Un = (1 - Tι)wT' + (1 - τk)k,
Uc
(22a)
(22b)
--ln Uc = r — δ — n — p.
dt
In this case, factor income taxation involves only static distortions as
the intertemporal tax wedge on capital income disappears. By embedding
equations (22) into the general equilibrium model, it can immediately be seen
k
that the first-best allocation is replicated if τk > 0 and τl =--τk < 0.21
wT '
This result, which is the exact opposite of our closed economy one, also differs
from the Abel (2006) finding, which instead implies that labor income should
be tax free.
This discovery can be summarized as follows:
Proposition 4 In a model with endogenous fertility, capital income taxation
combined with the exemption of capital expenditure requires that labor should
be subsidized with the scope of replicating the first-best allocation.
4.2 Small open economy
As the Abel (2006) tax proposal contemplates de facto a full expensing of
saving, i.e. gross capital accumulation, in an open economy we have to
21Abel (2006) shows that the Hall-Jorgenson proposal of capital income tax generates
the first-best equilibrium as a proposal based on consumption and labor tax mix, if the
normative prescription τl = —τc < 0 is satisfied (where τc is a proportional consumption
tax rate); that is, consumption and leisure must be taxed at a uniform rate. It is not
difficult to show that in our setup the co-existence of consumption and labor taxation
implies that for a positive consumption tax, the optimal labor subsidy rate that replicates
first-best allocation is given by τl
(FIT' + k) τ < 0
FlT' c < `
Note that this result violates
the Atkinson-Stiglitz (1972) principle that all commodities (and hence fertility) should be
uniformly taxed (this is because the capital stock enters the implicit cost of fertility).
22