The Impact of Optimal Tariffs and Taxes on Agglomeration

σP^{1 σ} [(1-σ)(1 -7)(1 -T₄) - γσ(1 - T₁ )] [σP∙^1-σT∙-7(1-L)]

+σ77P^1-σΘ*(1 - T_i)L

+(σ-1+7)[[σP*^1-σT* -7(1 -L)][σP^1-σT- γL] - 7²ΘΘ*(1 -L)L]

(14.3)

+7σ

(¹-TA )

l-₇

^-Y

(i-t_a)^1-y p^-γ

(1 - T_i) (σP^1-σT - γL + γσΘ(1 -L))
^{+ (1 -} a^{)(1 -} 7^{)(1 -} '/'₇^θ!∣ ^-L)

= 0,

[7(1 -L)-σP*^1-σT*] [σP^1-σ (1 -T_a-T)+ 7L]

P γ                +7 ²ΘΘ*(1-L)L

P*⁷ =    P*^1-σ7σ (1 - TA)^1-γ (1 - Ta)⁷ (1-L)Θ.

Substituting (14.4) in (14.3) and simplifying yields:

(14.4)

τ _ . — τ*      _

TA,Opt = ¹ A,Opt =
σ

(14)

while resubstituting (14) in (14.4) or (14.3) yields for T₁,_θpt and TI,_θpt the
following non-linear equation system:

7^θ*^l _{+ p}7_p*1-σ-γ _- ¹ -σTI
σ - 1               1 - T_i

(1-7 )P ∙¹-^σ + 7 (1-L) +      '* 1 =0,

σ-1

7 Θ(1 - L)       1-σ-₇ 1 - σT*

σ - 1 ⁺ P ^P  - Tif

(1 -7)P^1-σ+7L +

7σ(1 -L)Θ
σ - 1

(15)

23

= 0.