I disagree.
Why spend $5 for something that nature will solve anyway. Let the woman be fertile. Fertile females and high birthrates are nature's way of dealing with high mortality. Squirrels have lots of squirelettes, mice have lots of mice, etc. Nothing new here.
The way to fix is the problem is by letting them be. The problem will fix itself to something sustainable, instead of importing food into the area, let the population go down to where the land that the population is living on can sustain it. Or let the population increase their agricultural output in order to sustain its current level.
Ever see the program called Cellular Automata? Where you put in variables for life expectancy, beginning population, food, and space? The food isn't there, so the population has to decrease.
On a purely pragmatic level, what you say is true. Biologists can point out to countless studies on carrying capacities of an ecosystem.
However, should we treat other humans as we would a deer herd in an area with too few predators?
I am not the most religious guy in the world and am more agnostic than not. However, if there is a God and there is a Golden Rule, do we not have a moral obligation, not to feed an unsustainable population, but to encourage responsible birth rates?