Would rapid population growth in an economy lead to inflation issues?
I'm currently worldbuilding for a story where humanity has been trapped in a simulation by aliens, and humans are slowly starting to emerge from said simulation, having to rebuild modern civilisation from scratch. Only a few emerge at first, and begin planning on how to proceed.
As soon as their numbers grow beyond a few dozen, they start implementing a market economy with a fairly free market. Because they can choose who to free from the simulation next, assume they have at least one competent economist among them, whose advice is generally heeded.
At the same time, the server farm where the other humans are still trapped has been abandoned long ago, and it is unclear how much longer the hardware can keep running smoothly, creating time pressure to get all of humanity out of the simulation before it starts glitching out too hard.
Now, with a government that is economically competent, would the fact that the population of this new civilisation is rapidly growing lead to inflation issues, assuming the growth can be mostly planned? If yes, could this inflation be managed without having to introduce drastic measures like price controls? And how quickly could the population grow every year while keeping inflation at a tolerable level?