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ON LIMITS TO GROWTH


	1. Many  quantities grow exponentially  in time for  a while.
Examples include a  population of bacteria, the human population, the
industrial production of a country, and the use of electrical energy. 

	2. There are two  ways of arriving  at the conclusion that  a
quantity  is growing  exponentially.   First,  it  can be  determined
theoretically  that its rate of growth  is proportional to the amount
present.  This is true of populations when resources are abundant and
also of industrial economies when resources are abundant and there is
an abundant supply of  labor that can be  taken from unemployment  or
agriculture.  It is also true of the size of  a firm as long as it is
small  compared to  the economy.    The second  way of  arriving at  a
conclusion of exponential growth  is by fitting an exponential  curve
to observed data.  This applies  to the exponential curves for energy
usage.    Fitting exponential  curves  represents to  some  extent an
arbitrary decision, because one could fit other kinds  of curves just
as well. 

	3.  Both methods of  getting exponential  curves can  lead to
mistaken results if done blindly.  A growth model that does not  take
into account the  limitation of a resource  or a demand will  fit the
data  perfectly until this  limitation comes  into action.   When the
bacteria use up  all the  agar or  encounter the walls  of the  Petri
dish, the exponential  growth curve will be distorted.   Mark Twain's
famous example  of extrapolation should also be cited.  He noted that
the Mississipi river had shortened  by 100 miles in 100 years  by the
cutting off of  meanders and extrapolated to the  time when the river
would be  all  gone.   One  could  concoct another  such  example  by
considering fitting an exponential curve  to American beef production
between 1870  and 1890 and predicting that  if something weren't done
about it, each American would have to eat a cow a day by 1930. 

	4. In my opinion, the growth of the consumption of  energy in
the  United States  has  certain resemblances  to  the beef  example.
Namely,  we now have certain  uses for energy.  These  uses lead to a
demand that depends on the distribution of income  in the population.
However, the  present uses will  saturate at a  calculatable level of
energy production.  Further increase in demand beyond this point will
depend on the development of new uses.   Given the present collection
of  uses, we  can ask whether  we can  afford the energy  required to
saturate the demand, from both a resource and an  environmental point
of  view.     In  my  opinion,  the  scientific   knowledge  and  the
technological  development has  already proceeded to  the point where
this question can be answered affirmatively, not only  for the United
States but for the world.  If new major energy consuming applications
develop, we shall  have to  examine whether we  can afford  them.   I
don't really see any such applications now  but don't want to exclude
them.   My guess would  be that use  of energy will  saturate at less
than three times the present U.S.  per capita use. 

	5. The Limits of Growth book  by Meadows uses a model of  the
economy  in  which a  fixed  proportion  of  GNP is  reinvested  into
productive facilities.  Such a model is appropriate to a society that
is far from saturating the demand for goods and  services.  They then
predict  that  unless  we take  some  drastic  measures,  we will  be
overwhelmed by  the  consequences of  increased  production.   In  my
opinion, as soon  as further investment  will not produce  goods that
are a net  benefit to the population, this investment will stop.  The
Meadows view is like looking at  a man eating dinner and noting  that
if he doesn't eventually stop eating he will burst and proposing that
we  make him stop.  He will stop  when he has had enough.  Therefore,
the  question  that  needs  to  be  asked  about  American  or  world
production  is  not  what   will  happen  if  it  continues  to  grow
indefinitely, but merely whether the next increment is worthwhile.