Please note that without the latest version of Acrobat Reader, i.e. version 3.02, you may experience very minor problems. In particular, the greek letter "psi" is occasionally missing from equations (9) and (13) and some minus signs in exponents get dropped. I've also found that the paper prints more accurately on postscript printers.
December 3, 1998 -- Version 4.0
All growth models are linear in some sense, and the endogenous growth literature can be read as the search for the appropriate linear differential equation. Linearity is a "crucial" assumption, in the sense used by Solow (1956), and it therefore seems reasonable to ask that this assumption have an intuitive and compelling justification. This paper proposes that such a justification can be found if the linearity is located in an endogenous fertility equation. It is a fact of nature that the law of motion for population is linear: people reproduce in proportion to their number. By itself, this linearity will not generate per capita growth, but it is nevertheless the first crucial ingredient of such a model. The second crucial ingredient is increasing returns to scale. A justification for increasing returns, rather than linearity in the equation for technological progress, is the fundamental insight of the idea-based growth literature according to this view. Endogenous fertility together with increasing returns generates endogenous growth.