J. Bradford DeLong
Department of Economics, U.C. Berkeley
I construct estimates of world GDP over the very long run by combining estimates of total human populations with estimates of levels of real GDP per capita.
I take my estimates of human population from Kremer (1993), but it would not matter if I had chosen some other authority. All long-run estimates of human population that I have found are quite close together (with the exception of estimates of population around 5000 BC, where Blaxter (1986) (cited in Cohen (1995)) estimates a population some eight times that of other authorities). Note that this does not mean that the estimates are correct--just that they are the same.
Kremer (1993) sees human populations as growing at an increasing proportional rate from perhaps 125,000 in one million B.C. to 6 billion today. Population reached approximately 4 million by 10000 BC, 50 million by 1000 BC, and 170 million by the year 1. Population then reached 265 million by the year 1000, 425 million by 1500, and 720 million by 1750 before exploding to 1.2 billion by 1850, 1.8 billion by 1900, 2.5 billion by 1950, and 6 billion today. Up until 1950 Kremer calculates that the rate of growth of human populations was roughly proportional to their total level.