Optimal Taxation of Capital Income in Models with Endogenous Fertility

From (13a), it is clear that in an open economy (relatively to a closed
one) the opportunity cost of one unit of fertility is raised by b.Sincer is
pinned down by r* + δ, the input demand system (5) implies that the capital
k

intensity and the wage rate are fixed and tax invariant; that is, — = κ and
k

w = w , where κ = f' ¹(r* + δ) > 0, w = f (κ*) — κ f ^-(κ*) and f (—) = F(
k

— , 1) is the output-labor ratio.

Alternatively, in the case of source-based capital taxation, the arbitrage
condition between domestic and foreign assets requires that the after-tax
return on capital is equal to the world interest rate, i.e. (1 — τ_k)(r — δ) = r*,
where τ k represents the domestic capital income tax rate. Therefore, the
representative agent’s dynamic budget constraint becomes

..

k + b= (r* — n)(k + b) + (1 — τ ι)wl + q — c.            (14)

From the consumers’ standpoint, optimality requires that (13a) and the
following Euler equation

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