Real vs nominal: what inflation does to your pay

A pay slip from 1976 says $3,000 a year. Today the same job pays $36,000. Twelve times more! A student concludes that workers today are twelve times richer, and the test marks it wrong. The dollars are twelve times more; what the dollars buy is a different question. The two words that keep them apart are nominal and real.

Twelve times the dollars

Take Coralia, the island of the Macroeconomics course. In 1976 Amara's grandfather built boats for $3,000 a year. Amara builds boats in the same yard today for $36,000. Whether she is better off depends on one thing the pay slips do not show: how much prices rose in fifty years. Move the slider and watch grandpa's pay translated into today's dollars.

At × 10, what actually happened on Coralia, grandpa's pay is worth $30,000 in today's dollars. Amara's $36,000 is more, but by 20%, not by a factor of twelve. Slide to × 12 and the two bars meet: twelve times the dollars, exactly the same goods. "Who earned more?" has no answer until you know what prices did.

One number for all prices

How do we know prices rose ten times? The statistics office picks a market basket, a fixed list of things a household buys in a month, and prices the same basket every year. Coralia's basket is 10 kg of fish, 20 loaves of bread and 10 ferry tickets. It cost $40 in 1976 and $400 in 2026.

Then it turns the basket into a price index: pick a base year, give it 100, and give every other year its basket cost as a share of the base year's, times 100. With 1976 as base, 2026 gets $400 ÷ $40 × 100 = 1,000, and 1996, when the basket cost $120, gets 300. The index of what households buy is the consumer price index, the CPI. At 1,000, prices in general are ten times their 1976 level.

Real = nominal ÷ index × 100

Now any pay slip from any year can be put in the same dollars. Divide by the index of its year, multiply by 100, and the answer is in base-year dollars, here 1976 dollars.

The captain of 1996 earned three times grandpa's dollars and bought exactly what grandpa bought. Amara's $3,600 against $3,000 is the 20% of the first graph, reached by the other road: instead of pushing grandpa forward to 2026 dollars, we pulled Amara back to 1976 dollars. Both roads compare goods, not dollars, so both give the same answer.

A raise that is not a raise

The same rule tells you whether a raise is real. Kofi, a dive instructor on Coralia, earned $12,000 in 1996, when the index was 300. In 2016 the index was 750. His 1996 pay was $12,000 ÷ 300 × 100 = $4,000 in 1976 dollars. Slide his 2016 pay and see how much of each raise survives the prices.

At $30,000 Kofi's pay is 2.5 times bigger and buys exactly the same, because prices are 2.5 times higher too. At $22,500 he earns almost twice the dollars and has taken a real pay cut of 25%. For one year there is a shortcut: a raise of 3% while prices rise 5% is a real raise of about 3 − 5 = −2%. Over long stretches the shortcut drifts, so divide by the index. The same rule works for a whole country: Coralia's GDP doubled in dollars from 2006 to 2026, but with its price index at 160 real output grew only 25%.

The trap on tests

• Nominal is what the slip says. Real is what it buys. Twelve times the dollars is a fact about dollars, not about goods.
• Divide by the index, then multiply by 100. Forget the × 100 and Amara earns $36. A base-year amount never changes: its index is 100.
• Use the index of the amount's own year. Amara's pay is divided by 1,000 (2026), the captain's by 300 (1996). Mixing the years is the most common slip.
• A real raise of zero is an answer. Kofi's pay 2.5 times higher with prices 2.5 times higher means he buys the same, and that is what the question wanted.
• "Real" means base-year dollars, 1976 dollars here. Pushing an old amount forward into today's dollars is the same comparison in the other year's money.

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