The Impact of Optimal Tariffs and Taxes on Agglomeration

Hr₁

^Y α - Г)^Р^σ¹ (¹ — σT' + ₁-τ, (σ - P-‘⁽¹ ^θ) ' ɑ²*¹

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

σP^1-σ

+(1 -

LΘ*γ (1 -Ti )

+ σT₁ — 1+T— (σ — 1)

(1-L)ΘT_f

¹-^ti

P^σ-1 [σP *^1-σT * — Y (1 — L)]

σ — γ) (σLP*^1-σT* + γ(ΘΘ* — 1)(1 — L)L) = 0.

(12.9)

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:

^TI,Opt

^TA,Opt

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

(12)

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—-Y
dTι

— + γTP^-1dTι ⁺^y

dP
dTI

_ι(1 — T*)^1-γ P*^-γT dw* _ ₀

^b(1 — T_a)^1-γ P^-γT*( dTι ^,

(14.1)

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

0. (14.2)