The name is absent

Substituting the government budget constraint τk = (ι-α) W into (A.25) and
solving for λ, we obtain

^λ = ^po ^{(1 - α})(¹ + ^δ) (⅛) ^,

where we have used the fact that the absence of rents implies W = w = F_L . Equa-
tion (3.4) in Proposition 3 is found by substituting (A.27) and (A.28) into (A.24)
and rearranging. The fraction g⁰/u⁰ in (3.4) is the marginal rate of substitution
between private and public goods, and FL is the marginal rate of transformation.
Since ( ι-1α ) (_1-ε(1_-α)) > 1, it follows immediately from (3.4) that g⁰/u⁰ >F_L,
implying that public goods are underprovided relative to the first-best allocation.

Proof of Proposition 4: The proposition assumes that tax coordination starts out
from a tax competition equilibrium without rents where W = w = FL , u⁰_g = u⁰_p =
u⁰ and ug = up . Further, when the individual country takes τ as well as r as
given, it follows from the government budget constraint (2.22) that dW/ ∖dα∖ =
W∕α (1 — α). Inserting these relationships into (4.2) and dividing the resulting
expression by (4.1), we get

By Proposition 3 the initial tax competition equilibrium satisfies (3.4) which may
be substituted into (A.29) to give

α + αδ

MPB α + δ — ε (α + δ)(1 — α)'

From Proposition 2 and the assumption n → ∞ it follows that ε > δ/ (α + δ) in
the initial tax competition equilibrium without rents. The expression on the right-
hand side of (A.30) must therefore be greater than one, implying MPC > MPB.
Since MPC is the marginal political cost of reducing public sector employment
and MPB is the marginal political gain from spending the freed-up resources
on higher public sector wages, an unconstrained politician would thus want to
cut the public sector wage rate in order to expand public employment, but the
binding recruitment constraint W ≥ w prevents him from doing so. When tax

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