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hadow prices) to change as well and thus have
indirect effects throughout other sectors of the
economy. Consequently when large changes are
considered a different methodology is needed to
help us deal correctly with the big picture. Here, we
look briefly at the type of model an economic
planner would want to use for this purpose.
To be sure of capturing all indirect effects, we
would need to construct a dynamic general equilib-
rium model that incorporates all the interactions
(both static and dynamic) between and among
economic and environmental (or ecological) vari-
ables and use it to analyze aggregate planning
problems in which macro decisions are made on
associated decision variables. However, the practical
problems of implementing such a model are daunt-
ing. The number of variables necessary to specify
the ‘‘state’’ of this system is much too large to deal
with computationally much less analytically. The
best we can do with the current state of the art is to
construct stylized models with a significantly re-
duced state space and/or to ignore potential feed-
backs among certain sectors of the economy. Even
though these models are removed further from the
precision we need than those of the earlier sections,
they do provide some valuable insights.
MACRO PLANNING METHODOLOGY
In thinking about macro allocation problems, such
as the total allocation of an exhaustible resource
over time, the economist again is led to the use of
shadow prices. This is not because economists are
wedded to prices, but because constrained optimiza-
tion problems of the type that emerge are most
efficiently (and intuitively, we think) analyzed us-
ing shadow prices. To see the logic of this, consider
the following example. A pool of oil is to be divided
up among several competing firms. If firm i uses
amount m, it can generate a net social benefit f
i
(m).
Our problem is to allocate a fixed reserve Z to
maximize total contributions to social benefit. This
problem can be expressed mathematically as
Max
mi
oi
f
i
(mi
) with constraint oi
mi
# Z.
The method of Lagrange Multipliers is an efficient
way of solving this problem both analytically and
computationally. We emphasize here the computa-
tional aspects and later comment on the (perhaps
better known) analytic analog. We begin by replac-
ing our constrained problem with an unconstrained
one (generally much easier to solve). Namely we
form the Lagrangian: