Optimal Taxation of Capital Income in Models with Endogenous Fertility



instead, lowers the capital intensity and the capital stock, since the fertility
rate remains constant. The wage rate falls. Consumption, nonhuman wealth
and gross national income are reduced as well.18 The stock of net foreign
assets is, on the contrary, increased.

3.3 Normative analysis

Residence-based regime

In the small open economy, the implementability constraint is given by19

0{(c-q)Uc


ɪ—TTZ—[Un - (k + b) Uc] }e ρtdt — a0Uc[0],


(19)


18To work out the effects on consumption and financial wealth, write (18a) and (18c)
as follows

c = x(a; τk), xa 0; xτk 0;                           (18a’)

c = m(a,τk),ma 0; mτk 0;                      (18c’)

where

Uc2       .n          Uc2 (1 - τ 1)T'w'

> 0;


χa = -,--------c-------? > 0; χτι. = - т~~—------------?

a   (UcUcn - Un Ucc)       τk     (UcUcn - UnUcc)

.∩         τ kr*(f '- δ)   ∩

ma = ρ > 0; mτk = (1 - τk)2f ''0.

Therefore, the steady state multipliers of consumption and financial wealth -derived


from (18’)- are

dc = (xamτk - maxτk ) < 0; da = (mτk - xτk ) < 0;

k (Xa - ma) _      ; k (Xa - ma)     ;

where saddle-point stability requires xa >ma .

19 Equation (19) is obtained by integrating the consumers’ flow budget constraint
(12) forward, incorporating the condition preventing Ponzi games —that is,
limt→∞ a
e-∫o[(1-τa)r -n]ds=0- and using the relationship Uce-ρt = Uc[0]e- Jo[(1-τa)r -n]ds. The
implementability constraint (19) remains unaltered under the source-based regime of cap-
ital taxation even if the relationship (14), the proper ”no Ponzi game” condition and the
relationship
Uce-ρt = Uc[0]e-ʃo(r -n)ds are now employed.

18



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