When I read things like free economies it reminds me of a "free market economy" and I just wonder...are you a "kindred spirit"?
Anyway, as I was taught, the birth rate did go up in cities after that advent of monoculture agriculture due to the properties of the diet they were consuming. However, the death rate went up, too, due to being packed so closely together (disease), and the advent of a new group of killers caused by a grain-based, dairy-based diet, and possibly a diet dependant upon the deadly nightshade family, ie., potatoes, tomatoes, egg plant, peppers, etc...a compromised immune system in the form of the body trying to kill itself...autoimmune diseases such as arthritis, rhuematoid arthritis, MS, Lupus, Obesity, some forms of heart disease, and the grand daddy of them all...DIABETES. Before agriculture we do not see any traces of any of these diseases in the fossil record, but they become rampant early on in the fossil record of city dwellers, who quite naturally were dependant upon agriculture. The birth rate sky-rocketed and DEATH stalked the streets of early villages and cities in the above forms, and in complications caused from childbirth...women weren't as easily able to ward off many of the problems caused by childbirth due to their diet...again! This is still true, today. Of course, childbirth has always been extremely dangerous to the health and welfare of women and children, even without compromised immune systems and weakened bodies. The death rate really went up in the Industrial Revolution as white flour made its' appearance. So did the birth rate. White flour (pure gluey starch) and the birth rate seemed to go hand in hand at this time in the Western Countries. Also, in the rice- based, soy-based economies as hulled rice and soy products became a staples in the cities...(pure gluey starch! and other stuff that our bodies don't like such as alkaloids, etc.), and a growing dependance upon milk-based products, world-wide (another form of pure glue ala ELMER'S).
Now, we come to the present day. We now have modern medicine, which is surely helping to prolong life, no question. Better health practices, such as washing our hands with soap and water to keep the germs out of our insides, modern food preserving which keeps the bad bugs from entering our intestines, etc. We also have the growth rate slowing in the Western Countries due to societal changes and awareness factors, as well as economies which have caused woemn to enter the work force in huge numbers. However, in the Third World, I am of the understanding that the birth rate is climbing at alarming rates with no end in sight.