Additionally, Z is dependent on social and economic pressures. As the world becomes more urbanized, birth rates have been going down because it is becoming more expensive to raise children. This is occurring naturally without artificial limits imposed.
Example:
> In a 1994 study titled Food, Land, Population and the U.S. Economy, David Pimentel and Mario Giampietro estimated the maximum U.S. population for a sustainable economy at 200 million
The dangers of over-population myth assumes a naive view of a static society. For instance, we can reasonably have X land for food production, from that we can grow Y food and that can feed Z people so anything above Z would be harmful. The problem is that Y is dependent on human innovation and technology. Same can be said for most resources. We never did reach peak oil.
These predictions of inevitable decline have been wrong for a long time. I don't know why you put so much faith into the modern day equivalents.