Well, it's perfectly obvious that as soon as convenient and cheap birth control becomes widely available, then many people will not have children. This reduces the birthrate. HOWEVER, the people that do have children will have been, on average, self-selected. And one thing you can be sure of, they will be over-represented in the psychological category of "People who really like kids"

That being the case, one has to assume that all our descendents, ultimately, will be extremely philoprogenic. Because all the people that deliberately don't have kids, because kids are 'more trouble than they are fun', will have eliminated themselves from the gene pool. In fact, they may eliminate themselves in a single generation.

Which says to me that we will have a bottleneck of sorts -- birth rates will go down, maybe a lot, and so will the total population, but then, as the philoprogenics begin to dominate the gene pool -- birth rates will start to climb again. And more so every generation, I expect. It's a positive feedback loop.