Optimal Taxation of Capital Income in Models with Endogenous Fertility

up from (17b), since labor hours worked are increased. Consumption and
nonhuman wealth unambiguously rise.¹⁷ The stock of net foreign assets may
rise or fall. Domestic output and national income are increased.

Source-based regime

As in the long-run n = r* — ρ from (15), the steady state economy is
described by

Uⁿ(^c,r---^p) = ^{(1 - τ}ι)^w(^τk)T'(^r* ^- P⁾ + ^k + ^b,         (^18a)

Uc(c,r* — ρ)

k = κ(τ k )[1 — T (r* — ρ)],                     (18b)

[ρ + ∕_ι^{τ k} r ʌ ]k + ρb + w(τ k )[1 — T (r* — p)] = c + g. (18c)
(1 — τk)

A change in τ_l reproduces the same effects obtained under the residence-
based taxation of wealth income. By raising the cost of capital, a hike in τ_k ,

¹⁷The consequences on c and a can be derived as follows. Keeping τ_l fixed, (17a) and
(17c) can be written as

c = z(a; τa), za > 0; zτ_a < 0;                           (17a’)

c = c(a,τa),ca > 0; cτ_a > 0;                          (17c’)

^whe^re      U2               ₌  [UnUcn — UcUnn + U_e²(1 — τ ι)w*T "]

z^a   (U_eU_en — U_nU_ee)    ; z^τa              (U_eU_en — U_nU_ee)

Ca = (ρ + τar*) > 0; Cτa = (a + w*T')r* > 0.

Totally differentiating (17a’) and (17c’), the following multipliers are obtained

^dc = (zacτa ^— cazτa ) > 0; da = (cτa ^{— z}τa ) > 0;

dτa (Za — Ca)         ’ dTa (z_α — Ca)      ’

where the condition za >ca , assumed to be satisfied, ensures saddle-point stability.

17

<<   15   16   17   18   19   20   21   >>

More intriguing information