WBTC/DIGG AMM together with flexible supply - explained with example

Support
#1

Hello,
I realize that I do not understand how the digg/wbtc Uniswap pool would work in light of the fact that digg’s supply changes daily. Let’s take this simple example:

Say that WBTC = 50,000$ DIGG = 60,000$ = > WBTC = 0.833DIGG

You use 1 WBTC to buy 0.833 DIGG and then contribute 1WBTC and the 0.833 DIGG (you just bought) at Uniswap to get LP token…At that point in time (time 0) , value of your portfolio is 100,000$
Say 24hrs pass and the price of WBTC is still $50,000 and there are NO trades in Uniswap (no fees have been gained or Impermanent Loss has been incurred) but the supply of DIGG has been adjusted upwards by 17% (I know it doesn’t work this way but for the sake of simplicity let’s assume it does) so that now 1WBTC = 1 DIGG
The question I have is: What happened to the constant product formula? WHen I contributed at time 0 the constant product was 1 (wBTC) * 0.833 (Digg) = 0. 833 but now just because of the way digg works (I now have 1 digg instead of 0.833) the constant product won’t work as it will be 1WBTC * 1 DIGG = 1 How is this accounted for?
In my head, it should still be the case that the value of my portfolio is unchanged at 100,000$ - I now have 1 WBTC (=50,000$) and 1 DIGG (instead of 0.833) but the value of the 1DIGG is 50,000 (and not 60,000)…

#2

If there are no trades and therefore no fees, and if prices of both WBTC and DIGG does not change, then yes. The value of your portfolio is unchanged but now you have more DIGG as consequence of the rebase. In theory that is what happens.

In the practice, both prices (WBTC and DIGG) constantly change. So depending on the market, perhaps after the rebase the price of DIGG still goes up and then the value of your portfolio too. Or it can happen the other way around: the rebase might trigger a DIGG selloff meaning that you have more DIGG but the value is lower than before.

But this is the same with all tokens and all liquidity pools. The only exception is that in this case, DIGG gets rebases. This is an additional variable that could work sometimes for you, and other times against you. You take more risk when participating in LP versus just depositing DIGG in the app. This additional risk is somehow compensated by larger DIGG emissions.