Tariffs don't necessarily mean higher prices, they are likely to create more competition. Effectively, tariffs are taxes on corporations, i.e. the rich.
Exactly the opposite: tariffs necessarily mean higher prices and the consumers will pay it ("the rich" will not care much). You have to pay the price of the seller plus the tariff and it gives your home industry zero incentive to lower the prices. This is economy 101, seriously...
You may argue that it protects local jobs, which is true, but at the cost the consumers subsidizing via those higher prices. It is a handout without government mediation.
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Here is where you are missing it. Trump's promise to reduce regulations.
When you combine tariffs that are against the products from other countries, with the freedom from regulation in the US, Americans will jump right in and start manufacturing the now-expensive foreign products for themselves... expensive because of tariffs.
When this happens, America will start to out-produce other countries. Other countries will slow down their products coming into America. Less foreign products means less tariff money for government. Less tariff money means a reduction in tariff prices so more products can come in to give government their money. Reduction in tariffs means competition for the US manufacturer.
And that is what it is all about... the free market. It has to do with making America great... again if she wasn't for a while.