What is the function of "for more productivity" on this sentence?

If we rephrase it to say,

A rapid population increase drives the search for more productivity

it becomes self evident: A rapid increase in population [an increase of people] creates a push for more productivity, or, gives people the drive, or motivation, to find ways to become more productive [in tandem with population growth].

Productivity might refer to producing more food, more housing, more living needs, etc.