# The Maths of Ethereum Price

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What I’m about to spell out will change what you think about the future of Ethereum. The conclusion of this article is counterintuitive, but irrefutable. I have never heard anyone else state these facts, and can not draw from other articles.

Warning: I use the terms cost and price frequently, and it’s easy to confuse the two and get lost in the language; they are not interchangeable. Cost is an amount to be paid in total. Price is an amount per unit.

If demand for ETH goes up, then price will go up as well, all else being equal.

The following will show that even a massive increase in transaction volume will not increase demand for ETH, and therefore will not increase price. This sounds crazy — at first.

We need to recognise that there is a range of market price that the public will tolerate for a particular smart contract execution, measured in USD.

For example, the public is prepared to pay around \$50 USD to put their house title on the Ethereum blockchain, or something like that, it might be too cheap, but it doesn't really matter. The important part is that there is going to be a number give or take a few per cent that will be generally acceptable. Much more than that, and people will shy away. Much less than that, and it will be more attractive.

Next, look at these equations to see how everything is connected:

The first equation in diagram 1 shows that the overall amount of ETH the public will need to buy (and consume) to execute smart contracts is proportional to how much ETH is consumed per average transaction (red brace in diagram 1), and proportional to the overall number of smart contract transactions (Tx volume).

The amount of ETH consumed per transaction (red brace), is equal to the cost of gas per transaction (eg \$50 USD needed, blue arrow). The average cost of gas (in USD) is proportional to the average amount of gas consumed in an average transaction. The cost of gas is also proportional to the price of gas. Price of gas is the amount of ETH consumed per gas consumed (This price of gas can be converted to USD consumed per gas consumed using ETH price)

We can therefore rewrite the first equation like this:

The component within the blue brace in diagram 2 comes from the blue arrow in diagram 1, and I said earlier that it is relatively fixed.

So if transaction volume goes up (Tx volume), then Volume ETH demanded goes up, so ETH price goes up. Hooray!

Unfortunately, everyone stops here.

I kept digging because something intuitively doesn’t feel right.

What happens to the transaction costs (blue brace) when ETH price goes up?

Looking at diagram 2, Tx volume can be increased, increasing demand for ETH (left hand side of equation), which increases ETH price, which increases gas price. But gas price is within the blue brace! This is not allowed. Blue brace total must stay the same, because the public will not tolerate too much of an increase in cost for an average transaction.

To compensate, the gas price falls, and less ETH is consumed per gas consumed. That’s right. When more ETH is demanded because of more transactions, less ETH is demanded per transaction, because gas price falls. This is necessary, otherwise transaction costs will escalate an Ethereum will not be used.

This proves that the expected massive increase in ETH transaction volume does not increase the demand of ETH, or price of ETH.

What matters to ETH price is the average cost per transaction (in USD, but paid in ETH) that an average user is willing to pay. Trust me, it won’t be an astronomical amount.

So what makes ETH price go up? Speculative demand. (Or reduced supply)

If speculative demand is high, price goes up, gas price goes down, \$50 transaction costs (as per the original example) remains unchanged.

Speculation drives ETH price. Not utility. Similarly, the industrial properties of gold have not driven it to its current price of \$1580 per oz. Speculation of its monetary properties and SOV properties has done this.

For ETH to moon, it needs to compete against Bitcoin as money, and it can not. It has poor monetary properties compared to Bitcoin. Utility in the form of smart contracts is not a monetary property. Demand for utility, as I have shown, does not increase ETH price.

ETH is staying on Earth. Bitcoin is going to moon.