The Impact of Optimal Tariffs and Taxes on Agglomeration



Appendix

Optimal taxes and tariffs without coop., eq.(12):

To derive the optimal tax and tariff rates the corresponding partial deriva-
tives of the real income
Yr = (1 + Lw)T-1(1 TA)1-γPγ must be set to
zero:

dYR_ (1 1 ∙.    P ( dw ΓdT (1 γ)τl

dTA =     T 1,⅛- ⅛ τ-. JJ=0'  (m)

=- = -(1 - γ),                          (122)

1A

d^__      (1 γ)Yγ (γ(1 L) (1 ΘΘ*) σP*1-σT*)

dTA =  (^P*1-σT* γ(1 L))(σP1-σT γL) γ2ΘΘ*(1 L)L) '

(12.3)

Substituting (12.3) and (12.2) in (12.1) and solving for the optimal agriclu-
tural tax
TOpt yields:

oCtpt _

TA=


Ti (1 L)Θ
(1 Ti )


7Θ*L(^ L)Θ      L

σ (σP*1-σT* γ(1 L))   σ


P σ-1


(12.4)


The partial derivatives with respect to T1 are given by:

dYR
dTι


(1 TA)1-y P
T


dw

LdT1


dT + γTP-
dTI


dPV
dτ√.


= 0,


(12.5)


dP _ Pσ(1 L)Θ
dT
=  (1 Ti )2

(12.6)


dw

i


γY Θ(1l)
P 1-σ (1Ti )2


[(1 — σ)(1 — γ )(1 ta) — γσ(1 ti )]
× (σP*1-σT* + γ(1 L) [ΘΘ* 1])
+σγP1-σ Θ*T (1 T1 )

' (σP*1-στ*γ(1 L))(σP1-σT γL) '
γ 2ΘΘ*(1 L)L


(12.7)


21




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