Equilibrium Growth, Inflation, and Bond Yields - Duke University's ...

The intermediate firms face a cost of adjusting the nominal price a lá Rotemberg (1982), measured in terms
of the final goods as
G(Pi,t, Pi,t−1; Pt, Yt) = φR
2
� Pi,t
ΠssPi,t−1
�2 − 1 Yt
where Πss ≥ 1 is the steady-state inflation rate and φR is the magnitude of the costs. The source of funds
constraint is
Di,t = PtF (Ki,t, Ni,t, Li,t; At, Nt, Yt) − Wi,tLi,t − PtIi,t − PtSi,t − PtG(Pi,t, Pi,t−1; Pt, Yt)
where Di,t and Wi,t are the nominal dividend and wage rate, respectively, for intermediate firm i. Firm i
takes the pricing kernel Mt and the vector of aggregate states Υt = [Pt, Kt, Nt, Yt, At] as exogenous and
solves the following recursive program to maximize shareholder value Vi,t ≡ V (i) (·)
V (i) �
Di,t
(Pi,t−1, Ki,t, Ni,t; Υt) = max
+ Et Mt+1V
Pi,t,Ii,t,Si,t,Ki,t+1,Ni,t+1,Li,t Pt
(i) �
(Pi,t, Ki,t+1, Ni,t+1; Υt+1)
subject to
Pi,t
= J(Ki,t, Ni,t, Li,t; At, Nt, Yt)
�
Pt
�
Ii,t
Ki,t+1 = (1 − δk)Ki,t + Φk
Ki,t
�
Si,t
Ni,t+1 = (1 − δn)Ni,t + Φn
Ni,t
�
Ki,t
Ni,t
Di,t = PtF (Ki,t, Ni,t, Li,t; At, Nt, Yt) − Wi,tLi,t − PtIi,t − PtSi,t − PtG(Pi,t, Pi,t−1; Pt, Yt)
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