Price Indices & Calculating Inflation

You’ll be able to

Construct a price index from a market basket and a base year
Compute the inflation rate between two years from index values
Compare the CPI with the GDP deflator and identify each one's bias

An index is a ratio dressed up as a number

A price index tracks the cost of a fixed market basket relative to a base year. Cost the basket at current prices, divide by its cost in the base year, multiply by 100. The base year is therefore always exactly 100 — not a coincidence, a definition. An index of 125 means the basket costs 25% more than in the base year. The index value itself has no units and is not a price; only changes in it mean anything.

Index and inflation rate

CPI = (cost of basket now / cost in base year) × 100 · inflation = (CPI_new − CPI_old) / CPI_old × 100

The inflation rate divides by the OLD index, not the new one and not 100. Dividing by 100 is the most common error here.

Why the CPI overstates inflation

The CPI holds the basket fixed, which builds in two biases. Substitution bias: when beef gets expensive people buy chicken, but the fixed basket keeps buying beef, so the measured cost rises more than the cost people actually bear. Quality-change and new-goods bias: a phone that costs the same as five years ago is a far better phone, and treating the price as unchanged misses the improvement. Both push the same direction, so the CPI tends to overstate true inflation — which matters because social security and many contracts are indexed to it.

CPI versus the GDP deflator

The CPI tracks a fixed basket of what a typical urban consumer buys, including imports. The GDP deflator covers everything a country produces, excludes imports, and its basket changes every year with the composition of output. So they answer different questions: the CPI is the right measure for the cost of living and for indexing a pension, and the deflator is the right one for converting nominal GDP into real GDP. A jump in imported oil prices moves the CPI sharply and the deflator barely.

Worked example

A basket of 10 loaves and 5 shirts cost $50 in the base year 2020. In 2024 the same basket costs $62, and in 2025, $65. Find the 2024 and 2025 index values and the inflation rate from 2024 to 2025.

1.2020 is the base year, so its index is 100 by definition.
2.2024 index = 62/50 × 100 = 124.
3.2025 index = 65/50 × 100 = 130.
4.Inflation 2024→2025 = (130 − 124) / 124 × 100.
5.= 6/124 × 100 = 4.8%.

Answer: Index 124 in 2024 and 130 in 2025, with 4.8% inflation between them. Note it is not 6% — dividing the 6-point change by 100 instead of by the old index of 124 is the standard mistake.

Watch out

A change of 6 index points is not 6% inflation unless the old index was exactly 100. Points and percent coincide only in the base year, and the exam picks non-base years precisely to test whether you noticed.

Checkpoint

A price index rises from 150 to 165. The inflation rate is:

Checkpoint

The CPI is widely believed to overstate the true cost-of-living increase, in part because:

Checkpoint

Which measure would you use to convert nominal GDP into real GDP?

On the exam

Free-response calculations must show the setup, not just the answer. Writing "(130 − 124)/124 × 100" earns the method point even if the arithmetic slips, while a bare "4.8%" can lose everything if it is wrong.

Answer the 3 checkpoints as you read.