EMERYVILLE, a tiny city of 12,000 lying on the eastern shore of the San Francisco bay, is rather cruelly known by residents of its bigger neighbours primarily as a place to buy furniture. A huge IKEA, a Swedish homeware shop, greets visitors to the city, which has no fewer than four shopping centres. But Emeryville has a better claim to fame; its many shoppers are served by some of the best-paid retail staff in the country. Since July 2015 the city’s minimum wage, for all but the smallest firms, has been $14.44 an hour, nearly double the federal minimum of $7.25 and almost 50% higher than the state minimum of $10. Emeryville is one of dozens of cities across America to have boosted its minimum wage in recent years, but it has gone further than almost any other towards the $15 campaigners seek.

That goal emerged in New York in 2012, when 200 fast-food workers went on strike demanding higher pay and a union. Those strikes were repeated, grew, and then spread nationwide (the last national strike was in April). At the same time, local politicians began to take action. After more than a decade with barely any changes to local minimum wages, they rose significantly in a handful of places in 2013. The next year 12 localities raised them, including Bay-area cities Berkeley, Oakland and San Francisco. In 2015, sixteen more, including Emeryville, followed suit.

Most areas have not gone as far as Emeryville, but many promise to do so eventually. On June 21st, the city council in Washington, DC, the latest city to follow the trend, voted unanimously to raise the minimum wage to $15 by 2020. Only California and New York have taken comparable action at the state level. But, thanks mainly to local laws, almost 17m workers have benefited from higher minimum wages since the “fight for $15” began, according to the National Employment Law Project. At least 10m of those will eventually receive $15 an hour.

Campaigners claim that higher local minimum wages are necessary to alleviate poverty, particularly as minimum wages are often not adjusted for years at the state and federal levels. Prices are already 10% higher than in 2009, the last time lawmakers upped the federal rate. This argument carries particularly weight in Emeryville, where a one-bedroom flat commands rent greater than $2,000 per month, owing to an influx of rich techies into the area. Dianne Martinez, the city’s mayor, says $14.44 was picked based on an estimate of what it now costs to live in her city.

These justified concerns about poverty are often mixed up with anger about stagnant median incomes or inequality. Here, the thinking is sloppier. Minimum wages exert little pressure on middle-America’s earnings; neither do they restrain the pay of bankers or CEOs. Until recently it looked like low minimum wages did cause middle-earners to pull further away from very low-earners during the 1980s. But a recent study by economists David Autor, Alan Manning and Christopher Smith suggests that minimum wages explain only 30-40% of this trend.

Minimum-wages, then, are best viewed as one route to helping the lowest earners. Since nobody thinks that low pay is desirable, the argument against minimum-wages is that they destroy jobs. Campaigners deny this, with some justification. A canonical study in 1993 found that employment in New Jersey restaurants increased, rather than fell, in response to a minimum wage rise. More recent research, from 2010, examined all county-pairs that straddle a state border and found that, for the period from 1990 to 2006, differences in minimum wages had no effect on employment in low-wage sectors.

Other economists dispute these findings. But some jobs clearly can survive higher minimum wages. In 2015 more than half of workers earning at or below the federal minimum wage worked in restaurants, bars and the like. Such service jobs cannot be moved overseas, and many, such as cleaning the floor of a McDonalds, are hard to automate. These jobs will survive if firms can tolerate lower profits or raise their prices sufficiently. Soaring demand for services in fast-growing, high-income areas like New York and San Francisco typically enables them to do so. Seattle began raising its minimum wage in April 2015, initially from the state minimum, $9.32, to $11 for large firms. Yet the proportion of jobs in the Seattle area in the food service and preparation industry has grown from 7.2% in April 2015 to 7.4% today.

But in other industries, raising prices is harder. Match Analysis, an Emeryville business with around 35 local staff, collects data on soccer matches, which it sells globally alongside analytical software. The firm’s competitors hire exclusively in countries with lower wages, such as India and Russia, says Mark Brunkhart, who founded the business in 2000. That means it cannot raise prices; instead, the higher minimum wage has forced the firm to shed 13 data-collection jobs. This has mainly been achieved with a hiring freeze, but this month Mr Brunkhart had to lay-off six staff. These were the first redundancies in the firm’s history.

Some retail workers, who make up 13% of workers whose pay is at or below the federal minimum wage, are also under threat because of automation. Big shops are unlikely to speak out against minimum-wage changes because of the bad press it generates. But they are not immune to incentives. Target, one of the retail behemoths in Emeryville, has in the past month installed self-service checkouts, perhaps because of higher labour costs.

Caution is warranted because economists’ experience with minimum wages is limited to where they have been set modestly, relative to incomes. The average minimum-wage to median-income ratio in the OECD, a club of mostly-rich countries, is 50%. The highest, 68%, is in Turkey. Median hourly wages vary hugely by state, from less than $14 in Mississippi to over $22 in Alaska. That means even Hillary Clinton’s proposed $12 federal minimum-wage exceeds 75% of the median hourly wage in fully 16 states—well beyond the rates that have been well-studied.

Decentralised minimum-wage setting might therefore be desirable. But 19 states ban cities from raising minimum wages on their own; in February this stopped Birmingham, Alabama, from raising its rate to $10.10. In Emeryville, the minimum-wage to median-income ratio is around 85%, according to our calculations (see chart). Ms Martinez promises an economic impact study, but says “there are times where you have to take a leap of faith”.