Jyoti Amge is an actress known for her role in American Horror Story and measures roughly 2 feet tall and weighs 11 lbs. Since she is not mentally deficient, she is proof that the human brain can retain its full function at such a reduced size. Imagine if all humans were her size, and how much fewer resources that would consume. The most obvious decrease in resources would come from food, which would suddenly be fantastic in its abundance, but it would also be trivial to build cheap and efficient aircraft if the passengers only weigh 11 lbs (even a set of artificial wings could probably do the trick). Houses could be the size of a walk-in closet, and space travel would suddenly become cheaper by orders of magnitude. When you think about it, the most major factor that makes our civilization's engineering challenges so difficult is that we're so damn big and heavy.
Aside from the need to shrink our pets (especially cats) and the question of what to do with the existing gigantic infrastructure, what would be the complications and challenges from solving overpopulation by engineering smaller people?