What you're saying seems to be reasonable assumption on both the "common sense" and "intuitive" level, except for one thing; it's not true.
Historically, it's when incomes go UP, food-per-person goes UP, availability of post-secondary education goes UP, that birthrates plunge and childbearing bottoms out. Odd, I know.
Take a look at this: New York City's borough of Manhattan is the richest county in the United States. In particular, ZIP code 10021 on Manhattan's Upper East Side, with over 100,000 inhabitants and a per capita income of over $90,000, has one of the largest concentrations of extreme wealth in the United States. But fertility is far lower in Manhattan (1.3) than in Mexico City (2.22) and lower in Mexico City than in Iraq (4.1).
If you look at a chart showing world fertility rates (link) you find the opposite of what you would predict: the richer the country gets, the lower the fertility rate drops. Fertility is been dropping all over the world since 1970 or so, just as literacy and education become universal and over-all nutritional sufficiency is attained (with the main nutrition-related problems being obesity and diabetes.)
So in fact, when people get wealthy and well-fed, far fewer kids get born.
And the bottom 30 nations on this chart probably won't even exist as independent ethnic entities 60 years from now.
They'll be taken over by more-fertile immigration and invasion.
As you pointed out as the COST of living goes up the kids go down, why? In Europe people cannot afford to have kids, getting the same way here.
Yes but the subject isn’t fertility, it’s is libido, sex drive.
The problem with your analysis is that you are assuming a homogenious population, when in fact, the survivors of a dwindling society are quite different from the ones on the decline. Call it the Taranto effect, call it social Darwinism. The silly liberal twits who believe that gay relationships are equivalent to heteros, believe in abortion on demand, and do not believe in God are the ones in decline. The ones who are left have more common sense and will carry their values to their children.