Zabihullah Mujahid, a spokesman for the Taliban, said the accusations of burning down homes was under investigation.

The group’s public responses, though rarely sincere, play directly into a strategy meant to portray the insurgents as a comparable option to the Afghan government. And they ignore the fact that local feuds drive large amounts of the war’s violence, outweighing any official orders from the Taliban leadership.

On the battlefield, things are shifting quickly. Thousands of Afghan soldiers and militia members have surrendered in past weeks, forfeiting weapons, ammunition and armored vehicles as the Taliban take district after district. Government forces have counterattacked, recapturing several districts, though not on the scale of the insurgents’ recent victories.

But little reported are Taliban losses, aside from the inflated body counts announced by the Afghan government’s Ministry of Defense. The Taliban, with their base strength long estimated to be between 50,000 and 100,000 fighters, depending on the time of year, have taken serious casualties in recent months, especially in the country’s south.

The casualties are primarily from the Afghan and U.S. air forces, and sometimes from Afghan commando units.

Mullah Basir Akhund, a former commander and member of the Taliban since 1994, said that cemeteries along the Pakistani border, where Taliban fighters have long been buried, are filling up faster than in years past. Pakistani hospitals, part of the country’s unwavering line of support for the insurgents, are running out of bed space. During a recent visit to a hospital in Quetta, a hub for the Taliban in Pakistan, Mr. Akhund said he saw more than 100 people, most of them Taliban fighters, waiting to be treated.

But despite tough battles, the weight of a nearly withdrawn superpower, and the Taliban’s own leadership issues, the insurgents continue to adapt.

Even as they seek to conquer the country, the Taliban are aware of their legacy of harsh rule, and do not want to “become the same pariah and isolated state” that Afghanistan was in the 1990s, said Ibraheem Bahiss, an International Crisis Group consultant and an independent research analyst.

“They’re playing the long game,” Mr. Bahiss said.

Reporting was contributed by Asadullah Timory in Herat, Taimoor Shah in Kandahar, Ruhullah Khapalwak, Farooq Jan Mangal in Khost and Zabihullah Ghazi in Jalalabad.

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U.S. Aid to Central America Hasn’t Slowed Migration. Can Kamala Harris?

SAN ANTONIO HUISTA, Guatemala — An American contractor went to a small town in the Guatemalan mountains with an ambitious goal: to ignite the local economy, and hopefully even persuade people not to migrate north to the United States.

Half an hour into his meeting with coffee growers, the contractor excitedly revealed the tool he had brought to change their lives: a pamphlet inviting the farmers to download an app to check coffee prices and “be a part of modern agriculture.”

Pedro Aguilar, a coffee farmer who hadn’t asked for the training and didn’t see how it would keep anyone from heading for the border, looked confused. Eyeing the U.S. government logo on the pamphlet, he began waving it around, asking if anyone had a phone number to call the Americans “and tell them what our needs really are.”

soared in 2019 and is on the upswing once more.

have risen, malnutrition has become a national crisis, corruption is unbridled and the country is sending more unaccompanied children to the United States than anywhere else in the world.

That is the stark reality facing Ms. Harris as she assumes responsibility for expanding the same kind of aid programs that have struggled to stem migration in the past. It is a challenge that initially frustrated her top political aides, some of whom viewed the assignment from Mr. Biden as one that would inevitably set her up for failure in the first months of her tenure.

Her allies worried that she would be expected to solve the entire immigration crisis, irked that the early reports of her new duties appeared to hold her responsible for juggling the recent surge of children crossing the border without adults.

linked to drug traffickers and accused of embezzling American aid money, the leader of El Salvador has been denounced for trampling democratic norms and the government of Guatemala has been criticized for persecuting officials fighting corruption.

Even so, Ms. Harris and her advisers have warmed to the task, according to several people familiar with her thinking in the White House. They say it will give her a chance to dive squarely into foreign policy and prove that she can pass the commander-in-chief test, negotiating with world leaders on a global stage to confront one of America’s most intractable issues.

critics denounced as unlawful and inhumane. Moreover, members of the current administration contend that Mr. Trump’s decision to freeze a portion of the aid to the region in 2019 ended up blunting the impact of the work being done to improve conditions there.

But experts say the reasons that years of aid have not curbed migration run far deeper than that. In particular, they note that much of the money is handed over to American companies, which swallow a lot of it for salaries, expenses and profits, often before any services are delivered.

Record numbers of Central American children and families were crossing, fleeing gang violence and widespread hunger.

independent studies have found.

“All activities funded with U.S.A.I.D.’s foreign assistance benefit countries and people overseas, even if managed through agreements with U.S.-based organizations,” said Mileydi Guilarte, a deputy assistant administrator at U.S.A.I.D. working on Latin America funding.

But the government’s own assessments don’t always agree. After evaluating five years of aid spending in Central America, the Government Accountability Office rendered a blunt assessment in 2019: “Limited information is available about how U.S. assistance improved prosperity, governance, and security.”

One U.S.A.I.D. evaluation of programs intended to help Guatemalan farmers found that from 2006 to 2011, incomes rose less in the places that benefited from U.S. aid than in similar areas where there was no intervention.

Mexico has pushed for a more radical approach, urging the United States to give cash directly to Central Americans affected by two brutal hurricanes last year. But there’s also a clear possibility — that some may simply use the money to pay a smuggler for the trip across the border.

The farmers of San Antonio Huista say they know quite well what will keep their children from migrating. Right now, the vast majority of people here make their money by selling green, unprocessed coffee beans to a few giant Guatemalan companies. This is a fine way to put food on the table — assuming the weather cooperates — but it doesn’t offer much more than subsistence living.

Farmers here have long dreamed of escaping that cycle by roasting their own coffee and selling brown beans in bags to American businesses and consumers, which brings in more money.

“Instead of sending my brother, my father, my son to the United States, why not send my coffee there, and get paid in dollars?” said Esteban Lara, the leader of a local coffee cooperative.

But when they begged a U.S. government program for funding to help develop such a business, Ms. Monzón said, they were told “the money is not designed to be invested in projects like that.”

These days, groups of her neighbors are leaving for the United States every month or two. So many workers have abandoned this town that farmers are scrambling to find laborers to harvest their coffee.

One of Ms. Monzón’s oldest employees, Javier López Pérez, left with his 14-year-old son in 2019, during the last big wave of Central American migration to the United States. Mr. López said he was scaling the border wall with his son when he fell and broke his ankle.

“My son screamed, ‘Papi, no!’ and I said to him, ‘Keep going, my son,’” Mr. López said. He said his son made it to the United States, while he returned to San Antonio Huista alone.

His family was then kicked out of their home, which Mr. López had given as collateral to the person who smuggled him to the border. The house they moved into was destroyed by the two hurricanes that hit Guatemala late last year.

Ms. Monzón put Mr. López in one of her relatives’ houses, then got the community to cobble together money to pay for enough cinder blocks to build the family a place to live.

While mixing cement to bind the blocks together, one of Mr. López’s sons, Vidal, 19, confessed that he had been talking to a smuggler about making the same journey that felled his father, who was realistic at the prospect.

“I told him, ‘Son, we suffered hunger and thirst along the way, and then look at what happened to me, look at what I lost,’” Mr. López said, touching his still-mangled ankle. “But I can’t tell him what to do with his life — he’s a man now.”

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Why Apple and Google’s Virus Alert Apps Had Limited Success

Sarah Cavey, a real estate agent in Denver, was thrilled last fall when Colorado introduced an app to warn people of possible coronavirus exposures.

Based on software from Apple and Google, the state’s smartphone app uses Bluetooth signals to detect users who come into close contact. If a user later tests positive, the person can anonymously notify other app users whom the person may have crossed paths with in restaurants, on trains or elsewhere.

Ms. Cavey immediately downloaded the app. But after testing positive for the virus in February, she was unable to get the special verification code she needed from the state to warn others, she said, even after calling Colorado’s health department three times.

“They advertise this app to make people feel good,” Ms. Cavey said, adding that she had since deleted the app, called CO Exposure Notifications, in frustration. “But it’s not really doing anything.”

announced last year that they were working together to create a smartphone-based system to help stem the virus, their collaboration seemed like a game changer. Human contact tracers were struggling to keep up with spiking virus caseloads, and the trillion-dollar rival companies — whose systems run 99 percent of the world’s smartphones — had the potential to quickly and automatically alert far more people.

Soon Austria, Switzerland and other nations introduced virus apps based on the Apple-Google software, as did some two dozen American states, including Alabama and Virginia. To date, the apps have been downloaded more than 90 million times, according to an analysis by Sensor Tower, an app research firm.

But some researchers say the companies’ product and policy choices limited the system’s usefulness, raising questions about the power of Big Tech to set global standards for public health tools.

Stephen Farrell and Doug Leith, computer science researchers at Trinity College in Dublin, wrote in a report in April on Ireland’s virus alert app.

CA Notify in December, about 65,000 people have used the system to alert other app users, the state said.

“Exposure notification technology has shown success,” said Dr. Christopher Longhurst, the chief information officer of UC San Diego Health, which manages California’s app. “Whether it’s hundreds of lives saved or dozens or a handful, if we save lives, that’s a big deal.”

In a joint statement, Apple and Google said: “We’re proud to collaborate with public health authorities and provide a resource — which many millions of people around the world have enabled — that has helped protect public health.”

Based in part on ideas developed by Singapore and by academics, Apple and Google’s system incorporated privacy protections that gave health agencies an alternative to more invasive apps. Unlike virus-tracing apps that continuously track users’ whereabouts, the Apple and Google software relies on Bluetooth signals, which can estimate the distance between smartphones without needing to know people’s locations. And it uses rotating ID codes — not real names — to log app users who come into close contact for 15 minutes or more.

said last year in a video promoting the country’s alert system, called Corona-Warn-App.

But the apps never received the large-scale efficacy testing typically done before governments introduce public health interventions like vaccines. And the software’s privacy features — which prevent government agencies from identifying app users — have made it difficult for researchers to determine whether the notifications helped hinder virus transmission, said Michael T. Osterholm, the director of the Center for Infectious Disease Research and Policy at the University of Minnesota.

“The apps played virtually no role at all in our being able to investigate outbreaks that occurred here,” Dr. Osterholm said.

Some limitations emerged even before the apps were released. For one thing, some researchers note, exposure notification software inherently excludes certain vulnerable populations, such as elderly people who cannot afford smartphones. For another thing, they say, the apps may send out false alarms because the system is not set up to incorporate mitigation factors like whether users are vaccinated, wearing masks or sitting outside.

Proximity detection in virus alert apps can also be inconsistent. Last year, a study on Google’s system for Android phones conducted on a light-rail tram in Dublin reported that the metal walls, flooring and ceilings distorted Bluetooth signal strength to such a degree that the chance of accurate proximity detection would be “similar to that of triggering notifications by randomly selecting” passengers.

Kimbley Craig, the mayor of Salinas, Calif. Last December, when virus rates there were spiking, she said, she downloaded the state’s exposure notification app on her Android phone and soon after tested positive for Covid-19. But after she entered the verification code, she said, the system failed to send an alert to her partner, whom she lives with and who had also downloaded the app.

“If it doesn’t pick up a person in the same household, I don’t know what to tell you,” Mayor Craig said.

In a statement, Steph Hannon, Google’s senior director of product management for exposure notifications, said that there were “known challenges with using Bluetooth technology to approximate the precise distance between devices” and that the company was continuously working to improve accuracy.

The companies’ policies have also influenced usage trends. In certain U.S. states, for instance, iPhone users can activate the exposure notifications with one click — by simply turning on a feature on their settings — but Android users must download a separate app. As a result, about 9.6 million iPhone users in California had turned on the notifications as of May 10, the state said, far outstripping the 900,000 app downloads on Android phones.

Google said it had built its system for states to work on the widest range of devices and be deployed as quickly as possible.

Some public health experts acknowledged that the exposure alert system was an experiment in which they, and the tech giants, were learning and incorporating improvements as they went along.

One issue they discovered early on: To hinder false alarms, states verify positive test results before a person can send out exposure notifications. But local labs can sometimes take days to send test results to health agencies, limiting the ability of app users to quickly alert others.

In Alabama, for instance, the state’s GuideSafe virus alert app has been downloaded about 250,000 times, according to Sensor Tower. But state health officials said they had been able to confirm the positive test results of only 1,300 app users. That is a much lower number than health officials would have expected, they said, given that more than 10 percent of Alabamians have tested positive for the coronavirus.

“The app would be a lot more efficient if those processes were less manual and more automated,” said Dr. Scott Harris, who oversees the Alabama Department of Public Health.

Colorado, which automatically issues the verification codes to people who test positive, has reported higher usage rates. And in California, UC San Diego Health has set up a dedicated help line that app users can call if they did not receive their verification codes.

Dr. Longhurst, the medical center’s chief information officer, said the California app had proved useful as part of a larger statewide public health push that also involved mask-wearing and virus testing.

“It’s not a panacea,” he said. But “it can be an effective part of a pandemic response.”

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5 Tips to Take Command of Your iPhone

Last month, Apple released an update to its operating system, iOS 14.5, which gives users more control of their personal data. But if you’re looking to gain more control over the iPhone itself, you also have options. Want to put your favorite apps within easy reach, tag friends in Messages or set your preferred browser to open links? You can do all that and more.

Here are a few quick tips for enhancing the iPhone experience. Next week’s Tech Tip column will round up a few helpful hints for the Android faithful.

The Control Center — that handy panel of often-used settings summoned with a finger swipe — first appeared back in 2013 and got more useful when Apple began to let users add their preferred buttons a few years later. If you haven’t tinkered with your Control Center to add the features and functions you use the most, just open the Settings icon on the home screen, scroll down to Control Center and give it a tap.

Credit…Apple

From the list on the next screen, choose the icons for the apps and settings you want to live in your Control Center. While tools like the Flashlight are typically there by default, you can remove those you never use and add icons for apps you want, like the Magnifier, the QR Code scanner or even the Shazam music recognition feature. To rearrange the order of the icons on the screen, drag them up and down the list before you close the Settings app.

Back Tap feature to have your iPhone perform a specific action when you give it quick taps on the back.

Credit…Apple

To set it up, open the Settings, select Accessibility and then Touch, and scroll down to Back Tap. Once you select Back Tap, select either Double or Triple Tap and choose an action on the next screen, like opening the Spotlight search app or the Control Center or running a Shortcut you’ve set up with Apple’s Shortcuts app. You can assign two separate tasks to the Double Tap and Triple Tap functions — and Back Tap should work even if your iPhone is in a case.

Tired of the iPhone always opening the Safari browser instead of your favored DuckDuckGo when you tap a link, or firing up Apple’s Mail program instead of the Gmail app when you select an email address from your Contacts list? If your iPhone is running iOS 14 or later, you can choose the apps you want as your default programs.

Messages chat or get someone’s attention in a group conversation, just as you can on some social media platforms? You can do both.

Credit…Apple

To reply to a certain message in either a one-on-one or group chat where everyone is using the Messages app, press your finger on that message until a menu appears. Select Reply, enter your response and tap the blue Send arrow. To tag someone in a conversation so he or she gets a notification, put the @ symbol in front of the name or just type the name and select it when it pops up onscreen from your Contacts.

Apple’s Siri voice assistant, celebrating a decade on the iPhone this October, has been losing ground in knowledge and usefulness to Amazon’s Alexa and the Google Assistant in recent years. To boost Siri’s powers, Apple added more skills in iOS 14. And with iOS 14.5, it now includes a more diverse set of voices.

Credit…Apple

To change how and when Siri sounds, open the Settings icon on the home screen, select Siri & Search and make your selections. You can also opt to display your conversations on the screen by tapping Siri Responses and turning on “Always Show Siri Captions” and “Always Show Speech” to make sure you see the last word, too.

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The Big Deal in Amazon’s Antitrust Case

This article is part of the On Tech newsletter. You can sign up here to receive it weekdays.

Hoo boy, this is a moment. A government authority in the United States has sued Amazon over claims that the company is breaking the law by unfairly crushing competition.

The lawsuit, filed on Tuesday by the attorney general for the District of Columbia, joins the recent government antitrust cases against Google and Facebook. These lawsuits will take forever, and legal experts have said that the companies likely have the upper hand in court.

The D.C. attorney general, Karl Racine, however, is making a legal argument against Amazon that is both old-school and novel, and it might become a blueprint for crimping Big Tech power.

It’s a longstanding claim by some of the independent merchants who sell on Amazon’s digital mall that the company punishes them if they list their products for less on their own websites or other shopping sites like Walmart.com. Those sellers are effectively saying that Amazon dictates what happens on shopping sites all over the internet, and in doing so makes products more expensive for all of us.

told me that he believed that those price claims were the strongest potential antitrust case against Amazon on legal grounds. (He has since been picked to advise the White House on corporate competition issues.)

I don’t know if any of these lawsuits against Big Tech will succeed at chipping away at the companies’ tremendous influence. And I can’t definitively say whether we’re better or worse off by having a handful of powerful technology companies that make products used and often loved by billions of people.

the price of power is scrutiny.

How to fight back against bogus online information: The comedian Sarah Silverman and three of my colleagues are hosting a virtual event Wednesday about disinformation and how to combat it. Sign up here for the online event at 7 p.m. Eastern. It’s open only to New York Times subscribers.



fine social media companies for permanently barring political candidates’ accounts. The measure is most likely unconstitutional and unenforceable, Democrats, libertarian groups and tech companies told my colleague David McCabe, but it’s a response to Facebook’s and Twitter’s suspension of former President Donald Trump.

  • Posting is life. My colleague Taylor Lorenz explains how social media invitations to a teenager’s birthday party spread on TikTok and drew thousands of people and a police crackdown. The event got big partly because it was an opportunity for attendees to post compelling material online. SIGH.

  • POTUS loves Apple News? I don’t like it when computers and smartphones come with the device makers’ apps already installed, but it’s effective — even with the president of the United States. The Washington Post reported that during the 2020 campaign Joe Biden shared with aides human interest stories from Apple News, which came on his iPhone and he apparently hadn’t deleted.

  • The Linda Lindas are glorious. Here is the talented punk band of four girls between the ages of 10 and 16 — Bela, Eloise, Mila and Lucia — playing “Racist, Sexist Boy” at a Los Angeles public library. The Guardian interviewed them about their sudden internet fame.


    We want to hear from you. Tell us what you think of this newsletter and what else you’d like us to explore. You can reach us at ontech@nytimes.com.

    If you don’t already get this newsletter in your inbox, please sign up here. You can also read past On Tech columns.

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    Rolling Blackouts Hit Taiwan After Accident at Power Plant

    TAIPEI, Taiwan — An accident at a power plant in southern Taiwan on Thursday prompted the authorities to institute an emergency rolling blackout across the island, leaving millions without electricity in the middle of the workday.

    Taipower, the state-run utility company, said that the outage was caused by a grid failure at the Hsinta Power Plant in the southern city of Kaohsiung. Shortly after, at around 3 p.m., residents around the island received a government alert on their mobile phones warning of the coming blackouts. Then, several cities, including Tainan, Taoyuan, and the capital city of Taipei, saw electricity cut almost instantly.

    Taiwan’s president, Tsai Ing-wen, said Thursday afternoon that the power would be gradually restored as the government worked to resolve the issue. Chang Ting-shu, a spokesman for Taipower, said the utility was hoping to limit the blackouts so that residents would only experience 50 minutes of outage at a time. The utility is investigating the cause of the failure.

    The sudden outage caught many of the island’s 24 million residents off guard. In several cities, the police were forced to manually direct traffic. In the eastern city of Hualien, the local fire department received requests to assist people trapped in elevators and help at least one patient who was on a ventilator, according to Taiwan’s official Central News Agency. The government said it would prioritize restoring power for certain places like government offices, hospitals and military-related areas.

    global hub for high-tech manufacturing and is known for its computer chip industry, whose products are essential components for smartphones, cars and other gadgets.

    Taiwan Semiconductor Manufacturing Company, the chip manufacturing giant, said that some of the company’s facilities had experienced a power dip as a result of the outage but that electricity was being supplied as normal.

    “T.S.M.C. has taken emergency response measures and prepared generators to minimize potential impact,” the company said in an email.

    The Taipower spokesman said that the scale of the outage on Thursday appeared to be smaller than a previous islandwide power blackout in 2017. That outage, which lasted for five hours, resulted in about $3 million worth of losses for 151 companies in industrial parks and export processing zones, said the ministry of economic affairs at the time.

    Thursday’s outage came as Taiwan has been racing to subdue a recent outbreak of the coronavirus. On Wednesday, the island’s health authorities announced 16 cases of local transmission, the highest single day total since the pandemic began last year.

    On Thursday, officials from Taiwan’s Centers for Disease Control were holding a daily news briefing in Taipei to announce 13 new local cases when the room suddenly went dark.

    A video of the briefing showed officials sitting on the darkened stage in confusion as reporters talked among themselves, their faces lit by the glowing screens of their laptops. Shortly after, the power came back on.

    Raymond Zhong contributed reporting.

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    Despite Chip Shortage, Chip Innovation Is Booming

    “It’s a bloody miracle,” said Jim Keller, a veteran chip designer whose résumé includes stints at Apple, Tesla and Intel and who now works at the A.I. chip start-up Tenstorrent. “Ten years ago you couldn’t do a hardware start-up.”

    The trends are not necessarily good news for chip customers, at least for the short term. Scarce supplies of many chips have manufacturers scrambling to increase production, and are adding to worries in Washington about reliance on foreign suppliers. Extra demand could extend the shortages, which are already expected to last into 2022.

    High demand was evident in earnings for chip companies last quarter, which ended in March. Revenue grew 27 percent, for example, at NXP Semiconductors, a big maker of auto, communications and industrial chips, even though it temporarily closed two Texas factories because of a cold snap.

    The industry has historically been notorious for booms and busts, usually driven by purchasing swings for particular products like PCs and smartphones. Global chip revenue slumped 12 percent in 2019 before bouncing back with 10 percent growth last year, according to estimates from Gartner, a research firm.

    But there is widening optimism that the cycles should moderate because chips are now used in so many things. Philip Gallagher, chief executive of the big electronics distributor Avnet, cited examples like sensors to track dairy cows, the flow of beer taps and utility pipes, and the temperature of produce. And the number of chips in mainstay products like cars and smartphones keeps rising, he and other executives say.

    “This is a lasting growth cycle, not a short spike,” said Kurt Sievers, NXP’s chief executive.

    A longtime industry watcher, Handel Jones, who heads the consultancy International Business Strategies, sees total chip revenues rising steadily to $1.2 trillion by 2030 from roughly $500 billion this year.

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    Apple and Epic Head to Court Over Their Slices of the App Pie

    One Friday last August, Tim Sweeney, a billionaire game developer, sent an email to a contact at Microsoft: “You’ll enjoy the upcoming fireworks show.”

    A week later, Mr. Sweeney’s game Fortnite delivered good news to players on iPhones: They would get a discount on items in the game if they completed the purchases outside Apple’s payment systems.

    The change violated Apple’s rules and cut the iPhone maker off from collecting a commission on one of the world’s most popular games. Hours later, Apple kicked Fortnite off the App Store.

    immediately sued Apple in federal court. It also began a public-relations broadside that was months in the works, complete with a trending #FreeFortnite hashtag and a parody of Apple’s iconic “1984” ad depicting Apple’s chief executive, Tim Cook, as an evil corporate overlord with an apple for a head.

    up to 30 percent of their app sales to Apple.

    An Epic victory would also invigorate the antitrust fight against Apple. Federal and state regulators are scrutinizing Apple’s control over the App Store, and on Friday, the European Union charged Apple with violating antitrust laws over its app rules and fees. Apple faces two other federal lawsuits about its App Store fees — one from developers and one from iPhone owners — that are seeking class-action status.

    Beating Apple would also bode well for Epic’s upcoming trial against Google over the same issues on the app store for Android devices. That case is expected to go to trial this year and would be decided by the same federal judge, Yvonne Gonzalez Rogers of the Northern District of California.

    has also said he was OK paying commissions to companies like Microsoft and Nintendo because they sold their gaming consoles at or below cost and depend on the commissions, while Apple earns wide margins on all parts of its business.

    created an alliance with other app makers “to ensure we’re not the only voice,” according to an Apple court filing. Epic named the effort Project Liberty.

    Last June, Mr. Sweeney emailed Mr. Cook and a few of his deputies, asking to release a competing marketplace for games on the iPhone and to use Epic’s own payment system instead of Apple’s, enabling it to circumvent Apple’s 30 percent cut.

    Apple’s lawyers responded, writing that the company wouldn’t turn the App Store “into a public utility.”

    its own feud with Apple, had been scheduled to testify but dropped out.

    Apple has accused Epic of looking for a free ride. The game maker has not gone after other companies that distribute Fortnite. Microsoft, Samsung, Sony and Nintendo all charge the same commissions on games, according to a study funded by Apple. That study did not note that Apple popularized the 30 percent rate with the App Store in 2008.

    In response, Epic has pointed to the commission it charges in its own marketplace for game developers: 12 percent.

    halved its commission to 15 percent for developers that make less than $1 million on their apps. That new rate applies to about 98 percent of the developers that paid Apple’s commission, according to estimates from Sensor Tower, an app data firm.

    Yet it hardly affected Apple’s bottom line. According to Sensor Tower, more than 95 percent of Apple’s app revenues come from companies paying the full 30 percent rate.

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    U.S. Economy Rebounds as Pain Caused by Pandemic Eases: Live Updates

    the first-quarter growth rate was 6.4 percent.

    2019 Q4 LEVEL

    $20 trillion

    +1.6%

    FROM

    PRIOR

    QUARTER

    Gross domestic product,

    adjusted for inflation and

    seasonality, at annual rates

    2019 Q4 LEVEL

    $20 trillion

    +1.6%

    FROM

    PRIOR

    QUARTER

    Gross domestic product, adjusted for inflation

    and seasonality, at annual rates

    “This was a great way to start the year,” said Gregory Daco, chief U.S. economist at Oxford Economics. “We had the perfect mix of improving health conditions, strong fiscal stimulus and warmer weather.”

    “Consumers are now back in the driver’s seat when it comes to economic activity, and that’s the way we like it,” he added. “A consumer that is feeling confident about the outlook will generally spend more freely.”

    Looking ahead, economists said they expected to see even better numbers this quarter.

    “It’s good news, but the better news is coming,” said Ian Shepherdson, chief economist at Pantheon Macroeconomics. “There’s nothing in this report that makes me think the economy won’t grow at a gangbusters pace in the second and third quarter.”

    The expansion last quarter was spurred by stimulus checks, he said, which quickly translated into purchases of durable goods like cars and household appliances.

    “This demonstrates the value of government intervention when the economy is on its knees from Covid,” he added. “But in the coming quarters, the economy will be much less dependent on stimulus as individuals use the savings they’ve accumulated during the pandemic.”

    Cumulative percent change in

    G.D.P. from the start of the

    last five recessions

    Final quarter

    before

    recession

    5 quarters

    into recession

    Cumulative percent change in G.D.P.

    from the start of the last five recessions

    Final quarter

    before

    recession

    5 quarters

    into recession

    Overall economic activity should return to prepandemic levels in the current quarter, Mr. Anderson said, while cautioning that it will take until late 2022 for employment to regain the ground it lost as a result of the pandemic.

    Still, the labor market does seem to be catching up. Last month, employers added 916,000 jobs and the unemployment rate fell to 6 percent, while initial claims for unemployment benefits have dropped sharply in recent weeks.

    Tom Gimbel, chief executive of LaSalle Network, a recruiting and staffing firm in Chicago, said: “It’s the best job market I’ve seen in 25 years. We have 50 percent more openings now than we did pre-Covid.”

    Hiring is stronger for junior to midlevel positions, he said, with strong demand for professionals in accounting, financing, marketing and sales, among other areas. “Companies are building up their back-office support and supply chains,” he said. “I think we’re good for at least 18 months to two years.”

    Spending on goods like automobiles led the way in the first quarter, but demand for services like dining out should revive in the second quarter, said Rubeela Farooqi, chief U.S. economist at High Frequency Economics. “I think we will see a surge in services spending,” she said.

    As more Americans become vaccinated, many economists expect a decline in new unemployment claims.
    Credit…James Estrin/The New York Times

    Initial jobless claims fell last week to yet another pandemic low in the latest sign that the economic recovery is strengthening.

    About 575,000 people filed first-time claims for state unemployment benefits last week, the Labor Department said Thursday, a decrease of 9,000 from the previous week’s revised figure. It was the third straight week that jobless claims had dropped.

    In addition, 122,000 new claims were filed for Pandemic Unemployment Assistance, a federal program that covers freelancers, part-timers and others who do not routinely qualify for state benefits. That was a decline of 12,000 from the previous week.

    Neither figure is seasonally adjusted. On a seasonally adjusted basis, new state claims totaled 553,000.

    “Today’s report, and the other data that we got today, signals an improving labor market and an improving economy,” said Daniel Zhao, senior economist with the career site Glassdoor. “It is encouraging that claims are continuing to fall.”

    Although weekly jobless claims remain above levels reached before the pandemic, vaccinations and warmer weather are offering new hope. Most economists expect the slow downward trend in claims to continue in the coming months as the economy reopens more fully.

    But challenges lie ahead. The long-term unemployed — a group that historically has had a more difficult time rejoining the work force — now make up more than 40 percent of the total number of unemployed. Of the 22 million jobs that disappeared early in the pandemic, more than eight million remain lost.

    “The labor market is definitely moving in the right direction,” said AnnElizabeth Konkel, an economist at the online job site Indeed. She noted that job postings as of last Friday were up 22.4 percent from February 2020.

    Still, she cautioned that industries like tourism and hospitality would probably remain depressed until the pandemic was firmly under control. She also stressed that child care obligations might be preventing people ready to return to work from seeking jobs.

    “We still are in a pandemic — the vaccinations are ramping up but there is that public health factor still,” Ms. Konkel said. “We’re not quite there yet.”

    The NBC sitcom “The Office” became a big streaming hit for Netflix and is now back in the Comcast fold, available on its streaming service Peacock.
    Credit…Chris Haston/NBC

    If you want a clear picture of the state of the media industry in upheaval, Comcast offers a good snapshot.

    The company, which includes NBC, Universal Pictures, several theme parks, and the Peacock streaming service, beat Wall Street’s expectations in its first-quarter earnings report on Thursday as it continued to shift its emphasis from cable to digital.

    To start, take these figures from its results:

    Despite the regular pace of cord cutting, Comcast’s cable television business pulled in over $5.62 billion in revenue for the first quarter. That was flat compared with last year, but it’s still the company’s biggest business, accounting for a fifth of all revenue.

    Peacock, on the other hand, is the fastest growing, but it loses the most money. Last year, it approached $700 million in pretax losses. This year, the streaming platform is expected to lose $1.3 billion as Comcast spends big to load it up with original shows and sports programming with the aim of attracting more viewers.

    That’s the operating thesis behind every major media company today: replace the eroding base of profit-rich cable customers with loss-making streaming viewers in the hope that over time the digital audience will become more valuable. The Walt Disney Company, ViacomCBS, Discovery Inc. and AT&T’s WarnerMedia are all trying to make the transformation without entirely losing their shirts.

    Peacock’s 42 million sign-ups should also come with an asterisk. The service is free and easy to join, but that doesn’t mean everyone is watching. (The figure includes paid versions of Peacock, which feature more content and fewer commercials.) A February report from the tech news site The Information revealed that a little more than 11 million households were watching the service.

    Even so, the aim of Peacock is to replace the lost advertising from Comcast’s cable and broadcast channels as people continue to cut the cord. Peacock, which is available nearly everywhere, can also act as a hedge against other cable operators such as Charter or Cox when Comcast’s media division, NBCUniversal, negotiates carriage fees.

    Peacock offers some of the most popular streaming shows, including “The Office,” a top hit on Netflix before it lost the rights to the series in 2021 when the license expired and the show reverted back to its owner, Comcast.

    In a few years, Peacock will have the rights to stream National Football League games on Sunday alongside NBC as part of a new agreement. That could ruffle feathers with some of NBC’s affiliate stations if viewers drop TV and opt for Peacock to watch football. The streamer will also have some games exclusively. In March, the service added WWE.

    Comcast sells something that has proved more durable than sports and entertainment: broadband, the piping that carries all streaming platforms. The company saw a surge in subscribers during the pandemic. In the first quarter, sales increased 12 percent to $5.6 billion. It’s likely to overtake cable television as the company’s biggest business.

    At NBCUniversal, sales sharply dropped as movie theaters remained mostly shut and fewer people were visiting theme parks under the pandemic. Revenue fell 9 percent to $7 billion and pretax profit decreased 12 percent to $1.5 billion. Advertising at its television networks, which include NBC, MSNBC and Syfy, fell 3.4 percent to $2.1 billion.

    Overall, the company beat expectations, reporting adjusted profit of 76 cents a share on $27.2 billion in revenue, and its stock was climbing on Thursday morning. Investors were looking for 59 cents in per-share profit and $26.6 billion in sales.

    Microsoft will decrease the share of money it charges independent developers that publish computer games on its online store, starting in August, the company said on Thursday.

    Developers will keep 88 percent of the revenue from their games, up from 70 percent. That could make Microsoft’s store more attractive to independent studios than competitors like Valve’s gaming store, called Steam, which typically starts by taking a 30 percent cut. Epic Games’ store takes 12 percent.

    “We want to make sure that we’re competitive in the market,” said Sarah Bond, a Microsoft vice president who leads the gaming ecosystem organization. “Our objective is to have a leading revenue share and really a leading platform.”

    The share of revenue that developers get to keep has come under greater scrutiny across the tech industry. Google and Apple have faced antitrust questions for the 30 percent fees they charge developers whose programs appear in their app stores.

    Last year, Epic sued Apple and Google separately, claiming they violated antitrust laws by forcing developers to use their payment systems. Epic had tried to bypass the fees by letting customers pay for items in its Fortnite video game directly through Epic. That caused Apple and Google to boot Fortnite from their app stores.

    Apple and Google have since reduced fees for some developers. Epic’s lawsuit against Apple is set to head to trial on Monday in U.S. District Court in Oakland, Calif.

    A Shell recharging station for electric vehicles in the Netherlands. Despite investments in renewable energy, Shell’s profit last quarter was largely the result of rising oil and gas prices.
    Credit…Koen Van Weel/EPA, via Shutterstock

    Strong profit increases from two of Europe’s largest energy companies, Royal Dutch Shell and Total, demonstrated that what really matters for the financial performance of these companies remains the price of oil and natural gas.

    Their recent investments in clean energy, described by company officials as essential for the future, remain marginal.

    Total said that adjusted net income rose by 69 percent compared with the period a year earlier, when the effects of the pandemic were beginning to kick in, to $3 billion, while Shell said that what it calls adjusted earnings rose by 13 percent to $3.2 billion.

    The main factor in the improved performance by both companies was a roughly 20 percent rise in oil prices along with an increase in natural gas prices, leading to higher revenues. During a news conference to discuss the results, Jessica Uhl, Shell’s chief financial officer, said that a $10 jump in oil prices would translate into a $6.4 billion increase in cash for the company’s coffers on an annual basis.

    Shell, which cut its dividend last year for the first time since World War II, confirmed that it would increase the payout for the quarter by 4 percent, to about 17 cents a share.

    Both companies have tethered their futures to generating and distributing renewable sources of energy. Shell in February said its oil production had peaked in 2019, and it has been investing in various clean energy ventures, including a network of 60,000 charging stations for electric vehicles. And Total has, among other things, invested in options to build offshore wind farms off Britain.

    In its earnings statement, Total took the lead among the oil majors in providing details on its investments in renewable energy like wind and solar. The company said these businesses brought in $148 million for the quarter, measured as earnings before interest, taxes, depreciation and amortization. This figure was about 2 percent of the overall total for the company of $7.3 billion, according to analysts at Bernstein, a research firm.

    Although Airbus reported a quarterly profit after a full-year loss for 2020,  “the market remains uncertain,”  said Guillaume Faury, the company’s chief executive.
    Credit…Chema Moya/EPA, via Shutterstock

    Airbus announced Thursday that it had returned to a profit in the first quarter following a 1.1 billion euro loss last year because of the coronavirus pandemic, but its top executive warned that the economic toll would continue.

    “The first quarter shows that the crisis is not yet over for our industry, and that the market remains uncertain,” Guillaume Faury, chief executive of the world’s largest airplane maker, said in a statement.

    Airbus booked a net profit of 362 million euros ($440 million) between January and March, compared with a loss of 481 million euros a year earlier, as cost-cutting measures — which included more than 11,000 layoffs announced last year for its global operations — bolstered the bottom line. Revenue fell 2 percent to 10.5 billion euros.

    Airbus delivered 125 commercial aircraft to airlines in the three-month period, up from 122 a year earlier. Over all, Airbus delivered 566 aircraft to airlines in 2020, 40 percent less than expected before the pandemic.

    Airbus has previously warned that the industry might not recover from the disruption caused by the pandemic until as late as 2025, as new virus variants delay a resumption of worldwide air travel.

    Given the uncertain outlook, Airbus won’t ramp up aircraft deliveries this year. The company said it expected to deliver 566 aircraft on back order from airline companies, the same number as last year.

    It maintained its forecast for an underlying operating profit of two billion euros for the year.

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    Stocks on Wall Street jumped on Thursday, rising with European stock indexes, amid indications that the economy is moving toward a recovery to prepandemic levels.

    The Commerce Department reported Thursday that the U.S. economy expanded 1.6 percent in the first three months of 2021, compared with 1.1 percent in the final quarter last year, or 6.4 percent on an annualized basis.

    A day earlier, the Federal Reserve said that the outlook was improving and that it would continue to provide substantial monetary support, easing investors’ concerns that it would soon start easing the stimulus efforts it launched a year ago when the Covid-19 crisis forced a near shutdown of many parts of the economy.

    “While the level of new cases remains concerning,” Jerome H. Powell, the Federal Reserve chair, said, “continued vaccinations should allow for a return to more normal economic conditions later this year.” The central bank kept interest rates near zero and said it would continue buying bonds at a steady clip.

    The S&P 500 rose 0.7 percent. Market sentiment continued to rise after President Biden detailed more of his spending plans — which total $4 trillion — to fund expanded access to education and reduce the cost of child care, among other things.

    Oil prices rose. Futures of West Texas Intermediate, the U.S. benchmark, climbed more than 2 percent to above $5 a barrel.

    The Stoxx Europe 600 rose 0.3 percent as a measure of economic confidence for the eurozone surged higher.

    Amazon announced raises for half a million employees in its warehouses, delivery network and other fulfillment teams.
    Credit…Chang W. Lee/The New York Times

    Amazon will increase pay between 50 cents and $3 an hour for half a million workers in its warehouses, delivery network and other fulfillment teams, the company said on Wednesday.

    The action follows scrutiny of Amazon from lawmakers and an unsuccessful unionization push that ended this month at its large warehouse in Alabama. In 2018, Amazon raised its minimum pay to $15 an hour. In recent months, it has publicly campaigned to raise the federal minimum to $15, too.

    Amazon has been on a hiring spree during the pandemic. As more customers ordered items online, the company added 400,000 employees in the United States last year. Its total work force stands at almost 1.3 million people.

    Amazon typically revaluates wages each fall, before the holiday shopping season. But this year, it moved those changes earlier, said Darcie Henry, an Amazon vice president of people experience and technology. The new wages will roll out from mid-May through early June. Ms. Henry said the company was hiring for “tens of thousands” of open positions.

    Jeff Bezos, Amazon’s founder and chief executive, recently told shareholders in his annual letter that he recognized the company needed “a better vision for how we create value for employees — a vision for their success.” He said that Amazon had always striven to be “Earth’s Most Customer-Centric Company,” and that now he wanted it to be “Earth’s Best Employer and Earth’s Safest Place to Work” as well.

    Amazon is scheduled to report quarterly earnings on Thursday.

    Gary Gensler’s tenure leading the Securities and Exchange Commission is off to a rocky start: Alex Oh, who he named just days ago to run the regulator’s enforcement division, has resigned following a federal court ruling in a case involving one of her corporate clients, ExxonMobil.

    In her resignation letter on Wednesday, Ms. Oh said the matter would be “an unwelcome distraction to the important work” of the enforcement division.

    Ms. Oh’s resignation letter followed a ruling on Monday from Judge Royce C. Lamberth of the Federal District Court for the District of Columbia over the conduct of Exxon’s lawyers during a civil case involving claims of human rights abuses in the Aceh province of Indonesia.

    According to Judge Lamberth’s ruling, Exxon’s lawyers claimed without providing evidence that the plaintiffs’ attorneys were “agitated, disrespectful and unhinged” during a deposition. He ordered Exxon’s lawyers to show why penalties were not warranted for those comments.

    The ruling did not single out any lawyers by name. Ms. Oh was one of the lead lawyers for Exxon.

    The judge’s order also granted the plaintiffs’ motion that Exxon pay “reasonable expenses” associated with litigating their request for sanctions and with an accompanying motion to compel additional testimony from Exxon related to the deposition.

    Ms. Oh’s resignation letter did not mention the Exxon case by name, but a person briefed on the matter confirmed that the ruling from Judge Lamberth had prompted her to step down.

    Ms. Oh, a former federal prosecutor in Manhattan who worked for the elite firm Paul, Weiss for nearly two decades, was picked by Mr. Gensler to oversee the S.E.C.’s 1,000-attorney enforcement division on April 22. The same day, she filed a notice with the court in the Exxon case saying she had withdrawn from the matter because she had resigned from the firm to join the federal government.

    The civil litigation involving Exxon is nearly two decades old and involves allegations by the plaintiffs that Exxon’s security personnel “inflicted grievous injuries” on them. The lawsuit was brought under the federal Alien Tort Claims Act, which enables residents of other countries to sue in the United States for damages arising from violations of U.S. treaties or “the law of nations.”

    Mr. Gensler said in a news release that Melissa Hodgman, who had been the enforcement division’s acting chief since January, will return to that position. Ms. Hodgman has been an enforcement attorney with the agency since 2008. He thanked Ms. Oh for her “willingness to serve the country.”

    Ms. Oh could not immediately be reached for comment.

    Brad Karp, chairman of Paul, Weiss, said the firm would not comment on the matter because it involved ongoing litigation. “Alex is a person of the utmost integrity and a consummate professional with a strong ethical code,” he added.

    Ms. Oh is a highly respected lawyer, but her selection had been criticized by the Revolving Door Project, a good-government group, because she had been in private practice for so many years and had defended some of the largest U.S. companies.

    Increased supply-chain and freight costs for cereal makers could translate into higher retail prices for customers.
    Credit…Sara Hylton for The New York Times

    Before the pandemic, when suppliers raised the cost of diapers, cereal and other everyday goods, retailers often absorbed the increase because stiff competition forced them to keep prices stable.

    Now, with Americans’ shopping habits having shifted rapidly — with people spending more on treadmills and office furniture and less at restaurants and movie theaters — retailers are also adjusting, Gillian Friedman reports for The New York Times.

    The Consumer Price Index, the measure of the average change in the prices paid by U.S. shoppers for consumer goods, increased 0.6 percent in March, the largest rise since August 2012, according to the Bureau of Labor Statistics. Procter & Gamble is raising prices on items like Pampers and Tampax in September. General Mills, which makes cereal brands including Cheerios, is facing increased supply-chain and freight costs that could translate into higher retail prices for customers.

    At the beginning of the pandemic, companies were focused on fulfilling demand for toilet paper, cleaning supplies, canned food and masks, said Greg Portell, a partner at Kearney, a consulting firm. The government was watching for price-gouging, and customers were wary of being taken advantage of.

    Now that the economy is beginning to stabilize, companies are starting to rebalance pricing so that it better fits their profit expectations and takes into account inflation. “This isn’t an opportunistic profit-taking by companies,” Mr. Portell said. “This is a reset of the market.”

    Gary Gensler, the chair of the Securities Exchange Commission, has some expertise with cryptocurrencies.
    Credit…Kayana Szymczak for The New York Times

    For many cryptocurrency supporters and investors, regulatory approval of a Bitcoin exchange-traded fund in the United States represents the holy grail. It would allow the crypto-curious to get exposure to Bitcoin without having to buy the tokens themselves, signifying that digital assets are really, truly mainstream.

    But it’s not meant to be — yet. On Wednesday, the Securities and Exchange Commission delayed a decision on a Bitcoin E.T.F. proposal from the investment manager VanEck, saying it needs more time but offering no other explanation.

    Delay is not denial, and it may be a good sign, Todd Cipperman, the founder of the compliance services firm CCS, told the DealBook newsletter. When considering the concept of a crypto E.T.F. in 2018, the S.E.C. raised questions about investor protection issues and put a “wet blanket on the whole idea,” he said.

    Now, crypto is much bigger, and Gary Gensler, who taught courses about blockchain technology at M.I.T., is chair of the S.E.C. His expertise doesn’t guarantee success for crypto E.T.F.s, but it will be easier for an expert in the field to approve them, Mr. Cipperman suggested.

    The S.E.C. gave itself until mid-June, with the option to take more time, but it must decide before year’s end. The regulator has rejected every proposal to date, starting with the first Bitcoin E.T.F. pitch in 2013, presented by the Winklevoss twins, which was eventually dismissed in 2017 (and again in 2018). There are several E.T.F. proposals on the table now, including one from the traditional finance giant Fidelity.

    Canada is moving faster, approving all kinds of crypto E.T.F.s, after allowing its first Bitcoin E.T.F. in February. Hester Peirce, an S.E.C. commissioner and vocal crypto champion, told DealBook earlier this month that she has been “mystified” by her agency’s response to some prior applications, which met the standards in her view. With more players now engaging in the process, approval could be looming — eventually.

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