Eq. (19) yields
sign{α} = sign{tiktii + ki - tj ktji }
= - sign {|ег|- 0.5 },
where the last step follows from inserting ktii = -ktji (Eq. (3)) and rearranging. The term α
is positive (negative) provided the elasticity of the capital tax base |ег| is below (above) 0.5.
Proposition 3 implies that a low tax base elasticity leads to a less efficient tax mix, while a suf-
ficiently high elasticity leads to more efficient taxing incentives under decentralized leadership.
The result is intriguingly related to the federal transfer response. Recall, a rise in public con-
sumption in state i following an increase in the capital tax rate induces an inequality in public
consumption in both states. To correct it, the federal government cuts back on transfers to the
tax raising state. With capital mobility the neighboring state equally enjoys an increase in the
tax base which counteracts the imbalance of public consumption. If the relocation of capital
(i.e. |ег|) is sufficiently high, state i may still forfeit transfers (case (ii) in table 1), but at a
relatively low level. With a moderate retrenchment of transfers, state i benefits from a capital
tax higher than the Nash-level as more own-source tax revenues induce a reduced labor tax
burden. Increasing |ег| further, the cross-budget effect becomes strong enough such that state i
does not forfeit transfers (case (iv)) or even receives more federal funds (case (iii)). Now, the
transfer response weakly reinforces the impact of the federal tax response to tax mobile capital
at a higher rate.24
The implications for local public good provision are presented in Proposition 4.
Proposition 4: If α > (<) 0, local public good provision decreases (increases) relative to the
24It is instructive to analyze the interplay of the own and cross tax revenue effect in a federation with an
arbitrary number of symmetric states n ≥ 2. The influence of local tax policy on a single neighbor state’s tax
revenues becomes smaller when n rises, and it is negligible in the limit n → ∞ (small open state). Since the
own tax revenue effect is positive, federal transfers are adjusted so as to distribute the additional tax revenues
equally across all states; an effect which leaves the tax-raising state with almost no taxing incentives. Hence, in
the limit n → ∞ the capital tax differential will satisfy td - tN < 0. More generally, the reasoning suggests that
the interval of elasticity values supporting td - tN > 0 is decreasing in n and is empty for n → ∞.
20