### Charles I. Jones --
Population and Ideas: A Theory of Endogenous Growth

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### Abstract

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.