Uses of consumer price index number

1. NADEEM UDDIN
ASSOCIATE PROFESSOR
OF STATISTICS

2. 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

3. Year Consumer Price Index
2000 = 100
2000 100
2002 110
2004 120
2006 190
2008 200
Example-1 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.

4. 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

5. Example-2
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.

6. Example-3
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.

7. 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%.

8. Example-4
(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

9. 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)

10. (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.

11. 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.

12. Example-5
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%

13. Year Inflation Current Sales
2000
-----
100000
2001 5.3% = 0.053 109000
2002 4.7% = 0.047 128535
2003 5.8% = 0.058 130440
Solution:
Real Sale =
current sale
l + r
Index Number =
Real Sale
1000
Example-6
Calculate the Real Sale and Index Number (if inflation rate and
current sales are given while assume that base year is 2000 ):

14. 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

15. Example-7
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