The corresponding cost-minimizing prices are:
PC,t = [νCPTTC,t1-μC+(1-νC)PNT,t1-μ_ C]^ 1/(1-μC);
PTTC,t = [νTCPHT,t1-μTC+(1-νTC)PIMC,t1-μ_ TC]^ 1/(1-μTC);
PIM C,t = (sum over CO ≠ H of νIM CH,CO((PIM,tH,CO)/(ΓIM ^ CH,COdagger(IMtC,CO/QC,t)))1-μ_ IMC)1/(1-μIMC).;
(28)
(29)
(30)
The model features import-content of exports, which is modelled as in Brzoza-Brzezina et al. (2014), where export firms create a bundle of home-produced tradable goods for export, HTX,t and goods imported for the purpose of reexporting, IMX,t, and then export the bundle of both goods. The export bundle is:
EXt = [νX1/(μX)HTX,t(μX-1)/(μX)+(1-νX)1/(μX)IMX,t(μx-1)/(μX)](μX)/(μX-1).
(31)
Analogously to demands for goods in the consumption bundle, we have the demands for home tradable goods for exports and imported goods for reexports:
HTX,t = νX((MCT,t)/(MCX,t))-μXEX_ t;
IMX,t = (1-νX)(cfrac PIMX,t MCX,t)-μXEXt.;
(32)
(33)
Imported goods for the purpose of reexports are a bundle of imported goods from all other regions, subject to adjustment costs:
IMX,t = [sum over CO ≠ H of (νIM_ XH,CO)1/(μIMX)(IMX,CO,t(1-ΓIM^ XH,CO((IMX,CO,t)/(EXt))))(μIMX-1)/(μIMX)](μIMX)/(μIMX-1).
These give rise to bilateral demands for reexport goods:
(34)
IMX,CO,t = νIM^ XH,CO((PIM,tH,CO)/(PIMX,tΓIM^ XH,COdagger(IMX,CO,t/EXt)))-μ_ IMX(IMX,t)/(1-ΓIM^ XH,CO(IMX,CO,t/EXt))
(35)
The real price (in terms of consumption goods) of the export good is just its marginal cost, MCX,t, which is the weighted average of (real) marginal costs of home tradable goods, MCT,t, and the relative price of imported goods for reexport, PIMX,t:
MCX,t = [νXMCT,t1-μX+(1-νX)PIMX,t1-μ_ X]1/(1-μX),
(36)