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been extremely unequally distributed both between and within countries. The causes of this epochal rise in productivity are less well-agreed-on among social scientists. Economists tend to attribute it to a
change in ‘‘technology’’, stemming from an accumulation of scientific and technical knowledge that proceeds either autonomously as the fruit of human curiosity and ingenuity, or endogenously from
incentives for cost-reducing technological innovation.
Smith, who identified the division of labor as the underlying condition for technological progress, would perhaps not have been surprised by the unfolding patterns of world population and production.
For Smith a larger population would imply opportunities for a much wider and deeper division of labor, both at the detailed level in particular production processes, and at the social level through
regional specialization and trade. Smith’s vision implies, contrary to the postulate of diminishing returns, that a larger population, up to some limit, will have higher rather than lower productivity. If
this relationship holds, it has important consequences for the stability of the world population. Curiously, the economic increasing returns posited by Smith due to the division of labor is precisely
the condition necessary to stabilize human populations that are undergoing the demographic transition to lower fertility rates. These considerations suggest that the current world population may be quite
close to an equilibrium stabilized by falling fertility rather than rising mortality, Autonomous technical progress will have the consequence of lowering, rather than raising, this Smithian
equilibrium world population.
3. Malthus’ equilibrium
It is convenient to consider population dynamics in terms of ‘‘total female fertility’’, the average number of children born over the fertile phase of a woman’s life cycle. Assuming a sex ratio in births
close to 50, population will stabilize in the long run when total female fertility is 2. This measure focuses on average rates of reproduction, avoiding the complications of mortality rates among men
and women past childbearing age. By the same token, an analysis based on total female fertility will abstract from the age composition of the population and its transitional dynamics, issues which are of
central policy and social importance.
Malthus’ postulates of falling mortality, especially infant mortality, and rising fertility with a rising standard of living, imply that total female fertility will rise with the standard of living. We will
identify standard of living with household income, and assume that household income is proportional to per-capita economic output, x 5 X N, where X is Gross Domestic Product corrected for inflation,
and N is population. Measuring total fertility, f, on the horizontal axis and per-capita output, x on the vertical axis, Malthus’ assumptions apply to the positive segment of the income–fertility relation
sketched in Fig. 1.
In this figure a Malthusian demographic equilibrium, x , occurs at the per-capita output
M
corresponding to a fertility rate of 2 on the upward sloping segment of the income–fertility relation. This equilibrium will be stable if a rising population lowers per-capita output, x. Malthus and Ricardo
took this as axiomatic, relying on the presumption of economic diminishing returns to increases in labor and capital in the face of limited land. Thus Malthus’ theory implicitly assumes that the
economy lies on the downward sloping segment of the population–per-capita output relation sketched in Fig. 2.
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.K. Foley Economics Letters 68 2000 309 –317
Fig. 1. The theoretical income–fertility relation has both an upward sloping segment, corresponding to Malthus’ assumption of rising fertility with income, and a downward sloping segment, corresponding to the demographic transition in which fertility falls with income.
There are two equilibrium levels of per-capita output, at which total fertility equals 2, the Malthusian equilibrium x , and the Smithian
M
equilibrium, x .
S
4. The demographic transition and Smithian demographic equilibrium
