Federal Tax-Transfer Policy and Intergovernmental Pre-Commitment

and to the corresponding tax rates given by condition (27) in Lemma 1. □

In case (i), tⁱk_tⁱ_i + kⁱ > t^j k_t^j_i , which gives α > 0. Consequently, implied by Lemma 2 state
i chooses t^d < t^N . The decrease in sⁱ, following a marginal increase in tⁱ , dominates the positive
effect of a lower labor tax rate. In case (ii), tⁱk_tⁱ_i +kⁱ < t^j k_t^j_i and, thus, α < 0. Lemma 2 predicts
a tax rate choice t^d > t^N . In case (v), tⁱk_tⁱi + kⁱ = t^j k_t^j_i and, thus, α = 0. Consequently, t^d = t^N .

To infer how the federal government sets labor taxes and transfers in a symmetric equilibrium,
we evaluate how the FMCPF and the marginal benefit of transfer spending have changed due
to an adjustment in capital taxes (relative to the Nash outcome). First observe that at a
symmetric allocation the FMCPF is independent of the level of t^d, ceteris paribus. The reason
is that in any symmetric equilibrium capital employment is kⁱ = к which yields an identical
labor demand across regimes. Also, for a given τ, labor supply is unchanged - see (1). Thus,
equilibrium employment behavior is independent of the level of capital taxes once symmetrically
chosen. Furthermore, given s = s^N , b⁰(g) T b⁰(g^N) if t^d S t^N . Following the federal first-order
condition (11) and assumption (A), the federal government will choose τ^d T τ^N if t^d S t^N .
Since the federal government operates on the upward-sloping part of the federal tax revenue
curve (0 > ηⁱ > -1 - see (11)), s^d T s^N if and only if τ^d T τ^N which completes the proof of
Proposition 3.

References

[1] Akai, N. and M. Sato, 2005, Decentralized leadership meets soft budget, CIRJE Discussion
Paper, vol. 391 (F-series), Tokyo.

[2] Becker, G.S., 1981, A treatise on the family, Harvard University Press, Cambridge, MA.

[3] Bernheim, B. and M. Whinston, 1986, Common agency, Econometrica 54, 923-942.

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