International macroe.. - Free

290CHAPTER 9. THE NEW INTERNATIONAL MACROECONOMICS"c t (z ∗ qt (z ∗ # −θ))= C t , (9.119)P tForeign household demand for domestic z-goods and for and foreignz ∗ -goods are" #qc ∗ ∗ −θt (z) = t (z)Pt∗ Ct ∗ , (9.120)"p∗t (z ∗ # −θ)Ct ∗ . (9.121)c ∗ t (z ∗ )=Firms. Firms only employ labor. There is no capital in the model.The domestic and foreign production technologies are identical and arelinear in hours of worky t (z) =h t (z),P ∗ty ∗ t (z) =h∗ t (z).Domestic and foreign Þrm proÞts areπ t (z) = p t (z)x t (z)+S t qt ∗ (z)v t(z) − W t h t (z), (9.122)πt ∗ (z ∗ ) = p ∗ t (z ∗ )x ∗ t (z ∗ )+ q t(z ∗ )vt ∗ (z ∗ ) − Wt ∗ h ∗ t (z ∗ ). (9.123)S tThe domestic z-Þrm sets prices at the beginning of the period beforeperiod-t shocks are revealed. The monopolistically competitive Þrmmaximizes proÞts by choosing output to set marginal revenue equal tomarginal cost. Given the demand functions (9.118)—(9.121), the rulefor setting the price of home sales is the constant markup of price overcosts, 10 p t (z) =[θ/(θ − 1)]W t . The z-Þrm also sets the euro price of itsexports qt ∗ (z). Before period t monetary or Þscal shocks are revealed,the Þrm observes the exchange rate S t , and sets the euro price accordingto the law-of-one price S t qt ∗ (z) =p t (z). This is optimal, conditional onthe information available at the time prices are set because home and10 The domestic demand function is y = p −θ P θ C can be rewritten asp = PC 1/θ y −1/θ . Multiply by y to get total revenue. Differentiating with respectto y yields marginal revenue, [(θ − 1)/θ]PC 1/θ y −1/θ =[(θ − 1)/θ]p. Marginalcost is simply W . Equating marginal cost to marginal revenue gives the markuprule.