Every once in a while, one will hear an argument for protectionism that protectionist tariffs will ultimately lead to lower prices.  The argument they make is an adjusted form of the infant industry argument:  domestic firms do not expand because of the presence of foreign competition.  Tariffs will force foreign competition out of the market.  Prices will rise, causing new domestic firms to form.  These new firms enter the market and push prices down to the pre-tariff level (or even below the pre-tariff level).  In short, tariffs allow firms to expand their scale and push down prices.  

Like the infant industry argument, one can make an internally coherent prediction for tariffs along these lines.  But, like the infant industry argument, it suffers from the same fatal flaw: tariffs are not needed to accomplish these goals.  If it was profitable for firms to operate at such a scale as to match or beat the free-trade price, they would already be doing so.  The presence of capital markets ensures the profit opportunities of those firms can be realized.  Given all the political issues with tariffs, it’s quite improbable that the political marketplace would be better suited to realize those profit opportunities than the firms themselves and investors; I just have a hard time believing these people who are profit-seekers would leave billions of dollars in profit on the table.  In short, if firms could match the free-trade price, they already would.  

Financial markets allocate resources through time.  By borrowing, firms and individuals can sacrifice some consumption in the future for consumption now.  Firms in particular borrow to expand, fund new technology, fund new projects, etc., that could take years to payoff.  These sorts of transactions occur all the time, to the tune of trillions of dollars per day.  How could politicians properly identify profit opportunities those in the know do not know?  

Relatedly, imposing tariffs is a long, public process.  There are debates, votes, public hearings, etc.  If, by some miracle, the political process was able to identify profit opportunities better than the market participants, once the tariff is announced, it would become public knowledge.  Investors of all stripes would rush to the affected markets, eager to seize the profit opportunities.  The tariffs would be rendered moot.

In short, while it is possible for tariffs to lower prices, it’s quite unlikely.  Best case scenario, the tariffs simply recreate the status quo, but with more steps.  Since tariffs are not costless (there are administrative costs such as collection and enforcement), this suggests that using tariffs to lower prices would still be a worse outcome than the free-market outcome.