Federal Tax-Transfer Policy and Intergovernmental Pre-Commitment

tⁱ as the source-based capital tax rate levied in state i.¹⁵ The profit maximizing input choices
deduce from the familiar first-order conditions

f_lⁱ = wⁱ and f_kⁱ = r + tⁱ .

The factor market equilibrium follows from Eqs. (1), (2), the capital market clearing condition

k¹ + k² = 2к, and the labor market clearing condition li = Li.¹6 The responses of lⁱ, kⁱ, r and
wⁱ to a rise in capital or labor taxes are

∂kⁱ _ 1   ∂kⁱ _ -1   ∂r _ —fjk

W = ∆^, ∂t^j = Δ^^, ∂ti = ∆

and

∂li _ -1 ∂wi _ fl_l
∂τ σ ^, ∂τ σ ^,

with Δ := fklk + fkk < 0 and σ := — h⁰0(P^,) — f∖_l > 0. The comparative static results reflect
the interplay of the additive separability of preferences and of the assumption f_lⁱ_k = 0. They
insulate the labor (capital) market from capital (labor) taxation.

Incorporating optimal labor supply and factor demand choices and general equilibrium ef-
fects, we can write utility as a function of tax rates and public expenditures, V ⁱ(τ, tⁱ , t^j , gⁱ).
Noting that output is exhausted by factor payments, i.e. cⁱ = f (ki, li) — fkki — τli + rk, and
making use of Eqs. (1) - (4)

• ∙ ∙ ∙ '*⅛' ∙

Vi = — lⁱ, Vj = -kⁱ (= —к) and Vj = 0, i = j,                 (5)

with symmetric capital tax rate choices. The result V_tⁱj = 0 reflects the opposing effects a higher

tax rate in state j has on interest income and land income in state i. The income changes nullify

¹⁵ For simplicity, the production factor land is omitted from notation in the subsequent analysis.

¹⁶ The capital market clearing condition implies that capital is in fixed supply at the federal level. The assump-
tion is intended to reflect the differential degree of capital mobility in a federation (being highest at the local
level) in an analytically tractable way. If capital were in elastic supply for the federation as a whole, the labor tax
would be set at a lower (same) level if f_lⁱ_k > 0 (f_lⁱ_k = 0) ceteris paribus; see Bucovetsky and Wilson (1991). The
level effect on labor taxes applies to all decision-making scenarios considered in the paper; thereby suggestively
not compromising the relative policy evaluation.

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