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272CHAPTER 9. THE NEW INTERNATIONAL MACROECONOMICSM ∗ tP ∗t="γ(1 + i∗t )i ∗ tC ∗ t# 1², (9.29)where (1/²) is the consumption elasticity of money demand. 3Euler-equations for optimal “labor supply” are 4[y t (z)] θ+1θ=[y t (z ∗ ) ∗ ] θ+1θ="θ − 1ρθ"θ − 1ρθ##TheC −1t [C w t + G w t ] 1 θ , (9.30)C ∗−1t [C w t + G w t ] 1 θ . (9.31)It will be useful to consolidated the budget constraints of the individualand the government by combining (9.22) and (9.16) for the homecountry and (9.17) and (9.24) for the foreign countryC t =(1+r t−1 )B t−1 − B t + p t(z)y t (z)P t− G t , (9.32)Ct ∗ = −(1 + r nt−1)1 − n B t−1 + n1 − n B t + p∗ t (z ∗ )yt ∗ (z ∗ )Pt∗ − G ∗ t . (9.33)Because of the monopoly distortion, equilibrium output lies belowthe socially optimal level. Therefore, we cannot use the planner’s problemand must solve for the market equilibrium. The solution methodis to linearize the Euler equations around the steady state. To do so,we must Þrst study the steady state.The Steady StateConsider the state to which the economy converges following a shock.Let these steady state values be denoted without a time subscript. We3 The home-agent Þrst order condition is γ³M tP t´−² 1P t− 1P t C t+βP t+1 C t+1=0.Now using (9.26) to eliminate β and the Fisher equation (9.13) to eliminate (1 + r t )produces (9.28).4 “Supply” is placed in quotes since the monopolistically competitive Þrm doesn’thave a supply curve.