On the face of it, Rachel Reeves’s budget looks like a kind of economic suicide note: huge tax rises planned just before the next general election. The Office for Budget Responsibility says that by then she will be imposing the highest tax rate in history while overseeing anaemic growth in living standards and a borderline debt crisis. Privately she rejects all this, saying the OBR is too gloomy and that something big will turn up. She hasn’t explained what.

Over in the White House a similar belief underpins Donald Trump’s economic agenda. His One Big Beautiful Bill is a tax-and-spend package that official forecasters say will saddle the US with staggering amounts of debt. Those forecasts are wrong, says the White House. It has published its own scenario involving heroic economic growth, with a windfall in jobs and tax revenue.

The big hope in both Washington and London is artificial intelligence. A fascinating OBR paper, released alongside the budget, lists AI as the top potential “upside” surprise for UK growth and sketches what this could look like. Vanguard, one of the world’s largest investment firms, puts the chances of an AI-driven productivity surge at 50 per cent.

‘I’ll show ’em!’ cried Rachel, sounding unhinged

Essentially, it’s a coin flip. If it happens the tax revenues rise, debt stabilises and chancellors and presidents look like geniuses. If it doesn’t, we enter a doom loop of austerity, job losses and tax rises.

At The Times Budget Briefing in Westminster this week, a reader asked whether, given the potential of the AI era, the government has a plan for it. Mehreen Khan, our economics editor, replied that it’s not really a plan, more of a prayer. This sums it up. Rachel Reeves started off basing her economic agenda (she called it “securonomics”) on the policies of Joe Biden. She has ended up resorting to Trumpian blind hope. So this is more prayer-o-nomics, digital Micawberism. Hoping that the AI ship will come in sooner than expected.

In her defence, this is by no means a fantasy. The OBR’s paper says if AI goes well and helps workers achieve far more each day, productivity growth would be revised up to 1.5 per cent a year, from 1 per cent, by the next election. This would mean enough extra revenue to allow Labour to halt its tax rises. It would also change the national mood, setting the scene for the roaring Thirties.

This bullish case has serious advocates. Anthropic’s Dario Amodei argues that within a few years we could have AI systems smarter than Nobel laureates across biology, programming, maths and engineering, working around the clock at 100 times human speed.

If he’s right, the productivity surge isn’t a 0.5-point uplift but something closer to an industrial revolution, compressed into a single parliament. With some £200 billion more UK tax revenue a year by the end of the next decade.

Could this robot be a glimpse into London’s future?

You can see how these figures are so seductive for politicians — it’s like a discovery of digital magic beans. No need for the hard graft of welfare reform. No need even for an economic agenda: you plant those beans and sit back. And unlike other fantasies, the first results can already be seen.

Driverless taxis crawl the streets of Austin, Phoenix and Los Angeles. Warehouse staff using AI route-planning can pick 25 per cent more items per shift just because they walk less. Studies show AI is letting computer programmers achieve 20 per cent more. The tech is everywhere: I recently met a Swedish entrepreneur whose AI device scans logs, then instructs saws to cut in a way to get more usable wood per tree. These are not what-ifs or modelling but real-world results, now.

The big question is timing. Historical patterns regularly show new technology delivering game-changing boosts in prosperity. But the upswing can take about 20 years to show up after the breakthrough moment (as it was with electricity and desktop computers). We’re perhaps three years into the AI era, which would put the productivity surge somewhere in the 2040s. Too late for Reeves and Trump.

But there’s reason to think AI might move faster. The old technological revolutions needed physical infrastructure: power stations, copper wiring, factories full of new machines. AI runs on what we already have: computers and smartphones.

So the main bottleneck isn’t hardware but training people, redesigning workflows, encouraging staff to trust the machines. Asking workers to trust the “clankers” (a new, derogatory word for AI) may be hard; feeding energy-hungry bots will be costly. But it could all happen faster than HS2.

In the White House, the magic-beans scenario is being counted on as reality. Trump’s Council of Economic Advisers talks about a supercycle — of AI and more — doubling economic growth within a few years. In this world there’s no debt bomb: on the contrary, the debt-to-GDP ratio peaks in 2028 and then falls indefinitely. Goldman Sachs, Bank of America and Ark Invest have all published scenarios that make even those numbers look timid. The OBR’s paper is at the most cautious end of the estimates.

The political beauty of it, from Mar-a-Lago to HM Treasury, is that the jackpot arrives on precisely the right timetable. Cash comes flooding in by the mid-2030s when the British welfare state and Medicare trust funds would be otherwise heading over a cliff. No need to cut welfare, or clear the legalistic weeds that choke growth now. The bots will pay for Trump’s border wall, Keir Starmer’s defence spending pledges and everyone’s retirement.

Politicians, of course, have a long history of imagining such miracles. Harold Wilson’s promises about the “white heat” of scientific technology ended in the dark cold of the 1970s. Japan’s government spent the 1980s talking about fifth-generation computers and ended up with the “lost decades”. Gordon Brown, as chancellor, sold off half the UK’s gold reserves in the belief that gold no longer glittered in the era of the knowledge economy. Its value has since risen tenfold.

Rachel Reeves and Donald Trump are signing up to the oldest trope in politics: “this time it’s different”. Both want to believe the AI cavalry will ride over the hill before the bond vigilantes do. They could even be right. It is a seductive story — and, to be sure, a plausible one. But today it’s just a story. Perhaps the only one standing between Labour and oblivion.

Before he was prime minister, Starmer described himself as an atheist. When asked recently, he said he was brought up Christian — a shift, perhaps, born of necessity. As the saying goes, there are no atheists in foxholes. Until decent growth turns up in the real world, rather than in annexes and scenarios, prayer-o-nomics may well be all he has.