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292CHAPTER 9. THE NEW INTERNATIONAL MACROECONOMICSGovernment.seignorageGovernment spending is Þnanced by tax receipts andP t G t = P t T t + M t − M t−1 , (9.134)Pt ∗ t = P t ∗ t ∗ t ∗ − M t−1 ∗ . (9.135)In characterizing the equilibrium, it will help to consolidate the individual’sand government’s budget constraints. Substitute proÞts (9.122)-(9.123) and the government budget constraints (9.134)-(9.135) into thehousehold budget constraints (9.110)-(9.111) and use the zero-net supplyconstraint B ∗ t = −(n/(1 − n))B t from (9.137) to getP t C t + P t G t + δ t B t = p t (z)x t (z)+S t q ∗ t (z)v t(z)+B t−1 , (9.136)P ∗t C ∗ t + P ∗t G ∗ t −n δ t B t= p ∗ t (z ∗ )x ∗ t (z ∗ )+ q t(z ∗ )vt ∗ (z ∗ ) − n1 − n S t S tB t−1S t.1 − n(9.137)The equilibrium is characterized by the Euler equations (9.112)—(9.117),the consolidated budget constraints (9.136) and (9.137) with B 0 = G 0 =G ∗ 0 = 0, and the output equations (9.128)—(9.133).From this point on we will consider only on monetary shocks. Tosimplify the algebra, set G t = G ∗ t =0forallt. We employ the samesolution technique as we used in the Redux model. First, solve forthe 0-steady state with zero-international debt and zero-governmentspending, then take a log-linear approximation around that benchmarksteady state.(189)⇒The 0-steady state. The 0-steady state under pricing-to-market isidentical to that in the redux model. Set G 0 = G ∗ 0 = B 0 = 0. Dollarprices of z and z ∗ goods sold at home are identical, p 0 (z) =q 0 (z ∗ ).From the markup rules (9.124) and (9.125), it follows that the law ofone price, p 0 (z) =q 0 (z ∗ )=S 0 q0(z) ∗ =S 0 p ∗ 0(z ∗ ). We also have by PPPP 0 = S 0 P0 ∗ . (9.138)Steady state hours of work, output, and consumption are" # 1/2θ − 1h 0 (z) =y 0 (z) =h ∗ 0(z ∗ )=y0(z ∗ ∗ )=C 0 = C0 ∗ = . (9.139)ρθ