• Fahad Saleh

Volatility and Welfare in a Crypto Economy


Cryptocurrencies exhibit tremendous volatility. That volatility arises for many reasons, but one such reason becomes obvious once you translate crypto-jargon to foundational economics.

To understand the aforementioned reason, let’s think more concretely. For simplicity, let’s focus on Bitcoin. New bitcoins are created when “miners” solve some puzzle and receive newly-created bitcoins as a reward. Let’s not worry about why these “miners” solve this puzzle, what the puzzle is or even why we call them “miners.” The point is that “miners” receive newly-created bitcoins for solving a puzzle so that more puzzle solutions means more bitcoins.

What does that mean for price? To answer that question, let’s think about the supply and demand for bitcoins. The bitcoin demand curve slopes down because a higher bitcoin price means a higher opportunity cost for holding bitcoins. With regard to supply, a higher bitcoin price increases the incentive for a “miner” to solve a puzzle because the higher price means a larger reward for the “miner.” Thus, a higher bitcoin price leads to more puzzles being solved which leads to more bitcoins in circulation so that the bitcoin supply curve slopes up.

What does any of this have to do with volatility? Loosely speaking, volatility measures how much prices fluctuate, and prices fluctuate because of changes in either supply or demand. Demand is hard to control – for example, if people get richer, they might want to buy more of everything (including bitcoin) which would move the bitcoin demand curve up and therefore also move bitcoin’s price up. But by how much? That depends also on the supply curve. Figure (a) exhibits a positive demand shock for bitcoin and demonstrates that the bitcoin price moves from P0 up to P1 in response. That’s standard economics, but it does not characterize the bitcoin market correctly! The same demand shock would move bitcoin’s price more than depicted– that is, bitcoin would be more volatile than the aforementioned analysis suggests. Why?

Bitcoin targets a currency growth rate so that demand shocks do not (on average) affect bitcoin quantity. Figure (a) depicts not only a price increase (from P0 to P1) but also a quantity increase (from Q0 to Q1), but Bitcoin’s protocol is specifically designed to avoid the quantity increase (actually, Bitcoin’s protocol targets a specific quantity increase but that’s an irrelevant detail). How does the protocol achieve the desired outcome? When a positive demand shock occurs, the protocol makes the puzzle that “miners” must solve more difficult which increases the marginal cost of finding a puzzle solution and thereby shifts the supply curve back. Figure (b) depicts the positive demand shock and the negative supply shift. The negative supply shift succeeds in counteracting the demand shock to keep bitcoin quantity at Q0, but the supply shift also exacerbates the demand shock’s effect upon bitcoin prices: it moves bitcoin’s price from P0 beyond P1 to P2. In econ-speak, Bitcoin meets a positive demand shock with a negative supply shock which stabilizes quantities but magnifies price movements which means… more volatility!

The truth is, though, that Bitcoin’s protocol is even worse in terms of creating volatility. Here, I assumed that the protocol could perfectly target a bitcoin growth rate. In practice, for reasons I won’t discuss here, Bitcoin cannot perfectly target a growth rate. Rather, there is some additional randomness in the creation of bitcoins coming from how lucky “miners” are when they try to solve puzzles. That randomness, by construction, cannot counteract demand shocks which means it adds even further to bitcoin volatility.

So, yes, bitcoin is volatile… but well-established economic theory explains partially why. While we generally don’t like volatility, this is good news because curing a patient is easier when you understand why the patient is sick. That’s the thought process behind my most recent paper, “Volatility and Welfare in a Crypto Economy” which is available here. In that paper, I formalize the argument I made here, and I offer an alternative (which is a variant of something initially proposed by Iain Stewart – credit to him for that clever idea). Cryptocurrencies may have some undesirable properties – like high volatility – but that does not mean we cannot put forth new cryptocurrency designs that keep the good aspects while taking away some of those undesirable properties.

Fahad Saleh, McGill University


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