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

t
n ⎡
= y j,
k − ⎢ f n,
j,
k −∑
⎣
i=
f
n,
j,
k
α i,
j,
k i,
j,
k
(B26)
1
⎤
⎥
⎦
Given consistent aggregation in the nest, the following accounting identity must hold:
n
W i,
j,
kYi
, j,
k ∑ Fi,
j,
kTi
,. j,
k
i=
1
= (B27)
Linearising (B27), substituting (B25) and rearranging in terms of wj,k gives the linearised
composite intermediate input price in the nest:
n
w j,
k ∑ i,
j,
k fi
, j,
k
i=
1
= α (B28)
Substituting (B28) into (B26) gives a simplified version of the Cobb-Douglas Hicksian
demands for intermediate input ‘i’:
[ f − w ]
t n,
j,
k y j,
k − n,
j,
k j,
k
= (B29)
This linearised demand function has exactly the same interpretation as the CES primary
factor demands. The unitary value of the elasticity of substitution parameter is implicitly
recognised within the price effect component of the demand function.
Summary of Production Nest Input Demands
Composite Input/Factor Demands (Leontief)
y = z
j,
k k
(B2)
x = z
j,
k k
(B2)
Composite price in the nest:
p k S1
, k w j,
k + S2,
ku
2,
k
= (B5)
Primary Factor Demands (CES):
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