The term “economic bandwidth” was introduced by Ryan S. Adams to describe how ETH, Ethereum’s native asset, gives trustless liquidity to build trustless money applications. There seems to be a clear parallel with the “Pyramid of Money” (see for instance here) analogy, that of an economy whose breadth (or bandwidth) is governed by the angle at the very top of the pyramid. Decrease that angle, and you now have a pointy cone of discipline, where the initial mass of money (i.e., the one that’s “printed”, or more precisely borrowed on the money markets) yields less room for bottom layers to “print” more in the form of debt. Increase the angle and your money supply becomes more elastic.
What I particularly like about the concept of “Pyramid of Money” is the really clear two-way intuition that its visual form suggests: make arguments about the pyramid itself and you can project them back onto the actual technical nitty-gritty of money stuff. And though the concept of economic bandwidth sounds inherently visual, I do not believe an adequate image exists yet to represent its existence.
So in this notebook I want to try and build up one from what is arguably the centerpiece of the economic bandwidth edifice (as of February 2020), the DAI stablecoin system of MakerDAO. Hopefully, the visualisation is simple enough for newcomers to “get” what is meant by bandwidth, and for the rest of us to keep this image in head and derive intuition when necessary.
Let’s start with the fundamental building block of the DAI system: Vaults (the financial instrument formerly known as CDP). A vault has one very simple function: Capture your ETH and allow you to print DAI, with the reverse operation (paying back the DAI and unlocking the ETH) to adjust or close your position. Since DAI is morally expected to be worth one US dollar at all times, the vault asks that you put enough of your ETH into its belly to satisfy its craving for value. The vault gets hangry anytime the following equation doesn’t hold:
ETH locked in x Price of ETH > Printed DAI x 150%
And why shouldn’t it? You’ve put in 1 ETH into your vault (the collateral) back when it was worth $600, so you could print up to $400 DAI. Reasonable that you are (that’s what your parents like about you), you’ve decided to print only $300 DAI. The vault was happy, being 200% full (you gave it $600 and took out $300 out of it). Here is you now:
The dark green bar at the bottom is the DAI you printed, all $300 of it. Then you’ve got the lime green bar which tops your debt: that’s the extra debt you could issue for yourself before hitting the dreaded 150% ceiling. Since the orange bar, the highest of the three, is the value of your collateral (1 ETH, or $600 in this example), you would hit your debt ceiling by printing 400 DAI. Let’s add in some price information, which I’ll represent with a line (and explain why later on).
Now however the pumps have turned and your 1 ETH is only worth $500. The vault is still full enough (it has $500 in the belly and is still out $300, so about 166.67% full), but it’s looking at you, worried. “What if the price goes down more?”, it said. You didn’t have an answer for it. You wish you had, oh, you really did.
Powerless, you could only stand there, mouth agape, as the price took a turn for the worse and hit $450. The vault has reached its limit. It is already making its peace. And as the price tumbles further to $400, your innocent vault starts throwing up your ETH to who will seize it.
Your collateral was not enough to cover your debt anymore, so your lime green margin disappeared and the margin threshold crossed your darker green collateral. The vault is liquidated, you incur the liquidation penalty and use your remaining collateral to pay off some of the excess debt. You do not pass Go nor do you collect $200.
Now let’s reverse engineer the process, and start with a clean slate and the price at $600.
Your friends and yourself own various amount of ETH, respectively 0.5, 1 and 1.4 ETH each. You decide to open one vault each and put your ETH in there, printing respectively 100, 300 and 400 DAI each.
You are all above board! The darker green bar (the DAI you printed) is bounded above by the lime green bar (the DAI you could print with the current collateral you put in and the price level). Let’s shade the space we have to create debt.
Now what happens when the price falls, say to $420? Then our margin line falls to 2/3rds of that number, down to $280, and our “debt space” narrows.
We could call this economic amplitude: for a given level of debt, how much ETH (relative to the total supply) ought to be locked up to support that level? This is given by the angle of our margin line!
Economic bandwidth, on the other hand, refers to the “whole pie”, the total supply of ETH. Price increases give more amplitude to each individual application (today, MakerDAO, tomorrow, staking and optimistic rollups perhaps), reducing their use of the available bandwidth given a fixed level of output. For instance (and this is highly simplifying), for a security budget of the chain equal to a billion dollars, if we need 10 million ETH staked at $100, we need only 5 million at $200.
If we really want to appreciate the scale of economic amplitude, we need to visually represent the whole DAI ecosystem. Let’s come back to our three friends and their vaults.
We could plot the distribution of vaults, by collateral level, under the plot.
Let’s assume a fourth friend joins the fun, also putting in 1 ETH in a vault but printing $200 instead of your reckless $300. Let’s recap which vaults are in the mix now:
| Vault # | Collateral (ETH) | Print (DAI) |
|---|---|---|
| 1 | 0.5 | 100 |
| 2 | 1 | 200 |
| 3 | 1 | 300 |
| 4 | 1.4 | 400 |
If we group by collateral and average the debt in there:
| Collateral (ETH) | Average print (DAI) | Count |
|---|---|---|
| 0.5 | 100 | 1 |
| 1 | 250 | 2 |
| 1.4 | 400 | 1 |
So let’s plot our Count variable as a histogram under the vaults, with a single vault representing all vaults containing the same amount of collateral (or close to, if we bin more coarsely).
Now let’s generate some totally fake data and see what our chart looks like. 
Finally let’s put it back together: multiply our histogram (the bottom chart) with the vault bars (the top chart).
The dark green area is the amount of DAI printed. Given the current price p ($600), the lime green area shows how much more can be printed given the collateral in the system. But observe what happens when the price drops to $400.
We imagine a catastrophic worst-case scenario where none of the owners of a vault recollateralises while the price is dropping, so a lot of vaults get eliminated in the process. Even if they are recollateralised properly so that no one gets liquidated, it is clear that to achieve the same level of debt in the system (i.e., the amount of printed Dai), a lot more ETH (in absolute terms) needs to be locked up. This is one way to understand ETH as economic bandwidth: the higher the price, the more room for the debt to grow, as the slope of our margin line increases.
This might not be the meaning of economic bandwidth advocated by its creators. We haven’t touched upon the central notion of liquidity, although this is present in the Pyramid of Money too: the lower the version of money in the pyramid (i.e., the further we are from the central bank at the top), the more liquid that version of money is too. By liquidity we roughly mean that selling off our asset will be met with someone to pay for it. An illiquid asset is one that is hard to sell: for instance a house is much less liquid than plain cash.
In our “trustless” version of the Pyramid of Money, ETH is the pointy top. Locking ETH into a Vault gives you access to debt in the form of DAI. To maintain an equal total amount of debt in the system (currently, the debt ceiling is split between a SAI ceiling and a DAI ceiling), more ETH needs to be locked up when the price starts tanking, so the total fraction of ETH locked up (relative to the ETH supply) increases. A higher price reduces this fraction, giving more room.