The system of capitalism gets a little dicey is when that stable population isn't consuming at the rate of GDP growth.
Capitalism shines when there is excess production which goes into the creation of more capital, which results in either an increased quantity of what is produced, an increased quality, or both.
What will happen in this case (stable quantity of consumption) is that quality goes up, price goes down, or both.
A prerequisite for this virtuous cycle is a properly-functioning government that doesn't allow today's successful capitalists to prevent future competitors from arising, and potentially taking their place.
Socialist economies run in the opposite direction: they punish capital creation or saving in favor of redistribution, resulting in the steady consumption of overall capital. This is the basis of the statement "Socialism seems great until you've finished eating your seed corn. Then everybody starves."