International macroe.. - Free

9.1. THE REDUX MODEL 273restrict the analysis to zero inßation steady states. Then the governmentbudget constraints (9.16) and (9.17) are G = T and G ∗ = T ∗ .By(9.26), the steady state real interest rate isr =(1 − β). (9.34)βFrom (9.32) and (9.33), and the steady state consolidated budget constraintsareC = rB + p(z)y(z) − G, (9.35)PC ∗ = −r nB1 − n + p∗ (z ∗ )y ∗ (z ∗ )− G ∗ . (9.36)P ∗The ‘0-steady state’. We have just described the forward-looking steadystate to which the economy eventually converges. We now specify thesteady-state from which we depart. This benchmark steady state hasno international debt and no government spending. We call it the ‘0-steady state’ and indicate it with a ‘0’ subscript, B 0 = G 0 = G ∗ 0 =0.From the domestic agent’s budget constraint (9.35), we have C 0 =(p 0 (z)/P 0 )y 0 (z). Since there is no international indebtedness, internationaltrade must be balanced, which means that consumption equalsincome C 0 = y 0 (z). It also follows from (9.35) that p 0 (z) =P 0 .Analogously,C0 ∗ = y0(z ∗ ∗ )andp ∗ 0(z ∗ )=P0∗ in the foreign country. By PPP,P 0 = S 0 P0 ∗ , and from the foregoing p 0 (z) =S 0 p ∗ 0(z ∗ ). That is, the dollarprice of good z is equal to the dollar price of the foreign good z ∗ inthe 0-equilibrium.It follows that in the 0-steady-state, world demand isC w 0 = nC 0 +(1− n)C ∗ 0 = ny 0 (z)+(1− n)y ∗ 0(z ∗ ).Substitute this expression into the labor supply decisions (9.30) and(9.31) to gety 0 (z) 2θ+1θ =y ∗ 0(z ∗ ) 2θ+1θ =Ãθ − 1ρθÃθ − 1ρθ!![ny 0 (z)+(1− n)y ∗ 0 (z∗ )] 1 θ[ny 0 (z)+(1− n)y ∗ 0(z ∗ )] 1 θ .