Joe Hat

The Joe Hat Bonding Curve Contract is an Avalanche smart contract for trading HAT.

It uses the JoeHat, which is an ERC-20 token.

Why did we decide to build a brand-new contract

The inspiration of JoeHat comes from Unisocks, which uses a regular Uniswap v2 SOCKS/ETH pool seeded with 500 SOCKS.

Because we gave away 100 120 of 150 HATs, we had to change our approach to ensure a few things:

• Buying a HAT fron the bonding curve increases the price of the next HAT.
• We could account for the (unlikely) event that all 100 120 HATs were dumped.
• We could seed the bonding curve in an affordable way that without having the user to pay for the actual cost and shipment of the physical hat.

The general idea of this custom bonding curve contract is that it takes a small percentage of each sale that is used by the team to fund the cost and shipping of the hat.

How it works

The contract follow the xy=k curve that I explained on twitter.

When you buy a HAT, it calculates the amount you need in Avax.

When you sell HAT for avax, it calculates the price, reduced by ~5%.

For the last HAT, we choosed to price it 4 times the previous one. As the price of the previous one is k / reserveHat = k / 2, that means that the last HAT will be priced 4 * k / 2 = 2 * k

How it really works

For Hat from 1 to 149:

The first 149 hats will be priced following the Uniswap v2 curve, xy=k. We chose the hats to be priced at 15 avax per hats for the 30th, that means

k = reserveAvax * reserveHats = (30 * 15) * 30 = 13 500.

That means, that if you're buying the 56th HAT, the price in avax would be :

price = k / 56 - k / 57 = 4.23 avax

When you're swapping HATs for AVAX, i.e., selling it, the price will be approximately lowered by a/b%, in our case, 5%.

Let's say you're swapping 5 HATs for AVAX, and that there are 50 hats left in the contract, it will be calculated like so :

// This is the price for each of the 5 HATs? Or price for all 5 HATs? // This is the price of the 5 HATs, I don't know how to say that tho

price with fees = k / 50 - k / (50 + 5 * 0.95) = 18.85 Avax

Now let's say you want to sell some HATs for exactly 20 AVAX. And let's assume there's already 50 HATs in the bonding curve contract. First, that means there's k/50 = 270 AVAX in the contract.

Then to calculate how many HATs you'll get:

hats with fees = k / 270 - k / (270 - 20 * 1.05) = 4.22 HATs

For the last Hat (i.e., 1 to 0)

We really wanted the 150 caps to be purchasable, and Uniswap v2 curve doesn't allow that because as xy = k and x = k/y, then if y goes to 0, then the price goess to... infinity.

We chose to price the last HAT 4 times the last one. We have chosen a straight line function for the last HAT to make it as simple as possible because it's already hard to use 2 functions instead of only one to price an asset.

As there is only one HAT using this function, it's trivial to calculate the price:

// Can you elaborate on this equation a bit more? What does amount_bought mean? // amount bought is the quantity of the last hat you want to buy, so any values between [0, 1], I don't know how to explain that too tbh

price = amount_bought * last_hat_price = amount_bought * k * 2.

The hardest part

// This part needs more explanation. Don't really get the logic here. // True Everything looks fine, but what happens if you buy an amount of $HAT that crosses both function. Let's say 3 $HAT and there is only 3 left in the contract, we calculate the price like so:

oldHat = 3 - 1 = 2
newHat = 3 - 2 = 1

With those numbers, we just calculate the price with the first function, or the second one. If you want to sell tokens, it will be calculated with a new amount equals to

newAmount = amount / 0.95
or 
newAmount = amount * 0.95

It depends on if you're swapping an exact amount of $HAT for Avax, or $HAT for an exact amount of Avax.