A. Appendix
Analogously, one gets for CF equation (13):
Cf = (1 - n) Ppψ- C.
Plugging these two equations into the definition of C, one gets:
C=
n 1-n
■ P C ' P C
nn(1 - n)1-n
=(P)' P
C.
Solving this forP , one finally obtains equation (5):
=PHnPF1-
Consumption-based Producer Price Index, Demand Curves for Individual Goods The representative
domestic household maximizes
CH=
1
n^θθ г
θ-1
C ( h ) ~s~ dh
θ- 1
with respect to C(h) subject to the budget constraint
n
H CH =
0
(h)C(h)dh.
Hence,
Λ=
1
(;)θ
n / ∖θ-1
I с ( h) -τ- dh
0
θ
θ-1
λ nP (h)C(h)dh -PH CH
0
→ max
C(h)
∂Λ
⇒ ∂C ( h)
ɑ)' Г C ( h )
θ- 1
θ dh
1
θ- 1
1
(1) β C ( h ) -1 - λΡ ( h ) = 0 •
Solving this expression for C (h), one obtains the subsequent preliminary demand function for individual
domestic goods:
{x -θ
---------λ---ɪ---(
[( 1 )1 ;; C ( h )θ- dhθ-1 ( n ) »
Multiplying the preceding equation with Ρ (h), one obtains:
{4 -θ
---------λ---ɪ---(
[( 1 )θ RO C ( h ) θ^ dh]θ-1 ( 1 ) »
Taking the integral from 0 to n over both sides of this equation, one gets:
-θ
n Ρ (h)C (h)dh = n Ρ (h)1-θ dh
00
[( n )1 RO C( h )θ-1 dhiθ-1 ( n )1
29
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