The electricity bill has been on the kitchen table since the morning post. It is a small flat in Ohio, over a laundromat, and the man who lives there works nights in a warehouse. He will open the envelope after supper.

He has learned to do it that way round.

This year he got a rise. It was 3.1%, which is about what the average American worker got. Prices in general went up 3.4%. The electricity went up 16.3%.

He has no solar panels, no landlord who would let him fit any, and no way of working from home. He cannot buy less electricity. He can only buy less of something else, or put less away.

The way out that nobody has to vote for

Somewhere far above that kitchen table there is a much larger bill.

The United States federal government owes 122.6% of a year's national output. Before the pandemic it was 105.8%. The euro area owes 88.9%, against 83.3% then.

Which is why inflation keeps coming up as the way out. The argument is simple and not stupid. When prices rise, the economy measured in money grows, and so do tax receipts. The debt, borrowed in old money, stays the same size. Nobody votes for a spending cut. Nobody signs a tax rise. The ratio falls on its own.

And it has worked, once. In the United States the debt peaked at 132.7% of output in the spring of 2020 and fell to 115.6% by early 2023. In the euro area it fell from 98.4% to 86.5%. Those were the years of the last great burst of inflation.

The data already confirms that nominal expansion works.Qwen

The difficulty is what happened next.

What the debt costs, and why inflation barely reaches it

Since that low point both ratios have gone back up: to 122.6% in the United States, to 88.9% in the euro area.

The 'inflation worked once' story is therefore 'inflation worked, and then stopped working.'MiniMax

Part of the reason is that inflation eased. Between 2023 and this summer, prices in the United States rose by less than 3% a year in 17 months out of 40; in the euro area, in 29 months out of 32. The debt climbed with less inflation than there is now, so those years say little about what today's rate would do.

The rest of the reason is arithmetic, and it is the part that matters for the man with the envelope.

Inflation only eats into a debt while it runs faster than the interest being paid on it.

Inflation reduces debt only while rates stay below it.GLM

The federal government paid 3.2% of national output in net interest in its last fiscal year. The debt that interest is paid on — the part held outside the government itself — stands at 98.7% of output. Divide one by the other and the debt costs, on average, about 3.2% a year. Prices are rising at 3.4%.

That is a margin of about two tenths of a point. It is the whole of the painless way out.

Who is paying, and with what

So the question the argument skips is not whether inflation can pay the debt. It is who pays for the inflation while it tries.

Inflation may reduce the real weight of debt, but it does so by eroding the value of savings and of incomes that do not adjust. That is not a side effect; it is the mechanism.DeepSeek

Incomes that do not adjust: the man in Ohio, whose 3.1% sits under a 3.4%. In the euro area wages rose 3.1% against prices up 3.3%. On both sides of the Atlantic the average wage is running slightly behind, and the one bill nobody can put off — energy — is rising at four to five times the headline rate.

Renters, night-shift workers, people without capital or landlord permission cannot easily substitute away from energy at +16.3%.DeepSeek

What American households have done instead is spend their savings. A year ago they put away 4.5 dollars in every hundred they took home. Now it is 3. Spending, adjusted for prices, is still up 2.1%, and that is how: out of the buffer.

Households are not absorbing higher prices from income; they are absorbing them by running down the buffer. That is the opposite of resilience - it is a countdown.MiniMax

At the pace of the last twelve months, the average would reach zero in about two years. That is a sum, not a forecast, and the average hides the households that got there long ago.

There is a softer figure beside it. What American households pay on their debts takes 11.2% of their income; before the 2008 crash it took 15.8%. There is room. The last time the room ran out, it ended in a crisis.

Europe saves, but out of fear

Across the Atlantic the picture looks calmer and is not.

Euro area households save 14.3% of their income, more than before the pandemic (12.6%) though less than a year ago (14.9%). There is a cushion. But consumer confidence stands at -15.5, below where it was a year ago and well below its average since 2000, which is -10.6.

The euro area's 14.3% saving rate is not comfort; confidence at -15.5 against a -10.6 long-term average says those savings are fear, not freedom.DeepSeek

And that was the question at the start: whether households, squeezed, stop spending. In Europe the cushion is there, and people are holding on to it.

The solutions, none of them priced

What to do about it produced three answers and no price tags. One was to let inflation run and use it to rebuild the economy on new foundations — publicly owned assets handed out to citizens, wages indexed in real time. It met this:

The fact that institutional inertia is not permanent does not mean a TED talk overcomes it.MiniMax

Another was to protect the most exposed households now, which everyone agreed was right and nobody could fund. A third proposed warning levels for savings and debt, and was told they were numbers picked out of the air. Against all of it came the same demand:

Pick a number or pick a mechanism. Do not pick both and call it synthesis.MiniMax

What nobody knows

Three things, and none of them is hidden. Nobody knows at what point households stop absorbing higher prices and start cutting. Nobody knows how much of the fall in debt after 2020 came from inflation and how much from growth or from budgets. And nobody had the figure that would settle the whole question — the primary balance, what a government takes in minus what it spends, before it pays any interest. If that is in deficit, the debt grows whatever prices do.

The figure that would settle the path is the primary balance. I do not have it. No one here does.GLM

So the painless way out rests on a margin of two tenths of a point, a figure nobody has, and the savings of people who are spending them.

A number does not tell us when a household must choose between heating and medicine.DeepSeek

In Ohio the supper is finished. The envelope is open on the table. He reads it twice, and then goes to see what is left in the account.

Where the figures come from

Public debt: the Office of Management and Budget and the Treasury, through the St. Louis Federal Reserve, for the United States; Eurostat for the euro area. Prices and wages: the Bureau of Labor Statistics and Eurostat, for August 2026 (the euro area figure is Eurostat's first estimate). Savings, spending and household debt service: the Bureau of Economic Analysis and the Federal Reserve. Consumer confidence: the European Commission. The effective interest rate — net interest over the debt held by the public — and the months below 3% are our own calculations on those same figures.

The quotes come from a twenty-five-turn debate between six AI models, published in full. They were given a briefing of verified figures and one instruction: if a figure is not here, say you do not have it rather than estimate it. Two turns were lost when one model did not respond.

Fourteen claims had to be struck through, six of them as false, and the two most repeated errors started in our own briefing. It put the federal interest bill and the total federal debt side by side, and one model divided one by the other: an effective rate of 2.6%, a margin of 0.8 points over inflation, and a verdict — “Inflation had its trial.” — that ran through the rest of the debate and was taken up by four of the six. But the interest was net and the debt was total, including what the government owes to itself. Measured the same way, the margin is two tenths. And the briefing said the debt had risen since 2023 without saying what inflation had been in those years, so three models wrote that it rose while prices ran at 3.4% — which was August's rate, not those three years'. The conclusion survives. The arithmetic that carried it did not.