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growth in the system ultimately is limited by the
rate of growth of labor and under a variety of
behavioral assumptions the system converges over
time to a steady state in which the capital–labor
ratio and the consumption per person (standard of
living) are constant. Again, the basic story can be
understood using shadow prices. Capital assets now
pay a real dividend in terms of their productivity. If
this dividend exceeds the social rate of discount,
goods prices will be falling so that the net return on
capital (dividend plus capital gains) equals the rate
of discount, and vice versa. With goods prices
falling, consumption increases while investment
decreases and per capita growth slows down—it
stops completely when the dividend rate is reduced
to the discount rate. At this point, prices and the
standard of living become constant over time. The
process operates in reverse when goods prices are
rising.
This model is useful in exposing the fundamental
trade-off between current and future consumption
and the ways in which this trade-off depends on
discounting. It can be extended to incorporate
technological change in ways that allow for growth
in the standard of living even in the long run. These
models were developed in the 1950s at a time when
natural resource constraints did not seem so impor-
tant. However, they were rightfully criticized by
environmentalists for ignoring fixed factors (land
and space), exhaustible resources (oil and coal), and
renewable resources (trees and fish). It had been
argued as far back as Malthus, that the presence of
these resources ultimately would force a curtail-
ment of growth and even a fall in the standard of
living. We saw previously how this would work in
the case of exhaustible resources.
Naturally, reality lies between the two extreme
stories above. A realistic model of the economy/
ecology world would need to have (a) ‘‘state’’
variables for every type of stock variable (physical
and human capital, renewable and exhaustible re-
sources, and so on); (b) ‘‘control’’ variables (con-
sumption, investment, extraction, harvest, and so
on) specifying all the ways a planner might want to
interfere with this system; and (c) a determination
of how the systemevolves over time as a function of
such decisions. Constraints take the formof differen-
tial (or difference) equationsmuch as in intertempo-
ral ecology. For example, the exhaustible resource
constraint takes the particularly simple form: dz(t)/
dt 52m(t), where z stands for the resource stock
and m(t) is the rate of extraction at date t. Once
constructed, such a model could be analyzed using