“DON’T panic yet,” advises the sandwich king of Ohio. Robert Grote is chief executive of JE Grote Company, a family-run firm in Columbus that is a global manufacturer of pizza-preparation machines, bacon-slicers and automated sandwich-makers. Since about half of its $60m or so of annual sales comes from outside America and his firm buys speciality steel from Europe, he is closely following President Donald Trump’s recent efforts to upend the global trading order. Though European executives he knows are alarmed, he says his American peers believe Mr Trump’s threats are probably negotiating tactics and are willing to “let it play out”.

Mr Grote’s relaxed stance might seem reasonable. The Trump administration first caused shock waves on March 8th by unveiling a 25% tariff on imported steel and a 10% tariff on imported aluminium, but quickly granted temporary exemptions to countries responsible for most of America’s imports of those metals. These exemptions were due to expire on May 1st, but at the last minute America offered the European Union, Mexico and Canada extensions for another month. The Trump administration says it will use the additional time to conclude a renegotiation of the North American Free-Trade Agreement (NAFTA), and to push the EU into agreeing to “voluntary” quotas on exports. As for the threat of a trade war with China, Mr Trump’s dispatch this week of his top trade officials to Beijing fuelled hopes of a negotiated settlement.

Yet there are plenty of reasons to worry, too. Some are obvious. America’s trading partners could lash out. This week the European Commission declared, after news of the extensions, that “we will not negotiate under threat.” China has already imposed tariffs on dozens of American imports, ranging from wine to pork, in response to the tariffs on steel and aluminium, and proposed $50bn in tariffs targeting soyabeans, chemicals, cars and other products. If these were to come in, the impact on American firms would vary (see chart). The industries that will suffer most are ones, like aerospace and agriculture, that both sell a lot in China and that do not have many alternative markets.

Even if tensions de-escalate, some damage will already have been done. Devry Boughner Vorwerk of Cargill, an American grain-trading titan, points out that merely threatening to impose tariffs on China has harmed America’s reputation as a reliable supplier: “It’s not a good idea to insult your best customers.”

Businesses that consume steel and aluminium will pay higher prices for their inputs. A report released on May 1st by America’s Institute of Supply Management, an independent research outfit, confirms that price increases and shortages are already squeezing local firms. Among other examples, it cites a fabricator of metal products that has been forced to eliminate some products because of the difficulty and cost of acquiring raw materials. American steel and aluminium producers are certainly gearing up for greater demand. Jesse Gary of Century Aluminium says his firm is planning to invest over $100m to expand and modernise its production facilities in Kentucky.

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So much is relatively clear. Much harder to calculate is the exposure of American firms to supply-chain risk as a result of disruptions to international trade. Resilinc, a supply-chain analytics and management firm, has gathered data on the global purchasing and inventory transactions of nearly 30,000 manufacturers and suppliers worldwide. Bindiya Vakil, its boss, says that “most companies are unable to quantify the risk of a serious trade war,” in part because the relevant information is “siloed” in firms and not properly analysed. A senior executive at an American Fortune 100 firm admits that the firm has spent a month intensely studying the likely impacts of Mr Trump’s policies and still does not know how its suppliers and sub-suppliers will be affected.

But there is little doubt that supply chains and the geography of production will shift. Some firms have already been rejigging output to cope with the possible demise of NAFTA. Fiat Chrysler Automobile (whose chairman sits on the board of The Economist’s parent company) said in January that in 2020 it will move assembly of its Ram pickup trucks from Mexico back to Michigan. That would sidestep the imposition of tariffs of 25% if America were to exit NAFTA. Its plant in Mexico, which has free-trade agreements with a host of countries, will be used to make vehicles for export to other markets around the world. An executive at a giant American industrial firm says that if tariffs increase the cost of manufacturing substantially at its American plants, it will shift some production to its plants in Europe or Asia.

In many cases, then, American factories will not benefit. Eric Hillenbrand of Alix Partners, a corporate-restructuring firm, confirms reports that firms of various nationalities which used to import raw metals and process them in America (for example, bending or forging steel or aluminium into complex shapes) are preparing to shift that value-added work out of the country owing to the metals tariffs. Working out what the Trump administration intends on trade is hard enough. Working out what effects it will have is even tougher.