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How do economic variables correlate with a nation's age distribution (population pyramid)?

Abbreviated Question: 
How do economic variables correlate with a nation's age distribution (population pyramid)?
Answer: 

The question of how demographics relate to economic issues (e.g., poverty, economic growth) has been at the forefront of economics ever since its infancy as a science. For instance, Rev. Malthus (1766-1834) controversially suggested that population growth would erase any improvements in the standard of living due to technological advances. At present, various aspects of the question of how demographics affect (and are affected by) the economy are studied by many fields of economics. There isn't one single field that does it all.