The document discusses consumer price index (CPI), which is used to measure inflation. It provides examples of calculating CPI using the Laspeyre formula under the aggregate expenditure method and weighted average of price relatives method. CPI is used to measure changes in cost of living and purchasing power over time. It also discusses how CPI can be used to calculate real income by adjusting current income for inflation. Higher CPI indicates higher inflation and lower purchasing power of money.

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 = PoQo ; 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% .

12. USES of Consumer price index number:
PURCHASING POWER
1- Purchasing power means how your money can buy.
2- You gain Purchasing power when prices goes down .
3- You lose Purchasing power when prices goes up.
The formula of Purchasing power is
Purchasing Power =
1
CPI
x 100

13. Year Consumer Price Index
2000 = 100
2000 100
2002 110
2004 120
2006 190
2008 200
Example-4 Find Purchasing Power of the Rupees.
Solution:
Year Consumer Price Index
2000 = 100
Purchasing Power =
1
CPI
x 100
2000 100 1
2002 110 0.91
2004 120 0.83
2006 190 0.53
2008 200 0.50
Comments
Purchasing power shows a continuously decreasing in buying
of goods and services.

14. REAL INCOME
1- It is the amount of money you have and the buying power,
based on the rate of inflation.
2- If the inflation rate is high then the real income goes down
and purchasing power decreases.
3- If the inflation rate is low then the real income goes up and
purchasing power increases.
The formula of real income is
Real Income =
current Income
C P I
𝑥 100

15. Example-5
Find Real Income (Deflated Income).
Year Money Income
Rs.
Consumer Price Index
2000 = 100
2000 25000 100
2005 27000 120
2010 31000 160
2015 36000 200
Solution:
Year Money Income
(current Income)
Rs.
Consumer Price
Index
2000 = 100
Real Income
=
current Income
C P I
𝑥 100
2000 25000 100 25000
2005 27000 120 22500
2010 31000 160 19375
2015 36000 200 18000
Comments
Money income shows an increasing trend in the current income
while the real income shows a decreasing trend.

16. Example-6
The per capita income in a country has increased from $500 in the
year 2002 to $1000 in the year 2009. Taking base as 100 in the year
2002, the Consumer Price Index in 2009 stood at 160.
(a) Compute real per capita income and the purchasing power of
money, in the year 2009.
(b) Find the percentage increase/decrease in real income over the
same period.

17. Solution:
(a)
YEARS Income CPI Real
Income
Purchasing
Power
2002 500 100 $500 1
2009 1000 160 $625 0.67
(b) % of increases =
625−500
500
× 100 = 25%
Comments
In this example current income increased by 100% while the
real income is increased only 25%.

18. Example-7
(a) Calculate the changes in the cost of living figures in 2011 as
compared with 2010 are seen?
(b) Also Calculate the purchasing power of money and real per
capita income if current per capita income is estimated at Rs.
60000 per year.
Group Expenses
2011 2010
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

19. Solution:
Expenses
(W)
2011 2010
𝑰 =
𝑷𝒏
𝑷𝒐
× 𝟏𝟎𝟎
𝑰𝑾
Price in
Rupees (𝑃𝑛)
Price in
Rupees (𝑃𝑜)
35 150 145 103.45 3620.69
20 75 65 115.38 2307.69
15 30 30 100 1500
20 40 45 88.89 1777.78
10 25 23 108.70 1086.96
𝚺𝑾 = 𝟏𝟎𝟎 Σ𝐼𝑊
= 10293.12
CPI =
Σ IW
Σ W
CPI =
10293.12
100
CPI = 102.93%
(a)

20. (b) Purchasing Power =
1
CPI
x 100
Purchasing Power =
1
102.93
x 100
Purchasing Power = 0.9715
Real per capita income = (60000)(0.9715) = 58290
Comments:
In part (b) current per capita income is Rs.60000 while the real
per capita income is Rs.58290.

21. Inflation
The rate at which prices increase over time, resulting in a fall in the
purchasing value of money. OR
Inflation is a quantitative measure of the rate at which the
average price level of a selected goods and services (Basket) in an
economy increases over some period of time.

22. Example-8
Find the inflation rate in percentage by using CPI.
Year Consumer Price Index
2000 = 100
2000 100
2001 110
2002 120
2003 125
2004 140
Solution:
𝑅𝑎𝑡𝑒 𝑜𝑓 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑦𝑒𝑎𝑟 2000 − 2001 =
110 − 100
100
× 100 = 10%
𝑅𝑎𝑡𝑒 𝑜𝑓 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑦𝑒𝑎𝑟 2001 − 2002 =
120 − 110
110
× 100 = 9.09%
𝑅𝑎𝑡𝑒 𝑜𝑓 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑦𝑒𝑎𝑟 2002 − 2003 =
125 − 120
120
× 100 = 4.17%
𝑅𝑎𝑡𝑒 𝑜𝑓 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑦𝑒𝑎𝑟 2003 − 2004 =
140 − 125
125
× 100 = 12%

23. Real Sale =
current sale
l + r
Index Number =
Real Sale
1000
Year Inflation Current Sales
2000
-----
100000
2001 5.3% = 0.053 109000
2002 4.7% = 0.047 128535
2003 5.8% = 0.058 130440
Example-9
Calculate the Real Sale and Index Number (if inflation rate and
current sales are given while assume that base year is 2000 ):
Solution:

24. Year Inflation Sales Re𝐚𝐥 𝐒𝐚𝐥𝐞 =
𝐜𝐮𝐫𝐫𝐞𝐧𝐭 𝒔𝒂𝒍𝒆
𝐥+𝐫
𝐈𝐧𝐝𝐞𝐱 𝐍𝐮𝐦𝐛𝐞𝐫
=
𝑹𝒆𝐚𝐥 𝑺𝒂𝒍𝒆
𝟏𝟎𝟎𝟎
2000
-----
100000 100000 100
2001 5.3% = 0.053 109000 103513.77 103.51
2002 4.7% = 0.047 128535 122765.04 122.76
2003 5.8% = 0.058 130440 123289.23 123.29

25. Example-10
If the GDP and GNP of a country is $314.6 billion and $337.07
billion, while in this period CPI is 164.88.
Find the real GDP and GNP.
Solution
Real GDP =
current GDP
C P I
𝑥 100
Real GDP =
314.6
164.88
𝑥 100
Real GDP = $ 190.81𝑏𝑖𝑙𝑙𝑖𝑜𝑛
And
Real GNP =
current GNP
C P I
𝑥 100
Real GNP =
337.07
164.88
𝑥 100
Real GNP = $ 204.43𝑏𝑖𝑙𝑙𝑖𝑜𝑛