Why is inflation a problem? I ask because the common sense answer is wrong, whilst a standard answer among economists is out-of-date.

You might think the answer is obvious: inflation is making us poorer. Not so. Of course, wages haven't kept pace with prices, especially of food and fuel. But this, strictly speaking, isn't inflation. It is a change in relative prices. If utility bills were rising 17 percentage points faster than wages and food prices 12 percentage points we'd have a problem even if other components of the CPI were falling so that overall inflation were low.

Nor are higher mortgage rates a cost of inflation. They are a cost of bringing inflation down. And this is a policy decision in two senses: first to want to cut inflation; and secondly to do so through higher interest rates rather than through other means such as higher taxes or price controls.

We define inflation as a rise in the general price level, in which prices and wages rise at the same rates. What's so wrong with that?

For years, the standard view among economists was: not much, unless the inflation is unexpected. As Milton Friedman wrote (pdf):

Anticipated inflations or deflations produce no transfers from debtors to creditors which raise questions of equity; the interest rate on claims valued in nominal terms adjusts to allow for the anticipated rate of inflation. Anticipated inflations or deflations need involve no frictions in adjusting to changing prices. Every individual can take the anticipated change in the price level into account in setting prices for future trades. Finally, anticipated inflations or deflations involve no trade-offs between inflation and employment.

And in 1995 Robert Barro found that it was only high inflation - above 15% - that had a statistically significant impact in reducing economic growth.

Why, then, worry about inflation?

One answer is that it can raise taxes. If our wages rise by, say, 10% at a time when prices are rising 10% we are no better off. But that 10% rise will make us pay more tax, and push many of us into a higher tax bracket. Which is happening now. HMRC says that the number of people paying the higher rate of income tax rose by over 40% from 2020-21 to 2023-24.

I don't think this is a cost of inflation, though. It is a cost of the government's conscious decision not to index tax allowances to the rate of inflation - something which, thanks to the Rooker-Wise amendment of 1977, used to be the case.

Instead, Friedman's beef with anticipated inflation was different. Higher inflation and higher interest rates, he said, caused us to economize on holding cash; because it pays no interest it is more expensive the higher are interest rates. That in turn means that, rather than carry lots of cash on the hip, we have to make more trips to the bank which means we waste more time walking there and standing in queues. Economists called these "shoe-leather costs". In the late 90s, Bank of England economists estimated these to be significant - equivalent to £60bn at the time, which is almost £120bn in today's money.

But obviously, this is out-of-date. Many of us rarely use cash today; the quantity of notes and coins in circulation has fallen in the last two years, and many of these I suspect are sitting in vaults and jars rather than changing hands rapidly.

If shoe-leather costs are no longer so significant, then, what is wrong with inflation?

Maybe not much. Good judges have for years advocated raising (pdf) the inflation target, on the grounds that the benefits of low inflation are small and outweighed by a cost - of the risk of low inflation becoming a deflation which drags us towards the zero bound wherein monetary loses its efficacy.
I suspect, though, that there are reasons why inflation is a bad thing.

For one thing, it creates uncertainty; this is perhaps one reason why the inflations of the 70s and late 80s were accompanied by rises in the households' saving ratio.

The uncertainty here isn't just our reaction of "how much?!" when being charged £13 for a pint of beer and glass of wine at the Hornblower. It's deeper than that. Inflation enriches some at the expense of others. And it does so not on the basis of contribution to society but upon factors such as: how real interest rates move; whether one has a nominal fixed income (such as an annuity or contract to deliver goods at a given price); or - of course - one's bargaining power. As Maynard Keynes wrote (pdf):

The sight of this arbitrary rearrangement of riches strikes not only at security, but at confidence in the existing distribution of wealth... and the process of wealth-getting degenerates into a gamble and a lottery. Lenin was certainly right. There is no subtler, no surer means of overturning the existing basis of society than to debauch the currency.

Right now, this "arbitrary rearrangement" is benefiting higher earners and larger capitalists who can exercise their greater bargaining power.

You might think this is welcome from a capitalist point of view.

Not necessarily. Capitalism requires not just favourable conditions for profit-making but also legitimacy. And inflation undermines this by reminding us that the notion that incomes depend upon marginal product is an ideologized fiction. Although discontent for now is manifesting itself only in lukewarm support for an unimaginative Labour party from mortgage-saddled former Tories, there's no assurance people will remain so passive if inflation persists. The inflation of the 70s, remember, fuelled sincere talk of a "crisis of democracy", and earlier hyperinflations in Europe had nastier effects.

From the point of view of rentiers and some larger capitalists (if nobody else!) British capitalism was working well in the low inflation era. Why risk rocking the boat?