Master Thesis - Humboldt-Universität zu Berlin

4.2 Intermediate firms
Intermediate goods y j t are produced in a monopolistic competition by a continuum
of differentiated producers (indexed by i= [0; 1]) characterized with
sticky prices. The Calvo model makes some very specific assumptions about
the elasticity of demand, holding it constant. The previous case of wage
setting is such an example that follows Dixit-Stiglitz specification of a constant
mark-up. For the intermediate firms we follow Eichenbaum and Fisher
(2003), and allow for the possibility that the elasticity of demand is a function
of firm’s price. In order to define this elasticity first we need to define
the technology of the domestic good firm D t as :
∫ 1
0
G(y j t /D t ) = 1 (8)
Function G includes the relative price of individual producers P j
t and the
aggregate Pt
D , as well as elasticity. Following the specifications of Kimball
(1995), G is increasing, and strictly concave, G(1) = 1.
The standard Dixit-Stiglitz specification corresponds to the specific case:
G(y j t /D t ) = (y j t /D t ) 1
1+λp
(9)
The intermediate goods are produced with a Cobb-Douglas technology function
nested in a Leontieff production function:
v j t = ɛ a t · ˜K α j,t · L 1−α
j,t (10)
˜K j,t = z t K j,t−1 (11)
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