A tariff on imports increases the price of imports in the tariff nation. This decreases demand for the imported product in the tariff nation.
If that country is large and provides a substantial fraction of global demand, the decline in global demand will lead to a lower global price.
Since terms of trade refers to the ratio of export prices to import prices, and the tariff nation is a net importer of the tariffed good, the lower price on the global market of the tariffed good means that the overall ratio of export price to import price rises. That’s a terms of trade benefit.
My understanding of a Tariff is that it is a tax (additional cost) on imported goods. It is usually used to protect domestic production. If a large country did this it might make those products cheaper for the rest of the world, but the entire point of a tariff is to make the imported product more expensive so that the same domestic product has a price or profit advantage, there by encouraging the domestic production of that product.
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