Optimal Taxation of Capital Income in Models with Endogenous Fertility

The excess of national income over the aggregate demand gives the rate
of accumulation of net foreign assets; in per capita terms, we have

..

b= У + (r* - n)b — c- k -(δ + n)k - g.

3.2 Positive analysis

In this section, we study the comparative static effects of factor tax shifts
under the two fiscal regimes.¹⁶

Residence-based regime

Equation (13b) implies that n =(1- τ a)r^* - ρ in the steady state.

Therefore, the long-run model can be expressed as

Un^[c, ^{(1 τ} a^{)r     ρ}]   z∣ ∖ *^γγ∣∖(λ        ʌ * I I 7 I ?          ∕l^f7λ

Uc[c, (1 — τ a)r* — ρ] =⁽¹ — ^τl)wT ^[(1 — ^{τ a)}r — ^{P]+ k + b,      (}1^7a)

k = κ^* {1 - T[(1 - τa)r^* - ρ]},

(ρ+τar^*)(k+ b)+w^* {1 — T[(1 — τa)r^* — ρ]} = c+g.

Ariseinτl leaves the fertility rate and the capital stock unaffected. The
implied reduction in the after-tax wage stimulates the holdings of net foreign
assets. An induced rise in disposable income occurs, which in turn raises
consumption.

By lowering the after-tax return on wealth, a higher τa brings the fertility
rate down. As the capital intensity is unchanged, the capital stock is pulled

¹⁶ Note that the hypothesis of endogenous fertility ensures that the dynamics of an
infinitely-lived small open economy facing perfect capital mobility are non-degenerate (as
occurs in the corresponding setup incorporating elastic labor-leisure choices with adjust-
ment costs associated with capital accumulation), as the economy is saddle-point stable.

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