Investment and Interest Rate Policy in the Open Economy

2.1 Final Good Producers

The home final good (Z) is produced by a competitive firm that uses ZH and ZF as
inputs according to the following CES aggregation technology index:

θ

• 1 θ-ι                 1 ^θ-i -| θ-ι

a θ ZH,t ⁺ (^{1 -} a) θ ZF,t

where the relative share of domestic and imported intermediate inputs used in the pro-
duction process is 0 < a < 1 and the constant elasticity of substitution between aggregate
home and foreign intermediate goods is θ > 0. The inputs ZH and ZF are defined as the
quantity indices of domestic and imported intermediate goods respectively:

where the elasticity of substitution across domestic (foreign) intermediate goods is λ > 1,
andzH(i) and zf (j) are the respective quantities of the domestic and imported type i
and j intermediate goods. Let pH (i) and pF(j) represent the respective prices of these
goods in home currency. Cost minimization in final good production yields the aggregate
demand conditions for home and foreign goods:
where the demand for individual goods is given by

PH   PHH,iS)∖^-λ ₇             ,F PFF,jj)∖ -^λ ₇

^zH,t(ⁱ) = I PHt ) ZH,t^{,        z}F,t^j) = I PFt ) ZF,t∙           ⁽³⁾

Furthermore, since the final good producer is competitive it sets its price equal to marginal
cost

Pt = [aPH^-tθ + (1 - a)PF^-θ] ^1-θ ,                         (4)

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