Following up what I had to say about how demographics affect the economic prospects of various countrues , the Economist has an article on the subject. (It's again subscription only, unfortunately).

Essentially this point is this. When you reach a certain stage of development, the number of children per mother drops. For a while, you have a situation where you have relatively few old people to be looked after (because the old people had a relatively large numbers of children, the number of old people per working age person is small) and relatively few children, because the birth rate has dropped. Therefore, a large portion of the population can devote itself to economically productive activity, and the economy can get a large, one off boost. Eventually, this large group of people gets old, and then you have a demographic brake, because they did not have that many children. If this drop in the number of children occurs too rapidly, as has occurred in Japan, then the economy can really hit the wall when this type of crisis is reached. The trick is to use the one off economic boost without knocking things too far out of balance in the long term.

This also means there is only one window of opportunity. Low fertility eventually leads to a rising proportion of older people, raising the dependency ratio as the working population goes from caring for children to caring for parents and grandparents. Nor is the demographic dividend automatic. The right policies—a flexible labour market, investment and saving incentives, provision of high-quality health care and education—are still essential to making the working-age population more productive.

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If these observations are correct, developing countries entering their demographic transition have a unique chance to cash their population dividend. South Asia will reach its peak ratio of workers to dependants between 2015 and 2025. Richer Latin American countries have completed the transition, but poorer ones continue to lag; their peak is likely in 2020-30. In sub-Saharan Africa, however, only 11 countries are expected to reach that stage before 2050, and a lot still has to be done to reduce fertility levels. The rapid rise in AIDS deaths will also frustrate changes in age structure that would otherwise occur. And once the transition is over and the dividend pocketed, countries will face the next big challenge: how to care for the old.