The Conservatives are finally backing down on the public sector pay cap – but not without a fight, and not without confusing the maths. I’m guessing the government thought our fear of numbers wouldn’t allow us to work out that inflation of 2.9% means their announcement of 1.7% and 2% respectively for prison staff and police wasn’t really a pay rise. Luckily, we’re not quite that bad at maths. Unfortunately, the Conservatives are still persuading many with the dodgy maths of their public spending cuts.

Again and again we hear from ministers that the pay cap can’t be lifted as the country cannot afford to pay public sector workers more. Years of being miseducated on how the economy works – presenting the country’s debt as household debt and public spending as only a cost with no benefits for the economy – have led to widespread economic illiteracy, among politicians as well as the population. The real question should be: can we afford not to increase public sector pay? The costs of maintaining the pay cap are numerous, and the benefits of increasing public sector pay would be huge for the economy.

Hammond eases public sector pay cap, but the squeeze goes on Read more

Let’s start with costs of recruitment and retention. This is a big one. Job advertising isn’t cheap and new recruits take time to settle in. Last year, a study found there had been a 61% rise in advertising spend since 2010 in secondary schools alone, costing £56m in 2015. Shortages in the health service mean NHS Trusts are paying millions every month to agency and bank nurses to ensure there are adequate levels of staff on wards.

Stress-related leave has also increased in the public sector as workers are understandably getting run down working in understaffed schools and hospital wards. This is just staff – what about the costs to our children of being in classes too big for them to maximise their learning or to a sick individual who has an operation delayed?

There are also secondary costs of underinvestment in one part of a co-dependent system. An Age UK study estimated the NHS lost 2.4m bed days, costing it £669m over five years, as shortages of social care support means frail patients cannot be discharged. Once you start putting financial costs on all these outcomes, you quickly get into the billions.

Putting the direct costs of the pay cap to public services aside, there is also the so-called multiplier effect to consider. This means when you give someone a pay rise, there are larger positive implications for the economy because it can stimulate further rounds of spending. For example, if there is a £2bn increase in wages for NHS workers and they spend just half of this in shops, then shopkeepers will also receive income.

In turn, this increase in income will mean shopkeepers are more likely to employ more people and increase salaries themselves. The treasury would then not just receive more taxes from higher wages among NHS staff, but also the VAT on extra goods sold, and on higher income taxes from jobs created elsewhere.

The multiplier effect is thought to be higher for those on low-middle incomes, as they are much more likely to spend it than save it or put it in a tax haven. According to a Unison study based on International Monetary Fund figures, every 1% increase in public sector pay would generate between £710m and £820m for the government in increased income tax. Of course, there are debates about just how big these multiplier effects are – but we must stop thinking about a pay rise as purely negative for the public purse. We all know that our public service workers are worth every penny – but these pennies go well beyond their pay packets.

Public investment pays huge dividends over the longer term. For example, investing in universal childcare, paid parental leave and targeted interventions could save the UK £1.5tn in the long term by addressing the underlying causes of crime, mental health problems and drug abuse. Right now, we are barely paying for the upkeep of our public services, let alone getting them match-ready for Brexit, an ageing society, technological developments and our changing climate. It is this lack of investment now that will saddle future generations with huge costs – not the prospect of a larger national debt at a time of record low borrowing rates.

Trade unions are calling for a 5% pay rise across the public sector (3.9% in the NHS) to start to claw back some of the lost income public sector workers have experienced since rogue bankers crashed the economy. This would cost around £9bn. It seems like a lot of money, but any equation of public sector pay must be considered against the cost of no investment and the value lost to society as a result. The Treasury would do well to recalculate the supposed “costs” of ending the pay cap.

• Faiza Shaheen is director of the Centre for Labour and Social Studies