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Ooh! There was an episode of the Past, Present, Future podcast a couple of months ago that touched on this very subject. Tariff policy was set by congress up until the Smoot-Hawley act, which was considered such garbage that they decided that it should be left to the executive.
Back when it was a congressional power, it was also the source of some of the worst horse-trading, as representatives from rural areas would seek protection on agricultural imports (with low tariffs on imported machinery), while representatives from manufacturing areas would seek to lower food prices and increase the cost of imported manufactured goods.
Edit: Not saying that handing it to the executive is the best plan, as we can see by what's going on now, but letting congress do it was also problematic. It's funny how a lot of us grew up with the idea that no/low tariffs are the natural order, when it's actually been a fairly short-lived anomaly in historical terms.
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