A temporary reprieve in trade tensions between the United States and China has reduced, but not eliminated, the odds of a shock to the economy that carries a whiff of stagflation, a top official at the Federal Reserve warned on Monday.

Austan D. Goolsbee, president of the Federal Reserve Bank of Chicago, said tariffs and the uncertainty around President Trump’s policies still risked a combination of higher consumer prices and slower growth.

Mr. Goolsbee welcomed the decision by the United States and China to lower tariffs on each other’s imported products for 90 days. But he said the temporary nature of the deal and the extent of the levies still in place would weigh significantly on the economy.

“It is definitely less impactful stagflationarily than the path they were on,” Mr. Goolsbee, who is one of 12 Fed officials to vote on policy decisions this year, said in an interview. “Yet it’s three to five times higher than what it was before, so it is going to have a stagflationary impulse on the economy. It’s going to make growth slower and make prices rise.”

Under the agreement forged over the weekend, the United States reduced its tariff on Chinese imports to 30 percent from its current minimum 145 percent level, while China lowered its levy on American goods to 10 percent from 125 percent.

Taking into account these reductions, as well as the tariffs that remain in place with nearly all of America’s trading partners, economists estimate that consumers still face an effective tariff rate of around 15 percent.

The deal with China is the latest twist in what has been a tumultuous period for both the economy and global financial markets, as Mr. Trump has repeatedly changed which countries and products he wants to tariff and by how much. Before announcing the truce with China, the White House had also put in place a 90-day delay on so-called reciprocal tariffs that Mr. Trump had imposed on dozens of countries last month.

These policies, plus shifting plans related to forthcoming tax cuts and other central pillars of Mr. Trump’s agenda, have upended forecasts for the economy. Officials at the Fed have for weeks warned that tariffs will stoke higher inflation and slower growth. What is unclear is the magnitude of the shock, which will depend on which tariffs will actually stay in place and for how long, as well as how consumers and businesses respond.

Already, the uncertainty around these policies has started to have an impact. Surveys show that consumers have become increasingly downbeat about the economic outlook and that businesses are essentially frozen in place until there is more clarity about what Mr. Trump has planned.

“The way that we’re doing this is not free for the economy,” Mr. Goolsbee said. Businesses he has spoken to want to make big investments and hire people, but the prospects that any of these negotiated tariff truces could lapse have made decisions like that much more difficult.

As a result, the Fed is in a wait-and-see mode about whether and when it might restart interest rate cuts. The central bank paused reductions in January after reducing borrowing costs by a percentage point last year, arguing that a patient approach was prudent when it was not yet clear how much impact Mr. Trump’s actions would have on the economy.

Mr. Goolsbee again endorsed a waiting approach on Monday, pointing to the inherent uncertainty being stoked by the Trump administration.

“Their statements are coming with explicit recognition that this isn’t permanent and that it’s going to be revisited in the near future,” he said of the White House’s communications about tariffs. “Part of those announcements are explicitly putting off into the future major decisions, so that’s why it feels like there is in corporate America a lot of sitting on the hands. If they’re sitting on their hands, that backs into the wait-and-see posture of the Fed.”

Mr. Goolsbee said the Fed could afford to take its time before making any policy decisions. The labor market is still in solid shape, and there are not yet acute signs of strain. But the risks to inflation are not negligible, and it is still possible that tariffs of the nature that Mr. Trump is willing to keep in place could lead to a much more persistent problem, Mr. Goolsbee said.

“If we could get the dust out of the air, it would make sense to think that rates would be going down,” he said. “But the bar for action has to be high when there’s so much uncertainty.”

Mr. Goolsbee said that what would concern him was if either the labor market started to deteriorate notably or expectations about inflation over a longer time horizon started to rise significantly.

“Stagflation is a very uncomfortable situation for a central bank,” he said.

There’s a tale told about a miner who found copper cans in his garbage dump in the early days of mining. Wastewater from copper mining had flowed through his land, he said, and turned steel cans into copper.

The story might be apocryphal, but the process is real, and it’s called cementation. Montana Resources, the mining company that took over from the Anaconda Copper Company, still uses this alchemical trick in a process at its Continental Pit mine in Butte, Mont.

Next to the mine is the Berkeley Pit, which is filled with 50 billion gallons of a highly acidic, toxic brew. Montana Resources pipes liquid from the pit, enabling it to cascade onto piles of scrap iron. The iron becomes copper and is gathered for production.

While methods to remove metals from water have been around a long time, in recent years the global scramble for metals critical to manufacturing and technology advances has given birth to a new generation of extraction technologies and processes.

One of the mineral-rich sources researchers are focused on is wastewater, including the brine from desalination plants, oil and gas fracking water and wastewater from mining. Researchers at Oregon State University estimate the brine from desalination plants alone contains metals valued at about $2.2 trillion.

“Water is the ore body of the 21st century,” said Peter S. Fiske, director of the National Alliance for Water Innovation at the Department of Energy’s Lawrence Berkeley National Lab California. “Technology now is allowing us to pick through the garbage piles of wastewater and pick out the high-value items.”

Research on the extraction of rare earths, a set of metallic elements, from waste is widespread as the need for them increases significantly. Researchers at Indiana Geological and Water Survey at Indiana University, for example, are studying the potential for mining rare earths in coal waste, including fly ash and coal tailings. And researchers at University of Texas at Austin have created membranes that mimic natural ones to separate rare earths from waste.

Not only is mining wastewater more economical and faster than starting new mines, it is also cleaner.

Among the big waterborne prizes in the pit next to Butte are two light rare-earth elements (REEs), neodymium and praseodymium. They are vital for small, powerful magnets in electric vehicles, for medical technology and for defense purposes, such as precision-guided missiles and satellites. A single F-35 fighter jet uses 900 pounds of rare-earth metals.

“We’re turning a giant liability into something that’s contributing to defense,” said Mark Thompson, vice president for environmental affairs at Montana Resources. “There’s some high-level metallurgy going on here. Real egghead stuff.”

This is a critical time for research into domestic production of rare earths. Not only does the United States lag far behind China, but President Trump’s trade war has spurred China to threaten to further restrict rare-earth mineral exports as a result of the Trump tariffs. Experts with the critical minerals security program at the Center for Strategic and International Studies say the large gap would enable China to expand its defense capabilities far more quickly than the United States could.

Both Greenland and Ukraine are the focus of the Trump administration’s attention in large part because the countries have significant deposits of rare earths.

Mr. Trump also just ordered the government to move toward mining large portions of the ocean floor, including in international waters, for its mineral riches.

There are 17 types of metals known as rare earths, all of which have been found in the Berkeley Pit. They aren’t rare in prevalence, but they are called that because they are often scattered in small concentrations.

Rare earths are sorted into two kinds: heavy and light. Heavy rare earths — such as dysprosium, terbium and yttrium — have a greater atomic weight and are typically more rare, meaning they sell in smaller quantities and are prone to shortages. Light metals, by contrast, have a lower atomic weight.

Acid mine drainage is a highly toxic pollutant created when sulfur-bearing pyrite in rock is exposed to oxygen and water during mining. The drainage then oxidizes and creates sulfuric acid and poisons waterways. It’s one of the country’s biggest environmental problems, and tens of thousands of abandoned mines have contaminated 12,000 miles of streams.

However, the acid also dissolves zinc, copper, rare earths and other minerals out of the rock and into the water, providing an opportunity for the right technology to extract them — which didn’t exist until recently.

Paul Ziemkiewicz, director of the water research institute at West Virginia University, has researched the pit water in Butte for 25 years. He and a team of researchers from Virginia Tech and L3 Process Development, a chemical engineering firm, developed a method to extract critical metals from acid mine drainage in West Virginia’s coal mines, the same process used in Butte. Large, densely woven plastic bags are filled with a mudlike sludge from the water treatment plant. The water slowly percolates out, leaving a preconcentrate of about 1 to 2 percent rare earths that need further refinement, with chemical processes. The final step in the patented process is an extraction with solvents that creates pure rare-earth elements.

“One of the nice things about acid mine drainage is the concentrates we get are particularly enriched in heavy rare earths,” Dr. Ziemkiewicz said. “The light ones aren’t as valuable.”

The Butte project is awaiting word on a Department of Defense grant of $75 million to build a concentrator, the last step needed to refine the preconcentrate to rare earths and begin full-scale production.

Zinc is also plentiful in the acid-mine-drainage mix here and, because it fetches a higher price, is important as a way to pay for the process. Nickel and cobalt are also extracted.

While rare-earth elements are much in demand, China produces a majority and manipulates prices to keep them low, which forces out competition. That’s why the Defense Department is funding much of the work on rare-earth elements and other metals. The United States has just one operational rare-earths mine, in Mountain Pass, Calif., which produces around 15 percent of the global supply of rare earths.

The Berkeley Pit has been a festering sore since 1982, when, the Anaconda Copper Company closed the open-pit mine, turned off the pumps and let water fill it. The water is so acidic from acid mine drainage that when tens of thousands of snow geese flew over it on their migration in 2016, many landed on the surface and were quickly poisoned. About 3,000 birds died.

The Atlantic Richfield Company and Montana Resources are required to treat the pit water in perpetuity to keep it from reaching levels that could contaminate the area groundwater. (Montana Resources mines the Continental Pit, next to the Berkeley Pit.) The Clean Water Act requires that companies treat acid mine drainage, an expensive process. Adding another level of treatment to the Horseshoe Bend plant here is less costly than building a new one and can offset the costs of treatment or even turn a profit.

There have been dozens of research efforts to liberate the suspended metals from the water. Mr. Thompson displayed a map with lines radiating out from Butte, showing where water samples had been sent to research facilities across the country. But the metal-producing process that’s going on now is the first one that’s proven economical.

While the riches in the mineral soup here have been known for decades, a way to extract them was elusive, until Dr. Ziemkiewicz’s team developed the new method. He has been producing rare earths at two coal mines in West Virginia where acid mine drainage is a problem. Each mine produces four tons of rare earths a year.

The Berkeley Pit, however, has a much richer concentration of rare earths in solution and a higher volume of water and is expected to produce 40 tons a year. Dr. Ziemkiewicz believes this process if used at other mines could eventually provide nearly all of the U.S. imports of rare-earth elements needed for defense purposes, which, he said, currently amount to about 1,400 tons.

But demand for rare earths could increase by as much as 600 percent in the coming decades, according to some estimates.

In the global effort to clean water and produce critical minerals, the lab at Lawrence Berkeley researches an array of water-filter-related technology, especially experiments to improve membranes. It operates a particle accelerator called Advanced Light Source, which creates very bright X-ray light that enables scientists to study various membranes at the atomic scale.

The lab has worked with outside researchers to create a new generation of filters, called nanosponges, that are designed to trap a single target molecule, such as lithium.

“It’s an atomic catcher’s mitt,” said Adam Uliana, the chief executive of ChemFinity, a Brooklyn company studying the use of nanosponges for cleaning many different types of waste. “It catches one and only one type of metal.”

Lithium, cobalt and magnesium are critical minerals, in addition to rare earths, that have attracted considerable attention from researchers.

Ion exchange, a proven technique for removing metals and pollution from water, is gaining interest. Lilac Solutions, a start-up in Oakland, Calif., has developed the specialized resin beads needed to extract lithium from brine with ion exchange and plans to start its first production facility at the Great Salt Lake in Utah.

The company’s technology pumps brine through ion exchange filters, extracts the mineral and returns the water to its source, a process David Snydacker, the company’s president, said caused very little environmental disturbance. If it proves to work at scale, it could revolutionize lithium extraction and reduce or eliminate the need for underground mines and open pits.

Magrathea Metals is a start-up in Oakland that makes magnesium ingots from salty brines left over after seawater has been desalinated. The company allows the brines to dry, which leaves behind magnesium chloride salts. An electrical current — which can utilize off-peak renewable energy — heats the solution and separates the salts from the molten magnesium, which is cast into ingots.

Its chief executive, Alex Grant, said this process is extremely clean, though it has yet to be used to manufacture magnesium at a large scale. The Department of Defense has funded much of its work.

China produces 90 percent of the world’s magnesium. The metal is smelted with something called the Pidgeon process — . heated with coal-fired kilns to around 2,000 degrees, which is highly polluting and carbon-intensive. Dr. Fiske expects a lot more innovation.

“Three vectors are converging,” he said. “The value of some of these critical materials is going up. The cost of conventional mining and extraction is going up, and the security of international suppliers, especially Russia and China, is going down.”

President Trump has defended his decision to introduce tariffs on goods from other countries by arguing that it will lead companies to shift production to the United States, bringing back jobs.

For German companies, which have been producing their goods in the United States since the late 1800s, such arguments ring hollow. Thousands of German companies already have factories in the United States, accounting for 12 percent of the country’s foreign investments.

Automakers like BMW and Mercedes-Benz have long had plants in the United States. In 2023, the candy maker Haribo opened its first U.S. plant in Wisconsin, after decades of importing its gummy bears.

Many German companies are now calling that strategy into question. Recent surveys indicate that German manufacturers are pulling back from investing in the United States, and those that already have a footprint there are more gloomy about their futures.

The German Chamber of Commerce and Industry regularly polls the 6,000 German companies with U.S. factories to gauge their outlook on the economy. For years, those companies held an “above average” view, said Volker Treier, the head of foreign trade at the chamber. But since Mr. Trump announced the initial round of tariffs on April 2, sentiment has dropped.

“They have fallen against the trend,” Mr. Treier said. “Because tariffs are poison.”

Instead, it appears that many German firms are keeping their investments at home. Only 19 percent of companies in Germany said they were looking to invest in North America, down from 25 percent, according to a separate survey of 216 German financial executives by the consulting firm Deloitte.

German companies also appear to be more willing to invest at home, since a new government under Friedrich Merz was sworn in last Tuesday with a mandate to reduce bureaucracy and bring down energy prices. Many are also hoping to cash in on the 500 billion euros (about $564 billion) the government plans to borrow to invest in infrastructure over the next 12 years.

That excitement could change in the weeks before the 90-day suspension of tariffs ends in July, or if the European Union and Washington are able to reach a trade agreement.

In their first call since Mr. Merz took office, the chancellor and Mr. Trump “agreed to resolve the trade disputes quickly,” Mr. Merz’s office said.

Among the German industries hardest hit by the tariffs was the automotive sector, which has had a significant presence in the United States since the mid-1990s, when BMW and Mercedes-Benz set up plants in the South. Roughly a decade later, Volkswagen followed.

Leaders of the three companies have held talks in Washington, hoping to ease the tariffs. Both Mercedes and Volkswagen, which owns Audi, have said they were considering moving the production of some models to the United States, which the White House celebrated this month as proof that the president’s strategy was working.

Beyond the leading automakers, dozens of smaller German companies produce goods in the United States, contributing to Germany’s overall direct investment there, worth $657.8 billion in 2023. That was more than three times as much as the $193.1 billion that flowed into Germany from American companies in the same year.

That discrepancy is certain to feature in tariff negotiations involving Mr. Merz and Mr. Trump, who has zeroed in on the trade deficit, in which Germany sells more goods to the United States than it buys.

“We have invested more, our companies have created more jobs in the U.S. than American companies in Germany,” Mr. Treier said. “That to me is the most important starting point for when we talk about fairness.”

For German companies, the reason to set up production in the United States has been driven by factors like the ease of market access and a desire to produce locally.

Haribo’s move to Wisconsin was part of a shift to a locally focused strategy, said Christian Bahlmann, a senior vice president at the company. “We are pursuing this long-term plan — regardless of the current customs policy,” he said.

Stihl, a maker of chain saws and other power tools, is based in the southwestern German city of Waiblingen. But for decades, it has run a factory in Virginia.

“We did that in 1974 not because of administrative pressure, but because we believe in local production,” the chairman of Stihl, Michael Traub, told reporters recently, stressing that the move had been based on good business sense, not politics.

That locally focused approach is now helping Stihl to avoid some of the worst effects of Mr. Trump’s import taxes. But the company still relies on batteries and other components that are shipped to the United States from its factories in Europe and Brazil, which means that prices of some items will inevitably go up, Mr. Traub said.

“We will do everything to avoid increasing prices,” he said. “We believe that tariffs are taxes, and at the end of day, our consumers will have to pay them.”

Two Chinas inhabit the American imagination: One is a technology and manufacturing superpower poised to lead the world. The other is an economy that’s on the verge of collapse.

Each reflect a real aspect of China.

One China — let’s call it hopeful China — is defined by companies like the A.I. start-up DeepSeek, the electric vehicle giant BYD and the tech powerhouse Huawei. All are innovation leaders.

Jensen Huang, the chief executive of the Silicon Valley chip giant Nvidia, said China was “not behind” the United States in artificial intelligence development. Quite a few pundits have declared that China would dominate the 21st century.

The other China — gloomy China — tells a different story: sluggish consumer spending, rising unemployment, a chronic housing crisis and a business community bracing for the impact of the trade war.

President Trump, as he tries to negotiate a resolution of a trade war, must reckon with both versions of America’s arch geopolitical rival.

The stakes have never been higher to understand China. It’s not enough to fear its successes, or take solace in its economic hardships. To know America’s biggest rival requires seeing how the two Chinas are able to coexist.

“Americans have too many imagined notions about China,” said Dong Jielin, a former Silicon Valley executive who recently moved back to San Francisco after spending 14 years in China teaching and researching the country’s science and technology policies. “Some of them hope to solve American problems using Chinese methods, but that clearly won’t work. They don’t realize that China’s solutions come with a lot of pain.”

Just like the United States, China is a giant country full of disparities: coastal vs. inland, north vs. south, urban vs. rural, rich vs. poor, state-owned vs. private sector, Gen X vs. Gen Z. The ruling Communist Party itself is full of contradictions. It avows socialism, but recoils from giving its citizens a strong social safety net.

Chinese people, too, grapple with these contradictions.

Despite the trade war, the Chinese tech entrepreneurs and investors I talked to over the past few weeks were more upbeat than any time in the past three years. Their hope started with DeepSeek’s breakthrough in January. Two venture capitalists told me that they planned to come out of a period of hibernation they started after Beijing’s crackdown on the tech sector in 2021. Both said they were looking to invest in Chinese A.I. applications and robotics.

But they are much less optimistic about the economy — the gloomy China.

The 10 executives, investors and economists I interviewed said they believed that China’s advances in tech would not be enough to pull the country out of its economic slump. Advanced manufacturing makes up about only 6 percent of China’s output, much smaller than real estate, which contributes about 17 percent of gross domestic product even after a sharp slowdown.

When I asked them whether China could beat the United States in the trade war, nobody said yes. But they all agreed that China’s pain threshold was much higher.

It’s not hard to understand the anxiety felt by Americans frustrated with their country’s struggles to build and manufacture. China has constructed more high-speed rail lines than the rest of the world, deployed more industrial robots per 10,000 manufacturing workers than any country except South Korea and Singapore and now leads globally in electric vehicles, solar panels, drones and several other advanced industries.

Many of China’s most successful companies have gained resilience from the economic downturn and are better prepared for the bad days ahead. “They’ve been DOGE-ing for a long time,” said Eric Wong, the founder of the New York hedge fund Stillpoint who visits China every quarter, referring to the Trump administration’s cost-cutting effort known as the Department of Government Efficiency. “By comparison, the U.S. has been living in excess for a long time.”

But as we marvel at China’s so-called miracles, it is necessary to ask: At what cost? Not just financial, but human.

China’s top-down innovation model, heavily reliant on government subsidies and investment, has proved to be both inefficient and wasteful. Much like the overbuilding in the real estate sector that triggered a crisis and erased much of Chinese household wealth, excessive industrial capacity has deepened imbalances in the economy and raised questions about the model’s sustainability, particularly if broader conditions worsen.

The electric vehicle industry shows the force of the two Chinas. In 2018, the country had nearly 500 E.V. makers. By 2024, about 70 remained. Among the casualties was Singulato Motors, a start-up that raised $2.3 billion from investors, including local governments in three provinces. Over eight years, the company failed to deliver a single car and filed for bankruptcy in 2023.

The Chinese government tolerates wasteful investment in its chosen initiatives, helping fuel overcapacity. But it is reluctant to make the kind of substantial investments in rural pensions and health insurance that would help lift consumption.

“Technological innovation alone cannot resolve China’s structural economic imbalances or cyclical deflationary pressures,” Robin Xing, the chief China economist at Morgan Stanley, said in a research note. “In fact,” he wrote, “recent advances in technology may reinforce policymakers’ confidence in the current path, increasing the risk of resource and capital misallocation.”

The Chinese leadership’s obsession with technological self-reliance and industrial capacity is not helping its biggest challenges: unemployment, weak consumption and a reliance on exports, not to mention the housing crisis.

Officially, China’s urban unemployment rate stands at 5 percent, excluding jobless migrant workers. Youth unemployment is 17 percent. The real numbers are believed to be much higher. This summer alone, China’s colleges will graduate more than 12 million new job seekers.

Mr. Trump was not wrong in saying factories are closing and people are losing their jobs in China.

In 2020 Li Keqiang, then the premier, said the foreign trade sector, directly or indirectly, accounted for the employment of 180 million Chinese. “A downturn in foreign trade will almost certainly hit the job market hard,” he said at the onset of the pandemic. Tariffs could be much more devastating.

Beijing is playing down the effect of the trade war, but as negotiators held talks last weekend with their U.S. counterparts, its impact was obvious. In April, Chinese factories experienced the sharpest monthly slowdown in more than a year while shipments to the United States plunged 21 percent from a year earlier.

All of the economic fallout will be shouldered by people like a man I spoke to, with the surname Chen, a former university librarian in a megacity in southern China. He asked that I not use his full name and where he lived to shield his identity from the authorities.

Mr. Chen lives in the gloomy China. He stopped taking the vaunted high-speed trains because they cost five times as much as a bus. Flying is often cheaper, too.

He lost his job last year because the university, one of the top ones in the country, was facing a budget shortfall. Many state-run institutions have had to let people go because many local governments, even in the wealthiest cities, are deeply in debt.

Because he’s in his late 30s, Mr. Chen is considered too old for most jobs. He and his wife had given up on buying a home. Now with the trade war, he expects that the economy will weaken further and that his job prospects will be dimmer.

“I’ve become even more cautious with spending,” he said. “I weigh every penny.”

Fox Corp. revealed new details about its streaming service on Monday, including that it would debut this fall and would be called Fox One.

The announcement came ahead of the company’s upfront, an annual pitch to entice advertisers with a slate of upcoming shows. Lachlan Murdoch, the company’s chief executive and son of the Fox Corp. founder, Rupert Murdoch, previewed the service on a quarterly earnings call. The name Fox One, he said, was a reference to the combined heft of the company’s TV shows, cable channels and broadcast network, including National Football League games.

“Whether it’s the Super Bowl, the election cycle or the upfront, our company is at its best when we work together as one,” Mr. Murdoch said.

Mr. Murdoch did not say how much Fox would charge viewers, only that it would not be less than what its cable subscribers pay.

Unlike Disney or Warner Bros. Discovery, which have put paid streaming services at the center of their businesses, Fox Corp. has until now adopted a more piecemeal approach. The company, which owns the Fox News cable channel and the Fox broadcasting network, operates the Fox Nation streaming service and Tubi, a free ad-supported service with TV shows and movies.

The Fox Nation streaming service will continue to exist as a stand-alone product within Fox Corporation, but Fox One subscribers will be able to bundle their subscriptions with Fox Nation. Mr. Murdoch also said that Fox had been approached by operators of other streaming services about offering a bundled subscription, though he did not identify them.

Fox recently announced plans to team up with Disney and Warner Bros. Discovery on a sports-focused streaming service called Venu. That service was canceled before it got off the ground amid legal challenges.

Like Venu, Fox One is meant to coexist with the company’s lucrative traditional TV business. In his remarks, Mr. Murdoch said that the service was aimed at the “cordless” market, referring to viewers who do not have a pay-TV subscription. Traditional cable customers who already have access to Fox channels will be able to get Fox One free of charge.

“It would be a failure if we attract more connected subscribers,” Mr. Murdoch said, adding, “We do not want to lose a traditional cable subscriber to Fox One.”