The world economy was already grappling with a perplexing assortment of variables, from geopolitical conflicts and a slowdown in China to the evolving complexities of climate change. Then, President Trump unleashed a plan to uproot decades of trade policy.

       In starting a process to impose so-called reciprocal tariffs on American trading partners, Mr. Trump increased volatility for international businesses. He broadened the scope of his unfolding trade war.

       In basic concept, the argument for reciprocal tariffs is straightforward: Whatever levies American companies face in exporting their wares to another country should apply to imports from that same country. Mr. Trump has long championed this principle, presenting it as a simple matter of fairness — redress to the fact that many American trading partners maintain higher tariffs.

       Yet in practice, calculating individual tariff rates on thousands of products drawn from more than 150 countries poses a monumental problem of execution for a vast range of companies, from American manufacturers dependent on imported parts to retailers that buy their goods from overseas.

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       “It’s potentially a herculean task,” said Ted Murphy, an international trade expert at Sidley Austin, a law firm in Washington. “For every widget, every tariff classification, you can have 150 different duty rates. You’ve got Albania to Zimbabwe.”

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       Seamstresses working at a factory in Cartagena, Colombia, last month. Mr. Trump has challenged the merits of companies moving plants out of China by threatening tariffs on imports from Colombia and other countries.Credit...Alejandro Cegarra for The New York Times

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