Like so many proprietors across this host city, restaurateur Albert Siu could almost hear the cha-ching of Olympic gold. But almost a week into the Games of the XXX Olympiad , he stood amid empty tables at his eatery in the normally bustling West End theater district this week and asked the same question being posed by so many Londoners: Where have all the tourists gone?

Britain gambled $15 billion on hosting the Olympics, an investment being watched closely across crisis-battered Europe, where the debate over stimulus vs. austerity has reached a fevered pitch. But early evidence is suggesting just how hard it can be for modern host cities to cash in on the Games.

The 2000 Summer Games brought an influx of international tourists who packed hotels across Sydney. But, like Athens and Beijing, which saw net declines in summer visitors in 2004 and 2008, respectively, the London Games have turned into a tale of two economies.

“We employed more staff because we were told millions of people were coming to London,” said Siu, 54, the manager of the Melanie Italian Restaurant, around the corner from the Palace Theater, which is staging the musical “Singin’ in the Rain.” “Now we’ve realized it’s not getting busy, and we’ll have to give them notice.”

On one hand, a thriving events-related market is chugging along near stadium sites in East London, Wimbledon and Greenwich, where businesses with captive audiences of ticket holders are reporting bang-up sales. But with non-Olympic visitors apparently scared away from one of the world’s largest tourist destinations by the talk of crowds and chaos — and with large numbers of Londoners opting to go on vacation or work from home during the Games — other parts of this typically thriving city of 8.1 million people have suddenly turned into ghost towns.

Traffic on roads in Central London is down 20 percent. London tour operators are reporting drops of 30 percent or more. At some of London’s hottest museums, the normally long entrance lines have disappeared. London’s famous Black Cab drivers are griping about a rare shortage of fares.

Luxury hotels tapped by Olympic organizers to provide rooms for the Games, as well as many of those near event sites, appear to be doing quite well. But some other one-to-four-star London hotels, many of which had tried to jack up prices by 50 to 80 percent, are half-empty. The West End show “Sweeney Todd” is taking a partial hiatus during the Olympics. Excess seats to hits such as “Singin’ in the Rain,” for which tickets can run upward of $130, were being offered by online discounters this week for as little as $23 ($39.50 with dinner).

Things were eerily quiet this week at the Victoria and Albert Museum, home to the world’s largest collection of decorative arts and usually packed this time of year. During the Olympics, the museum even pushed closing time back from 5:45 p.m. to 10 p.m. to accommodate crowds. But evenings have been surprisingly slow — so slow that on Monday after 8 p.m., only two people attended a fashionable exhibit on British glamour.

Echoing Londoners who are scratching their heads over the early forecasts of Olympic mobs, Sophie-Anne Caie, a 24-year-old gallery assistant at the museum, said, “London seems deserted.”

The tourists who do come are likely to spend less on attractions outside the Olympics venues. During the 1984 Summer Games in Los Angeles, for instance, theme parks saw a decline in revenue.

This year, little salvation

Olympic supporters contend that economic activity during the Games accounts for a relatively small part of the financial jolt for host cities. Olympic-related building, including the new 500-acre Olympic Park in a reclaimed urban wasteland of East London, helped buoy Britain’s construction sector during and after the world economic crisis of 2008. A massive new mall built near the Olympic Park also opened late last year, bringing 10,000 jobs and boutiques such as Prada and Omega to a corner of the city better known for tough housing complexes and youth unemployment. And a rash of luxury condominium towers are going up in the area.

But with the British economy mired in recession, including a deeper-than-expected plunge of 0.7 percent in the second quarter, many businesses were looking to the London Olympics for economic salvation this year.

Some may get it. Howard Archer, chief European economist for IHS Global Insight in London, projected that, overall, Britain would see a 0.3 percent gain in gross domestic product from Olympic-related economic activity. But he cautioned of a “downside risk” to that estimate, in part because of the “displacement” effect of the London Games, which are bringing some tourists in but keeping others away.

Parts of Olympic London, however, are indeed mobbed. London transit officials said tube ridership was up 30 percent over the weekend, with weekday traffic up by about 5 percent, largely due to “Olympic-related travel.” But those figures are well below the doomsday scenarios of more than 1 million additional passengers a day on the London Underground system.

Hard to quantify

To some extent, Britons appear to be opening their wallets for the Games, too. In the weeks ahead of the Olympics, TV sales increased nationwide, although economists say that could just as easily be because of the recent elimination of analog broadcasts in Britain that forced those with old rabbit ears to go digital. Locals and tourists alike are also gobbling up Olympic memorabilia at pop-up stores from Hyde Park to East London.

At the gleaming new mall in Stratford next to the Olympic Park, sales were booming at restaurants and on any item that seemed remotely British but were sluggish on big-ticket consumer electronics and jewelry. Amy Myles, 28, a customer service manager at the Twinings tea shop in the middle of the mall, said that sales had doubled since the Olympics began and that the shop brought on five temporary workers to cope. It was, in effect, selling tea to China, with many of the biggest customers being free-spending Chinese tourists in town for the Games.

But so much of the economic impact from the Olympics is hard to quantify. Amid the gilded halls of Lancaster House, a British Foreign Office-owned mansion in Central London, the government was trotting out the likes of “Harry Potter’s” Ronald Weasley (Rupert Grint) and “Downton Abbey” creator Julian Fellowes for visiting foreign entrepreneurs in an effort to drum up investment during the Games. Among their claimed successes this week: Neoglory, China’s largest jewelry and accessories company, plans to open a branch in London, and Japanese gamemaker Sega aims to launch a development facility in Britain.

Officials conceded that many of the deals being announced were underway before the start of the Games, and they were hard-pressed to name any fresh pacts made as a result of the Olympics.

But British Olympic officials say the real gold being struck in London is a juggernaut of global publicity.

A record 40.7 million Americans, for instance, tuned in to the stunning if quixotic Opening Ceremonies on Friday night, with the city hoping the positive exposure will lure millions more to travel here.

“Long term, given the images of London that are being sent around the world from the opening ceremony, the torch relay and these events, it will be a huge economic boost to the capital,” said Paul Deighton, chief executive of London’s Olympic organizing committee.

Karla Adam contributed to this report.