Cost of Living Index — Class 12 Statistics Notes (GSEB)

What is Cost of Living Index?

The Cost of Living Index (CLI) measures the change in the cost of maintaining a certain standard of living over time. It tells us how much more (or less) a family needs to spend to buy the same basket of goods and services compared to the base year.

CLI is based on CPI (Consumer Price Index). It uses weighted average of price relatives, where weights represent the proportion of income spent on each item.

Think of it this way

If your family spent ₹20,000/month in 2015 and the same lifestyle costs ₹26,000 in 2024, the CLI = (26000/20000) × 100 = 130 — a 30% rise in cost of living.

How CLI is Constructed

The process flows from collecting prices to applying wage adjustments:

Current Prices

P₁ of each item

Weight by Expenditure

W = P₀q₀

Compute Index

ΣRW / ΣW

Apply DA

Wage revision

Formula — Weighted Average of Price Relatives

Cost of Living Index

CLI = \frac{\sum RW}{\sum W} = \frac{\sum \left(\frac{P_1}{P_0} \times 100\right) \times W}{\sum W}

R = Price Relative

R = (P₁ / P₀) × 100

W = Weight

Expenditure on item

Base Year CLI

Always = 100

If CLI > 100 → cost of living has risen. If CLI < 100 → cost of living has fallen. Workers receive Dearness Allowance (DA) to compensate for the rise.

Worked Example

A family's expenditure pattern and current prices:

Item	Weight (W)	P₀	P₁	R = P₁/P₀ × 100	RW
Food	45	100	115	115.0	5175.0
Housing	15	100	110	110.0	1650.0
Transport	12	100	120	120.0	1440.0
Clothing	10	100	108	108.0	1080.0
Education	8	100	125	125.0	1000.0
Others	10	100	112	112.0	1120.0
Total	100				11465.0

CLI = ΣRW / ΣW = 11465.0 / 100 = 114.7

Cost of living has risen by 14.7% compared to the base year

Applications of CLI

Limitations of CLI

Important limitations to remember:

⚠Does not account for quality improvements — a 2024 phone costs more but does far more than a 2015 phone.
⚠Assumes a fixed consumption basket — but people substitute expensive items with cheaper ones over time.
⚠Based on averages — individual families may have very different expenditure patterns.
⚠Does not capture new products — smartphones didn't exist in the 1990s CPI basket.

Key Takeaways

CLI measures the change in cost of maintaining a fixed standard of living — constructed using CPI.
Formula: CLI = ΣRW / ΣW — weighted average of price relatives.
Base year CLI = 100. If CLI > 100, cost of living has risen.
Used for Dearness Allowance (DA), wage revision, and pension adjustment.
DA = [(CLI - 100) / 100] × Basic Salary — compensates workers for price rises.
Limitations: ignores quality changes, assumes fixed basket, based on averages.