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



4. Market Clearing under Flexible Prices


4. Market Clearing under Flexible Prices

Before introducing nominal rigidities in Section 5, one should first consider the benchmark case of market
equilibria in a world with completely flexible prices.


4.1. World Bond and Goods Markets


For the derivation of the subsequent equations and their relation to one another see Appendix A.3.

Begin with the equilibrium conditions on the world markets for domestic and foreign goods denoted in
domestic currency:


Pt,HYt = PtCtw ,

Pt,F Ytt = PtCW,


(26)

(27)


where the left-hand side of equation (26) denotes global supply of and the right-hand side global demand
for domestic goods.


Note that an analogous interpretation for (27) also holds abroad.


Equations (26) and (27) immediately collapse to the definition of the terms of trade (TOT):


T    Pt,F _ StPt,F _ Yt

t :   Pt,H Pt,H Y^t ,


(28)


which is the ratio of imported goods’ and exported goods’ prices from the home country’s perspective.


Using the domestic intertemporal budget constraint (17) plus further manipulations eventually yield the
domestic and foreign balance of payment identities:


Pt,HYt-PtCt+it-1Bt-1  ≡  Bt -Bt-1,

Pt,FYtt - PtC + it-1 Bt-1  ≡  Bt - Bt-1


(29)

(30)


with the left-hand side of equation (29) representing the home country’s current account and the right-
hand side its capital account.

Note that an analogous interpretation for (30) also holds abroad.


Internationally tradable bonds are supposed to be in zero net world supply:

nBt + (1 - n)Btt = 0.                                                                         (31)

Assuming that international bond holdings have initially been zero B0 = B0t = 0 together with (14),
(29), (30), and (31) implies that
Bt = Btt = 0 at all times according to Corsetti/Pesenti (2001, pp.

430-432) and Obstfeld/Rogoff (2001, p. 8). Then equations (29) and (30) simplify to the following:


Ct


Ctt


Pt,H Yt

Pt   ,

Pt,F Ytt

Pt


(32)

(33)


10




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