Tariff Escalation and Invasive Species Risk

^τIFG

denote τ ≡ -FG^ and measure deadweight loss, DWL, associated with DI in terms of the
τ_I

relativeτ, we have:

ɪ _r ɪ    ²--θ  ɪ 1 - θ —    1 - θ 1  — ɪ

DWL = (τ - 1)τ^1-θ - [ x ^1-θdx = τ' ' - τ ^θ--(τ^1-θ -1) =---τ^1-θ - τ^1-θ.

¹                   2-θ2-θ2-θ

Therefore,

∂DWL   θ ₍

--------=-----τ^1-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 ( τ_I^N_F^N_G < τ_IFG ) works its way as in proposition 1 and reduces the externality. However, the
reduction of the raw-input tariff (τ_I^NN < τ_I ) 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 τ_I^N_F^N_G
should at least offset the increase in raw-input imports caused by the lowerτ_I^NN . This condition
insures that the marginal externality β does not increase with the joint reform or
∂β     ∂β

that----dτ +--dτ_n~ ≤ 0 ∙ Next, we formalize these sufficient conditions linking tariff

IIFG

∂τ_I       ∂τ_IFG

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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