---
title: Price Indexes and Inflation
url: https://doc.liz6.com/en/general-education/economics-foundations/18-price-indexes-and-inflation
locale: en
area: general-education
tags:
- General Education
- Economics Foundations
- General education
- Economics foundations
date: 2026-09-12
modified: 2026-09-12
description: 'Food prices have risen, but ticket prices have remained unchanged, yet two families report that their cost of living has increased by 25% and 10%, respectively. Who calculated it wrong? Possibly neither: they purchase different goods and assign different expenditure weights. Price indices synthesize many prices into a single number; the first step is to specify what is in the basket and how it is weighted.'
---
# Price Indexes and Inflation
Prerequisites: [GDP and National Income](/en/general-education/economics-foundations/17-gdp-and-national-income)
Food prices have risen, but ticket prices have remained unchanged, yet two families report that their cost of living has increased by 25% and 10%, respectively. Who calculated it wrong? Possibly neither: they purchase different goods and assign different expenditure weights. Price indices synthesize many prices into a single number; the first step is to specify what is in the basket and how it is weighted.
This article uses two fixed shopping baskets for calculations, distinguishing between price levels, inflation rates, and real purchasing power. The numbers are set for teaching purposes; in reality, the selection of goods, treatment of housing, quality adjustments, and weight updates in CPI compilation follow specific statistical rules, so this two-good example should not be taken as a complete method of compilation.
## Record quantities first, then calculate the bill
In the base period, food costs 2 yuan per unit and transportation costs 4 yuan per trip. Family A buys 10 units of food and 5 trips of transportation per period; Family B buys 5 units of food and 10 trips of transportation. Now, food prices rise to 3 yuan, while transportation prices remain unchanged.
| Family | Base Period Food Expenditure | Base Period Transportation Expenditure | Base Period Total | New Bill at Original Quantities | Increase |
| --- | ---: | ---: | ---: | ---: | ---: |
| A | 20 | 20 | 40 | 30+20=50 | 25% |
| B | 10 | 40 | 50 | 15+40=55 | 10% |
Food prices themselves rose by 50%, but the total bills for both households did not rise by 50%, because only a portion of their expenditures was allocated to food. Family A's base period food weight was 50%, and Family B's was 20%; in this fixed basket example, the total increases are `50%×50%=25%` and `20%×50%=10%`, respectively.
A fixed basket price index is typically written as "cost of purchasing base period quantities at current prices / cost of purchasing the same quantities at base period prices × 100". Family A's index goes from 100 to 125, and Family B's from 100 to 110. An index of 125 does not mean 125 yuan, but rather a level relative to the base period of 100.
**Change conditions, check results**
Base index 100; food weight 50%, food rise 50%, and unchanged transport give index 125. Weight and price rise can change separately.
First, keep the food price increase at 50% and only change the base period food weight. The results show how the same price change corresponds to different living experiences; it does not change the food price due to changes in your weight. Then, fix the weight and change the increase rate to distinguish between "prices changed" and "the synthesis method changed."
## A decline in inflation does not mean things have become cheap again
Family A's price index went from 100 to 125, so the inflation rate in the first period was 25%; in the next period, it went from 125 to 127.5, with an inflation rate of `(127.5−125)/125=2%`. Although the inflation rate has dropped significantly, the price level is still 2% higher than the previous period and 27.5% higher than the initial period.
| Period | Price Index | Increase Relative to Previous Period |
| --- | ---: | ---: |
| Base Period | 100 | — |
| Period 1 | 125 | 25% |
| Period 2 | 127.5 | 2% |
Slowing price increases are usually referred to as disinflation; a decrease in the price level is deflation. A drop from 125 to 122.5 would be −2%. Interpreting "inflation falling to 2%" as "prices dropped by 2%" confuses the rate of change with the level.
When comparing year-on-year and month-on-month figures, one must also look at the base. If prices remain unchanged in a certain month, the year-on-year increase may still decline if there was an abnormal price surge exactly one year ago; this does not automatically imply that current demand or production capacity has changed by the same magnitude.
## Wages rose, so why did purchasing power still fall
Family A's nominal disposable income increased from 40 to 44, a rise of 10%, while the price of the same basket increased from 40 to 50, a rise of 25%. Previously, one basket could be bought; now, only `44/50=0.88` baskets can be purchased, representing a 12% decline in purchasing power.
The precise relationship for real change is `(1 + nominal growth rate) / (1 + price increase rate) − 1`, which here is `1.10/1.25−1=−12%`. Simply subtracting 10%−25%=−15% yields only the difference and cannot masquerade as the precise real growth rate when increases are large; subtraction is a common approximation only for small changes.
Similarly, with a deposit interest rate of 5% and a relevant price increase of 2%, the change in real purchasing power after one year is `1.05/1.02−1≈2.94%`. Taxes and the price index used must also be considered, but separating nominal from real values prevents automatically equating an increase in account balances with an equivalent increase in wealth.
## Adding back substitution behavior and quality changes
After food prices rose, Family A might reduce consumption of certain foods and switch to substitutes. If the basket is no longer fixed, the actual bill may not rise by 25%; however, a bill that does not rise could also be due to buying less or lowering quality, so one cannot immediately conclude that the cost of living has not changed.
Conversely, if the quality of new goods improves, a rise in the sticker price may not be entirely due to "the same thing becoming more expensive." Real-world statistics handle specification replacements, quality differences, seasonality, and weight updates, with each method having its own scope of application. Fixed basket indices, other weighted indices, and the ideal cost-of-living concept cannot be interchanged without explanation.
CPI typically focuses on consumer prices for residents and is not equivalent to all asset prices or the prices of all domestic output; GDP price indices cover a different set of objects. Core inflation excludes certain volatile items according to specific indicators to observe trends, which does not imply that these items are unimportant to households.
## How prices are measured and why they rise are two different questions
The same index rise may stem from increased demand, energy supply disruptions, exchange rate changes, cost pass-through, or multiple factors. An index merely describes the price outcome first and does not automatically tell us which cause is responsible.
If the primary cause is a rise in imported energy prices, increased enterprise costs may push up prices and suppress output; if demand broadly exceeds existing production capacity, the short-term changes in prices and output may differ. To distinguish between these, one needs to combine component prices, quantities, wages, capacity, orders, and expectations, rather than just seeing inflation and filling in a single unique cause.
Expectations also affect current wages, quotes, and financing conditions. Long-term stable price expectations can alter the transmission of a one-time shock, but "expectations" should be supported by surveys, contracts, or market evidence, and cannot serve as a catch-all explanation when nothing else fits. The sections on fiscal and monetary policy will separately track demand and financing paths.
## Verify with a new basket
A family's base period food expenditure accounts for 30% of the total. Food prices rise by 20%, while other goods remain unchanged, and quantities are fixed. To what does the index rise from 100? If income rises by 5%, how does real purchasing power change?
Expand Reasoning
The basket increase is `30%×20%=6%`, so the index becomes 106. The change in real purchasing power is `1.05/1.06−1≈−0.94%`. One cannot substitute the food price increase of 20% for the total basket increase, nor can one assert real improvement simply because nominal income has risen.
Expand Reasoning
Yes. 3% still indicates that the overall price level is rising, just more slowly; supermarket goods may also have different weights and changes compared to the overall basket. First, verify the period, whether it is year-on-year or month-on-month, and the component versus overall indices, before judging if there is a contradiction. Individual bills differ from statistical indices, and this does not automatically mean one of them is wrong.