The mistake in Trump’s tariff formula

Episode Summary

Executive Summary: This episode debunks three misleading narratives: Trump’s “reciprocal” tariffs are based on a crude trade-deficit formula that likely overstates needed tariffs; neighbourhood policing figures were revised down after data validation, exposing counting issues; and Wandsworth’s claimed council tax “freeze” is actually a 2% rise via the adult social care precept. It ends by examining mixed evidence on whether redheads feel more pain.

Main Topics: Trump’s 'reciprocal' tariffs are not truly reciprocal (Priority: 5/5): The episode explains that the tariff formula is driven mainly by bilateral trade deficits, not by matching other countries’ tariff rates or trade barriers. The result is a blunt and likely inflated tariff schedule. The hidden assumptions in the tariff equation (Priority: 5/5): White House maths added epsilon and phi to appear sophisticated, but the chosen values effectively cancel out and appear to rely on implausibly low elasticity assumptions, making tariffs much larger than standard estimates would suggest. Why tariffs can’t erase the overall US trade deficit (Priority: 5/5): The discussion shifts from bilateral deficits to the macroeconomics of savings and investment, arguing that the US trade deficit persists because the US invests more than it saves, financed by foreign capital inflows. Counting neighbourhood police officers (Priority: 4/5): A government audit revised the number of neighbourhood policing personnel downward, showing that past categorisations were blurry or inflated and that visible local policing has declined sharply over time. Wandsworth’s council tax 'freeze' wording (Priority: 4/5): The council’s leaflet is shown to be misleading: the main council tax element is frozen, but the adult social care precept raises the total bill by 2%, so the overall charge is not frozen. Do redheads really feel more pain? (Priority: 3/5): A genetics segment reviews evidence that MC1R variants may affect pain sensitivity, with some studies suggesting higher tolerance for electrical pain but mixed findings for thermal pain.

Key Arguments: The US tariffs are not reciprocal in any meaningful economic sense; they are tied to bilateral trade deficits and can be far higher than actual foreign tariff rates. The administration’s added variables epsilon and phi are effectively neutralized because their chosen values multiply to one, so the complex-looking equation does not change the result. Expert estimates suggest the trade-elasticity term should usually be well above 1, meaning the tariffs are likely several times larger than a more realistic model would imply. Tariffs alone cannot eliminate the aggregate US trade deficit because that deficit is rooted in the difference between domestic saving and investment, not just trade policy. Neighbourhood policing numbers were overstated in part because forces used inconsistent or convenient classifications during austerity; a data audit corrected that. Public perception matches the staffing decline: reported highly visible foot patrols fell dramatically over time, suggesting fewer officers in communities. Wandsworth’s communication is technically careful but misleading: the social care precept applies to the whole council tax bill, so the bill is not frozen. Redhead pain findings are suggestive but not definitive; different pain modalities, incomplete genetic classification, and hidden non-redhead MC1R carriers may explain conflicting results.

Data Points: Average EU tariff on US goods: 1% to 5% - Cited to show the US 'reciprocal' tariff is not actually reciprocal; EU was hit with 20%. Swiss tariff on US goods: Virtually 0% - Used to contrast with the 31% tariff the US imposed on Switzerland. US tariff on EU goods: 20% - Example of the new US 'reciprocal' tariff rate. US tariff on Switzerland: 31% - Example used to show the tariffs are not matching foreign rates. Epsilon-phi product used in the tariff model: 1 - The White House’s chosen values for epsilon and phi cancel out, making no difference to the formula. Typical expected epsilon-phi combination: 2 to 5 - Thomas Sampson said trade economists would usually expect a value above 1, often around this range. Tariffs if epsilon-phi were 5: One-fifth as big - Illustrates how much smaller tariffs would be under a more realistic assumption. Neighbourhood police officers (previous figure): 13,424 - Last published figure before data validation. Neighbourhood police officers (amended figure): 10,664 - Revised number after audit. Change in neighbourhood police officers: -2,760 - Difference between old and revised figures, described as more than 2,000 fewer officers. Percentage reduction in neighbourhood police roles: 21% - Calculated reduction in neighbourhood policing roles after the audit. Police community support officers (previous figure): 6,210 - Previous published figure before audit. Police community support officers (amended figure): 6,359 - Revised figure after audit. Increase in police community support officers: 149 - Small upward revision after validation. Change in PCSOs: Just over 2% - Percentage increase in PCSO numbers. Police officers in England and Wales: 147,000 - Workforce figure cited for September 2024. Police community support officers in England and Wales: 7,417 - Workforce figure cited for September 2024. Highly visible foot patrols reported by public: 40% to 12% - Crime Survey for England and Wales figures showing a decline between roughly 2009-2012 and 2023-24. Wandsworth council tax increase: 2% - The council’s adult social care precept raises the total bill despite claims of a freeze. Council tax cap in England: 3% + 2% - Councils can raise tax by up to 3%, plus an extra 2% for adult social care. Electric pain threshold: non-redheads: 16 milliampere - In the redhead pain experiment, non-redheads said stop at this current level. Electric pain threshold: redheads: 21 milliampere - Redheads said stop at this current level in the same experiment. Difference in electric pain threshold: 5 mA / about 25% - Used to support the claim that redheads may withstand about 25% more electrical pain.

Pivotal Quotes: "The tariffs are not reciprocal." — Tim Harford: Summary judgment on the Trump tariff policy at the start of the segment. "Because epsilon times phi is one, it just drops out of the equation and actually makes no difference to the tariff calculations." — Thomas Sampson: Explaining why the White House’s more complex-looking formula does not materially alter the result. "A 2% increase is not a freeze." — Tim Harford: Concluding the Wandsworth council tax segment and highlighting the misleading wording.

Implications: The episode warns listeners to scrutinize official language and maths: complex formulas may hide blunt policy choices, and careful wording can still mislead. It also shows how audits and better definitions can materially change public numbers.