What happens to the birth rate of a country when the economy develops? Why?

When a country has economic development, the birth rate usually falls. People are working more and wait later in life to have children. While some others now choose to not have any children at all. For a population to be stable, a woman needs to have 2 children, it has fallen over the years in developed countries. This can be problematic for future generations because the newer generations are the ones to support the retiring generations. Labor forces will shrink and this will then hurt the economy.