>From Man-Hours and Distribution, 
by M. King Hubbert, 1940

http://www.technocracy.org/pamphlets/man-hours-distribution.html

Growth of Production with Time

"Every physical quantity that changes with time does so under very definite
physical limitations. Industrial production, being, a physical process,
therefore proceeds under ordinary physical limitations. One of the most
common types of physical growth is that in which a quantity increases by a
fixed percentage of itself in equal time intervals. This is exactly
equivalent to the increase in the principal of a sum of money at compound
interest, where the interest is compounded continuously rather than per
year. We shall speak of this as being a compound-interest type of growth. 

"Practically all industrial. production in its earlier stages increases with
a compound-interest type of growth. From the Civil War to the World War,
American industrial growth was at such a rate as to double itself once about
every twelve years. This would correspond to an instantaneous rate of
increase of about 6 percent per annum. 

"One of the basic principles of any such growth is that it is physically
impossible for it to continue more than temporarily, for otherwise it would
soon reach such proportions as to require more materials than exist in the
entire earth. It also would outrun the capacity of the public to consume. 

"It follows, therefore, that the next stage of physical growth must be one
of leveling off. The leveled-off stage may continue, or else be followed by
a declining stage in which the quantity may become stabilized at a lower
level than its maximum, or else continue to decline to zero. 

"The point at which the transition from the first stage of growth (that
where the increase each year is greater than that of the year before) to the
second stage, where the growth is definitely slowing down and the curve is
leveling off, is called the point of inflection of the curve."  

Regards, 

Tom Walker
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