τIFG
denote τ ≡ -FG^ and measure deadweight loss, DWL, associated with DI in terms of the
τI
relativeτ, we have:
ɪ r ɪ 2--θ ɪ 1 - θ — 1 - θ 1 — ɪ
DWL = (τ - 1)τ1-θ - [ x 1-θdx = τ' ' - τ θ--(τ1-θ -1) =---τ1-θ - τ1-θ.
1 2-θ2-θ2-θ
Therefore,
∂DWL θ (
--------=-----τ1-θ > 0 .
∂τ1 -θ
Hence, any menu that decreases both policies so that the relative τ falls is welfare improving in
terms of allocative efficiency, and abstracting from the eternality.2 3
The last component to worry about is the externality. The reduction in the final-good
tariff ( τINFNG < τIFG ) works its way as in proposition 1 and reduces the externality. However, the
reduction of the raw-input tariff (τINN < τI ) increases raw-product imports, hence increases the IS
risk and associated external cost β. Establishing sufficient conditions for a reduction in IS under
joint tariff reform hinges upon having two offsetting effects on raw imports I, such that the IS
externality is not exacerbated. There are several ways to do this. A sufficient condition is that the
decrease in raw-input imports from the lower derived demand for DI caused by the lower τINFNG
should at least offset the increase in raw-input imports caused by the lowerτINN . This condition
insures that the marginal externality β does not increase with the joint reform or
∂β ∂β
that----dτ +--dτn~ ≤ 0 ∙ Next, we formalize these sufficient conditions linking tariff
IIFG
∂τI ∂τIFG
reductions and the marginal externality so that a win-win outcome arises. Noting that
dDI =(DI / (1-θ))( dln τIFG - dln τI )]
2 A similar argument can be developed for the DWL associated with the supply DFG which is also increasing in τ.
3 This argument holds for the single tariff reduction case considered previously too.
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