The Price Elasticity of Demand for “Sound” Money

A meme in the crypto community is that because Bitcoin’s supply is capped – as opposed to fiat money – Bitcoin is “sound” money. While the principle of “limited” supply, with predictability, has long been touted as being sound, in this article I highlight why digital currency – though on the surface – looks like being a “capped” supply instrument, the limits to supply are only notional. Beneath this supply cap operates the principle of ultra-high divisibility wherein the digital currency can be divided and sub-divided into very small sub-units.

Coming down to the principles of economics of demand and supply, if the supply of a commodity is predictable, at constant demand price of that good would remain the same. However, if the demand increases the price of the good would increase. This ratio of change in demand to change in price is what economists call the price elasticity of demand.

Price elasticity of demand (P(e) = Delta(Q)/Delta(Price))

For this discussion we assume positive values for both numerator and denominator. If the price elasticity of demand is greater than 1 it means that price increases slower than demand. However, if the price elasticity is less than 1, it means that the price increases faster than demand. If the price elasticity of demand is 1 that means price and demand are correlated highly – a very unusual condition in markets.

Now, with Bitcoin, the supply is capped at about 21 Million because of the way in which the bitcoin protocol’s algorithm is designed to reduce the marginal supply of Bitcoin into markets. However, this definition of sound money need not necessarily be sufficient in the context of digital currency. Digital currency per-se is divisible nearly infinitely (in this case a sat(or satoshi) is at 1/10^9 Bitcoin) and each small sub-unit possesses the same properties as its main unit on the demand side. On the supply side, however, only the main unit i.e., Bitcoin is relevant, since Bitcoins are what result as rewards from the production function (or mining)

However, on the demand side the sub-unit of digital currency which is a Sat (or a milli-sat) is as important as the bitcoin itself since it shares all properties of Bitcoin, is a result of the same production function i.e., mining, and can be used to hold/transfer/accumulate value. Now coming back to the price elasticity of demand principle which is relevant to analyze Bitcoin, as the price elasticity decreases more and more and approaches 0, the market for Bitcoin as a unit of exchange in its entirety per-se will cease to exist because very rarely will a full Bitcoin be traded at that point. This could be because Bitcoin now becomes a valuable asset that all its holders will want to hold for ever – almost like precious art. As the production of new bitcoin will come to standstill around 2030, all existing Bitcoin will be locked up in wallets and accounts, and only a small fraction of these Bitcoins will be traded by speculators.

At that point, the sub-units otherwise “sats(satoshis)” or “milli-satoshis” will suddenly become relevant and there would be a shift in the supply perception of sats. The Bitcoin market would shift to becoming a “Satoshi” market. Please note that here – there is only a perception of an increase in supply because each “sat” will now suddenly become important. At such a point in time when the Satoshi market takes over, the “Bitcoin’s” price elasticity of demand which was ever so close to zero will now lead to a “Satoshi’s” price elasticity of demand which is much greater than 1. Now these two markets – i.e., the Bitcoin market and the Satoshi market have completely different properties in terms of the price elasticity of demand. Bitcoin’s price elasticity of demand will be close to 0, and Satoshi’s price elasticity of demand will be several orders greater than 1 until such a time when Bitcoin hits 100000000$ in value. Such a shift in market perception will need significant infrastructure alteration at exchanges.

Market Perception Shifting from Bitcoin to Sats means two important things for users

a) Users will start treating Satoshis as the base pricing mechanism as opposed to Bitcoin.

b) Demand elasticity of Bitcoin << 1 will be replaced by the demand elasticity of Satoshi (Sats) >> 1, which means that there is significant space to grow for this market.

Already, there are large investors calling for the shift in exchange listings from Bitcoin to Satoshis, so as to accelerate the shift in markets. This shift in markets would remove the artificial supply shortage (of 21 million Bitcoins) and would suddenly create a market of the abundance of “sats”, which will eventually increase the trade, accumulation, value-transfer capabilities of Bitcoin. This shift in markets is similar to what happens when a stock splits, except that in this case, 1 Bitcoin becomes 10^9 sats – each of which is now tradeable as independent units in markets. Such a decision to convert the unit of sale from Bitcoin to Satoshis will at some point be driven by major exchanges such as Coinbase, Binance, FTX, etc. When the property of markets change, from price elasticity of demand close to 0 to a number much greater than 1, it will demonstrate that the market has a significant supply and is awaiting an increase in price of sats, on the overall increasing the price of Bitcoin even further. At the point this shift in market perception happens – Bitcoin’s position as “sound” money will possibly no longer hold, since supply-perceptions have changed overall in the market owing to a change in the price elasticity of demand.

Applying this analogy to the Ethereum market – where anyways the market caps the supply to about 110 Million Ethereum when Proof of Stake becomes the predominant mode of mining. EIP1559 has already introduced a deflationary supply whereby Ethereum is burnt for each transaction after meeting a ceiling transaction fee, disincentivizing price gouging miners who wait to earn high rents based on the time of day/time of the transaction in these markets. When deflationary coin supply occurs in crypto markets, the demand elasticity of Ethereum would increase and the effect of such a change on price would compound. This is one of the reasons why Ethereum is called “Ultra-sound” money, because not only is supply capped after Proof of Stake rollout, supply reduces at a rate faster than the generation of additional Ethereum through a controlled burn of tokens through EIP-1559.