How to understand the constant product formula?

Question

Let's use this transaction as an example.

Here 1 BUSD was transferred to Zombie / BUSD LP in exchange for 172054109197 Zombie tokens. (3511308350 (2%) Zombie tokens were burned as part of the transaction.)

Here is the Swap event:

amount0In: 0
amount1In: 1000000000000000000
amount0Out: 175565417547
amount1Out: 0

Prior to the Swap, the reserve values were:

reserve0: 1203765031
reserve1: 6402195517789394391

after Swap, reserve values were updated to:

reserve0: 173257874228
reserve1: 44614233592769925

Everywhere that I've read, it is stated that constant product formula (x*y=k) requires that the k remains constant. However, this isn't the case here.

1203765031*6402195517789394391=7,706,739,085,939,811,390,553,341,121
173257874228*44614233592769925=7,729,767,272,594,744,235,790,992,900

Am I misunderstanding the function of the formula or is something else going on here?

Answer 1

The product k would actually be constant, if the swap fee was 0%. Since AMMs usually have a fee, the product of the reserves is not really a constant in practice.

The name ‘constant product market’ comes from the fact that, when the fee is zero (i.e., γ = 1), any trade ∆β to ∆α must change the reserves in such a way that the product RαRβ remains equal to the constant k.

Source: An analysis of Uniswap markets