Master Thesis - Humboldt-Universität zu Berlin

Households use the following rule for discounting:
Ṽ j
t (P j
t ) =
∞∑
i=0
ɛ i pE[Λ t,t+k tDiv j t+i (P j
t+i )] (70)
Λ t = λ t
P C
t
(71)
Λ t,t+i = β i λ t+i
λ t
P C
t
P C
t+i
(72)
As discussed in the introduction of the model, prices are also sticky and
not all firms will optimize their price in each t. Therefore the firm chooses
to maximize the following function subject to (57).
Ṽ j
t ( ˜P j t )=∑ ∞
i=0 ξi p Λ t,t+i[( ˜P j t (P D t−1+i /P D t−1 )γp ¯π i1−γp −MC t+i)y j t+i −MC t+iΦ] (73)
The firms that cannot optimize the prices, will index them acordingly:
P j
t+i = ˜P j
t (P D
t−1+i/P D
t−1) γp (¯π i /ɛˆπ t ) 1−γp (74)
Following a procedure similar to the wage setting, obtain the domestic
1
goods inflation, with
ɛλ p+1
defined before and an additional term, not explicitely
modeled to account for the feed back of a shock in consumption
inflation on domestic prices:
[
ˆπ t D= 1 βˆπ 1+βγp t+1 D +γpˆπD t−1 + (1−βξp)(1−ξp) 1
·
ξp ɛλp+1 · ˆmcD t
]
+λ p,t−cpy·η P C
t (75)
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