The Impact of Optimal Tariffs and Taxes on Agglomeration

^Y α - Г)^{Рσ 1} (¹ — σT' + ₁-τ, (σ - P-‘⁽¹ ^θ) ' ɑ²*¹

Substituting (12.6)-(12.8) in (12.5) yields:

If both, tax rate and tariff, are chosen to optimize welfare (12.4) and (12.9)
must be solved simultaneously for T_i and TA:

σP *^ι-^σ t * — γ (1 — L) — γLΘ*
σ²P*^1-σT* — γσ(1-L) — γLΘ*^,

.

σ

Resubstituting φ and T from (3) and (7) and simplifying yields:

⁽¹ — ^{L) (}Y(^σ —^{1) + σ}(¹ — Y⁾⁽¹ — ^tA))⁺L^θ* f^σ(¹ — Y)⅛⁺Y(^σ — l)ɔ

T_i =-------------------------------------w---------^f~_t--------⅛ > 0,

^{(1 —} L)^σ (γ(^σ — ¹)^+σ(¹ — γ^{)(1 — t}*))⁺L^θ* (^^σσ(¹ — γ)l-TA+γ(^σ2 — ¹)J

which is positive as long as γ < 1 < σ.

Optimal taxes and tariffs under coop., eqs. (14,15):

The partial derivatives of the the overall welfare (13) with respect to domestic
taxes and tariffs are given by:

L^W +Y(1—Y) ⁽1 — T (1 — Ta)-i) + <¹ — T*P*^T (1—L)dW*
dTA          ' ^V             (1 — T_a)^1-γ P-yT*^{V ,}d^rAA

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