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

The time t budget constraint of the household is
PtCt + Bt+1
= Dt + WtLt + Bt
Rt+1
where Pt is the nominal price of the final goods, Bt+1 are nominal one-period bonds, Rt+1 is the gross
nominal interest rate set at time t by the monetary authority, Dt is nominal dividend income received
from the intermediate firms, Wt is the nominal wage rate, and Lt is labor supplied by the household. The
household’s intertemporal condition is
where
1 = Et
� ⋆ Ct+1 Mt+1 = β
C ⋆ t
�
� 1−γ
θ
Pt
Mt+1
Pt+1
� Ct+1
Ct
�
Rt+1
is the stochastic discount factor. 9 The intratemporal condition is
Wt
Pt
= τCt
L − Lt
� �
−1 1−γ
Ut+1 Et[U 1−γ
t+1 ]
� 1 1− θ
Final Goods A representative firm produces the final (consumption) goods in a perfectly competitive
market. The firm uses a continuum of differentiated intermediate goods Xi,t as input in the CES production
technology
Yt =
�� 1
0
X ν−1
ν
i,t di
� ν
ν−1
where ν is the elasticity of substitution between intermediate goods. The profit maximization problem of
the firm yields the following isoelastic demand schedule with price elasticity ν
Xi,t = Yt
� Pi,t
Pt
where Pt is the nominal price of the final goods and Pi,t is the nominal price of intermediate goods i. 10 The
inverse demand schedule is
Pi,t = PtY 1
ν
t X
9 See the appendix for a derivation.
10 A derivation of the demand schedule is in the appendix.
7
� −ν
1 − ν
i,t