THE COMPOSITION OF GOVERNMENT SPENDING AND THE REAL EXCHANGE RATE
Yn = AN G(Ln,Kn ) = (An Z βZ )LβN KN (2)
where L and K stand for labor and capital, while Z stands for the public capital stock.
That is, we assume that total factor productivity in each sector is a composite of a sector-
specific term (AT, A*n) and the level of public capital.3 Accordingly, productivity in both
sectors is enhanced by a larger stock of public capital but we allow for the impact to
be potentially different across sectors (if αZ 6= βZ). We assume that αL + αK = 1, but
βL +βK < 1. That is, we incorporate a fixed factor of production (normalized to 1) in the
nontraded sector such that the production function in that sector exhibits diminishing
returns to labor and capital.4 The price of the traded good is equal to world price of the
good and is normalized to 1, while the price of non-traded goods is PN.
The accumulation functions for the private capital stocks in the traded and nontraded
sectors are given by
∆KT = ITK - δKT (3)
∆KN = INK - δKN (4)
where I denotes the level of gross investment and δ is the depreciation rate. The public
capital stock evolves according to
∆Z = IZ - δZ
(5)
We assume that private capital formation in the traded and nontraded sectors only re-
quires the traded good as an input, while public capital formation uses only the non-
traded good as an input.5 The representative household has an instantaneous utility
function over the goods defined as
with the implication that optimal household expenditure shares on traded and non-
traded goods are fixed at (1 - γ) and γ respectively, with a unit elasticity of the relative
consumption of nontradables in relation to the relative price of nontradables.
C=
1-γ γ
CT CN
(1 - γ)1-γγγ
(6)
3See also Barro (1990) on the inclusion of public capital in the production function.
4By incorporating a fixed factor, this allows demand-side factors to influence the structure of long-run
relative prices. As is well known, demand-side factors are irrelevant for long-run relative prices if both
sectors show constant returns to scale in mobile factors (Obstfeld and Rogoff 1996). The main results do not
change if we also allow for a fixed factor in the traded sector.
5In fact, the details of the investment process are not important for our analysis. These polar assumptions
just simplifies the presentation of the model.