The formal dynamics of controlled populations and the echo, the boom and the bust.

This paper analyzes the pattern of fluctuations of births in an age-structured population whose growth is subject to environmental or economic constraint. It synthesizes the traditional demographic analysis of age-structured renewal with constant vital rates and the economic analysis which treats population change endogenously. When cohort fertility depends on relative cohort size, or when period fertility depends on labor force size, fluctuations of forty or more years replace the traditional "echo" or generation-length cycle. Twentieth-century U. S. fertility change agrees well with the theory, as the "Easterlin Hypothesis" suggests; but the period model fits better than the cohort model.