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You'd have thought Lester Brown would have heard of Malthus and his 1798 treastise on the limits to population.
http://www.ac.wwu.edu/~stephan/malthus/malthus.0.html
Thanks EconLog for reminding us that even 200 year old bad ideas refuse to die and constant vigilance is required.
[Note from the Econlib Editor: Let me suggest reading any of the original and definitive editions of Malthus's Essay on the Principles of Population online:
1st edition (1798) http://www.econlib.org/library/Malthus/malPop.html
6th edition (1826), as revised by Malthus. http://www.econlib.org/library/Malthus/malPlong.html
Malthus's evident point was not about any limit to population. His observations were that individuals, families, and governments historically have made and continue to make choices, including those that affect family size and hence population. Individuals and families in every culture and country choose well in life, looking to the future of their children and themselves, about when to marry, have children, pursue health care for the young and the elderly, and how much to tolerate, save, risk, or plan in advance for life-or-death extremes that affect family and children, including war, famine and food availability, disease, government decisions, etc. Malthus's striking and extreme original example of the ability of food production to expand--at its maximum--less quickly than human reproduction could expand--at its maximum!--was an example that lives in infamy and misrepresentation. Malthus spent his whole life trying to clarify what is obvious to those who read the original: if people did not not react, the population would reach a limit per natural means; but it is precisely because humans react and make choices that the natural limits are not met. Neither food production, human reproduction, nor human health care typically ever reach those extremes because of the human ability to look to the future and react in advance.
--Lauren Landsburg, Econlib Editor]
Historically, when a new large population segment starts eating meat several times a week you do tend to get a spike in grain prices, but after a few years the spike goes away.
Starting to eat meat causes grain prices to spike because it takes about 7 pounds of grain to generate one pound of meat so you get a jump in grain demand. But after a lag demand expands to fill the increased demand.