Federal Tax-Transfer Policy and Intergovernmental Pre-Commitment

constraint (6) with respect to tⁱ and the federal policy instruments sⁱ and τ :

∂tⁱ                ∂tⁱ

— = 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, t^j ,tⁱkⁱ + s^l) + μ X (s^l — τlⁱ)

^s1,s2,τ           i=1,2                                      i=1,2

subject to {kⁱ = kⁱ (tⁱ , t^j)}_{i=1,2 i}6₌j , {lⁱ = lⁱ (τ)}i=1,2 , and {tⁱ = tⁱ (sⁱ)}i=1,2 . The first-order
conditions are

sⁱ :   Vⁱ_g + Vjt^j_si + V_g^jgjts_i + μ = 0 and τ :   X(Vi + μ(-lⁱ — τl^l₇-)¢ =0,     i= j, (13)

i=1,2

which have already been simplified using V_tⁱi + V_gⁱg_tⁱi tⁱ_si = 0 (by Eq. (8)). Imposing symmetry,
inserting Eq. (5) and rearranging, the first-order conditions reduce to

1

b⁰(g)(1+ g_titisi) = 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 g_t^j_i tⁱ_si . 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 (t^c, τ^c, s^c) and (t^N , τ^N , s^N) the optimal policy under
centralized leadership and Nash-behavior, respectively, we can state the following result:

14

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