Apple’s profit jumps to $34.6 billion in holiday quarter.

Apple also benefited from strong growth in its services business, which includes its App Store. The services business was up nearly 24 percent in the quarter from a year ago, to $19.5 billion.

Apple also said it planned to use nearly $27 billion of its cash to pay dividends to shareholders.

Apple’s positive results came near the end of a week of wild trading on the stock market that was due in part to fears about how quickly the Federal Reserve might raise interest rates in an attempt to curb inflation. Higher interest rates make riskier investment, like technology stocks, less appealing, adding to concerns that the pandemic-fueled boost to technology companies could soon be ending.

But Microsoft and Tesla, despite dealing with supply chain woes of their own, posted record profits this week and beat industry expectations. Next week, Alphabet, Google’s parent, and Amazon will report their results for the last three months of 2021, providing insight into the health of online advertising and retail.

The disagreement about his compensation in coming years had unfolded in recent months, The New York Times reported in December. Mr. Son and other SoftBank executives balked at Mr. Claure’s request, fearing it would upset investors in Japan, where such big payouts are frowned on. Mr. Claure was already one of the highest-paid executives in the country, making $17 million in 2020.

He privately told people inside and outside the company that he deserved a big payday for various cleanup jobs, including straightening out SoftBank’s investment in WeWork, the office-space leasing giant, which went public in October, as well as the future value he could bring to SoftBank.

Mr. Claure has played a central role at WeWork, taking over as executive chairman after its failed 2019 initial public offering. He negotiated directly with the WeWork co-founder and chief executive Adam Neumann on a severance package that paid Mr. Neumann roughly $180 million to give up his voting control of the company.

Mr. Claure later helped recruit Sandeep Mathrani, a veteran of the real estate business, to be the chief executive of WeWork, which ultimately went public through a special purpose acquisition company. Mr. Claure is expected to leave WeWork’s board as part of his departure from SoftBank, a person familiar with his plans said.

But Mr. Claure will remain on the boards of T-Mobile, which merged with Sprint in 2020, and the company that results from a merger of Grupo Televisa’s television content business and Univision Communications, a deal that’s expected to close soon, according to the two people familiar with the negotiations of his departure. Mr. Claure will also retain his personal stakes in T-Mobile and the merged entity.

Mr. Claure’s personal investments were a source of consternation for some SoftBank executives. Although the conglomerate did clear his transactions, it no longer allows executives to take personal stakes in companies that SoftBank may be interested in ahead of its own investments, unless they agree to sell them back to the company at their initial value.

The details of Mr. Claure’s exit package were not immediately clear. But the two people said he would be permitted to retain his stake in the profits of SoftBank’s $5 billion Latin America Fund, a venture he spearheaded. His stake in potential profits was recently estimated to be worth $300 million to $400 million.

SoftBank, which has a market capitalization of around $71 billion, is facing a drooping stock price. Its shares have fallen roughly 50 percent over the past year as tech stocks have been hit and after a regulatory crackdown in China that has weighed on Chinese stocks. Alibaba, the Chinese online retailing behemoth, is SoftBank’s largest holding.

In dismissing the convictions of Mr. Connolly and Mr. Black, the appellate panel said the prosecutors hadn’t proved that the bids submitted by the bank were not rates that it could have borrowed at. “The government failed to show that any of the trader-influenced submissions were false, fraudulent or misleading,” the panel wrote. It added, “The Libor submissions were not false.”

Kenneth Breen, a lawyer for Mr. Connolly, said his client had been “fully exonerated in this contrived case.” Seth Levine, a lawyer for Mr. Black, said his client had committed no crime and was “deeply appreciative” that the appeals panel agreed.

The Justice Department did not immediately comment.

The crackdown on the manipulation of what was formally known as the London Interbank Offered Rate was one of the major criminal prosecutions to arise from the financial crisis of 2008. Big lenders including Deutsche Bank paid billions of dollars in penalties to authorities in the United States and Britain to resolve accusations that their traders sought to rig Libor. Some banks pleaded guilty in deferred prosecution agreements.

The investigations helped prompt international banking officials to phase out Libor as the primary benchmark for setting rates on loans and in derivatives contracts.

The New York Stock Exchange has delisted both companies, along with China Mobile, and President Biden also said last year that Americans could not invest in any of the three companies.

The Trump administration also ran a lengthy campaign against the Chinese telecommunications company Huawei, warning allies that they should not use the company’s equipment in their next-generation 5G wireless networks and cutting off access to core components for its smartphones.

In 2020, the White House unsuccessfully tried to force ByteDance, a Chinese internet company, to sell TikTok, the viral video app, to an American owner, also citing national security reasons. Mr. Trump initially appeared to have forced a deal that would see much of the app sold to the enterprise software company Oracle. The sale was never finalized.

To offset those costs and maintain profit margins, McDonald’s, like other fast-food chains, increased menu prices by about 6 percent last year. While individual franchise owners make decisions about how much prices should increase, McDonald’s executives said there was a lot of discussion and examination around further price increases and the restaurant chain’s desire to still be seen as a good value to its customers.

“That’s where we keep a really close eye as we take pricing, is how customers are reacting, both in terms of customer research and how they view value and whether they’re still coming in from a transaction standpoint,” said Kevin Ozan, the chief financial officer for McDonald’s.

Share price performance since the start of 2021

“A new generation turned the act of investing into a mass movement,” Robinhood said in a statement on Tuesday about the market events last year. “We never want our customers to be surprised with trading restrictions again,” it added, noting that it had bolstered its risk and compliance infrastructure, among other things. On Wednesday, the S.E.C. chairman, Gary Gensler, issued a brief statement saying the agency was still working on recommendations to make the market “as fair, orderly, and efficient as possible.”

Robinhood said on Thursday that it had lost $3.69 billion last year, including $423 million in the last three months of 2021. Revenue in the quarter was up 14 percent, to $363 million, compared with the same period in 2020. That year it made a profit of $13 million, including $7 million in the last quarter of that year.

“We had a momentous year, nearly doubling the number of customers on the platform and making critical investments in our team and infrastructure to support growth,” Vlad Tenev, the co-founder and chief executive, said in a news release accompanying the financials. “This year, we’ll expand our ecosystem of products.”

Analysts had expected the company to say it lost more than $300 million in the fourth quarter.

Robinhood’s stock dropped 15 percent in aftermarket trading on Thursday, and has lost about two-thirds of its value since it went public this summer, stoking rumors that it could become a takeover target. Lingering issues from the meme stock rally — and related trading restrictions — has marred the outlook, but the company did get good legal news on Thursday before reporting its finances.

This month, a 27-year-old truck driver from Connecticut secured from the Financial Industry Regulatory Authority the first arbitration award stemming from Robinhood’s halt of meme stock trading. The $30,000 award is a small sum for Robinhood, which has a market cap of more than $10 billion, but Jorge Altamirano, a lawyer whose firm represented the investor in the arbitration, said he had heard from hundreds of others who said Robinhood’s actions had led to losses that “represented life-changing money for them and their families.”

Robinhood still faces a proposed class-action lawsuit in Florida that consolidates claims from around the country accusing it of antitrust and securities law violations. (On Thursday, the judge dismissed the plaintiffs’ claims of negligence.) The company had won a motion to dismiss the antitrust claims, but the plaintiffs were allowed to file an amended complaint for that portion of the case; a Robinhood spokeswoman said the new filing “doesn’t make their collusion allegations any more plausible.”

The company also may face regulatory scrutiny on payment for order flow, in which the broker sells its trades to big institutions to execute. This key element of its commission-free business model drew attention when trading was halted, raising concerns about conflicts of interest.

Shares of Tesla, one of the largest companies in the S&P 500, which gives greater weight to more valuable companies, fell 11.6 percent on Thursday after the company warned on Wednesday afternoon that supply chain troubles could constrain production its electric vehicles through the coming year.

Stocks rebounded as much as 1.8 percent in early trading after the Commerce Department reported that gross domestic product — the broadest measure of the goods and services produced — expanded 1.7 percent in the last three months of 2021. At an annual rate, the economy expanded at its fastest pace since 1984.

Economists saw several positive signals in the report. A jump in consumer spending, which the government said reflected an increase in spending on services like health care and recreation, was one. Also notable was a buildup in inventories despite the supply chain headwinds that companies have said are holding them back.

“While normally such a large inventory build would be very negative for future growth, in today’s environment it points to an easing of supply-chain snarls and means consumers will have more products to purchase once the winter lull passes,” Kathy Bostjancic, an economist at Oxford Economics, wrote in a note.

In a separate report on Thursday, the Labor Department said weekly claims for state unemployment benefits fell last week after three consecutive weeks of increases. There were 260,000 new claims for unemployment insurance, down from 290,000, a dip that might suggest a slowdown of the Omicron variant’s effects on the labor market.

“The downtrend will likely continue given demand for labor remains strong and businesses remain reluctant to lay off workers amid a persistent labor shortage,” Rubeela Farooqi, chief U.S. economist at High Frequency Economics, wrote in a note.

But stocks have swung between gains and losses each day this week. On Wednesday the major indexes tumbled after the Federal Reserve fueled investor concerns that it may move too quickly as it starts to raise interest rates.

The S&P 500, which is down about 9 percent since the start of the year, is on track for its worst month since the start of the pandemic.

The market volatility is likely to persist beyond the Fed’s first rate increase, which is expected to be in March, as indicators continue to provide reasons for the central bank to move on with its plan to remove support for the economy. The Omicron variant’s effect on supply chain backlogs could lead to a slowdown in 2022, reversing the surge in inventories in the last three months of last year. Also, if rising inflation continues to show no signs of deceleration, the Fed will seem obligated to move quickly on raising interest rates to tame it.

Markets in Europe swung between gains and losses, with the Stoxx Europe 600 ending the day up 0.7 percent. Asian markets closed lower, after Wednesday’s drop on Wall Street.

Shares of Southwest Airlines fell 2 percent after the company said in its quarterly earnings report that it expects to report a loss for the first three months of 2022 amid headwinds caused by the Omicron variant.

Are market corrections common?

If the market’s decline continues, it will be the 11th correction in the S&P 500 since the turn of the century, according to Yardeni Research. Of the 10 corrections so far, three turned into bear markets, defined as a more severe decline of at least 20 percent:

Does this mean stocks will continue to fall?

Not necessarily.

Some corrections don’t last very long, like the one in early 2018, which spanned less than two weeks. Others can be more drawn out, generally when they develop into full-fledged bear markets.

That said, the previous bear market, at the start of the pandemic, was severe but relatively short — it erased just about 33 percent in value from stocks in just over a month. Less than three months later, stocks had regained their previous peak.

The basic story here is simple. The reopening of the economy after the initial lockdowns brought a surge in demand, which was bolstered by the trillions of dollars in aid that the federal government provided to households and businesses. But supply chain bottlenecks, labor shortages and other issues meant that businesses could not fully meet that demand. Strong demand plus limited supply is a recipe for inflation.

What happens next is less clear. If companies are able to hire more workers and pick up production, then supply will be able to meet demand. In that scenario, the dark blue line would start to look more like the light blue one — growth would be strong in terms of real output, not just nominal dollars.

But if supplies can’t rebound, then either we will continue to burn off excess demand in the form of inflation, or demand will have to fall. Either scenario would make it harder for the economy to rebound fully from the shock of the pandemic.

The problems continued this month. Southwest said it has canceled more than 5,600 flights in January, taking a $50 million toll on operating revenue for the month. Omicron also weighed on ticket sales and led to an increase in customer cancellations. The airline now expects to report a loss for the first three months of 2022.

“Despite our fourth-quarter profit, we had a challenging start to 2022 as we continue to recover from the pandemic,” Mr. Jordan said. He added that the airline had also pared flight plans for the first half of the year to “provide additional buffer to the operation.”

Still, Southwest expects operating revenue in the first quarter of 2022 to be down only about 10 to 15 percent from the same period in 2019. The airline also said it hoped to restore most of its route network and return to typical productivity levels by the end of next year.

Despite the challenges, Southwest hired about 5,000 people last year and expects to hire an additional 8,000 this year as travel continues to recover. To remain competitive, the airline raised its minimum wage to $15 an hour on Aug. 1. It is in discussions with its unions for another increase to $17.

Southwest was the only one of the nation’s largest airlines to report a profit for the final quarter of last year. Delta Air Lines lost more than $400 million, United Airlines nearly $650 million and American Airlines more than $930 million. On Thursday, Alaska Airlines said it had eked out an $18 million profit for the quarter, while JetBlue Airways reported a $129 million loss.

The fall of Mr. Ghosn, who fled Japan after being arrested on charges of financial wrongdoing during his time at the head of the alliance, was widely seen as a result of a power struggle between Renault and Nissan that some feared could lead to a breakup that they could ill afford.

That has only become more true since the pandemic: Both companies have taken a significant hit from plummeting sales and tightened supply chains, which have limited production.

“We have gone through, the three companies, a very strong crisis in the past few years, and officially we were not brilliant in terms of competitiveness,” said Jean-Dominique Senard, the chairman of the alliance.

But the companies have hammered out their differences, he said, putting an end to years of bitter division: “We are demonstrating clearly that our ties are extremely strong, and I think today are in effect unbreakable.”

The investments in battery vehicles will significantly expand the alliance’s offerings, but the group still lags behind its competitors in its commitment to the vehicles, despite grabbing an early lead in the market with the Nissan Leaf, which was introduced in 2010.

Competitors like General Motors have said they intend to eliminate combustion engines from their lineups during the 2030s, but the alliance is hedging its bets. Nissan, for example, has put forward a much more modest goal: aiming for electric cars to make up 40 percent of its U.S. sales by 2030.

The executives attributed the slower adoption to the alliance’s global market presence, especially in developing countries where high prices for electric cars and less reliable power grids make consumers reluctant to make the switch.

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The strong fourth-quarter growth was driven in part by consumer spending, which “primarily reflected an increase in services, led by health care, recreation and transportation,” the Commerce Department said. Private investment and an increase in inventories were also major factors.

“This is really strong data,” said Jane Oates, an assistant labor secretary during the Obama administration and the president of Working Nation, a nonprofit group focused on employment issues. The inventory increase, she said, “shows at least incremental improvement in supply chains.”

Consumer spending and private investment were revived after the pandemic’s initial blow as a result of vaccination efforts, cheap credit conditions and additional rounds of federal aid to households and businesses. The labor market has recovered almost 19 million of the 22 million jobs lost near the peak of virus-induced suspensions in activity.

The initial momentum provided by government stimulus and the post-vaccine resurgence in many sectors is projected to fade further, and the Federal Reserve is planning to use its policy tools in the coming months to rein in inflation, which in December hit its highest level in 40 years.

“Fiscal and monetary policy committed to supporting the economy aggressively during the pandemic, and it worked,” said Julia Coronado, a former Federal Reserve economist and a professor of finance at the University of Texas at Austin. “Not only did we meet the goal of shortening the recession,” she said, “we exceeded all expectations” on the speed of re-employment.

As recently as last February, the Congressional Budget Office predicted that it might take until 2024 to reach the current unemployment rate of 3.9 percent, down from a peak of 14.7 percent in April 2020.

President Biden hailed the year’s economic growth and job gains as evidence that his policies were yielding substantial fruit. “The G.D.P. numbers for my first year show that we are finally building an American economy for the 21st century,” he said in a statement on Thursday.

But the economic recovery has been overshadowed recently by the highest rates in inflation since 1982. Consumer price increases — which reached 7 percent in the year through December — began to intensify in the spring when demand overstrained supply networks already discombobulated by the pandemic.

Import prices, for instance, were 10.4 percent higher in December than a year earlier, according to the Labor Department. Many businesses, large and small, are preparing for such supply chain issues to stretch beyond the summer — an unwelcome sign for workers whose wages have grown at the fastest pace in decades, while their purchasing power as consumers has been dented by costlier goods.

A Gallup survey conducted this month found that Americans view the economy more negatively than positively — with only 29 percent saying that the economy is improving, while 67 percent believe it is getting worse.

Still, 72 percent say it is a good time to find a quality job.

“It’s all about what you prioritize,” said Allison Schrager, an economist and senior fellow at the Manhattan Institute, a conservative think tank. Policymakers in Washington decided to err on the side of delivering too much pandemic aid rather than too little — and Ms. Schrager is among the analysts who say the trade-offs of that decision are becoming evident. If there had been less stimulus, she said, “inflation wouldn’t be as bad as it is.”

At a news conference on Wednesday, Jerome H. Powell, the Fed chair, conceded that “bottlenecks and supply constraints are limiting how quickly production can respond to higher demand in the near term” and that “these problems have been larger and longer lasting than anticipated.”

As analysts mull the direction and degree of price increases this year, many see the spring months as a crucial pivot point, said Ellen Zentner, a managing director and the chief U.S. economist at Morgan Stanley. This is partly because the Consumer Price Index reports in March and April of this year will provide the first relatively stable year-over-year comparisons that experts will have seen in three years: 2020 data was juxtaposed with the prepandemic normal of 2019; reports in 2021 after the economy reopened were measured against the abnormal, partly depressed environment of the vaccine-less economy in 2020.

“The hope is that changes as we’re getting into the second quarter,” Ms. Zentner said. And that high-single-digit inflation “doesn’t drag on further into the year.”

During quarterly earnings calls, JPMorgan Chase and Bank of America, which serve a combined 140 million households, have reported that families’ finances are technically better off than before the pandemic. Bank of America said its customers spent a record $3.8 trillion in 2021, a 24 percent jump from 2019 levels. But analysts note that dwindling savings and continuing price increases — along with any new coronavirus variants — could curb consumption.

The report on Thursday indicated that the cash reserves many Americans were able to build up during the pandemic continued to dwindle: Real disposable personal income decreased by 5.8 percent in the fourth quarter, and the personal saving rate — the percentage of overall disposable income that goes into savings each month — was 7.4 percent, compared with 9.5 percent in the third quarter.

Although factory production was up 3.5 percent in December from a year earlier, manufacturing output fell by 0.3 percent last month, a weaker showing than most forecasts. The spread of the Omicron variant appears to be extending manufacturers’ struggles with finding consistent labor, as infections drive absences. With businesses outbidding one another to get to the front of the line for supply parts that make up their finished products, materials shortages for hard-to-source components, such as computer chips, also remain a headache.

Core capital goods shipments — a popular gauge of business investment in U.S. equipment spending — were up a strong 1.3 percent in the fourth quarter, yet flat in December. Some industry analysts are emphasizing the broader quarterly trend as a sign that the private sector believes strong growth will persist through both inflationary pressures and speed bumps associated with coronavirus variants.

The average business owner “sees a very strong environment right now,” said Oren Klachkin, the lead economist for U.S. industry and regional research at Oxford Economics. “They want to ramp up investment because they want to meet that demand — and they have every reason to invest.”

The International Monetary Fund, citing tighter Fed policy and an anticipated halt to any further stimulus spending by Congress, this week reduced its U.S. growth forecast for 2022 by 1.2 percentage points, to 4 percent — though that increase would still outpace the annual average from 2010 to 2019.

Ben Casselman contributed reporting.