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Token Velocity is Good!

And other implications of analyzing MV = PQ from first principles

About the writer

Madhumitha Harishankar is a PhD Candidate in Carnegie Mellon University studying the application of network economics in wireless networks for resource sharing. She is advised by Prof. Patrick Tague and works closely with Prof. Carlee Joe-Wong. She also advises blockchain-based IoT service provider Nodle on token design and modeling.

Introduction

The equation of exchange (EoE), derived by John Stuart Mill, has become a popular approach for valuing medium of exchange crypto tokens. With P as the average price level of final goods and services produced in the economy and Q as the quantity of these final goods and services (also called the real GDP), PQ represents the nominal GDP of the economy — i.e. the total economic value of goods and services produced. With M as the amount of money supply and V as the average amount of times unit money exchanges hands in the purchase of final goods and services, MV represents the total monetary spending in the economy on final products. The equation of exchange is then the identity: MV = PQ.


Interpreting EoE in its intended context

Firstly, MV is the effective buying power in the economy. Consider, for instance, an economy with $1. If this $1 is exchanged for an ice-cream, and the ice-cream seller now uses this $1 to buy $1 worth of chips, then this $1 resulted in a $1 * 2 => $2 worth of buying power (since it facilitated 2 transactions of value $1 each). In this extremely simplified instance, M = 1, V = 2.

  • It assumes that V is constant. V is a measured quantity of people’s spending behaviors and is believed by monetarists to be largely unchanging over time. The long-term effect of changes in M are hence claimed to be observed in P, holding V constant.
  • This theory completely assumes that money is demanded for transactional purposes and not for its own sake; i.e. it has no speculative purposes (is not used for hoarding by people).

Interpreting EoE in crypto context

Since cryptocurrencies (especially utility tokens) can be considered as a medium of exchange, we can try interpreting MV = PQ in this context and see what we get. Let P represent the average price level of goods and services produced by the crypto company (in $) and Q the total quantity of transactions the company has with customers. Hence, PQ represents the economic worth, in dollars, of the company’s services. Further, define α as the number of coins comprising the circulating supply in the market and let 1 coin equals β USD; the money supply in this economy is β*α USD.

If we are concerned about whether there will be a market of customers who would like to use these newly available coin supply on the exchange to avail the company’s services, the Equation of Exchange can do nothing to answer this. When instantaneous coin supply suddenly increases due to hodlers dumping, the exchange rate of the coin may well decrease if this yet-untapped market does not exist. This is not captured by velocity. Equation of Exchange does not characterize spontaneous supply/demand dynamics and is too static a model for this kind of analysis.

Looking at the EoE then, it may be unclear what to conclude about V when hodled coins are released in this way without knowing if there is a market for these coins. However, it is impossible for V to decrease: these coins have now been made available for transactions with the company — hence, if they are purchased by customers at all, it only increases V since customers then exchange it for the company’s services and products. If there is no demand for the coins hodlers are making available, then coin velocity remains the same.


Contrasting with popular interpretation

There are a few popular ways that MV=PQ have been explained in the crypto context previously. I’ll review these below:

Chris Burniske and Vitalik Buterin’s versions:

Note that in Vitalik Buterin’s version, M and P are expressed in terms of tokens and are not fiat-dominated. Regardless, per their interpretation, V increases when long-term speculators start to sell their holdings back on the exchange, which appears inversely correlated with M and may hence result in a decrease in the market cap of the coin. This does not hold based on our analysis above. Speculators dumping their holdings on the exchange does not increase velocity but the “GDP-contributing supply”, so to speak, that was hoarded earlier. Whether this un-hodled supply meets with adequate demand or not is beyond the scope of the EoE. However, as we’ve shown, V increases regardless in this case. 1) If the exchange rate drops due to an excess supply and more coins are required per transaction now for the same fiat-based price level, thereby increasing V for same Q. Or 2) there exists previously unrealized demand for the company’s services which is realized now by consuming these coins, increasing the transactions Q, the network GDP, and either retaining the same exchange rate β or increasing it.

Kyle Samani’s version:

Kyle Samani defines velocity as the quantity of transactions/average network value; and concludes that the problem with utility tokens is that the quantity of transactions may increase multifold without necessarily the network value increasing since the velocity may be increasing proportionally. This is indeed a likely scenario; as we’ve seen above, rate of velocity growth η may well equal rate of transaction growth δ. However, this is not as much an issue as a feature of crypto-tokens, which I’ve discussed in detail in a separate post here. Coins buy privileges to access the services of a platform, not the platform itself. So it makes sense that their value will fluctuate with real-time dynamics of supply/ and demand for the platform’s services. Since tokens are not stocks and they do not pay dividends, it makes sense for their value to not grow directly with growth in demand. It grows with growth in instantaneous demand. As shown in my analysis in this post, if η grows beyond a certain market/application-driven threshold, then β starts to increase, and hence the market cap.


In Summary

  • Token velocity is crucial for medium of exchange tokens. For a given supply of tokens and price level of services, higher token velocity means more transactions with the network, aka higher real GDP for the network and potentially higher exchange rates and market cap.
  • However, the market rate and token velocity could change exogenously under different market conditions, and have different impacts on the Network GDP and token valuation that cannot be determined wholly by just the EoE.
  • Speculators holding utility tokens and over-valuing them may cause the value of the token to increase beyond the transactional value of the token (i.e. its medium-of-exchange value). The dynamics of this is not characterized by the equation of exchange or the token velocity.

nodle

Nodle​ is a decentralized network provider specializing in…

Madhumitha Harishankar

Written by

I am a 4th year PhD Candidate at Carnegie Mellon University. I enjoy applying economics, optimization and machine learning to wireless networks and sensor data.

nodle

nodle

Nodle​ is a decentralized network provider specializing in detecting and connecting the internet of things (IoT). The Nodle Network is simple, dense (5m+ active nodes, 92M+ detected devices), global (70+ countries) and uses existing hardware.

Madhumitha Harishankar

Written by

I am a 4th year PhD Candidate at Carnegie Mellon University. I enjoy applying economics, optimization and machine learning to wireless networks and sensor data.

nodle

nodle

Nodle​ is a decentralized network provider specializing in detecting and connecting the internet of things (IoT). The Nodle Network is simple, dense (5m+ active nodes, 92M+ detected devices), global (70+ countries) and uses existing hardware.

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