may be found from the simultaneous system consisting of the government budget
constraint (2.22), the political equilibrium condition (4.6) and the capital market
equilibrium condition
(1 — α) k (r + τ) — k = 0 (4.7)
which follows from (2.12) when all countries are forced to change their capital tax
rate in a coordinated manner. In analysing this system, we assume that countries
start out from a situation where the public sector recruitment constraint has just
ceased to be strictly binding so that W = w in the initial equilibrium. The effects
of a coordinated rise in τ on W , α and r are given in equations (A.18) through
(A.20) in Appendix 2. Using those results we obtain
Proposition 6: Once tax coordination has raised public goods provision to the
point where the recruitment constraint W ≥ w is no longer strictly binding, the
following condition is necessary and sufficient to ensure that politicians will use
part of the revenue from further tax increases to offer rents to public sector work-
ers:
δ + α [1 + α + γσc (α + δ)]
+ε μ ) ∙δ + γσc (α + *)+ f α+δ) f ɪ — i)l > 0, (4.8)
y α j 1 — α yαy y 1 + δ j
W
Y ≡-----=.
W + rk
Proof: See Appendix 3.
A sufficient (but far from necessary) condition for (4.8) to hold is that σg ≥
1+ δ. As mentioned in footnote 14, empirical estimates of the coefficient of relative
risk aversion in private consumption (σc) are typically far above unity, so if the
corresponding CRRA parameter for public consumption (σg) is not much smaller,
it will most likely exceed 1+ δ (since δ will not realistically be far above one).
Moreover, even if σg < 1+ δ, all the other positive terms on the left-hand side of
(4.8) are likely to ensure that the condition will hold. For all plausible parameter
values it then follows from Proposition 6 that once tax coordination is carried
beyond a certain point, it will start to generate rents to public sector workers.
Clearly this accords with the Public Choice view that tax coordination stimulates
27
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