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

deterministic steady state. 12
The law of motion for Ni,t is
� �
Si,t
Ni,t+1 = (1 − δn)Ni,t + Φn Ni,t
Ni,t
� �
� � 1 1− ζn
Si,t
Si,t
Φn =
+ α2,n
Ni,t
Ni,t
α1,n
1 − 1
ζn
where Si,t is R&D investment (using the final goods) and the function Φn(·) captures adjustment costs in
R&D investments and has the same functional form as the capital adjustment cost equation of Jermann
(1998). The parameter ζn represents the elasticity of new R&D investments relative to the existing stock of
R&D. The parameters α1,n and α2,n are set to values so that there are no adjustment costs in the determin-
istic steady state. 13
Substituting the production technology into the inverse demand function yields the following expression
for the nominal price for intermediate goods i
Pi,t = PtY 1
�
ν
t K α �
i,t AtN η 1−η
i,tNt Li,t
≡ PtJ(Ki,t, Ni,t, Li,t; At, Nt, Yt)
Further, nominal revenues for intermediate firm i can be expressed as
Pi,tXi,t = PtY 1
�
ν
t K α �
i,t AtN η 1−η
i,tNt Li,t
≡ PtF (Ki,t, Ni,t, Li,t; At, Nt, Yt)
� 1−α � − 1
ν
� 1−α � 1− 1
ν
For the real revenue function F (·) to exhibit diminishing returns to scale in the factors Ki,t, Li,t, and Ni,t
requires the following parameter restriction:
or
�
[α + (η + 1)(1 − α)] 1 − 1
�
< 1
ν
η(1 − α)(ν − 1) < 1
12
Specifically, α1,k = (∆Zss − 1 + δk) 1
ζk and α2,k = 1
ζk−1 (1 − δk − ∆Zss).
1
13
Specifically, α1,n = (∆Nss − 1 + δn) ζn 1
and α2,n = (1 − δn − ∆Nss).
ζn−1
9