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)-θ
PH CH
Ro P(h)1 -θdh
Plugging this into the definition of CH , one gets:
1
P (h)-θ
PH CH
Ro P(h)1 -θdh
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 -θ
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 μM∙V-ε 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—
,Γt(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,Lt,λt
30
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