Master Thesis - Humboldt-Universität zu Berlin

5.4 Final goods sector: Optimization problem
Final goods sector follows next on our list of log-linearized equations. Given
the presence of adjustment costs, the representative consumption goods distributor
chooses a contingency plan for D f t and M d t to minimize its discounted
expected costs of producing the aggregate consumption good:
max
∞∑
0
[
]
β i Λ t,t+i Pt+iF C
t+i − Pt+iD D f t+i − P M d
t+i Mt+i d − Pt+iO o f t+i
(81)
The first order conditions for equations (13) and (14) are being displayed
below:
F t (1 − θ) = Θ t (82)
F t θ = M f t (83)
The optimization problem for D f t andMt
d is very complicated, as showed
in the first draft of the paper. Instead of solving analitically, the authors
follow Corsetti et al. (2003) and introduce another parameter, namely the
proportion of imports in final goods χ:
Θ t (1 − χ) = D f t (84)
Finally, for the distribution sector:
Θ t χ = M d t (85)
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