- dd ln Uc = (1 - Ta)r*
- n - ρ.
(13b)
From (13a), it is clear that in an open economy (relatively to a closed
one) the opportunity cost of one unit of fertility is raised by b.Sincer is
pinned down by r* + δ, the input demand system (5) implies that the capital
k
intensity and the wage rate are fixed and tax invariant; that is, — = κ and
k
w = w , where κ = f' 1(r* + δ) > 0, w = f (κ*) — κ f -(κ*) and f (—) = F(
k
— , 1) is the output-labor ratio.
Alternatively, in the case of source-based capital taxation, the arbitrage
condition between domestic and foreign assets requires that the after-tax
return on capital is equal to the world interest rate, i.e. (1 — τk)(r — δ) = r*,
where τ k represents the domestic capital income tax rate. Therefore, the
representative agent’s dynamic budget constraint becomes
..
k + b= (r* — n)(k + b) + (1 — τ ι)wl + q — c. (14)
From the consumers’ standpoint, optimality requires that (13a) and the
following Euler equation
— — ln Uc = r* — n
dt
ρ,
(15)
are satisfied.
The demand for capital (5a) along with the condition of perfect capital
mobility implies that (1 — τ k)[Fk(k, —) — δ]=r*. From this relationship, we
k
get that — = κ(τk) (with κ =
(with w' =
κ(f ' — δ)
f4 <0).
(f ' — δ)
------—- < 0) and, using (5b), w = w(τk )
(1 — τ k)f ''
In each capital income tax regime, revenues from labor and wealth taxa-
tion finance the exogenous stream of government expenditure.
15