Investment and Interest Rate Policy in the Open Economy

where P is the consumer price index and PH and PF are the respective price indices of
home and foreign intermediate goods, all denominated in home currency:

We assume that there are no costs to trade between the two countries and the law of one
price holds, which implies that

_P* _ PFt
PFt =
t _et

where e is the nominal exchange rate. Letting Q = ^e-p- denote the real exchange rate,
under the law of one price, the CPI index (4) and its foreign equivalent imply:

and hence the purchasing power parity condition is satisfied only in the absence of any
bias between home and foreign intermediate goods (i.e. a = 0.5). The relative price T,
the terms of trade, is defined as T ≡ -PF-.

2.2 Intermediate Goods Producers

Intermediate firms hire labor and rent capital to produce output given a (real) wage rate
wt and capital rental cost rrt . A firm of type i has a production technology:

yt(i) = Kt(i)^αLt(i)^1-α,

where K and L represent capital and labor usage respectively, and the input share is
0 < α < 1. Given competitive prices of labor and capital, cost-minimization yields:

^w=mc_t(¹—^α) (ʌ) (Ka)                (8)

rrt=-( ⅛ )( ≡ Γ          (9)

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