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Empirically there is a strong inverse association between population density and body size. It holds in human societies at dierent levels of economic development; in biology it is known as "Damuth's law", with bearing on all mammalian species. Yet this intriguing trade-o between size and number of people lacks a microfounded theoretical explanation. This paper develops a bio-economic growth theory that provides one. We hypothesize that individuals face a fundamental choice of dividing resources between the number of children and how well to nourish them. The costs of childbearing are conceived as the metabolic costs needed for carrying the child through weaning, as well as a more standard time cost. The metabolic cost component creates a natural trade-o: expanding fertility limits the amount of nutrition per child since parents need to consume more for themselves. In the long-run steady-state, body size, population size and per capita income is constant. Adult consumption is at the level of subsistence, which itself is endogenously determined.

A Bioeconomic Foundation of the Malthusian Equilibrium: Body Size and Population Size in the Long-Run