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

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:

n 1-n

■ P C ' P C

nⁿ(1 - n)¹^-n

=(P)' P

Solving this forP , one finally obtains equation (5):

=PHⁿP_F¹^-

Consumption-based Producer Price Index, Demand Curves for Individual Goods The representative
domestic household maximizes

CH⁼

n^θ^θ г

θ-1

C ( h ) ~s~ dh

θ- 1

with respect to C(h) subject to the budget constraint

H CH ⁼0

(h)C(h)dh.

Hence,

Λ=

(;)^θ

ⁿ / ∖θ-1

I с ( h) -τ- dh
0

θ
θ-1

λ ⁿP (h)C(h)dh -PH CH

→ max
C(h)

∂Λ

⇒ ∂C ( h)

ɑ)' Г C ( h )

θ- 1

^θ dh

1
θ- 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- dh^θ-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 dhi^θ-¹ ( n )¹