I have to disagree with both your premise, and the one you are refuting. Neither population growth nor growth of consumption is a problem. The Malthusian question is always asked with faulty axioms. It assumes that there is a fixed quantity of resources which is slowly being depleted. The history of the human species refutes that. Due to willful creativity, a power that no other species possesses, we invent new technologies that redefine what a resource is. Therefore, before we consumed all the world’s firewood, we learned to use fossil fuels, a much, much cleaner alternative per unit of energy produced. Of course, both firewood and fossil fuels are simply solar energy that has been condensed and made more efficient through long-term biological and geological processes. And, there is a finite amount of solar energy that reaches the earth per unit of time. If we have any brains at all, we will hurry up and move to non-solar energy, nuclear fission in the short term, and fusion in the long term. Trying to capture solar energy with photovoltaic cells is a step backward in efficiency, like trying to pan the ocean for gold (there’s a lot of it there, and it’s free! But it’s too diffuse to be worth the trouble.)
The concept of “carrying capacity” is also completely wrong, scientifically. It would be applicable if we were protozoa or termites, but we’re not. The reason the population density of Taiwan is so much higher than the population density of Sudan is not due to the mineral wealth or arability of the soil. It is the quality of the man-made infrastructure which enables the land to sustain greater numbers of humans.