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-γ ( dw ΓdT (1 — γ)τl∖
dTA = T 1,⅛- ⅛ τ-. JJ=0' (m)
=- = -(1 - γ), (12∙2)
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-γ
T
dw
LdT1
⅛dT + γTP-
dTI
dPV
dτ√.
= 0,
(12.5)
dP _ Pσ(1 — L)Θ
dT∣ = (1 — Ti )2
(12.6)
dw
Hγi
—γY Θ(1—l)
P 1-σ (1— Ti )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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