The number of job vacancies has topped the 1m level for the first time. Firms are screaming out for staff. Labour shortages abound. Wage growth is accelerating. There are calls from industry lobby groups for the government to ease the pressure by granting more visas for EU workers.

At which point it may be worth taking a second or two to ask a simple question: if labour shortages are driving up the wages of low-paid workers then what is wrong with that?

There may well have been worse decades than the 2010s to be a wage earner but you would have to go back to the 19th century to find one comparable. It took 12 years for average earnings to exceed the level reached before the 2008 financial crisis – a dismal trend that led to entirely appropriate criticism not just of the UK’s economic model but of rising inequality.

If that way of doing things – in which the flipside of over-reliance on unskilled, cheap labour has been persistent underinvestment – is now coming apart then that is a welcome development and not a bad thing. There is something seriously wrong about an economy where more than half the people living below the official poverty line are from working households and where a large chunk of the welfare bill is spent supplementing the incomes of those who do not earn enough to get by.

Employers have only a limited range of options if they find themselves short of staff and it is not possible to call up reinforcements from overseas. They can invest more in labour-saving equipment; they can invest more in training to raise skill levels; or they can pay more in order to attract staff. It is not immediately obvious why any of these should be either impossible or undesirable.

Naturally, companies cannot solve immediate labour shortage issues by ramping up training or buying new kit. Both take time to organise and to have any real impact. That only really leaves the option of paying higher wages, which explains why Tesco is offering a £1,000 sign-on bonus for new lorry drivers.

Employers have expressed doubts whether higher pay will solve labour shortages either, although the basic laws of economics suggest that it will if the incentives are big enough. As things stand, it is the only real card companies have in their hands to play, because they are unlikely to get much joy out of the government with calls for a relaxation of migration rules.

There are a few reasons for this. The first is that there is no guarantee that easing controls would work. As Samuel Tombs, of the economics consultancy Pantheon Macro, points out, there are EU nationals who returned home during the pandemic last year who could come back to Britain if they chose to do so. “Legally, most of these people can return if they wish. Indeed, applications for pre-settled and settled status have exceeded the official number of EU nationals in Britain at the end of 2019,” he says. “Nonetheless, current labour shortages in sectors reliant on migrant labour indicate that enthusiasm to return is low.” That, of course, could change if EU nationals thought it was safe to come back and if the jobs on offer were well enough remunerated.

The second reason is that the government would rather not cope with labour shortages through migration. As the ministers responsible for the economy, it may be thought that the chancellor, Rishi Sunak, and the business secretary, Kwasi Kwarteng, would be in favour of plugging gaps in the workforce in this way, but that is not the case. Both think there are UK citizens who can be trained to fill the large number of vacancies.

The third reason is political, with the government seeking to entrench its support among low-paid, traditional Labour supporters, who backed Brexit and voted for the Conservatives at the 2019 election. Ministers sense that this section of the workforce is quite happy with a state of affairs where, for the first time in years, there is the possibility of screwing a decent wage rise out of their employer.

There has been much academic work done into the impact of migration on wages in the UK. The evidence is that where workers from overseas complement home-grown workers, they boost earnings. This tends to benefit those at the top end of the income scale.

It is a different story at the other end of the labour market, because wages are held down when migrant workers compete with domestic workers. The competition tends to be greatest in low-paid jobs, such as hospitality and social care.

That is not quite the end of the story, because increasing the supply of overseas workers also boosts demand. The new employees are also consumers and spend the money they earn like everybody else. The extra demand creates more jobs, although mainly in low-paid sectors.

Against this backdrop, it is perhaps unsurprising that Brexit divided the nation in the way it did. If you were in a relatively well-paid job and not at risk of being replaced or undercut by a worker from overseas, you were likely to vote remain. The Polish plumber was cheaper, the Lithuanian nanny was better educated, so what was not to like?

If, on the other hand, you were part of Britain’s casualised workforce, needing two or more part-time jobs to get by, you were much more likely to vote leave, on the grounds that tougher controls on migration would lead to a tighter labour market, which in turn would push up wages.

For those who have nothing to fear from open borders, labour shortages are evidence Brexit is flawed. For those not so fortunate, it is doing what it was supposed to do.