Inflation & Price Indexes
The CPI fixes quantities and lets prices move — the exact mirror of real GDP. To move money across years, multiply by new CPI ÷ old CPI. And r = i − π: real activity responds to r, not i.
Formulas
Converting across time — two worked cases
| Item | Then | CPI then → now | In today's dollars | Actual today | Verdict |
|---|---|---|---|---|---|
| Cal in-state tuition, 1985–86 | $1,296 | 108.94 → 300.536 | $3,575 | ≈$14,796 | Real tuition rose enormously |
| Good desktop computer, 1996 | $4,000 | 156.85 → 300.536 | $7,664 | ≈$1,000 | Real price of computing collapsed |
The basket goes stale
Smartphones and electric cars did not exist in 1983, so the BLS updates the basket, now annually. Old basket = Laspeyres, new = Paasche, geometric average = Fisher, usually chained. Edwards says the details are not on the exam; that the basket changes, and why, is fair game. Quality improvements are netted out of price rises; new goods count as new ways of obtaining utility.
Why care about inflation?
- The case for not caring
- Expenditure equals income in aggregate, so if all prices and incomes rise together nothing real changes — like arguing about Daylight Saving Time.
- Redistribution
- Unexpected inflation transfers from lenders to borrowers and hurts fixed nominal incomes.
- Psychology
- People feel price rises as theft and wage rises as merit, so inflation feels worse than the arithmetic. It moves elections.
- Efficiency
- Volatile prices make real signals harder to read and plans harder to make.
- How bad it gets
- Chronically high, as in Argentina since 2002; or hyperinflation, as in Venezuela 2018–2020.
The Fisher relation is the bridge to everything
Real activity responds to r, not i. The real rate is the price of spending today — the opportunity cost of what you forgo tomorrow — and it can go negative: policymakers pricing today's spending low enough to induce it. It explains the Great Depression's worst mechanism. Nominal rates fell, but consumer prices collapsed, so π went sharply negative and the real rate soared — borrowing turned ruinous exactly when the economy needed spending.
Rules that earn points
- To compare money across years, multiply by new CPI over old CPI. Sanity-check the direction.
- To judge a real price change, compare the good's growth factor to the CPI's growth factor.
- Whenever interest rates appear, convert to real: r = i − π.
- Flipping the CPI ratio. Converting an old amount to today's dollars must make it bigger.
- Confusing the CPI's fixed quantities with real GDP's fixed prices.
- Reasoning about spending with the nominal rate. Use the real rate.
A good desktop computer cost about $4,000 in 1996, when the CPI was 156.85. The CPI is now 300.536. In today's dollars that 1996 price is:
- A$2,088
- B$4,000
- C$7,664
- D$1,000
Answer
C — $7,664.
$4,000 × (300.536 / 156.85) = $7,664. Since a comparable desktop costs about $1,000 today, the real price of computing collapsed.
A is the trap: it inverts the ratio, 4,000 × (156.85 / 300.536) = $2,088. Converting an old amount into today's dollars must make it bigger, because today's dollars are worth less. Check the direction before you reach for a calculator.
Which statement correctly contrasts the CPI with real GDP?
- ABoth fix base-year prices and let quantities move
- BThe CPI fixes base-year quantities and lets prices move; real GDP fixes base-year prices and lets quantities move
- CThe CPI fixes base-year prices and lets quantities move; real GDP does the reverse
- DBoth fix base-year quantities and let prices move
Answer
B — CPI fixes quantities, real GDP fixes prices.
The CPI asks what a fixed basket costs as prices change. Real GDP asks what changing output would be worth at fixed prices. They are exact mirror images, which is why the base-year quantities in the CPI are called the weights.
C is the trap: the right structure, the wrong way round. If you can only remember one, remember that a cost-of-living index must hold the shopping basket constant.
A savings account pays a nominal interest rate of 10% while inflation runs at 9%. The real return is:
- A10%
- B9%
- C1%
- D19%
Answer
C — 1%.
r = i − π = 10 − 9 = 1. The nominal rate is compensation for inflation plus the real return; almost all of this one is compensation.
A is the trap, and it is the mistake that makes high-inflation periods look like good times to save. Real activity responds to r, not i.
During the early Great Depression nominal interest rates fell, yet the real interest rate soared. Why?
- ANominal rates actually rose once taxes are accounted for
- BConsumer prices collapsed, so π turned sharply negative and r = i − π rose
- CInflation rose faster than nominal rates
- DThe Fed raised its target above 2%
Answer
B — severe deflation.
Subtracting a large negative π from a small positive i produces a high real rate. Borrowing became ruinously expensive exactly when the economy needed spending, and the real burden of existing debts rose.
C is the direction flip. Rising inflation would have lowered the real rate — which is the opposite of what happened after 1929.
A Big Mac cost $1.60 in 1986 and $5.65 in 2021, about 3.5 times higher. Over the same period the CPI went from about 110 to about 271, about 2.5 times higher. (a) Has the real price of a Big Mac risen, fallen or stayed flat? (b) Can making and serving a Big Mac be automated, and what does that imply for its marginal cost over time?
Model answer
(a) The real price has risen. The Big Mac rose by a factor of 3.5 while the general price level rose by a factor of 2.5. The good outpaced the basket, so it costs more in inflation-adjusted terms: if your income grew at the rate of inflation, you can buy fewer Big Macs in 2021 than in 1986.
(b) No — it requires workers and a physical facility. Cooking and serving are hard to move into a factory, so the mechanism that drove down the real price of manufactured goods — factory automation cutting marginal costs — is largely unavailable. Marginal cost stays tied to labor costs, which rise with wages, so the real price drifts up. Contrast the desktop computer, which fell from $7,664 in today's dollars to about $1,000.
- Comparing growth factors, 3.5 against 2.5 — not raw dollar amounts.
- Stating the verdict as real price rose, with the reason attached.
- The purchasing-power restatement: fewer Big Macs on an inflation-indexed income.
- In (b), naming automation and marginal cost as the mechanism, not just "it's a service."
- A contrasting good whose real price fell, with a number.
Cal in-state tuition and fees were $1,296 in 1985–86, when the CPI was 108.94. The CPI is now 300.536, and tuition and fees are now about $14,796. Express the 1985–86 figure in today's dollars and interpret the result.
Model answer
So 1985–86 tuition was equivalent to about $3,575 in today's dollars. Actual tuition and fees are roughly $14,796 — more than four times as much.
Real tuition and fees have risen enormously, far faster than general inflation. This is not a price-level story; it is a real change in the cost of public higher education.
- The formula written with the ratio the right way up: new CPI over old.
- A converted figure larger than $1,296 — the direction check.
- Comparing $3,575 against the actual $14,796, not against $1,296.
- Saying the increase is real, i.e. over and above inflation.