The PROVIDE Project Standard Computable General Equilibrium ...

PROVIDE Project Technical Paper 2003: 3 October 2003
Production relationships by activities are defined by a series of nested Constant Elasticity
of Substitution (CES) production functions. The nesting structure is illustrated in Figure 3,
where, for illustration purposes only, two intermediate inputs and three primary inputs (FD k,a ,
FD l1,a and FD l2,a ) are identified. Activity output is a CES aggregate of the quantities of
aggregate intermediate inputs (QINT) and value added (QVA), while aggregate intermediate
inputs are a Leontief aggregate of the (individual) intermediate inputs and aggregate value
added is a CES aggregate of the quantities of primary inputs demanded by each activity (FD).
The allocation of the finite supplies of factors (FS) between competing activities depends
upon relative factor prices via first order conditions for optima. The base model contains the
assumption of full employment, but this can be relaxed.
3. Algebraic Statement of the Model
The model uses a series of sets, each of which is required to be declared and have members
assigned. For the majority of the sets the declaration and assignment takes place
simultaneously in a single block of code. 8 However, the assignment for a number of the sets,
specifically those used to control the modeling of trade relationships is carried out
dynamically by reference to the data used to calibrate the model. The following are the basic
sets for this model
c =
a =
f =
h =
g =
{ commodities}
{ activities}
{ factors}
{ households}
{ government}
and for each set there is an alias declared that has the same membership as the corresponding
basic set. The notation used involves the addition of a ‘p’ suffix to the set label, e.g., the alias
for c is cp.
However, for practical purposes, mainly associated with reading in the data, these basic
sets are declared and assigned as subsets of a global set, sac,
{ c, a, f , h, g, ent, kap, dstoc, row,
total}
sac = .
All the dynamic sets relate to the modeling of the commodity accounts and therefore are
subsets of the set c. The subsets are
8 For practical purposes it is often easiest if this block of code is contained in a separate file that is then
called up from within the *.gms file. This is how the process is implemented in the worked example.
© S. McDonald
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