How to compile an INDEX like the CPI
This explanation is in conjunction to page 379 in your textbook. It explains on a small, small scale
how StatsSA go about to compile the CPI.
Imagine a basket filled with goods and services that a
household consume on a monthly basis. For our example
we will work with only three (to keep it simple, but you can
use a million different goods and services if you wish). Our
example uses transport () food () and housing ().
Our household uses 3 (); 2 () and 5 () per month.
Each of these items has a price tag on and every year the
price increases. Take a look at the table below with the
prices for these items for 2 separate years.
Product
•
•
•
Quantity
•3
•2
•5
P 2010
P 2017
• 10
• 20
• 12
• 12
• 22
• 14
Step 1: Calculate the amount spent per product in 2010 (base year).
Thus: Quanity x P2010
•  3 x 10
•  2 x 20
•  5 x 12
Total spent in 2010 was
= 30
= 40
= 60
= 130
Step 2: Calculate a weight for each item.
Tells us what proportion (%) of total amount was spent on each item.
 30 ÷ 130 = 0.23
These are the weights of each item in your
 40 ÷ 130 = 0.31
basket. (the proportion we spent on each
item compared to the total)
 60 ÷ 130 = 0.46
The sum of these weights MUST = 1 (0.23 + 0.31 + 0.46 = 1)
How to compile an INDEX like the CPI
Step 3: Calculate a Specific Price Index for each item.
Specific Price Index = (Price in specific year ÷ Price in base year) x 100
Specific year 2010 (base year
2010)
Specific year 2017 (base year
2010)
•  (10 ÷ 10)x100
•  (20 ÷ 20)x100
•  (12 ÷ 12)x100
•  (12 ÷ 10)x100
•  (22 ÷ 20)x100
•  (14 ÷ 12)x100
= 100
= 100
= 100
When: (base year ÷
base year) you will
ALWYS get 100!!!!
= 120
= 110
= 116
Step 4: Calculate composite price index.
Composite Price Index = Sum of (Specific Index x Weight)
Composite Price Index = SUM of (Answers Step
.
If you do the same calculation
but use the base year values
(100) your composite index
value will be 100. It will always!
• 120 x 0.23 = 27.6
• 110 x 0.31 = 34.1
• 116 x 0.46 = 53.36
• SUM
= 115
2 x Step 3)
Composite index value
The CPI is a Composite Price Index like the one above!!! StatsSA follow the above steps for 12 groups
of consumer products (we used only 3) to compile the CPI. From the CPI values we calculate the
national inflation rate. To calculate the “inflation rate” for the items in our example:
Inflation rate =
CPI in specific year − CPI in base year
CPI in base year
Inflation rate =
(115 − 100)
100
Inflation rate = 15 %
𝑥𝑥 100
𝑥𝑥 100