revenue is spent on additional public sector employment, as witnessed by (4.3).
Using these results, we can prove
Proposition 5: Starting from a tax competition equilibrium where ε > δ/ (α + δ)
so that all rents have been eliminated, an internationally coordinated rise in taxa-
tion will unambiguously increase social welfare, and the welfare gain will be directly
proportional to the initial degree of underprovision of public goods, measured by
the magnitude /u/u^— ŋ of the initial deviation from the Samuelson condition.
Proof: See Appendix 3.
Since public goods are underprovided in the initial equilibrium, and since Pro-
position 4 established that none of the extra revenue from tax coordination will
be spent on rents, it is not surprising that some amount of coordination will raise
social welfare. Indeed, as long as g0/u0 >FL and MPC > MPB, i.e., as long
as public goods are underprovided and politicians have no incentive to spend the
revenue from tax coordination on rent creation, welfare will be boosted by further
coordinated tax increases.
4.2. Tax coordination with rent creation
But could tax coordination improve social welfare even if it is carried beyond
the point where rents start to emerge? To investigate this, we must derive the
effects of further tax coordination on W, α and r when the supply of public goods
has already been raised to a level where politicians would like to spend part of
a further revenue gain on rents. In that situation politicians will offer a fiscal
policy package (W, G) (with G = α) that satisfies the political optimum condition
MPC = MPB. Using (4.1) and (4.2) and noting from the government budget
constraint (2.22) that dW/ ∣dα∣ = W∕α (1 — α) when the individual country takes
τ and r as given, we find that the condition MPC = MPB implies
(1 + δ) g0 (α) + u (W + rk) — u (w (r + τ) + rk) =
(α+δ) u(w+rk μ.w ).
(4.6)
When the public sector recruitment constraint is no longer strictly binding, the
effects of tax coordination on W , . and r in the representative small country
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