and the price of reexport good is the weighted average of the import prices from the regions where its components came from:
PIMX,t = (sum over CO ≠ H of νIM^ XH,CO((PIM,tH,CO)/(ΓIM^ XH,COdagger(IMtX,CO/EXt)))1-μ_ IMX)1/(1-μIMX).
(37)
Non-tradable (YN,t) and tradable (YT,t) intermediate goods are produced using a Cobb-Douglas technologies:
YN,t = zN,tKG,tαGKN,tα_ NNN,t1-α_ N-ψ_ N;
YT,t = zT,tKG,tαGKT,tα_ TNT,t1-α_ T-ψ_ T;
(38)
(39)
where ψN and ψT are fixed costs. The inputs are homogenous capital services, KN,t and KNTt, and labour services, NN,t and NN,t. Capital services are supplied by domestic households under perfect competition, yielding that demand for capital is determined by its marginal product being equal to the rental rate, while labour demand is determined by the marginal product of labour at intermediate goods firm being equal to the cost of labour determined by labour packers, as described in the main text. zN,t and zT,t are sector-specific productivity shocks.
Note that the labour market clearing implies that the total labour services provided must equal to the labour demanded by intermediate goods firms:
nt = NN,t+NT,t.
(40)
Goods markets for non-tradable and tradable goods clear by equating supply and demand. Demand for non-tradable goods comes from demands for non-tradable consumption and investment goods, (NTC,t and NTI,t), and from government (Gt), which is fully biased towards non-tradable goods. Demand for tradable goods comes from demands for tradable consumption and investment goods (HTC,t, HTI,t) and from trading partners' imports (IMCO,H,t). sN,t, sHT,t, and sX,tH,CO are price dispersions in non-tradable, tradable, and export sectors:
YN,t = sN,t(NTC,t+NTI,t+Gt)
YT,t = sHT,t(HTC,t+HTI,t)+ sum over CO ≠ H of sX,tH,COIMCO,H,t
(41)
(42)
Price setting follows the standard Calvo (1983) framework. Intermediate goods firms, however, set prices differently, depending on the market to which they are pricing their goods. This applies to non-tradable, home tradable and to export goods, in the latter case also for each export market separately (the so-called local currency pricing framework). Prices that are not reset are indexed to a composite of past inflation and inflation target.