International macroe.. - Free

9.2. PRICING TO MARKET 291foreign market elasticity of demand is identical. Although the Þrm hasthe power to set different prices for the foreign and home markets itchooses not to do so. Once p t (z) andqt ∗ (z) are set, they are Þxed forthe remainder of the period. The foreign Þrm sets price according to asimilar technology.Since the elasticity of demand for all goods markets is identical andall Þrms have the identical technology, price-setting is identical amonghome Þrms and is identical among all foreign Þrmsp t (z) =S t qt ∗ (z) = θθ − 1 W t, (9.124)p ∗ t (z ∗ )= q t(z ∗ )= θS t θ − 1 W t ∗ . (9.125)Using (9.124) and (9.125), the formulae for the price indices (9.108)and (9.109) can be simpliÞed toP t = h np t (z) (1−θ) +(1− n)q t (z ∗ ) (1−θ)i 1(1−θ), (9.126)Pt ∗ = h nqt ∗ (z)(1−θ) +(1− n)p ∗ t (z∗ ) (1−θ)i 1(1−θ). (9.127)Output is demand determined in the short run and can either be soldto the domestic market or made available for export. The adding-upconstraint on output, sales to the home market and sales to the foreignmarket arey t (z) = x t (z)+v t (z), (9.128)" # −θpt (z)x t (z) =nC t , (9.129)P t" # −θpt (z)v t (z) =(1 − n)C ∗S t Pt∗t . (9.130)The analogous formulae for the foreign country areyt ∗ (z∗ ) = x ∗ t (z∗ )+vt ∗ (z∗ ), (9.131)"px ∗ ∗t (z∗ ) = t (z ∗ # −θ)(1 − n)Ct ∗ , (9.132)v ∗ t (z ∗ ) =Pt∗"St p ∗ t (z ∗ )P t# −θ(1 − n)C t . (9.133)⇐(186-187)