Federal Tax-Transfer Policy and Intergovernmental Pre-Commitment

where h(∙) and b(∙) are strictly increasing and strictly concave. The time endowment is normal-
ized to unity which implies labor supply Lⁱ = 1 - `ⁱ . Each household has a capital endowment
fc. Utility is maximized subject to the budget constraint
• ∙ ∙ '

ci = Iⁱ + (wⁱ - τ) Li + rk,

where Iⁱ is income generated from a fixed factor (say land), wⁱ is the wage rate in state i,
τ denotes the labor income tax rate, and r is the interest rate. The labor supply decision is
characterized by the first-order condition¹⁴

wⁱ - τ - h' ('ⁱ ) = 0.                                      (1)

The optimality condition implies that an increase in the net wage rate wⁱ - τ leads to an increase
in labor supply.

Each state produces a single good with a constant returns to scale technology. Output can
be used either for private or public consumption on a one-to-one basis. For analytical simplicity
the technology is additively separable in labor lⁱ and capital kⁱ . We should note that the results
developed in the paper are not specific to the assumption. In a note (available upon request
and posted on the author’s web-page) we outline the qualitative robustness of the results when
accounting for complementarity between labor and capital in production.

Invoking a linear production technology would generate the peculiar result that capital com-
pletely flows to the region which offers the more favorable tax treatment. To preclude the
“buy-out” result, we introduce land as a productive factor (Kuhn and Wooton, 1987). The
production technology f (Bⁱ, lⁱ, kⁱ) satisfies f_jⁱ > and f_jⁱ_j < 0, j ∈ {Bⁱ, lⁱ, kⁱ}, where Bⁱ denotes
the amount of productive land in state i. Furthermore, f_Bⁱ _j < 0, j ∈ {lⁱ, kⁱ}, and f_lⁱ_k = 0.

The representative firm in each state maximizes profits πⁱ = f(kⁱ, lⁱ) - wⁱlⁱ - (r + tⁱ)kⁱ with
¹⁴Derivatives are indicated by ⁰ . Subscripts of functions denote partial derivatives.

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