1 A Recursive Dynamic Computable General Equilibrium Model For ...

Appendix B: A Linearised representation of a nested production function
Consider a 2-stage nested production function (this approach can also be applied to a
utility function), where final output is a Leontief function of a ‘composite’ intermediate
input and composite primary factor. In the lower portion of the nest, the composite
input/primary factor is subdivided into specific types ‘i’. The intermediate input nest is
characterised using CD substitution possibilities, and the value added nest is specified as
CES.
The aim of the exercise is to present a range of possible linearised functional forms
typically used in nested CGE model structures. Moreover, it will provide some insight into
the interpretation of linearised functions which will be employed freely in the discussion in
subsequent chapters.
Notation
Z k ⇒ Output in industry ‘k’.
k ⇒
⇒
P The output price in industry ‘k’.
Y j,
k Demand for the composite intermediate input, ‘j’ in industry ‘k’.
W j,
k ⇒
X j,
k ⇒ Demand for value added composite, ‘j’ in industry ‘k’.
U j,
k ⇒ The input price of composite primary factor, ‘j’ in industry ‘k’.
T i,
j,
k ⇒
The input price of composite intermediate input, ‘j’ in industry ‘k’.
Input demand for intermediate input of type ‘i’, in composite intermediate input
nest ‘j’ in industry ‘k’.
⇒ The price of intermediate input ‘i’.
F i,
j,
k
V i j,
k
, ⇒ Input demand for primary factor of type ‘i’, in composite value added nest ‘j’, in
industry ‘k’.
R , , ⇒ The price of primary factor ‘i’.
i j k
Lower case letters are the percentage change equivalent of the upper case ‘levels’ variable.
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