If tariffs don't work, why do so many nations still use them?

Because it benefits a developing industry in a country.

Let’s say a country sees it has an opportunity to become a clothing manufacturer. If there were no tariffs, each aspiring clothes manufacturing company would have to compete with every other clothes manufacturer in the world — many of which have already a large global market share, experienced workforce, better contacts, state-of-the-art machinery, etc.

Sure, clothes are more expensive in such a country than they would be in a free-market situation, but then again, there is a future for the people in that country.

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There has been plenty of criticism aimed at Western proponents of global free markets. These countries developed their own manufacturing capabilities while protected by tariffs, and when third-world countries try to do the same, they are lectured about free trade benefitting everyone.

But if the country now puts tariffs to foreign clothes imports, this evens out the playing field, and enables local aspiring clothes manufacturers to gain experience, machinery, connections, etc. before having to compete with global competitors on a level playing field.

They wouldn’t be able to compete with foreign imports — neither in price, nor in quality — and would simply go bankrupt.

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This enables the existence of local businesses doing local manufacturing, providing jobs, money, and meaning to local residents.