The excess of national income over the aggregate demand gives the rate
of accumulation of net foreign assets; in per capita terms, we have
..
(16)
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 ? ∕lf7λ
Uc[c, (1 — τ a)r* — ρ] =(1 — τl)wT [(1 — τ a)r — P]+ k + b, (17a)
k = κ* {1 - T[(1 - τa)r* - ρ]},
(17b)
(17c)
(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.
16