I’m due a haircut and in the past week received a message from my barber containing the news that the price will be 10% higher than the last time I went for a trim.

If I call in for a coffee on my way to work it will be a similar story. After recent price rises, I can expect to pay the thick end of £4 for a flat white.

These are two examples of what Rachel Reeves calls the everyday economy in action, and they tell us something about the challenge facing the chancellor as she seeks to improve the UK’s poor economic performance.

It’s not hard to see why a haircut and a cup of coffee are going up in price. Rents are higher, insurance is more expensive and so are fuel and labour.

Businesses have a choice: they can either absorb these extra costs themselves or they can try to pass them on to their customers. Many are doing the latter, which is why inflation in the services sector is running at 5.7% while overall inflation is at 2%.

This matters. These days, the UK is primarily a service-sector economy. Manufacturing and construction are still important, but services account for about 80% of national output. Prices have risen by about 20% in the past three years and labour shortages have made it harder for employers to resist pressure for higher pay to compensate. Much of the service sector is labour-intensive and, unsurprisingly, workers don’t want to see their living standards eroded.

The very nature of the service sector makes productivity improvements hard to chisel out. My haircut takes as long as it did a year ago; the flat white comes in the same-sized cup and tastes the same. As a customer, I am getting the same service but paying more for it. As a nation, output per worker is up by 1.5% in the four years since the start of the Covid-19 pandemic; in the public sector – where Reeves is contemplating above-inflation pay awards this year – productivity is 6% lower.

Productivity is easy to measure in a car factory but harder to assess in the NHS. If a GP spends five minutes more per patient but by doing so saves lives does that count as productivity loss, because of the extra time spent, or (as it should) a productivity gain?

Similarly, a restaurant meal might take as long to produce as it did a year ago but be of a higher quality. If this means the customers have a better time than they did before then that’s a productivity improvement in any meaningful sense of the term. But time-wise, it’s no better.

Nor is it impossible to think of ways in which technology has helped to boost service-sector productivity. Checking a fact or referring to a previously written article meant a visit to the cuttings’ library when I started as a journalist many moons ago. Now search engines make the process quicker and simpler.

Even so, the fact that the UK is a labour-intensive service-sector economy has made the Bank of England warier about cutting interest rates than it might otherwise have been. A blog on Threadneedle Street’s Bank Underground site by a staff member, Tomas Key, found that trend (underlying) wage growth is currently 6%, double its pre-pandemic level.

This raises two questions. The first is whether higher wage growth is merely a response to higher inflation and will come down now that prices are rising less quickly. That appears to be the case. The annual growth in average earnings was 5.1% in the year to May compared with 8.2% in the same month of 2023.

The second is whether the Bank can do much to bring down wage growth, short of keeping interest rates at a punitive enough level to cause economic distress. The answer is no, not really. Higher interest rates are a crude tool that work by making businesses too nervous to risk raising prices and by forcing workers to accept below-inflation pay increases through the fear of losing their jobs.

So far, the evidence is that the economy has withstood a year of interest rates at 5.25% much better than might have been expected. There was a short, shallow, technical recession in the second half of 2023 but activity is now gently recovering. It would be doing so more quickly were it not for the 14 increases in official borrowing costs between December 2021 and August 2023.

All that said, the answer to Britain’s productivity weakness does not lie with the Bank of England. Instead, it will depend on changes to the supply side of the economy. Reeves will chair the first meeting of the Treasury’s new growth mission board on Tuesday.

Higher levels of private and public investment would help boost productivity and growth. If manufacturing represented a bigger share of national output that would help too because there is more scope for labour-saving efficiencies in a factory than in a care home. Productivity growth would be faster were Britain’s industrial base bigger.

AI has the potential to be an a gamechanger, because it will have an impact on all sectors of the economy and not just manufacturing. Indeed, there is already evidence of that happening. Labour is unsure how to regulate AI but if it wants faster productivity growth then AI is going to be an important part of the mix.

Even then, though, it is important to be realistic. Britain is going to remain predominantly a service-sector economy and there are services that do not readily lend themselves to productivity gains. A robot cutting my hair? I don’t think so.