Would a small enough world population and excess of resources downplay the role

No. It seems you're talking about the micro/neo-classical perspective, the one that says that all economics is is allocation of scarce resources.

Anyway, this perspective is concerned with allocation, so it would still have significance in your scenario. Also, human wants are generally assumed to be non-satiated (never completely satisfied), so the excess of resources would still not be enough, unless they are infinite.

But anyway this is only one perspective on economics. I consider the issues of (evolving) production, growth and living standards just as important as allocation of scarce resources.
 
The role of economics in...?

Your scenario describes the ideal conditions in which capitalism can flourish. As resources become more limited and population more excessive, capitalism in its true sense leads to severe income inequality and a de facto oligarchical government.
 
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