from the $1.9 trillion federal stimulus package: $5.95 billion in direct aid and another $4 billion for schools, a City Hall spokeswoman said.

While that addresses immediate needs, the city still faces an estimated $5 billion budget deficit next year and similar deficits in the following years, and a changing work culture could hobble New York’s recovery.

The amount of office space in Manhattan on the market has risen in recent months to 101 million square feet, roughly 37 percent higher than a year ago and more than all the combined downtown office space in Los Angeles, Atlanta and Dallas. “This trend has shown little signs of slowing down,” said Victor Rodriguez, director of analytics at CoStar, a real estate company.

At least one industry, however, is charging in the opposite direction. Led by some of the world’s largest companies, the technology sector has expanded its footprint in New York during the pandemic. Facebook has added 1 million square feet of Manhattan office space, and Apple added two floors in a Midtown Manhattan building.

And the surge in available commercial real estate has actually been a boon for some new businesses that have been able to find spaces at rents that are lower than they were before the pandemic.

“I’ve seen the obituary for New York City many times,” said Brian S. Waterman, the executive vice chairman of Newmark, a commercial real estate services firm. “The office reboarding will start to occur in May, June and July, and you are going to have a much fuller occupancy once we hit September.”

rally behind an idea that seemed unthinkable before the pandemic: converting distressed office buildings in Manhattan into low-income housing.

The record vacancy rate has been driven by companies across almost all industries, from media to fashion, that have discovered the advantages of remote work.

Beside the cost savings of operating a scaled-down office or no office at all, modern technology and communications have allowed workers to stay connected, collaborate from afar and be more productive without lengthy commutes. Parents are also clamoring for more flexibility to care for their children.

“We believe that we’re on top of the next change, which is the Distributed Age, where people can be more valuable in how they work, which doesn’t really matter where you spend your time,” said Alexander Westerdahl, the vice president of human resources at Spotify, the Stockholm-based streaming music giant that has 6,500 employees worldwide.

For now, Spotify does not plan to reduce its New York footprint, but as of February, the company told its United States employees — 2,100 of whom had worked at the Manhattan office — that they could work from pretty much anywhere.

“The change is mainly driven by globalization and digitalization, and our tools are much, much better at allowing for people to work from anywhere,” Mr. Westerdahl said.

Remote work, of course, is not without significant downsides.

The blurry lines that already existed between work and personal life have been all but obliterated during the pandemic. Without the time spent commuting in the morning and at night, people are logging on to work earlier in the day and staying connected later into the night.

And despite modern technology and video conferencing capabilities, companies are struggling to foster workplace cultures and make employees, especially new hires, feel welcome and part of a team.

Those concerns have weighed heavily on executives at Kelley Drye, a law firm founded in 1836 in New York, which is moving from Park Avenue near Grand Central Terminal to 3 World Trade Center in Lower Manhattan.

“Zoom and Teams are great,” said Andrea L. Calvaruso, a lawyer who is the chair of the firm’s trademark and copyright group, but she added that “there’s no substitute for sitting down in a beautiful new collaborative and working together without distractions.”

But Ms. Patellos, despite being unprepared after being stuck in California — she had to buy a keyboard and monitor — soon found herself connecting with colleagues all over the world just as she had in her New York office.

“I fell into a rhythm,” said Ms. Patellos, who is still deciding where to eventually move. “I maintained a bit of East Coast hours, starting my days a little earlier and ending a bit earlier. Before I knew it, it became the norm and a routine.”

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Google reduces some app-store fees amid criticism.

Google is cutting in half its commission on developers’ first $1 million in app sales, following a similar move by Apple that is aimed at appeasing developers and regulators who accuse the companies of abusing their dominance of the smartphone industry.

Google said that starting July 1, it would take 15 percent of the first $1 million developers take in from certain app sales, down from 30 percent. Google will still charge 30 percent after the first $1 million.

Apple last year said it was halving its app-store commission to 15 percent on companies that earn less than $1 million a year in app sales.

The dual actions reverse years of resistance by the companies to change their app-store commissions, which have become important to their growth.

Rivals have intensified their criticism of the rates, saying they are artificially high because the companies have a duopoly on the distribution of mobile apps. Regulators around the world have begun investigating the commissions as part of larger antitrust probes, and lawmakers in several states are considering bills that would make it more difficult for Apple and Google to impose the fees.

Apple has been largely the focus of the criticism because it forces developers to use its app store to reach iPhone users. Google’s Android software allows users to download apps outside of its flagship app store, called the Play Store. Still, Android is the dominant smartphone operating system around the world, underpinning roughly 85 percent of the world’s smartphones, according to IDC, a market research firm.

Google said its change would halve the app-store fees for 99 percent of Android developers. But while Apple’s and Google’s moves have earned them positive headlines, they will likely have little impact on the companies’ bottom lines, because most of their app-store revenues come from larger developers.

Apple’s new policy, for instance, will affect roughly 98 percent of the companies that pay Apple a commission, but those developers accounted for less than 5 percent of App Store revenues last year, according to estimates from Sensor Tower, an app analytics firm.

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A Push to End Germany’s Status as ‘Paradise for Patent Trolls’

BERLIN—Germany has long been a magnet for global patent litigation, ensnaring companies like Apple Inc., Samsung Electronics Co. and Alphabet Inc.’s Google.

Now a coalition of German blue-chip firms and foreign multinationals, including big U.S. tech firms, is pushing legislation that would lessen the country’s appeal for those seeking to assert their intellectual property.

Germany’s main patent courts, in Munich, Mannheim and Düsseldorf, systematically order injunctions, or temporary sales bans, for products subject to patent suits. That makes them attractive legal venues for patent holders.

Key targets of the legislation are so-called nonpracticing entities, or NPEs, which amass portfolios of patents that they license instead of using them in their own products. Critics call them patent trolls.

The proposed rules aim to make it harder for a plaintiff to win an injunction. The initiative has split Germany’s typically unified business community, pitting some of the country’s biggest patent users against its biggest patent holders.

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Companies That Rode Pandemic Boom Get a Reality Check

Will the online shopping and entertainment habits forged in confinement continue to accelerate the trends toward e-commerce and video streaming?

No one knows for sure, but the view of Bay Area technologists and investors, not surprisingly, leans toward a long-term Covid bump for tech companies.

Rich Wong, a general partner at Accel, a Silicon Valley venture capital firm, sees “a truly credible case” that the growth of “these digital transformations have actually increased by a major step and, with that, the size of the opportunity in technology and venture investing.”

Stock market gyrations can shelve plans by start-ups to sell shares to the public. But the gaming site Roblox, which is popular among children and tweens and has thrived in the stay-at-home economy, made its stock-market debut on Wednesday. After its first day of trading, Roblox was valued at $45 billion, up from $4 billion just over a year ago.

At the end of last week Coursera, the digital learning network, filed the documents necessary to go public in the coming weeks. The company and its venture backers are convinced that adult education and skills training will increasingly be online, and that investors will agree. In its filing, Coursera reported that its revenue jumped 59 percent last year, to $294 million.

So far, there is little evidence of a retreat from online life in general.

SimilarWeb, an online data provider, compared traffic at the top 100 websites in the United States during last March and April, when web use spiked at the start of the pandemic, with the first two months of this year. Total traffic was up more than 12 percent this year. No “peak web” yet.

Mr. Readerman, portfolio manager for Endurance Capital Partners, has been a technology company analyst and investor for 30 years. He is mainly a longer-term investor in companies he views as tech innovators with strong managements.

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