Optimal Taxation of Capital Income in Models with Endogenous Fertility

Equation (11c) can be rewritten with the aid of (11a) as

^- ^π ^ln Wc = τp^{k +} Fk ^{- δ - n -} ρ.
dt        W_c

In the steady state, (4c) and (5a) imply that (1 - τ_k)(F_k - δ)=ρ + n.
Combining this equation with the long-run version of (11c’), one gets the
optimal capital tax rate τk_k; that is,

Wk

-------^k---- < 0.
(Fk - δ)Wc

Normatively speaking, physical capital should be subsidized in the long-run.
The efficient labor income tax rate, obtained by the government budget con-
straint after using τk, should instead be positive. □

Our long-run results are to be ascribed to the fact that per capita cap-
ital enters the demand for fertility. This wealth effect is obtained because
the opportunity cost of fertility depends on nonhuman wealth as population
growth erodes its stock in per capita terms. Since the static efficiency con-
dition for fertility enters the implementability constraint (9) and hence the
pseudo-welfare function of the social planner, the capital stock appears di-
rectly in the maximand function of the ”Ramsey problem”, thus altering the
Chamley-Judd optimal capital tax rule.¹⁴

The ratio of this optimal tax configuration is imputable to the fact that
-when labor is taxed and hence fertility is stimulated and capital diminished-
capital subsidization becomes necessary in order to dampen population growth
and increase capital formation, thus allowing the economy to attain a higher
level of consumption and welfare of consumers.

¹⁴This is consistent with the methodological remarks on the zero capital tax rule put
forward by Jones, Manuelli and Rossi (1997, p. 105-06).

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