Trump's Percentage Problem: The Math Behind the Drug Price Claims

The recent speech at Davos brought a fascinating case study in how percentages can be manipulated for political effect. When Trump claimed pharmaceutical price reductions of "up to 90%" while simultaneously defending his previous claims of "5-, 6-, 7-, 800%" reductions, we got a rare glimpse into the mechanics of political numeracy.

The Percentage Paradox

Let's establish the baseline mathematics first. A price reduction from $100 to $10 represents a 90% decrease. The calculation is straightforward: (100 - 10) / 100 = 0.90, or 90%. This is the standard method taught in every introductory economics and mathematics course.

However, there's another way to express this same price change. If we calculate the ratio of the new price to the old price, we get 10/100 = 0.10, meaning the new price is 10% of the original. This is mathematically equivalent but semantically different.

The confusion enters when we consider what "reduction" means. A 90% reduction leaves you with 10% of the original price. Some political communicators have exploited this ambiguity by saying "prices fell by 90%" and "prices are 90% lower," which mean the same thing, while others have tried to claim "prices fell to 90% of original" and "prices fell by 90%" interchangeably.

The 900% Claim

Trump's earlier claim of 900% reductions reveals a different mathematical approach entirely. If a price increases from $10 to $100, that's a 900% increase: ((100 - 10) / 10) × 100 = 900%. By symmetry, a price drop from $100 to $10 should be a 900% decrease using the same formula: ((100 - 10) / 100) × 100 = 90%.

Wait—that's where the logic breaks down. The formula for percentage decrease is always (original - new) / original × 100. So from $100 to $10: (100 - 10) / 100 × 100 = 90%.

The 900% figure comes from using the wrong denominator. If you calculate (100 - 10) / 10 × 100, you get 900%. But that formula calculates how many times the new price fits into the reduction amount, not the percentage reduction relative to the original price.

The Davos Correction

What makes the Davos speech interesting is the apparent correction. "Up to 90%, depending on the way you calculate. You could also say 5-, 6-, 7-, 800%. There are two ways of figuring that."

This statement acknowledges the existence of multiple calculation methods while maintaining that both are valid. They are not. In standard mathematics and economics, there is one correct way to calculate a percentage reduction: (original - new) / original × 100.

The "other way" being referenced is likely one of these:

1. Using the new price as denominator: (100 - 10) / 10 × 100 = 900% - mathematically incorrect for expressing reduction
2. Expressing the new price as percentage of old: 10/100 × 100 = 10% - this shows what's left, not what was reduced
3. Relative to some baseline: Comparing to a hypothetical higher price - this creates a different metric entirely

The Pattern of Selective Numeracy

This isn't isolated to drug pricing. The pattern appears consistently:

• Net worth statements: "Whatever I feel it should be on a given day" suggests subjective valuation
• Crowd size estimates: Different counting methods yield different numbers
• Election results: Various interpretations of the same vote counts

The common thread is treating mathematics as a flexible tool rather than a fixed system. In standard practice, mathematical formulas produce consistent results regardless of who's calculating or why. The "two ways of figuring" approach suggests mathematics is negotiable.

The Real Impact

Focusing solely on the percentage calculation misses the larger question: will these drug pricing deals actually reduce costs? Percentage claims, whether 90% or 900%, depend on:

• Baseline prices: What starting point is used for comparison?
• Timeframe: Are these immediate reductions or phased over years?
• Scope: Which drugs, which companies, which markets?
• Enforcement: What mechanisms ensure compliance?

Without transparent reporting of actual price changes for specific medications, percentage claims remain political rhetoric rather than measurable policy outcomes.

What Proper Reporting Looks Like

When discussing price reductions, credible sources provide:

• Specific examples: "The price of insulin dropped from $300 to $30 per vial"
• Clear methodology: "Based on average prices across major pharmacies"
• Verification: Links to price databases or regulatory filings
• Context: Comparison to international prices or historical trends

The percentage calculation method becomes irrelevant when the underlying numbers are transparent and verifiable.

The Broader Pattern

This case illustrates a broader trend in political communication: the treatment of quantitative claims as persuasive devices rather than factual statements. When "there are two ways of figuring" applies to basic arithmetic, it creates space for any number to serve any purpose.

For technical professionals watching this pattern, the lesson is clear: precision in quantitative communication matters. Whether we're building financial models, analyzing data, or explaining technical metrics, the formulas we use must be consistent, transparent, and defensible. The alternative is a world where numbers mean whatever we need them to mean—which is to say, they mean nothing at all.

The drug pricing debate will continue, but the mathematical questions raised here have clear answers. Percentage reductions follow standard formulas. There aren't "two ways" to calculate a 90% drop. The real question is whether the underlying price changes materialize, and whether they're reported with the same precision we apply to the percentages themselves.