constraint (6) with respect to ti and the federal policy instruments si and τ :
∂ti ∂ti
b00 ( gi )
∂ti ( ⅛ ´ - b00 (gi)gi
(12)
— = 0 and —-
∂τ ∂si
A change in the federal tax rate does not affect the choice of ti, i.e. state i’s best-response
effectively is ti = ti (si). To sign state i’s reaction to a marginal increase in transfers, note that,
by the second-order condition of the state’s optimization problem, the denominator is positive.
This together with the assumption b00(gi) < 0 implies that state i’s capital tax rate is decreasing
in the amount of transfers received.
Federal Government The federal government solves:
max L = X Vi(τ, ti, tj ,tiki + sl) + μ X (sl — τli)
s1,s2,τ i=1,2 i=1,2
subject to {ki = ki (ti , tj)}i=1,2 i6=j , {li = li (τ)}i=1,2 , and {ti = ti (si)}i=1,2 . The first-order
conditions are
si : Vig + Vjtjsi + Vgjgjtsi + μ = 0 and τ : X(Vi + μ(-li — τll7-)¢ =0, i= j, (13)
i=1,2
which have already been simplified using Vtii + Vgigtii tisi = 0 (by Eq. (8)). Imposing symmetry,
inserting Eq. (5) and rearranging, the first-order conditions reduce to
1
b0(g)(1+ gtitisi) = 1+ψ > 1, i= j. (14)
Unlike the case of Nash-behavior the federal government anticipates a reduction in ti when rais-
ing si . The induced inflow of capital in state j increases tax revenues in state j as captured by
the term gtji tisi . Since the federal government considers the substitution of own state tax revenues
by federal transfers (financed by distortionary labor taxes ) as undesirable, the strategic effect
increases the marginal cost of labor taxation; yielding a lower labor tax (and thus transfers) and
by Eq. (12) a higher capital tax. Denoting (tc, τc, sc) and (tN , τN , sN) the optimal policy under
centralized leadership and Nash-behavior, respectively, we can state the following result:
14
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