Population and Ideas: A Theory of Endogenous Growth

All models of sustained growth 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 key ingredient of such a model. The second key 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.