Consumer price index number

1. NADEEM UDDIN
ASSOCIATE PROFESSOR
OF STATISTICS

2. Consumer price index number:
Consumer price index number is also known as cost of living index
or retail price index number. It is designed to measure the changes
in the composite price of a specified “basket” of goods and
services during the given period as compared with the base period.
The basket of goods and services include the followings.
i- Food and beverages
ii- House Rent
iii- Clothing and footwear
iv- Fuel and lighting
v- Education
vi- Services
vii- Miscellaneous items

3. The cost of living index numbers are constructed to examine the
effects of rise in prices on the family budgets of different classes.
We use any of the following two methods for CPI computations.
a) The Aggregative Expenditure method:
In aggregative expenditure method , quantities consumed in
the base period are used as weights, therefore we use
Laspeyre’s formula.
𝐶𝑃𝐼 =
Σ𝑃𝑛𝑄𝑜
Σ𝑃𝑜𝑄𝑜
𝑥 100

4. b) Family Budget or House Hold Budget Method:
Family budget method is also known as weighted average of
price relatives method. In this method family budget enquiry
is conducted to estimate the total expenditure of an average
family upon different commodities.
𝐶𝑃𝐼 =
Σ IW
Σ W
Where W = Po Qo ; 𝐼 =
𝑃𝑛
𝑃𝑜
𝑥 100

5. Example-1
Construct cost of living index number of 2016 on the basis 2014 using ;
a) Aggregate expenditure method and
b) Family budget method.
Article Quantity
consumed
in 2014
Unit Price in
2014
Rs.
Price in
2016
Rs.
Rice 6 Kilo Kilo 6.00 6.50
Wheat 6 Kilo Kilo 5.00 8.00
Grain 1 Kilo Kilo 6.00 9.00
Tea 4 Kilo Kilo 8.00 10.00
Ghee 2 Kilo Kilo 8.00 8.00
Sugar 1 Kilo Kilo 20.00 16.00

6. Solution:
(a) Quantity
consumed
in 2014(𝑄𝑜)
Price in
2014
Rs.( 𝑃𝑜)
Price in
2016
Rs.( 𝑃𝑛)
𝑃𝑜𝑄𝑜 𝑃𝑛𝑄𝑜
6 Kilo 6.00 6.50 36 39
6 Kilo 5.00 8.00 30 48
1 Kilo 6.00 9.00 6 9
4 Kilo 8.00 10.00 32 40
2 Kilo 8.00 8.00 16 16
1 Kilo 20.00 16.00 20 16
Σ𝑃𝑜𝑄𝑜
= 140
Σ𝑃𝑛𝑄𝑜
= 168
𝐶𝑃𝐼 =
Σ𝑃𝑛𝑄𝑜
Σ𝑃𝑜𝑄𝑜
𝑥 100
𝐶𝑃𝐼 =
168
140
𝑥 100
𝐶𝑃𝐼 = 120%
Comments:
The Prices increased by 20% in the year 2016 with respect to 2014.

7. (b)
Quantity
consumed
in 2014(𝑄𝑜)
Price in 2014
Rs.( 𝑃𝑜)
Price in
2016
Rs.( 𝑃𝑛)
𝑊 = 𝑃𝑜𝑄𝑜
𝐼 =
𝑃𝑛
𝑃𝑜
× 100
IW
6 Kilo 6.00 6.50 36 108.33 3900
6 Kilo 5.00 8.00 30 160 4800
1 Kilo 6.00 9.00 6 150 900
4 Kilo 8.00 10.00 32 125 4000
2 Kilo 8.00 8.00 16 100 1600
1 Kilo 20.00 16.00 20 80 1600
Σ𝑊 = 140 Σ𝐼𝑊
= 16800
𝐶𝑃𝐼 =
Σ IW
Σ W
𝐶𝑃𝐼 =
16800
140
𝐶𝑃𝐼 = 120%
Comments:
The Prices increased by 20% in the year 2016 with respect to 2014.

8. Example-2
Calculate the changes in the cost of living figures in 2011 as compared
with 2010 are seen?
Group Expenses
2010 2011
Price in
Rupees
Price in
Rupees
Food 35 150 145
Rent 20 75 65
Clothing 15 30 30
Fuel 20 40 45
Misc. 10 25 23
Solution:

9. Expenses
(W)
2010 2011
𝐼 =
𝑃𝑛
𝑃𝑜
× 100
𝐼𝑊
Price in
Rupees (𝑃𝑜)
Price in
Rupees (𝑃𝑛)
35 150 145 96.67 3383.45
20 75 65 86.67 1733.33
15 30 30 100 1500
20 40 45 112.5 2250
10 25 23 92 920
Σ𝑊 = 100 Σ𝐼𝑊
= 9786.78
𝐶𝑃𝐼 =
Σ IW
Σ W
𝐶𝑃𝐼 =
9786.78
100
𝐶𝑃𝐼 = 97.87%
Comments:
The Prices decreased by 2.13% in the year 2011 with respect to 2010.

10. Group Index Number Weights
Food 352 48
Lighting Fuel 220 10
Clothing 230 8
Rent 160 12
Miscellaneous 190 15
Example-3
Prepare the cost of living index number.
Solution:

11. Group Index Number
(I)
Weights
(W)
𝐼𝑊
Food 352 48 16896
Lighting Fuel 220 10 2200
Clothing 230 8 1840
Rent 160 12 1920
Miscellaneous 190 15 2850
Σ𝑊 = 93 Σ𝐼𝑊
= 25706
𝐶𝑃𝐼 =
Σ IW
Σ W
𝐶𝑃𝐼 =
25706
93
𝐶𝑃𝐼 = 276.41%
Comments:
The Prices increased by 176.41% .