As far as I can recall, Lem deals with the exponential rise in numbers of the inhabitants on a planet in two books.
In Fiasco it is described in the Section where DEUS describes how the power blocks balances shifted (because of the emerging nations, participating in the project of maintaining the ice ring just like the others, were superior only in the number of their population)
In the Futurological Congress it is the Central Theme and in shortened, abbreviated form handled in the first speech held in the Congress.
I have always wondered why no cultural or economic system on Earth has yet taken into account how many inhabitants consuming how much planet Earth can actually support. All we hear is that we consume to much and that its going to be bad.
But discreet or concrete measures as mentionedin the Congress are not executed in the scope necessary to make an impact so it seems. Or they are not publicly discussed at all.
So I wonder whether the globalized culture of man on Earth is lacking its reason in this vital part of their civilization, namely to sustain its own existence.