Optimal Taxation of Capital Income in Models with Endogenous Fertility

4 Fertility choices and capital taxation with
capital expenditure expensing

Abel (2006) investigates the general equilibrium effects of capital income tax-
ation when gross investment is immediately expensed from the tax base as
proposed by Hall and Jorgenson (1967). He discovers that, in an infinitely-
lived closed economy with an endogenous labor supply the first-best alloca-
tion is replicated if the positive capital income tax is accompanied by a zero
tax rate on labor income. The non-distortionary nature of this tax struc-
ture, which is also valid for the short-run, is due to the exemption of saving
from the burden of taxation or, in the Abel (2006) interpretation, to a zero
effective capital tax rate.

Here, we study how the Hall and Jorgenson (1967) and Abel (2006) tax
proposal works in general equilibrium models with elastic fertility and what
its normative implications for factor income taxation are. We discover that
endogenous fertility choices imply that the policy prescriptions for eliminat-
ing the allocative distortions of the capital levy may involve different tax
rules from those obtained in models with an endogenous labor supply.

4.1 Closed economy

When gross investment can be deducted from taxable capital income, the tax
base in levels is given by rK- K -δK (where K is the level of the capital
stock). Therefore, the dynamic budget constraint of consumers, expressed in
per capita terms, is given by

k =(r - δ - n)k + [(1 ^{- τ}l)^{wl + q -} cl.              (21)

(1 - τk)

The first-order conditions for the maximization of (1) subject to (3) and
(21) are

21

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