Bradford DeLong has a fantastic blog post on the relationship between population size and economic growth and development. He writes:
In Kremer’s model, population will grow and eventually population will be high enough that research and development will proceed fast enough to push income per capita high enough to trigger the demographic transition and thus break the Malthusian proportional link between resources and technology on the one hand and population on the other. After that link is broken, economic growth will predominantly take the form not of Malthusian increases in population but rather Industrial Revolution and Modern Economic Growth increases in living standards and labor productivity.
The breakthrough to an Industrial Revolution, Modern Economic Growth, and our present prosperous global post-industrial economy is therefore baked into the cake. It is an all-but-inevitable event in human history produced by the simple fact that when it comes to generating useful ideas two heads are better than one: “the fundamental nonrivalry of technology as described by Paul Romer (1986)…”
DeLong then tests an alternative theory in which the economic takeoff of WENA countries after 1750 could have been a fluke, and concludes that the British industrial revolution at most saved the world 150 years — that is, “if you take the association between global populations and global economic growth back before the British Industrial Revolution seriously, as a causal relationship.”
The whole post is worth reading. The empirical bits are clear and easy to follow. See also here.
In my Political Economy of Development class I make sure that my students understand the relationship between demography and human development — (i) the impact of demography on state development; and (ii) the impact of state development on markets and economic growth and development. To that end I often use these three illustrations.
Up until the mid 1990s tiny Europe had more people than all of Africa. In the next 30 years Africa’s population will grow by about 800 million people. By 2050 the Continent is projected to have 2 billion people; and half of the children being born in the world will be African. There is no reason to believe that the African experience after these demographic changes will not follow established correlations between population size, state development, and technological change.
kenopalo.com 
I agree with DeLong. A huge population spurs innovation and also provides ready market for those innovations. That’s why I anti the aggressive population control campaigns in Africa.. it happens naturally. As more people get richer, they get fewer children..
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That’s nice. It’s a real pity that the world’s climate has changed, and won’t be able to afford this. If your industrialisation and rise in productivity follows similar trends as before, then 3-4C warming is practically a certainty, and that will easily wipe out all the gains.
The real truth of our times is that the living standards the “Western world” had for the past 50 years or so (or rather, their consumption standards, since the actual quality of living stopped rising by 1978), are an unsustainable, ugly peak that needs to be brought down if the rest of us are to have a chance. “Second World” standards of Russia/China/Iran/South American nations are likely the highest we can reach globally without endangering the long-term survival of our species. Otherwise, we’ll blow through so much of the carbon budget that (real, non-hyperbolic) DPRK living standards will begin to look appealing for the young people come 2086.
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