Some Notes on Population and Living Levels - Villard, Henry H. (The Review of Economics and Statistics, 1955)
IT is today rather generally accepted that the gloomy future which Malthus predicted as a result of the application of an increasing population to a fixed quantity of resources can be warded off by increases in the quantity of capital and improvements in the techniques of production. This will undoubtedly be true for a century or so; but it cannot be true for periods which are, after all, fairly short in terms of human history. Specifically, at the present time world population is probably increasing at an annual rate of about one and one-half per cent, which means that population is doubling every fifty years. If this rate of increase were to be maintained until 4250 A.D., the population of the world would weigh six sextillion, six hundred quintillion short tons, which is also the estimated weight of the world. Given the law of conservation of matter, it follows that there is nothing that science will be able to do even in an atomic age to increase output sufficiently to maintain the present rate of population growth until 4250 A.D.; sometime well before that date the increase must come to an end. Note that only the timing depends on the one and one-half per cent rate of population increase that has been used. If the correct rate were three per cent, only half the time would be required; if it were 34 per cent, twice as much time would be needed. It follows that if the time period is long enough, diminishing returns are always with us despite improvements in techniques and increases in capital.