Optimal Taxation of Capital Income in Models with Endogenous Fertility

Fl(k, l)=w.

The resource constraint is given by

.

F(k, l)=c+ k +(δ + n)k + g.

Finally, the government balances its budget by financing public expendi-
tures through factor income taxation

τk(r - δ)k + τlwl =g+q,                      (7)

where g denotes the exogenous per capita government consumption expen-
diture.

2.2 Positive analysis

In the steady state, the macroeconomic model can be succintly written as⁸

Un(C^,n) = (1 - τι)Fι[k, 1 - T(n)]T'(n) + k,            (8a)

Uc(c,n)

(1 - τk){Fk[k, 1 - T (n)] - δ} = ρ +n,              (8b)

F[k,1 - T (n)] =c+(δ +n)k+g.               (8c)

We assume that lump-sum transfers q adjust endogenously to maintain the
government budget in equilibrium, while g is given.

⁸ The dyamic properties of the model are studied in Palivos (1995). The model exhibits
saddle-point stability if the condition T'²Fll — FlT'' < 0 is satisfied.

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