Federal Tax-Transfer Policy and Intergovernmental Pre-Commitment

goods as characterized by the Samuelson condition b⁰(gⁱ) = 1. As states are symmetric, we will
look at symmetric Nash equilibria which inherently feature production efficiency.

4 Simultaneous Policy Choice

In this section, we characterize the policy outcome when both levels of government simultane-
ously decide on the policy instruments under their discretion (Nash-behavior). The decision
sequence of the game is:

First Stage: Both levels of government choose their policy instruments {tⁱ , sⁱ, τ }i=1,2 simulta-
neously, i.e. they take the policy instruments which is under the discretion of other governments
as given. They account for the effect of their decisions on the behavior of households and firms.

Second Stage: Firms and households decide on {kⁱ, lⁱ}i=1,2 for given policy instruments
{tⁱ, sⁱ, τ}i=1,2.

The game is solved by backward induction to identify a symmetric subgame-perfect equilib-
rium.

State Government State government i’s problem is to

max   V ⁱ(τ, tⁱ, t^j , tⁱkⁱ + sⁱ)

tⁱ

subject to kⁱ = kⁱ(tⁱ, t^j). The first-order condition for tⁱ becomes:¹⁹

V_tⁱi +Vgⁱ(tⁱk_tⁱi +kⁱ) =0.                                         (8)

Inserting (5) and rearranging yields:

b⁰(д^г) = —-—г > 1 with eⁱ := ki ^.                          (9)

"' 1      1 + е^{г                                   t}i k^{i                                              v !}

¹⁹Although corner solutions may exist, we only report on interior solutions to all optimization problems analyzed
in the paper. Naturally, a corner solution does not exhibit strategic interaction in upper and lower level government
policy choices which is however the issue addressed in the paper.

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