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- An analogous procedure allows us to …nd all Foreign steady-state values, i.e.: Nn = e1 a2 (1 ) vN ' (70) Nf = (1 ) e1 vN' S 1 t + (1 ) ( + (1 ) S1 ) (71) + e1 vN ' + (1 ) S 1 1 Document de Travail du Centre d'Economie de la Sorbonne - 2009.65 halshs-00429600,version1-3Nov2009
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- Document de Travail du Centre d'Economie de la Sorbonne - 2009.65 halshs-00429600,version1-3Nov2009 7. APPENDIX 7.1. The detailed optimization program of the borrower. Utility function: max E0 ( X t=0 t U (Ct; Nt) ) Complete budget constraint, in nominal terms: PT;tCT;t+Pn;t (Cn;t (1 ) Cn;t 1)+Rt 1Dt 1 qtRt 1Dt 1 Dt qtDt +WtNt+ X where D are the bonds issued at Home in Home currency and D are bonds issued in the Foreign country in Foreign currency. The individual budget constraint in real terms of tradable consumption is: CT;t + xt (Cn;t (1 ) Cn;t 1) + Rt 1 dt 1 T;t qtRt 1dt 1 PT;t 1 PT;t (57) dt qtdt PT;t PT;t + WtNt PT;t + X
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- Document de Travail du Centre d'Economie de la Sorbonne - 2009.65 halshs-00429600,version1-3Nov2009 Substituting (60) and (62) in (14) we obtain the steady-state level for net external debt in Home: b = (1 ) (1 ) vN' e1 a1 + (1 ) S1 (66) and the one in Foreign: b = b (1 ) S1 + S1 + 1 We pin down steady-state levels for Nh; Nn and N by substituting (60) and (62) in (37),(38) and(39); i.e.: Nh = e1 vN' + (1 ) S1 1 (67) + (1 ) e1 vN ' (1 ) + S1 1 [ + (1 ) S 1] Nn = (1 ) vN' e1 a1 (68) N = Nh + Nn (69) The terms of trade, S, are pinned down by substituting all above steady-state values in (43).
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- Notice however that for ! 0; this result is reversed and we recover Monacelli (2008) result with a slightly dierent collateral constraint. Moreover, if we impose the following constraint: bt = (1 ) (1 ) Et Cn;txt+1 T;t+1 Rt Document de Travail du Centre d'Economie de la Sorbonne - 2009.65 halshs-00429600,version1-3Nov2009 as in Monacelli (2008), the impact of an increase in t pushes up the user cost of durables as long as x (1 ) [ T (1 ) n] > 0 which is comfortably satis…ed with our benchmark parametrization. This has important implications for consumption patterns, see Monacelli (2008).
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