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

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 ) ^{- 1}_r

Ct,H   =   n ∖  Pt '/ Ct^,

Ct,F  =  (1 - n) μPF-)   Ct.

Now we should make use of the fact that world consumption C^w 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

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
C_t , M_t , B_t , and L_t :

WtLt+(1+it-1)Bt-1+Mt-1+Γt(h) ≥PtCt+Mt+Bt+Ptτt.

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). i_t-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) i^θ1 Ch
∂P (h) ^l M Ph ]    Ph

11

12

w_w,_h.    r~^,(_h ʌɪn    ∖n*(_h∖   ∖^p( ( h )] ^-θ P^pHH-- '■    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

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