The mistake in Trump’s tariff formula

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Live in the Bay Area long enough, and you know that this region is made up of many communities, each with its own people, stories, and local realities.

I'm Erica Cruz-Guevara, host of KQED's podcast, The Bay.

I sit down with reporters and the people who know this place best to connect the dots on why these stories matter to all of us.

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BBC Sounds, Music, Radio, Podcasts.

Hello, and welcome to the last in this series of More or Less.

We're making a list, we're checking it twice, just to make sure we haven't accidentally tariffed some penguins, and I'm Tim Harford.

This week, when is a tax freeze not a tax freeze?

Hello, hello, hello.

Strange goings-on in the world of counting police officers.

Charlotte MacDonald tells me why redheads are tougher than I am.

But first, let's start with Liberation Day, the day U.S.

trade policy liberated itself from the shackles of rationality.

In a few moments, I will sign a historic executive order instituting reciprocal tariffs on countries throughout the world.

Reciprocal.

That means they do it to us and we do it to them.

Very simple.

Can't get any simpler than that.

Let's just get the obvious stuff out of the way.

These tariffs are not reciprocal.

The average tariff the EU puts on the US is somewhere between one and five percent, depending on who's counting.

They got a reciprocal tariff of twenty percent.

Switzerland puts virtually no tariffs on US imports.

They got a 31% tariff.

Aha, but trade is complicated.

Maybe the US has used a clever calculation to account for other trade barriers, such as bans on certain kinds of products, hormone-treated beef, chlorine-washed chicken, those chocolate bars that taste a little bit like sick.

That sort of thing might annoy a red-blooded US exporter.

They rip us off, it's so sad to see.

It's so pathetic.

Nope, none of that was involved.

Writer James Suruecki was the first to twig what was going on.

He noticed that the new tariffs had nothing to do with that.

All that mattered was the value of the goods each country sold to the US and how much each bought from the US.

To get the tariff numbers, you use a basic formula.

Your so-called reciprocal tariff equals the value of exports to the US minus the value of imports, aka the bilateral trade deficit, and then convert it into a percentage by dividing the whole thing by imports.

Then, to get the tariff the US would impose, the answer was divided by two.

Why?

Well, that was because President Trump was being kind.

We are being very kind.

We're kind people.

Very kind.

When James Surwicky posted this on Twitter...

It's called X now, Tim.

Not in my programme.

We eat marathons and opal fruits, we clean with JIF, and we post on Twitter.

So, as I was saying, James posted this on Twitter, and people were astonished that there hadn't been a complicated process that looked in detail at tariffs and trade barriers, but just a very simple formula.

People started to laugh and poke fun.

Sad.

So the White House Press Department replied to James Surowicki to say that the formula was actually much more complex, and they issued a complicated equation full of Greek letters.

The increase in tariffs equals exports minus imports divided by imports multiplied by epsilon and phi.

They said learning ancient Greek for ten years was pointless.

Nathan, you just showed them.

The new equation is divided by two additional terms, epsilon and phi, which were multiplied together.

But the values of these terms were 4 and 0.25.

Always 4 and 0.25 for every country.

Now those of you who are particularly good at mental arithmetic will realize that if you multiply 0.25 and 4 together, you get 1.

And if you multiply by 1, it doesn't make any difference to the rest of the equation.

Now it is tempting therefore to dismiss the importance of these terms, but actually including them in the formula did make sense, but there was a problem.

There were good reasons to think that the values were wrong.

Thomas Sampson is an associate professor at the London School of Economics.

The idea is that the epsilon tells you about how much, if you increase tariffs and therefore you increase the price of imports, how much trade responds.

And the phi is telling you if you increase tariffs, how much of that is passed through into import prices.

So the combination of the epsilon and the phi tells you if I increase tariffs, what is the proportional change in trade as a response?

So that, in fact, is a really important parameter for anyone who studies international trade.

It's what trade economists call the trade elasticity.

Yeah, if I increase a tariff, do people respond by cutting back or not?

Or do they just swallow the tariff and keep exporting?

Exactly.

But there's a catch, which is that the values of the epsilon and phi they've chosen to use actually multiply together to just give one.

And so because epsilon times phi is one, it just drops out of the equation and actually makes no difference to the tariff calculations.

So the actual calculations they do are as if the epsilon and the phi aren't there.

So

they could play an interesting role, but in practice they don't because they've used values that make them drop out.

Sorry, my head is hurting a little bit.

So the

is there is there a reason, I mean, are epsilon and phi,

by definition, going to equal one when you multiply them together?

Does it just happen to be that the values they've chosen happen to equal one?

It just happens to be that the values that they've chosen happen to equal one.

And in fact, we know something about what those numbers should be.

And typically, we would think that they should be a number bigger than one once you multiply them together, maybe somewhere between, you know, two at a minimum, maybe closer to five on average.

So they've, in fact, chosen a very low value for that epsilon phi combination.

And I'm just going to hazard a guess.

Does that very low value that they've chosen mean very high tariffs?

Absolutely.

It does.

For example, if the epsilon times phi were equal to five instead of one, the tariff would be one-fifth as big.

Rather than dividing by one, they should be dividing by a bigger number, making the tariff much smaller.

How did this happen?

The administration's press release cites an academic paper suggesting that this phi value is 0.25.

But the academic paper in question actually says that the value of phi is slightly less than one,

which, much as Thomas Sampson suggests, means all those tariffs are almost four times too high, even according to their own calculations, relying on their own hand-picked sources.

Now that might end up being the difference between a global downturn and a global depression.

But hey, friends don't argue over little differences like that.

So we have an awful lot of maths.

A lot of the maths appears to be fake maths and the real maths appears to be fake economics.

When push comes to shove, what what we've got is countries with whom the US has a big trade deficit are going to have a lot of tariffs imposed on their imports to the U.S.

Is that likely to eliminate or reduce the trade deficits?

It will certainly have an effect on trade, and for some countries it might reduce the trade deficits.

But the other thing we need to bear in mind is that what drives the aggregate US trade deficit is not anything to do with US tariff policy.

It's the fact that the US invests more than it saves domestically.

Now for some economists like me, that seems a perfectly natural thing to say, but I'm guessing that some of you will be quite puzzled by that statement.

What have savings and investments got to do with any of this?

If the US has a trade deficit, it means it's buying more from the outside world than it's selling to them.

That's a bit like spending more than you earn.

How is that possible?

The answer is that the extra money the US spends on imports comes from foreigners investing in the US.

They might do that by buying US property or shares in US companies or just by buying US promises to pay later.

We call these bonds and treasury bills.

You could think of it like this.

Instead of exporting t-shirts or microwave ovens, the US is exporting shares in Apple and Google.

The US has been doing this for a long time and because it's very good at generating new financial assets it's been a stable way to pay for all those lovely imports and US households would rather spend their last few dollars at the end of the month on buying more stuff from Asia than do a lot of saving like they do in China.

Fundamentally, you can't close a trade deficit by imposing tariffs.

You can only close a trade deficit by changing the macroeconomics of the US, maybe by persuading the American consumer to do more saving and investing rather than buying consumer goods.

Or maybe by making the US a less attractive place for foreigners to invest in.

Well, the White House might manage that one yet.

You never know.

So unless there's a change in that savings investment balance in the US, the US is still going to run an aggregate trade deficit.

And if you're running an aggregate trade deficit, then there's got to be at least some countries you run a bilateral trade deficit with.

So fundamentally, we wouldn't expect this to eliminate those deficits.

Of course, there might be a great 4D chess master plan behind these tariffs, but working on what we actually see, they are calculated to reduce US trade deficits with every country involved to zero.

They appear to be massively overpowered to do that, maybe four or five times bigger than they need to be by their own calculation.

And without changing the saving and investment balance, they can't do that anyway.

You're listening to more or less.

Politicians are always talking about the importance of bobbies on the beat and this government is no different.

They're promising more, 13,000 more neighbourhood police to be precise.

To get the ball rolling, they decided to find out how many there actually are bobbing on these beats already.

And there were

not as many as they thought, nearly 3,000 fewer, in fact.

Hello, hello, hello.

We obviously wondered, what's all this then?

Gavin Hales is a senior associate fellow at the Police Foundation think tank.

So how we've got to where we are is a history of kind of boom and bust in neighbourhood policing.

which started with a great deal of investment in the early 2000s.

We then got to austerity from 2010 and neighbourhood policing was one of the the victims of austerity and policing.

And now we've got a new government and they're making a commitment to reinvest in neighbourhood policing and so suddenly it matters a great deal that we can count exactly how many people work in neighbourhood policing today.

I think that through the austerity years there were in some cases police forces who perhaps tried to mask the impact of cuts by for example

deciding that all of their response police officers responding to 999 calls would be counted as neighbourhood police officers.

And in a way that was perhaps an attempt to preserve the impression that neighbourhood policing had been protected when it hadn't.

The definitions here are obviously a bit blurry.

What if an officer on patrol responds to a 999 call?

But the current government asked police forces to unblur them, to do an audit.

They called it a data validation exercise and check that everyone knew who was doing what, at least most of the time.

And it turned out they didn't.

The number of police officers in neighbourhood roles was thought to be 13,424 the last time these figures were published last July.

The amended figure for them is 10,664.

So it's a reduction of more than 2,700 officers or about 21%

in those neighbourhood roles.

For the police community support officers, they actually found that there was slightly more than was previously thought.

So they've gone up from 6,210 to 6,359, which is an increase of 149 or just over 2%.

Police community support officers are the people who patrol in uniform but don't have arrest powers.

So I should say that these numbers all apply to England or Wales.

And the last time the police workforce data was published, there were 147,000 police officers in England and Wales in September 2024.

And at the same time, there were 7,417 police community support officers.

So in terms of the police officers, there weren't a massive number categorised as neighbourhood police in the first place, under 10% of the total.

And then a load of them disappeared.

What happened to them?

Gavin says they went AWOL for a few different reasons.

Partly it was an unwinding of these slightly iffy categorisations that made the number look bigger than it actually was.

Some were apparently just mistakes.

But we don't have to rely on figures from the police.

We can look at things from the public's perspective.

So one of the pieces of evidence we can bring in here is from the Crime Survey for England and Wales, which is a survey of householders in England and Wales, which typically asks them about their experiences of crime and antisocial behaviour, but it also asks them about things like whether police patrols are highly visible in their local area.

What that tells us is that there was a fall from 40% of respondents reporting highly visible foot patrols in their local area in the years between sort of 2009 and 2012, to only 12% of people reporting that by 2023-24.

So the public have noticed that the police are no longer as present in their local communities and clearly this policy to increase the number of neighbourhood police officers is in part an attempt to address that gap.

As to the question of whether Bobbies on the beat actually prevent crime, the somewhat unsurprising answer is that they can if you target the right areas and do the right things.

So it's not enough just for police officers to be seen in public.

They also need to be actively tackling the problems that are affecting local people, whether that's crime or antisocial behaviour.

For the government, you might think that the missing officers might be bad news for their promise, a promise which includes both police officers, including part-time volunteers, and police community support officers.

But as some of the promised extra bobbies can be reclassified from the existing police officer pool, that might not be the case.

One of the effects of this may be that it makes it slightly easier for the government's commitment to put an additional 13,000 police personnel into Napole Policing.

It'll be slightly easier to reach because it's starting from a lower base.

Thanks to Gavin Hales from the Police Foundation.

Suffs, the new musical has made Tony award-winning history on Broadway.

We demand to be home.

Winner, best score.

We demand to be seen.

Winner, best book.

We demand to be quality.

It's a theatrical masterpiece that's thrilling, inspiring, dazzlingly entertaining, and unquestionably the most emotionally stirring musical this season.

Suffs, playing the Orpheum Theater, October 22nd through November 9th.

Tickets at BroadwaySF.com.

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Never let it be said that we don't hold ourselves to the same high standards we hold others.

So, time for an apology about a mistake we made in an episode two weeks ago.

Talking about the way the Office for National Statistics were re-evaluating pension wealth, for some reason I said that interest rates were high from 2018 to 2020.

As one anonymous emailer, signing off only as loyal listener, pointed out to us, they were actually very low.

Since I should have known and could have checked, I am not exactly sure how this one got through.

Possibly I was distracted by events.

As I worked on the script, there have been quite a lot of events.

In any case, sorry.

And thanks to our loyal listener for pointing out our error.

If you see anything we've got wrong or have any other questions or comments for us, our email address is more or less at bbc.co.uk

Last week, citizens up and down the country found themselves presented with increases in a whole swathe of bills.

Water, energy, car tax.

For millions of people, these went up.

Another big one was council tax, as many councils across the country increased their rates substantially.

But the Labour-controlled Wandsworth Borough Council in South London had reassuring words for their residents, proclaiming in their quarterly magazine, Wandsworth Council is freezing your council tax for the third year in a row.

Great news for Wandsworth residents everywhere.

Ought to be more specific.

Wandsworth.

But wait, we received an email from Louis Redman, a loyal listener and self-described, concerned resident of Wandsworth.

He had received that very magazine from the council assuring him that his council tax was going to be frozen.

But when he got his bill, that is not what it said.

Far from being frozen, the portion of council tax that Wandsworth Borough Council controls is going up by 2%.

We asked Professor Tony Travers, an expert in local government from the London School of Economics, to help us get to the bottom of this.

The leaflet that the Council sent out is very carefully written.

So the leaflet talks about the Council freezing its share of the Council tax, but then goes on to talk about a so-called social care precept which the Council is allowed to put up, the Government allows it to put it up within the capping rules that Central Government sets for local authorities in England each year.

Why is Adult Social Care being broken out here?

Well because a few years ago ago it was realised by central government that the pressure they put on council budgets was such that social care was effectively massively underfunded.

So the government allowed councils not only to put up council tax by say 3% a year but 3% plus 2 with the extra 2%

being to fund social care.

Councils in England have limits on how much they can put up council tax.

The cap starts at 3%,

but they're allowed to add an extra 2% to help them meet the costs of providing adult social care, taking them up to a total of 5%

if they want.

What Wandsworth Borough Council have done is very strange.

On the one hand, they claim they've frozen the main element of council tax.

They also talk about an increase of 2% in what is called the adult social care precept.

But this makes it sound like the 2% increase only applies to some separate and smaller portion of the council tax bill while the rest of the bill is frozen.

That's also strongly implied in a separate guide to council tax that Wandsworth sent out to residents.

But this is definitely not what's happening.

The 2% increase applies to the whole bill.

The whole bill is going up by 2%.

The truth is, if you look at it in the round, what they are doing is putting the council tax up by 2%.

But they're disguising the way they say it in the language they're using in the document that they've sent out.

I mean, this strikes me as.

Well, you described it as carefully written.

I mean, I might

say Prime Minister euphemisms is very carefully written.

But I mean, it's truth.

It's true that I think it would be very easy to read this document and be misled that the council tax as a whole wasn't going up by 2% for one's share of it.

And it would have been easy to say that the council tax is going up by 2%, which is less than the 5% we could have put it up by, because they could have put it up by the full 5%.

And we still have the lowest council tax in England.

But they've worded it in a way that, you know, in the end, has made the listener worried.

Yeah.

Well, they said they've frozen it, and they haven't.

They haven't frozen it at all.

They put it up, in effect, by 2%.

But the way it's written, you might think they'd frozen it and some other component was going up by 2%.

And it's just an unfortunate use of language, to put it kindly.

On the subject of the lowest council tax in England, I mean this seems to usually be true for Wandsworth.

Why?

How are they able to do that?

I think all the way back when it began in 1990 with the poll tax and then 1993 with the council tax, big efforts were made in government to ensure every sinew was stretched to ensure that the allocation of government funding to them at the time, to these councils, including Wandsworth, was helpful in delivering a low tax.

And it's lived lived through all the way since.

And I have to tell you, many councils outside London are slightly resentful of the very low tax, even these days, even though the residents presumably love it.

Tony Travers, thank you very much.

You are a very kind man.

Thank you, too.

We put all this to Wandsworth Borough Council.

They told us...

Wandsworth Council has frozen the main element of council tax for the third year in a row.

The 2% increase reflects the adult social care precept, which is ring-fenced to fund vital support for older and vulnerable residents.

This misses the point, which is that the 2% increase for adult social care applies to all of the council tax bill that Wandsworth controls, not to some smaller element.

And though it seems mad to have to repeat this, a 2% increase is not a freeze.

You're listening to more or less.

What do Lindsay Lohan, Ron Weasley, and our very own Charlotte MacDonald all have in common?

Now they haven't all driven a magic car, they're all natural redheads.

Outing me like this on the radio.

Ah, Charlotte, red is a lovely hair colour.

Indeed, red is the colour of my true love's hair.

Well, I appreciate it now, I guess, but growing up I always ran the risk of being bullied or, you know, being burned at the stake for witchcraft.

Did you grow up in medieval Europe?

Well, actually, it was the East Midlands in the 80s.

I'm sure it's the same thing.

Pretty much.

But anyway, whilst running the risk of some bullying, it turns out redheads could actually have a special ability.

According to an article in the New York Times magazine, redheads can withstand up to 25% more pain than their blonde and brunette peers.

And the reason for this special ability?

Our secret ingredient, MC1R.

Isn't that a classic 2000s emoband?

No, that's my chemical romance.

MC1R is a gene.

In fact, it's the thing thing that makes most of us redheads in the first place.

I'll let Professor Jeff Mogill explain.

He's the Canada research chair in genetics of pain.

Genetics of pain?

That definitely is a classic chemoband.

So the MC1R gene is the gene that codes for, that provides the instructions for the creation of a protein known as the melanocortin-1 receptor.

And the melanocortin-1 receptor has a number of roles, but its most well-known is its involvement in producing melanin, which is the pigment that makes skin and hair turn different colors.

And redheads, essentially, are those who have inherited variants of that gene such that the protein, once it's made, doesn't work.

And so melanocortin-1 doesn't do what it's supposed to do.

And so instead of having brown hair like you're supposed to and somewhat darker skin, you end up having red hair and somewhat lighter skin, which is usually prone to freckling.

Right.

So that's the redhead part.

What about the pain?

My lab showed that redheaded mice

were more sensitive to a particular class of opioid drugs called kappa opioid drugs.

And we found this completely by accident.

We were not interested in redheads.

We were not interested in red-headed mice.

We were trying to find what the gene was that was responsible for how much kappa opioid analgesia mice would have.

We eventually found the the gene and the gene happened to be MC1R and that's when we said to ourselves, oh, hmm, we could do this same experiment in humans because we can go get red-headed women that are very likely to have these variants of MC1R.

And indeed, we showed that redheads were more sensitive to the drug as well.

So analgesia, that is the fancy word for pain relief.

He's saying that these mice needed to take fewer opioid painkillers than regular mice to get the same pain relief.

But what about this figure of withstanding 25% more pain?

Well, that's Jeff living up to his title of chair in genetics of pain.

His team wondered whether the reason that redheads needed fewer opioids could be because the MC1R gene already acted as a natural pain inhibitor.

So they joined up with the team in the Netherlands.

to electrocute redheads.

Wait, what?

Only a bit, though.

So in this study, we gave them electrical current to their arm.

The intensity of that electrical current was slowly increased until they said, stop.

I've had enough.

The non-redheads said stop when the electric current was up to 16 milliampere,

and the redheads didn't say stop until it was up to 21 milliampere.

So, that's a difference of five out of 16.

So, yeah, about 25%.

So, it seems that redheads can withstand 25% more pain.

Job done?

Uh, not quite.

A paper published around the same time found that redheaded mice were more sensitive to thermal pain, so hot and cold temperatures.

If that's true, why are there so many redheads in Scotland?

I don't know, but I do know that there could be two reasons for redheads having higher pain tolerance for one thing and not the other.

Is it that different types of pain elicit different responses and are processed by the body in a different way?

Smart.

Yes, that's the first possible reason.

The second takes us back to genes again.

Explain.

Not all redheads have the right genes.

It turns out that the melanocortin I receptor accounts for about 75 or 80% of redheads, but not all.

We actually looked at the genetics of our subjects to find out: were they really melanocortin-1 receptor redheads?

And the US group didn't.

So it is theoretically possible that the people less able to handle thermal pain didn't have the MC1R gene.

Theoretically, yes.

But there's another twist in the tail.

Enter the secret redhead.

It turns out that some people with MC1R variants, through the additional effects of other genes, end up being blonde and not red-haired, but they too have non-functional melanocortin-1 receptors.

So yeah, it's possible that there are some blondes out there that have the same pain phenotype as redheads.

Very interesting indeed.

But Charlotte, in the end, what I am hearing is that you really might be able to withstand 25% more electrical pain than others.

Yeah.

Wait, Tim, why are you holding that cattle prod?

I might have the wrong genes, Tim.

Hmm.

Thank you, Charlotte.

And that is all we have time for this week, and indeed this series.

Don't worry, we will be back in the summer, and no doubt there will be one or two matters for us to look into by then.

If you want more more or less in the meantime, our Saturday podcast is available all year round.

Search for more or less behind the stats.

And my other podcast, Cautionary Tales with Tim Harford, is also available weekly from BBC Sounds.

Meanwhile, please keep those questions and comments coming in to moreorless at bbc.co.uk.

We will be back on Radio 4 in June.

Until then, goodbye.

More or less was presented by me, Tim Harford.

The producer was Tom Coles, with Nathan Gower, Charlotte MacDonald, and Lizzie McNeil.

The programme was recorded and mixed by James Beard.

Our production coordinator was Brenda Brown.

And our editor is Richard Varden.

I'm Joanna Page.

I'm Natalie Cassidy.

And we want to tell you all about our podcast.

Off the teller.

It's basically both of us chatting about what we've been up to.

On and off screen.

It's just brilliant.

Who and what we just can't resist?

With plenty of behind-the-scenes stories and gossip.

Yeah.

Cracking.

We always say cracking now.

Really?

Everything's cracking.

It's definitely the place for what's occurring.

Oh, Joe, you do that so well.

Off the telly.

Listen to all new episodes on BBC Sounds.

Sucks.

The new musical has made Tony award-winning history on Broadway.

We the man to be honest.

Winner, best score.

We We demand to be seen.

Winner, best book.

We demand to be quality.

It's a theatrical masterpiece that's thrilling, inspiring, dazzlingly entertaining, and unquestionably the most emotionally stirring musical this season.

Suffs!

Playing the Orpheum Theater October 22nd through November 9th.

Tickets at BroadwaySF.com.