3. New Open Economy Macroeconomic Model
relative to the respective domestic or foreign PPI.10 Note that θ does not only denote the elasticity of
substitution between any two individual goods, but also the price elasticity of demand for any individual
good faced by each producer.11 Equation (2) implies that the demand curves for the composite domestic
and foreign goods, CH and CF , are given by:
r μ Pt,H ) - 1r
(12)
(13)
Ct,H = n ∖ Pt '/ Ct,
Ct,F = (1 - n) μPF-) Ct.
Now we should make use of the fact that world consumption Cw equals the population weighted sum of
total domestic and total foreign consumption, where C w then denotes per capita as well as total world
consumption as world population is normalized to 1:
CW := nCt + (1 - n)C*t. (14)
Combining (14) with equations (8), (10), (11), (12), and (13) one finally obtains the global demand
functions for individual domestic and foreign goods in terms of (total) world consumption:12
Ctw(h)
Ctw(f)
|
• Pt ( h ) ■ |
-θ μ Pt,H ʌ-1 rw ∖Hp∏) Ct |
|
• Pf |
-θ μPF ) -1CW |
(15)
(16)
3.2. Households
The representative domestic household maximizes its ob jective functional (1) sub ject to the following
sequence of intertemporal budget constraints (in nominal terms) with respect to the decision variables
Ct , Mt , Bt , and Lt :
WtLt+(1+it-1)Bt-1+Mt-1+Γt(h) ≥PtCt+Mt+Bt+Ptτt.
(17)
As an example for a typical flow budget constraint, inequality (17) states that the household’s period
t expenditure must not exceed period t income.13 W denotes the endogenously determined nominal
wage being the remuneration for supplying labor, which is identical across households (L = L(h)) on
the assumed to be perfectly competitive labor market, an assumption differing from Clarida et al.
(2002). it-1 denotes the nominal interest rate between period t - 1 and period t on riskless one-period
non-government bonds Bt-1 carried over from period t - 1. These nominal bonds are denominated in
10
∂c(h) = (-θ)ι ∙ p(h) iθ1 Ch
∂P (h) l M Ph ] Ph
< 0.
11
∂C (h) P(h)
’ '(h),p(h) := ∂P(h) C(h)
(-θ )1
n
∙ P ( h)1 -θ-1
L Ph J
CHpthP IP(h)!θ --1
---P ( h ) n ---- C-1
Ph 7L Ph h
-θ.
12
ww,h. r~,(h ʌɪn ∖n*(h∖ ∖p( ( h )] -θ PpHH-- '■ 1 ^., ∖t3( ( h )] -θ Pt3HH-- 1 nw
Ct (h) = nC((h) + (i - n)Ct(h)= I PtH I ( -j^- ) [nC( + (1 - n)Cd= I PtH I ( ) Ct .
13
P(C( = P(,H C(,H + P(,F C(,F =
n P((h)C((h)dh + 1
0n
P((f)C((f)df.