Macroeconomic Interdependence in a Two-Country DSGE Model under Diverging Interest-Rate Rules



A. Appendix

with 0n P (h)C (h)dh = PHCH. Now combine the preceding equation with the preliminary demand

function from above. Then one gets for C (h):

C(h) = P (h)


PH CH

Ro P(h)1 dh


Plugging this into the definition of CH , one gets:


1

P (h)


PH CH

Ro P(h)1 dh


Dividing this formula by CH and raising both sides of the resulting equation to the power of (θ — 1)/θ, I
obtain:

1'∙∙ ndι‰R-rrP^.


θ-1


dh,


which can be solved for PH to finally obtain the domestic PPI given by equation (6):

1


PH =

Plugging this formula into the last given equation in C (h), one eventually gets equation (10):

PH


θ

CH.


A.2. First Order Conditions for a Utility Maximum

The representative household maximizes

,   ,.ʃv--‘ C-'+ X μMV   γ r--i∏

Ut = ; I -β      Pf + 1—ɪШ -'Ls J∫

with respect to the decision variables Ct , Mt , Bt , Lt subject to the intertemporal budget constraint (in
real terms)

Wt            Bt-1  Mt-1

— Lt + (1 + it-1) ~P~ +P—


t(h)    c ,Mtdt    Bt

+     = Ct + τ+ π+τ,'


Hence,

Λt


Et


X β

=t


C1-ρ


—- Ls + (1 + is
P


1)


G9


1-ε


L1-ξ


Γ(h)


])


max


Ct,Mt,Bt,Ltt


30




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