Yeah that is true. Maybe I'll just say that the size of the cake (economy) grows but is fairly independent of how you slice the cake. So printing money doesn't increase the size of the economy.

Yes, but with a larger cake, it makes sense to have more slices.

There are other reasons that inflation is good too, having to do with sticky wages and recessions. I'm not sure how to work that into the cake analogy though.

Yeah the reality is that the size of the cake changes, and slicing the cake in different ways can feed back to the growth of the cake.

The perceived value of each slice relies a lot in the psychology of the public.

It's the job of the central bank to make sure the slices are proportioned properly and the perceived value of each slice of cake is maintained.

Key observation. In recessions (liquidity crunches) the cake grows more slowly. Maybe if we increase liquidity a lot (i.e. print money) and give it to the bottom tiers who will spend it (increase velocity) then the cake will grow faster!

We don't have good models for how the economy actually works. Until 2008 most models didn't even have a financial sector. Currently economic models can't accurately predict the velocity of money or even explain changes after the fact very well. We still have no consensus among economists as to what causes recessions.

So this is an experiment but the claims that it is "obviously" going to lead to inflation are flat wrong. We are going to learn a lot from this experiment. If we need to pull back to bring down inflation, we have tools for that.

The entire reasoning behind inflation is that thanks to productivity increases there is always a slice left behind. If nobody eats the slice then the cake shop will make smaller cakes with less slices. If we give someone money to buy the last slice then the cake shop is incentivized to make another left over slice until it is so busy making cake that it cannot make more.