Consumer price index (cost of living index): family budget method
Business Statistics · Unit V · Topic 15 of 15 · 5 min read
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1. Meaning
A consumer price index (also called cost of living index) measures the average change in the retail prices of goods and services consumed by a defined class of people (industrial workers, agricultural labourers, urban employees) between a base period and the current period. It answers the question: how much more must this class spend now to maintain the base-period standard of living?
The general wholesale price index does not answer this, because different classes buy different things, pay retail not wholesale prices, and spend in different proportions. Hence a CPI is always made for a specific group and place.
In India, consumer price indices (Rural, Urban and Combined) are compiled by the National Statistics Office under the Ministry of Statistics and Programme Implementation; the CPI for Industrial Workers is compiled by the Labour Bureau. The headline CPI (Combined) is the measure used for the RBI’s inflation target.
2. Uses
- Wage and dearness-allowance fixation: DA of government and industrial employees is linked to the CPI.
- Real wages and purchasing power: real wage = money wage / CPI × 100; purchasing power of the rupee = 100 / CPI.
- Monetary and fiscal policy: the inflation rate on which the central bank acts.
- Deflating national income and sales figures into constant prices.
- Market and wage negotiation: settlements, rent agreements, escalation clauses.
3. Steps in construction
- Decide the class of people and the area (e.g. middle-class families in Mumbai).
- Family budget enquiry: a sample survey of families to find what they buy and how much they spend on each item; this gives the weights.
- Group the items: food, clothing, fuel and lighting, housing (rent), miscellaneous.
- Collect retail prices of the items in the shops where this class buys, for the base and current periods.
- Compute price relatives and combine them with weights by one of the two methods below.
4. The two methods
(a) Aggregate expenditure (aggregative) method: CPI = Σp1q0 / Σp0q0 × 100, i.e. Laspeyres with base-year quantities as weights. Used when quantities consumed are known.
(b) Family budget method (weighted average of relatives): CPI = ΣIW / ΣW, where I = p1/p0 × 100 for each item (or the group index if given) and W = value weight, p0q0, or the percentage of expenditure. Both methods give the same answer when W = p0q0.
5. Worked: group indices given (January 2026)
Construct the cost of living index for 2009 on base 2005.
| Group | Index (I) | Weight (W) | IW |
|---|---|---|---|
| Food | 122 | 32 | 3,904 |
| House rent | 140 | 15 | 2,100 |
| Cloth | 112 | 18 | 2,016 |
| Fuel | 116 | 10 | 1,160 |
| Miscellaneous | 106 | 25 | 2,650 |
| Total | 100 | 11,830 |
CPI (2009) = 11,830 / 100 = 118.30. The cost of living rose by 18.3% between 2005 and 2009.
6. Worked: indices for two years (January 2025)
| Item | W | I (2008) | IW (2008) | I (2012) | IW (2012) |
|---|---|---|---|---|---|
| Food | 33 | 140 | 4,620 | 210 | 6,930 |
| Clothing | 10 | 220 | 2,200 | 300 | 3,000 |
| Fuel | 5 | 125 | 625 | 140 | 700 |
| Housing | 12 | 150 | 1,800 | 200 | 2,400 |
| Others | 11 | 135 | 1,485 | 160 | 1,760 |
| Total | 71 | 10,730 | 14,790 |
- CPI 2008 = 10,730 / 71 = 151.13.
- CPI 2012 = 14,790 / 71 = 208.31.
- If asked for 2012 on 2008 as base: 208.31 / 151.13 × 100 = 14,790 / 10,730 × 100 = 137.84, i.e. a 37.84% rise.
Note that the weights total 71, not 100; divide by ΣW, whatever it is.
7. Worked: prices and percentage weights (August 2024)
Budgets of middle-class families in Mumbai. What change in the cost of living in 2013 has taken place compared with 2002?
| Item | W (%) | p0 (2002) | p1 (2013) | I = p1/p0 × 100 | IW |
|---|---|---|---|---|---|
| Food | 20 | 300 | 500 | 166.67 | 3,333.33 |
| Rent | 10 | 100 | 200 | 200.00 | 2,000.00 |
| Clothing | 5 | 40 | 300 | 750.00 | 3,750.00 |
| Fuel | 3 | 120 | 80 | 66.67 | 200.00 |
| Electricity | 8 | 95 | 220 | 231.58 | 1,852.63 |
| Vegetables | 12 | 40 | 98 | 245.00 | 2,940.00 |
| Refreshments | 12 | 85 | 100 | 117.65 | 1,411.76 |
| Miscellaneous | 30 | 500 | 600 | 120.00 | 3,600.00 |
| Total | 100 | 19,087.72 |
CPI (2013) = 19,087.72 / 100 = 190.88. The cost of living of these families rose by about 90.88% between 2002 and 2013.
8. CPI and WPI compared
| Point | CPI | WPI |
|---|---|---|
| Prices | Retail | Wholesale |
| Coverage | Goods and services consumed by a class | Goods only, at the first stage of bulk sale |
| Purpose | Cost of living, DA, inflation targeting | General price level in trade and industry |
| Compiled by (India) | NSO (MoSPI); Labour Bureau for CPI-IW | Office of the Economic Adviser, DPIIT |
Limitations of CPI: based on a sample of families, so not exact for any one family; consumption patterns change and the fixed basket ages; quality changes are hard to capture; retail prices vary from shop to shop.
How this is examined
Cost of living index from group indices: January 2026 and January 2025 (six marks). Family budget method from prices and percentage weights: August 2024 (ten marks). Theory: “Write a short note on Consumer Price Index” (January 2026) and “Write a note on cost of living index” (June 2025). In the note, cover meaning, uses, steps and the two methods with their formulas.
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