International macroe.. - Free

9.1. THE REDUX MODEL 267c t (z ∗ ) ="St p ∗ t (z∗ )P t# −θC t . (9.6)Analogously, foreign household lifetime utility is⎡Ã∞XM∗Ut ∗ = β j ⎣ln Ct+j ∗ t+j+j=0γ1 − ²with consumption and price indicesP ∗t+j! 1−²− ρ 2 y∗2t+j(z ∗ )⎤⎦ , (9.7)⇐(150)⇐(151)C ∗ t =P ∗t =·Z n0⎡Z n⎣0c ∗ θ−1t (z)θ dz +Z 1nà ! 1−θ Z pt (z)1dz +S t n¸ θc ∗ t (z∗ ) θ−1 θ−1θ dz∗ , (9.8)⎤[p ∗ t (z∗ )] 1−θ dz ∗ ⎦11−θ, (9.9)and individual demand for z and z ∗ goods" # −θc ∗ t (z) = pt (z)S t Pt∗ Ct ∗ ,"pc ∗ ∗t (z∗ ) = t (z ∗ # −θ)Ct ∗ .Every good is equally important in home and foreign householdsutility. It follows that the elasticity of demand 1/θ, in all goods marketswhether at home or abroad, is identical. Every producer has theidentical technology in production. In equilibrium, all domestic producersbehave identically to each other and all foreign producers behaveidentically to each other in the sense that they produce the same levelof output and charge the same price. Thus it will be the case that forany two domestic producers 0