Price Indices and Inflation: Study Guide (Macroeconomics 2.4)

Why we need a price index

Prices of thousands of goods change every year. Some rise, some fall, and they change by different amounts. A household wants to know one thing: how much more money do I need to keep the same standard of living? A price index answers this with a single number.

Key definitions:

• Price level: the average level of prices in the economy.
• Inflation: a sustained rise in the overall price level.
• Deflation: a fall in the overall price level (the inflation rate is negative).
• Disinflation: the inflation rate falls but stays positive. Prices are still rising, only more slowly.
• Inflation rate: the percentage change in a price index from one period to the next.
• Nominal variable: measured in the money of its own time (for example, this year’s wage in this year’s currency).
• Real variable: a nominal variable adjusted for changes in the price level, so it measures purchasing power.

The consumer price index (CPI)

The consumer price index measures how the cost of a typical consumer’s purchases changes over time. It is built in four steps.

1. Choose a market basket. This is a fixed list of goods and services, with fixed quantities, that represents what a typical household buys.
2. Choose a base year. This is the reference year that every other year is compared with.
3. Price the same basket in every year. The quantities stay fixed; only the prices change.
4. Divide and multiply by 100:

CPI in year t = (cost of the basket in year t ÷ cost of the same basket in the base year) × 100

In the base year the two costs are equal, so the CPI is always 100 in the base year. A CPI of 108 means the basket costs 8% more than in the base year. A CPI of 95 would mean it costs 5% less.

Because the quantities are fixed, the CPI shows the change in income a household needs to buy exactly the same basket. That is why it measures the change in the cost of maintaining a standard of living.

Our fictional economy: Valdoria

Valdoria is a fictional country. Its currency is the valda, written VD. The statistics office chooses 2022 as the base year and this weekly market basket for a typical household:

Item	Quantity	2022 price	2023 price	2024 price	2025 price
Bread (loaves)	20	VD 3.00	VD 3.30	VD 3.45	VD 3.40
Cooking oil (litres)	5	VD 8.00	VD 9.00	VD 9.40	VD 9.20
Bus rides	30	VD 1.50	VD 1.60	VD 1.70	VD 1.70
Haircuts	2	VD 27.50	VD 28.50	VD 29.50	VD 30.00

All prices are fictional.

Worked example 1: calculating the CPI and the inflation rate

Question. Calculate the CPI for each year from 2022 to 2025 (base year 2022), and the inflation rate for 2023, 2024 and 2025. Describe what happened to the price level.

Step 1: cost of the basket in each year (quantity × price, then add).

Item	2022	2023	2024	2025
Bread	20 × 3.00 = 60	20 × 3.30 = 66	20 × 3.45 = 69	20 × 3.40 = 68
Oil	5 × 8.00 = 40	5 × 9.00 = 45	5 × 9.40 = 47	5 × 9.20 = 46
Bus	30 × 1.50 = 45	30 × 1.60 = 48	30 × 1.70 = 51	30 × 1.70 = 51
Haircuts	2 × 27.50 = 55	2 × 28.50 = 57	2 × 29.50 = 59	2 × 30.00 = 60
Total cost	VD 200	VD 216	VD 226	VD 225

Step 2: CPI = (cost in year ÷ VD 200) × 100.

• 2022: (200 ÷ 200) × 100 = 100.0 (base year)
• 2023: (216 ÷ 200) × 100 = 108.0
• 2024: (226 ÷ 200) × 100 = 113.0
• 2025: (225 ÷ 200) × 100 = 112.5

Step 3: inflation rate = (new CPI − old CPI) ÷ old CPI × 100.

• 2023: (108 − 100) ÷ 100 × 100 = 8.0%
• 2024: (113 − 108) ÷ 108 × 100 = 5 ÷ 108 × 100 = 4.63%
• 2025: (112.5 − 113) ÷ 113 × 100 = −0.5 ÷ 113 × 100 = −0.44%

Interpretation. From 2023 to 2024 Valdoria had disinflation: prices still rose, but the inflation rate fell from 8.0% to 4.63%. In 2025 the price level fell slightly, so Valdoria had deflation of about 0.44%.

Check. The 2024 rate is not 13% − 8% = 5%. The 5-point rise in the index is divided by the 2023 index (108), not by 100. Only when the old index is 100 do index points equal percentages.

Using an index to compare values across years

Money values from different years cannot be compared directly, because a valda buys different amounts in different years. A price index converts a nominal value into a real value, measured in base-year money:

Real value = (nominal value ÷ price index) × 100

To express a value from one year in the money of another year, scale by the ratio of the indices:

Value in year B money = value in year A money × (index in year B ÷ index in year A)

Percentage change in a real value ≈ percentage change in the nominal value − inflation rate. This shortcut is close when rates are small; the exact method is to compare the real values.

Worked example 2: is the worker better off?

Question. A Valdorian bus driver earned VD 500 a week in 2022 and VD 560 a week in 2024. (a) Calculate her real weekly wage in 2024, in 2022 valdas. (b) Did her purchasing power rise or fall? (c) What wage would she need in 2025 to have the same purchasing power as in 2022?

(a) Real wage 2024 = 560 ÷ 113 × 100 = VD 495.58 (in 2022 valdas). Her 2022 real wage is 500 ÷ 100 × 100 = VD 500, because 2022 is the base year.

(b) Her nominal wage rose by (560 − 500) ÷ 500 × 100 = 12%. Prices rose by 13% over the same period (CPI 100 → 113). Her real wage changed by (495.58 − 500) ÷ 500 × 100 = −0.88%. Her purchasing power fell slightly, even though she earns more valdas. The shortcut 12% − 13% = −1% gives almost the same answer.

(c) Wage needed = 500 × (112.5 ÷ 100) = VD 562.50 a week.

Check. The 2025 CPI is below the 2024 CPI, so the 2025 wage needed (VD 562.50) is just below the wage that would have matched 2024 prices (500 × 1.13 = VD 565).

Why the CPI may overstate inflation

The CPI prices a fixed basket. Real households do not buy a fixed basket. This is why the CPI tends to overstate the true rise in the cost of living.

• Substitution bias. When one good becomes relatively more expensive, consumers switch to relatively cheaper substitutes. The fixed basket ignores this switch, so it overstates how much more people really need to spend. In Valdoria, if oil prices jump, households may cook with less oil or switch to a cheaper fat, but the CPI still prices 5 litres of oil.
• Quality changes. If a product’s price rises because it has improved (a faster phone, a safer car), part of the price rise buys more quality. The CPI may count all of it as inflation.
• New goods. New products often enter the basket only years after they appear, after their prices have already fallen. The early fall in their prices is missed.

The course requires you to explain that the CPI has shortcomings, such as substitution bias. Quality changes and new goods are further examples you can use.

Out of scope here. The producer price index (PPI) is beyond the course. The inflation rate can be found from any price index, including the GDP deflator, with the same percentage-change formula; calculating the GDP deflator itself is in Topic 2.6, Real v. Nominal GDP.

Common misconceptions

• “A CPI of 113 means inflation is 113%.” No. It means prices are 13% higher than in the base year.
• “Inflation rate = difference in index points.” Only when the earlier index is 100. From 108 to 113 the rise is 5 points but 4.63%.
• “Falling inflation means falling prices.” A lower but positive inflation rate is disinflation; prices still rise. Prices fall only with deflation.
• Dividing by the new index. The percentage change uses the earlier index as the denominator.
• “Inverting the CPI ratio.” The CPI is cost in the given year ÷ cost in the base year, not the other way round.
• “A higher nominal wage means a better standard of living.” Only if it rises faster than prices. Compare real wages.
• Changing the quantities each year. The basket must stay fixed; otherwise the index mixes changes in prices with changes in what is bought.
• “The CPI understates inflation because of substitution.” Substitution makes the CPI overstate inflation.

Where this leads

Next you will look at who gains and who loses from inflation (Topic 2.5), then use a price index to separate real from nominal GDP (Topic 2.6). Try the practice questions now, then use the revision notes and the checklist to consolidate.