Gregory Clark's book
The Farewell to Alms re-popularized the Malthusian model (for the relevant chapter go
here). The basic idea is that population dynamics and the so-called demographic transition do have an important impact on economic growth. Robert Malthus' idea is relatively well known, even if there is an incredible amount of confusion in the way it is explained by modern neoclassical authors.
As all classical authors, Malthus assumed that real wages tended to be at subsistence levels. He emphasized more than others, eg. Smith or Marx, the physiological elements associated to subsistence, and his theory of population influenced David Ricardo (friends sometimes will push you in the wrong direction, but this should not be exaggerated; Ricardo was no Malthus). And this has nothing to do with some Iron Law of Wages (again this reflects the fact that mainstream authors like Clark have limited, to say the least, understanding of the surplus approach; for Ricardo and other classical authors on real wages see Stirati
here).*
At any rate, Malthus notion was that if wages increased, population growth would ensue and bring them back to subsistence levels, hence real wages could not grow. In the mainstream story this is connected with lack of growth of income per capita. The economy would be in a Malthusian trap.** Population growth is bad in this Malthusian world, that is why the good reverend, like modern Republicans (and I would assume more than a few neoclassical economists), was for abstinence and delayed marriages.
The idea is that higher population, for a given technology, leads to more mouths to feed. Classical ideas that suggest that the extent of the market (and, hence, population) might have a positive impact on the division of labor (who said that?) are not discussed by modern neoclassical authors (also explains their dislike of Kaldor-Verdoorn Law). At any rate, the modern theory of economic growth is still dominated by supply-side explanations, in which technological progress is either exogenous (Solow) or endogenously determined by spending on education (or some variation of the topic in the endogenous growth literature).
Demographic transitions, in which the rates of mortality and fertility decline have in this view particular effects on growth. The notion is that the initial fall in fertility leads to a lower youth dependency ratio (less youngsters to feed), and is growth enhancing. Further, mainstream authors assume that workers in the labor force would have a higher savings rate (given life cycle hypothesis arguments) and that would lead to investment (yes, Say's Law). Jeff Williamson suggests (see
here) that this, the so-called demographic dividend, in part explains the Economic Miracle in parts of Asia.
On the other hand, the same population dynamics leads to higher old age dependency ratio, and that should have (even if evidence is mixed on that) a negative impact on growth. Note that
Eichengreen and his co-authors, suggest that slowdowns in growth are associated to falling productivity (not population dynamics), even if they measure that using Total Factor Productivity (which is not a measure of productivity, but of the changing patterns of functional income distribution; see
here).
Mind you there is a more reasonable, demand-led, explanation for why population transitions might have an impact on growth. As the process of structural transformation from agricultural to industrial societies continues, more workers are incorporated in industrial jobs with higher pay, and even if income distribution might worsen, the expansion of urban population (and higher real wages) means an expansion of demand. Obviously once the transition is done, the expansion of real wages (not just from the rural workers moving into cities) must continue. In this case, the main cause for the limits to real wage expansion (demand expansion), and continued growth, come from the balance of payments, since higher wages and consumption lead to increasing imports.
There are many more limitations in the resurgence of Malthusian views in the mainstream. Including the Social Darwinist flavor of Clark's ideas, as noted by Deirdre McCloskey (
here). But I'll leave those for another post.
* The main point that mainstream intepretations of classical authors miss is that there is no systematic decreasing relation between real wages and employment in Ricardo and other classical economists, something that Stirati makes clear.
** Note also that some authors suggest that this is the basis for Carlyle's epithet the 'dismal science' for Political Economy. As noted before by Vienneau (see
here): "Thomas Carlyle did not coin the phrase 'The dismal science' to refer to Thomas Malthus's anti-utopian theory of population."