Federal Tax-Transfer Policy and Intergovernmental Pre-Commitment

Nash level of g, i.e. g^d < (>) g^N. If α = 0, local public good provision is unaltered, i.e. g^d = g^N.

Proof: The proof involves a comparison of the FMCPF evaluated at (t^N , τ^N) and at (t^d, τ^d),
respectively. Based on the first-order condition (11) we then infer how public spending levels
will adjust. Note first that labor supply, and thus the FMCPF, is independent of capital taxes if
symmetrically chosen. Precisely, symmetric capital tax rate changes influence the interest rate
which however has no effect on labor supply behavior - see (1). By (A) the FMCPF is positively
affected by τ which yields

Now, following the first-order condition b⁰(gi) = ^+1^ (Eq. (11)) the comparison (22) implies

^b0⁽gi)l(td,τd) T ^b0⁽gi)l(tN,τN)^{if τd} T^τN.

By the strict concavity of b(gⁱ), we can conclude that

g^d S g^N if τ^d T τ^N

Relating the labor tax differential τ^d - τ^N to α, as stipulated by Proposition 3, completes the
proof. □

In contrast to the finding under centralized leadership a more efficient tax structure translates
into a more efficient provision of local public goods. Proposition 3 and 4 thus readily allows us
to infer the welfare differential (relative to simultaneous policy formation). When α > (<) 0
efficiency deteriorates (improves) over all decision margins which yields lower (higher) welfare.

The welfare result can be rationalized by the concept of fiscal externalities. The total effect
of an incremental rise in tⁱ on indirect utility V ^j is given by

dV ^j

— = Vj Tti + Vj sj + Vj t^j kj, i = j.                      (23)

21

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