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time, the stock looks like a free good since its supply
would exceed current demand at any positive price.
However, itwould bewrong to set the shadowvalue
to zero since there is an opportunity cost of units
used today measured as lost consumption later.
Rather we should treat the stock as a common
resource to be shared over many units of time and
assign a positive value to it. It is not immediately
clear how to set this price, but we can say how it
should evolve over time. If extraction rates are
optimal, the marginal unit of oil left in the ground
should earn a rate of return equal to the social
discount rate; if it earns a lower rate of return, then
the unit should be extracted immediately (rather
than left for later consumption). Conversely if the
return is higher, then we should leave the extra unit
in the ground longer. Since oil does not do anything
for us while it is sitting in the ground (it is implicitly
assumed here that oil in the ground does not have
any ‘‘existence value’’), the only way it can earn a
positive return is if it appreciates in value. It follows
that the shadow price of oil in the ground (mea-
sured in labor time—we normalize by setting the
wage equal to one) should grow at the social rate of
discount.
Thus, oil above the ground should be allocated
using a shadow price (in terms of labor) equal to the
marginal extraction cost plus an oil asset price that
increases over time. Consequently, the effective
price of oil should rise over time at a rate positively
associated with the rate of discount (assuming that
this rate is positive). It follows from this that if there
were no productive assets in the economy, the
standard of living should fall over time—the purchas-
ing power of labor (real wage) declines with time. In
this bleak view of things, we currently are living
above ourmeans by using a finite resource provided
‘‘for free’’ by nature.
Of course there are productive assets such as
capital equipment and renewable resources. The
earliest dynamic macro models dealt only with
these and painted a much rosier picture.We outline
briefly the best known of these as an illustration of
the opposite extreme and then comment on more
realistic intermediate cases.
NEOCLASSICAL GROWTH
In the neoclassical growth model, the only unpro-
ducible resource is labor, and there is a single
produced good that is used for both consumption
and investment in capital (plant and equipment). If
the technology for producing goods fromcapital and
labor is assumed stationary over time, the rate of