For years I have been telling a story about car washes. Why is it that in some countries you are more likely to drive your car through the roller brushes of a giant machine, while in others a group of (often immigrant) men will descend on your car with washcloths?

My answer is that when wages are high, employers economise on labour, investing in machinery, digitisation or other steps to get more out of every hour worked. In turn, that allows them to pay those higher wages. In economies where labour is cheap, businesses find it profitable to forgo capital investment and employ enough low-productivity workers to do what machines could otherwise have done.

The car wash analogy explains Scandinavia’s combination of high productivity and relative egalitarianism. Rather than a paradox, the high productivity is because wages are high.

Since the British Conservative party conference last week, fans of my car-wash parable have asked me what I think of Prime Minister Boris Johnson’s new economic message. His government is telling business to stop complaining about worker shortages — such as that of HGV drivers — because ending low-wage immigration will shift the country to a high-wage high-productivity economy. Unusually, Johnson’s deeds are (for now) as good as his words; he has largely resisted calls for substantial emergency visa schemes.

So, is the government doing what I have been recommending all along? I am not convinced.

Lip service to a high-wage, high-productivity economy is not a true strategy for getting there. A real plan would signal that wage levels will be permanently higher and that businesses must adapt or die. If Conservatives are serious about this, they should steal a march on Labour by committing to an early target of a £15 minimum wage. (That would also monumentally troll the Labour left, which last month picked and lost a fight with party leader Sir Keir Starmer over just this.)

The government would also show it understands the most likely way high wages drive productivity. That is not because every business finds previously unexploited sources of productivity, but because those that don’t (typically smaller, less professionalised ones) lose out to those that do (larger, more efficient groups). If this government is steeling itself for a wave of small business bankruptcies, it is not telling us.

Nor is there ambition to spend much more on education or sustain aggregate demand so more productive businesses have the long-term confidence to expand. These have been essential to make the strategy of productivity from high wages work in Scandinavia. In sum, it is not at all clear the British government really desires to take the economy down the path to the promised land.

There is a strain of Conservative party thinking that does. Forcing productivity increases by raising minimum wages was the secret Scandinavian ingredient of George Osborne’s 2015 Budget. But this is not the 2015 Tory party. For the current lot, the “strategy” smacks of political opportunism, though I would love to be proved wrong.

Even if the government really did want to force higher wages on business, the end of EU free movement of labour, and Brexit generally, would be the worst ways to achieve this. Any potential pay-induced productivity gains can be cancelled out by other frictions that leaving the EU creates — such as more red tape for cross-border trade. Global Britain must run just to stand still.

Brexit-induced labour shortages may also not even lead to higher wages. The economic evidence is unambiguous that immigration for work exerted at most only a small downward pressure on wages. So ending it should not be expected to push them up.

Britain’s low-wage economy is arguably entirely homegrown, a result of domestic policies such as poor labour law enforcement and a big informal economy. After all, some countries avoided a low-wage economy even with free movement. Norway welcomed many more Europeans after eastern Europe joined the EU in 2004 than the UK, and has extended collectively bargained wage floors to exposed sectors, effectively creating sectoral legal minimum pay — including for HGV drivers.

In contrast, UK employers’ ability to pay little caused low-productivity sectors to expand — with immigrant labour. With those workers gone, the consequence may be not generalised high wages and high productivity, but that more dispensable sectors — fruit and vegetable exports, hospitality and tourism — simply shrink to give up labour to more essential ones, such as trucking. What happens to car washes is anyone’s guess.

martin.sandbu@ft.com