Appendix: The equivalence of a specific tariff and an ad valorem tariff
Ad valorem tariffs are a very simple way to think about the effects of a tariff on the equilibrium outcome because such a conceptualization removes the need to adjust for changes in the quantities traded as a result of the tariff. Ad valorem tariffs simply scale up the imported good’s world price by a factor equal to the tariff rate; that is, by multiplying the world price of the imported product by (1 + the tariff rate).
It is easy to demonstrate that, for fixed prices, any specific tariff can be expressed as an ad valorem tariff. Here are some examples:
Say the price of a good is $100 in the domestic country, and suppose that the government places a $5 specific tariff on imports of this good. Solve for the equivalent ad valorem tariff rate t that, when levied on a $100 good, would result in $5 of revenue collected by the government for the import:
$5 = t x $100 [latex]\rightarrow[/latex] t = $5 / $100 = 0.05, or 5%
If the good was $200, then a $10 specific tariff would be equivalent to the ad valorem tariff of 5%:
$10 = t x P [latex]\rightarrow[/latex] t = $10 / $200 = 5%
A $50 specific tariff on a $400 imported good is converted into an ad valorem tax using the same approach:
t = $50 / $400 = 12.5%
Because this equivalency depends on prices being unchanged throughout the analysis, it is especially helpful in the context of the small open economy which is by definition too small for its demand or production to affect world prices. The tariff’s impact is captured in the analysis of a change in relative prices experienced in the domestic economy.
