. In other words, all resources in the economy have been fully utilized, and increasing the money supply will not lead to changes in real GDP.

2. Suppose V is constant. V is used to measure people's consumption behavior, and monetarists believe that consumer behavior is largely unchanged over time. Therefore, when Q and V are relatively stable, the change of M will affect the change of P.

Fisher believes that under the premise that the actual transaction quantity Q is exogenous, Q and V remain stable, and the change in the money supply M leads to a proportional change in the price level P of goods and services. This theory assumes that people hold money for the purpose of daily transaction payments for trading purposes (transactional motives), not for speculation. This assumption is debatable, but it is undeniable that this theory has certain applicability. Take the US economy as an example. This assumption can explain the relationship between money supply and inflation under the control of the Fed. After adjusting the trading equation, we get

M=PQ/V

When the money supply M increases, the currency depreciates (the money supply is greater than the actual demand of the currency), in which case the money becomes less valuable, causing the price P to continue and rise generally – this is inflation.

However, unlike Fisher's hypothesis, the increase in money supply M may also affect the velocity V of currency, as advocated by Keynesian theory of money demand: the rise in price P leads people to need more money. In order to purchase the goods they need, the currency circulation speed V may drop.

When inflation is too high, the Fed can issue bonds to reduce the money supply M. At this time, the currency appreciates, causing the demand for money to fall, and the price P to fall. The Fed can also adjust the interest rate to fight inflation, and the Fed raises interest rates to hold the currency. Increased costs.

According to the EoE and inflation effects, if the currency circulation rate V remains stable, the real GDP Q increases by x%, and the growth of the money supply M will exceed x%, and the price P will increase accordingly.

Therefore, the premise of EoE's “no speculative motive in money demand” has been controversial.

It should also be noted that controlling the velocity of money V is not a good solution to the currency problem. When the money supply M is constant, the higher the velocity V of the currency, the higher the nominal GDP PQ, if so If we solve the problem of poverty in the world, then why do governments not introduce policies to ban hoarding of money?

In fact, the velocity of money V needs to be synchronized with the value people create in the economy. It is itself a function of GDP, not an independent variable.

For example, Alice designed a program and sold it to Bob for \$500. Then she went to IKEA to buy a sofa for \$500, and Ikea used the \$500 to upgrade.

In the process, Alice created a value of \$500 through the design process. He can exchange value with the US dollar as a carrier; IKEA creates a value of \$500 by making a sofa, and IKEA can use the sofa to exchange other services. PQ implies value creation in the economy, so V is not a constant, it is affected by many factors.

## Cryptographic currency and EoE

Since cryptocurrency can also be considered a medium of exchange, we can try to analyze it from the perspective of EoE.

We use P to represent the average price level of revenue generated by goods and services on the cryptocurrency platform (in US dollars) and Q to represent the total amount of transactions.

Therefore, PQ represents the economic value of the cryptocurrency platform. In addition, we define α as the number of cryptocurrencies in circulation, and in dollar terms, setting each token equal to β dollars, so the total supply of tokens in economic operations is β*α dollars.

There is a problem to be aware of when defining the speed of circulation V: we must distinguish between a general encrypted transaction and a cryptocurrency that only causes network consumption. When the exchange medium is money, any currency exchange behavior that occurs in this economy directly contributes to GDP, so the higher the circulation speed V, the higher the GDP. In cryptocurrency, one token may be purchased by speculators, speculators may sell it to the next person, and the next person can continue to sell the token, but the process is not encrypted. Network GDP contributes. Therefore, we define V' as the average number of token transactions conducted for speculative purposes over a period of time, defining V as the average number of token transactions for a non-hodling transaction for a period of time.

That is to say, the miner "mining", generating the token as a reward, the process is calculated in V, and the trade that the miner sells the token to the encrypted speculator is not counted in V. But if the speculator finally sells the token to a consumer of goods or services that pay for the platform, then the transaction will be counted in V. At the same time, the transaction in which consumers pay for goods or services with tokens will also be counted in V.

In summary, V represents the number of average transactions that have contributed to the encrypted network GDP. We can eliminate the ambiguity that may exist when we define V from the process of generating cryptocurrency, purchasing tokens from miners or speculators, and paying for goods or services with tokens. This method of disambiguation has no effect on the rest of the analysis.

So we got the encrypted EoE:

βαV=PQ

We reserve Fisher's hypothetical premise as mentioned above, treating V and Q as constants. In cryptocurrency, the encryption platform sets and controls the cryptocurrency number α in circulation and the average value of the revenue of goods and services generated by the cryptocurrency platform. In traditional finance, a central bank such as the Federal Reserve directly controls the money supply. The amount M.

In the case where the service price level P remains unchanged, the token supply α is increased, and the price β of the cryptocurrency will be proportionally reduced to β', requiring more tokens to be traded (from P/β to P) /β'). And if P also increases at the same time, the change in β will depend on the increase in P.

There may be a significant increase in the P value as the potential economic value of the goods/services of the encryption platform increases. If α does not change at this time, β will increase.

Then, if we take the quantitative theory of money and treat P and α as constants, how will Q and V change again? After rearranging the encrypted EoE formula, we can get:

β=PQ/αV

We can think about the change in β when V changes.

Whether V increases or decreases, as long as the PQ changes in proportion, β is not affected. When α and P are given, the increase in Q causes V to also increase, and if the magnitude of Q increases is greater than the magnitude of V increase, β will also increase β. Therefore, when α and P are fixed, V must be increased to promote the growth of encrypted GDP.

Therefore, the increase in the circulation rate V has increased the purchasing power of goods and services in the encryption economy, directly contributing to the growth of encrypted GDP (PQ).

The key here is whether the growth rate of Q (set to δ) is greater than the growth rate of V (set to η). EoE is essentially a static model that assumes that several factors are in equilibrium and briefly describes the economic behavior that is generated.

However, we know that the essence of economic life is dynamic, and β is actually a function of real-time supply and demand dynamics. So, we are out of the monetary quantity theory to explain the encryption EoE:

First, as long as no external factors affect β, the value of η cannot be larger than δ, because η does not increase the supply or demand of tokens in isolation, but refers to the net increase in the transaction rate of tokens that contributes to the overall gdp. Therefore, if the overall transaction ratio in this system increases, then in the worst case, β will remain the same or grow. If the growth of η exceeds a certain limit, then the high probability is because the market demand is too high, in response, β will rise. This means that in order to maintain the same P, the number of tokens required for each transaction is reduced. At this time, V is higher, which increases the number of tokens α in circulation, resulting in an increase in the number Q of transactions.

The above explanation may be puzzling, because the increase in β leads to an increase in the number of transactions, which seems to contradict the supply and demand theory in traditional finance. However, it should be noted that the token price β and token transactions are based on cryptocurrency, and the price level of the services provided by the platform is a fixed value with market competitiveness. Therefore, as more people recognize the platform and demand for the service, the value of the token will increase, which will lead to an increase in the price level of the token. In other words, the number of tokens that can be bought in one dollar will decrease. Will reach more deals.

What makes V exogenous from the beginning? Different market factors may cause V to produce different changes. For example, if a base product and service extension provided by a platform becomes more differentiated, then their customers may trade more frequently, and new customers may also flock. Alternatively, V may be affected by the behavior of the holder.

One of the basic assumptions in the theory of quantity of money is that money (or the tokens analyzed in the text) is not held for speculative purposes. In Keynes's interpretation of EoE, people hold money for preventive motives and convenience, and the proportion of money in non-trading (ie, holding) purposes in people's income depends on the opportunity cost of holding money (such as alternative assets). Interest earned in).

So EoE may run counter to our original purpose. The token market has obvious speculative nature. When most investors lose interest in holding tokens; or they think that the token market is relatively liquid and buys tokens according to their own needs, rather than for preventive motives, this will lead to an increase in supply. .

We also need to know that there are actually participants of different beliefs in the market. They may buy and sell tokens for different times. Sometimes the tokens on the market only flow between investors, resulting in temporary price increases. What is produced at this time is V' instead of V.

EoE is static and not dynamic. It does not take into account homogeneous users, balanced market behavior and non-speculative currency use. This is one of the reasons we consider using other models to replace EoE, and the encryption market is these. A multi-equal game composed of complex factors (as Vitalik Buterin said).

The following situation is also worthy of our analysis: Most token holders look at empty tokens (for example, most tokens do not have room for appreciation), so there are some tokens that have not been absorbed by the market. These tokens that are not absorbed by the market have an external influence on the number of transactions V that contribute to the encryption of GDP.

However, the act of speculators selling their tokens to the exchange will not immediately lead to an increase in V, but will increase the “supply that can contribute to the crypto-GDP”. There is a view that V is thus increased. It implies that consumers who are supposed to have these tokens that have not been absorbed by the market have been interested, and use it to purchase goods or services, resulting in an increase in V value.

So, is there really such a group of consumers who are willing to use the tokens on the market to buy services? EoE can't tell us the answer. When the supply of contemporary coins suddenly increases due to dumping by hoarders, β is likely to decline if there is no token payment in exchange for goods and services. EoE cannot be used to describe spontaneous supply and demand dynamics, which is too "static" for this type of analysis.

At this point V will not decrease, because if these tokens are ultimately purchased by the consumer for payment, this will only result in an increase in V; if no consumer pays with it, then V will remain unchanged.

How to describe the relationship between V, β and Q at this time? We can go back to the formula β=PQ/αV. If these tokens that have not been absorbed by the trading market have not been accepted by the consumer for payment, then β will fall, meaning that a larger number of tokens are needed to make the same transaction as the previous price level P.

Therefore, when V is increased, since the change of β is exogenous, Q does not increase greatly. On the other hand, if these tokens that are not absorbed by the trading market can be accepted by consumers with the same β, then Q and V will increase at the same time. Whether β is increased or not depends on the size of η and δ we mentioned earlier.

Obviously, we need a more appropriate encryption dynamic model to truly understand the valuation changes in different types of market behavior and at different times. Another question worth pondering is, if the platform's service price level P is only symbolic, how will it analyze the impact between them?

## Different views on MV=PQ

Vitalik Buterin believes that:

M and P are uncontrolled. In any case, according to their explanation, when long-term holders start selling the tokens they hold on the exchange, V will increase, V and M have a negative correlation, and may lead to a decline in the market value of the token. But according to our analysis above, this conclusion does not hold.

The speculators selling the tokens they hold to the exchange do not increase the circulation rate V, but increase the “supply that can contribute to the encrypted GDP”. As we said above, EoE can't answer whether there is such a group of consumers who are willing to use the tokens on the market to buy services. In our conclusion, V will grow in this case. First, if β falls due to oversupply, then the number of tokens required for each transaction now increases under the same P, resulting in an increase in Q. Second, if these tokens are used by consumers to pay for the services of the platform, the number of transactions Q and the crypto GDP will increase, and β will remain the same or increase.

And Kyle Samani believes that:

V is the average of the transaction volume/network value. When the transaction quantity Q of the utility token (the token can be used directly and meaningfully in the buyer's hands) may multiply, the network value may be increased due to the possible increase of V. P will not necessarily increase.

According to the above analysis, this is indeed a possible situation because the growth rate η of V may be the same as the Q growth rate δ. Tokens can be used to purchase services for the platform, not the platform itself. Therefore, the value of the token will fluctuate with the dynamic supply and demand dynamics of the platform service. Since the token is not a stock and does not have to pay dividends, its value does not increase directly as demand increases. But if η exceeds a certain market/application-driven threshold, then β begins to grow, so the market value increases.

## to sum up

First of all, the token transaction speed V is crucial for trading tokens. For a given token supply alpha and service price level P, the token transaction speed V means more online transactions, which means higher encryption network GDP, while beta and market value increase. Sex.

Second, under different market conditions, β and V cannot be completely determined by the EoE equation. They may also be affected by other external factors, which in turn affects the encrypted network GDP and token value.

Finally, when speculators hold or overestimate the utility token, it may lead to an increase in the value of the token, even more than the transaction value of the token (ie, the intermediate exchange value); the dynamics of the encryption market cannot simply be EoE or token transaction speed. V to explain.

Original | Token Velocity is Good. And Other Implications of Analyzing MV = PQ from First Principles

Compile | Hash Pie – Adeline

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