SBP Working Paper Series STATE BANK OF PAKISTAN

3.1 Firms
3.1.1 Final Good Producing Firms
The final good producing firms produce final good for consumption and investment by combining the
differentiated goods produced by intermediate good producers according to the following Dixit-Stiglitz
bundling technology:
p
p
1
1
p
1
=
j
p
y ( )
t
yt
dj
(2)
0
j
th
Here y
t
, yt
and
p
represent intermediate good produce by j intermediate firm, final output and
constant elasticity of substitution between intermediate products, respectively. For given price and
j
elasticity of substitution, the final good producers choose the quantity y
t
of each intermediate good in
such a way that maximizes their profit. The result of this profit maximization is the following demand
th
function for the j intermediate good:
y
j
t
p
j
P
t
= yt
(3)
Pt
The equation (3) shows that the demand for intermediate good j is inversely related to its relative price
and directly related to aggregate output. Aggregating across all intermediate goods and using equation (2),
we get the aggregate price level
P
t
j 1 p
p
P
dj1
1
t
1
=
(4)
0
3.1.2 Intermediate Good Producing Firms
Intermediate goods producers demand capital and labour for given wages and rental rate of capital in
competitive factors market. In addition, they set price of their differentiated product while exploiting
some degree of monopoly and considering uncertainty regarding their ability to change prices in future.
The Calvo (1983) model is used to capture the intermediate good producing firms’ behavior under this
uncertainty.
Demand for Labour and Capital
The intermediate good producing firms are assumed to follow a Cobb-Douglas production function with
constant returns to scale (CRS)
j
j
k h
1
j
y = exp( a )
(5)
t
where
way.
t
t
a
t
t1
t
a = a
is a stochastic technology shock that affects all intermediate firms in the same
a
a
t
a
a
is the persistence parameter and
t
~ N(0,
) is an i.i.d. random shock to total factor
productivity (TFP). The parameter is the share of capital in production. Also,
capital and labour utilized by firm j respectively.
j
kt
and
j
ht
are physical
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