The name is absent

rent seeking. However, this does not necessarily mean that a further coordinated
tax increase is undesirable once rents start to emerge. More precisely, we have

Proposition 7: When tax coordination has raised public goods provision to the
point where the recruitment constraint W ≥ w is no longer strictly binding, a
further coordinated rise in the level of taxation will increase social welfare if and
only if the following condition is met:

γ^σc(^α+^δ) ^α+^δ -(1—^α) >^δ+^α(2—^α)⁺μ^α+δyμ^{α + δ} ɔ.(4.9)
α + αδ                           1+δ α (1 - α)

Proof: See Appendix 3.

Condition (4.9) may very well be satisfied. For example, suppose that ρ = 0.12,
γ ≡ WWrk = 0.8 and α = 0.13. The inequality in (4.9) will then hold for all values
of σc above 3.74. The empirical estimates in Hall (1988) imply that σc is at least
5 and possibly much higher, while the estimates by Attanasio and Weber (1995)
suggest that σ_c lies in the interval between 1.5 and 4.7. Hence tax coordination
may be welfare-improving even when it generates rents (recall from Proposition
6 that a coordinated rise in taxation will almost surely create rents when the
recruitment constraint ceases to bind). The reason for this result is that public
goods are still underprovided in the initial equilibrium, so if politicians spend part
of the extra tax revenue on an increase in public goods supply - as indeed they
will, given the parameter values assumed in the numerical example above - the
resulting positive welfare effect may outweigh the loss from the distortions caused
by the introduction of rents.¹⁸

¹⁸To see that public goods are underprovided initially, note from (A.29) in Appendix 3 that the
political equilibrium condition MPB = MPC implies g⁰/u⁰ >FL . The fact that a coordinated
rise in τ will increase public goods provision (and not just induce a rise in rents) follows from
(A.18) in Appendix 2 by inserting the assumed parameter values.

Introducing positive rents causes a rise in the private consumption of public sect₀or wo₀rkers
(if their wage rate rises by more than their tax bill) which may increase the ratio g FFGO/)g . In
that case the pre-existing distortion to public goods supply will increase from the perspective
of public sector workers so that no unambiguous conclusion on the overall welfare effect can be
drawn, even though the distortion to public goods supply will certainly be reduced from the
viewpoint of private sector workers.

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