CPA PAPER 5

Index numbers

By the end of topic, participants should be able to;

1. Appreciate the usefulness of index numbers in monitoring changes over time 1. Calculate simple indices

2. Determine simple aggregate price indices

3. Use laspeyre’s and Paashe’s price indices to determine weighted indices.

What is an index number?

An index number is a statistical measure designed to show/ monitor changes over a period of time in the price, quantity or value of an item or a group of items. It compares the value of a variable at any time with its value at another fixed time called the base period. There are different types of index numbers eg. Price index numbers, cost of living index numbers, sales index numbers etc.

The base year

A base year can be defined as the year against which all other years are compared. The base year selected should be a stable/ normal year where you do not have prices changing rapidly. It should not be too distant from the current year. The price or quantity of base year is represented by 100 and those of other years measured against it. An index relative

An index relative sometimes just called a relative is the name given to an index number which measures the change in a single distinct commodity

Simple indices

Index for a period = value in a period

Value in base period

Price index (price relative) = Price at given year x 100

Price at base year Index relative

Price index (price relative)

= Pn/Po x 100

Quantity relative

Quantity relative = (qn/qo) x 100

Example

In 1990 the price of a certain commodity was shs 40 whilst in 1995 its price was shs 60. Taking 1990 as the base year, find the price relative. Solution

Price relative = Price at 1995 x 100

Price at 1990

= 60 x 100

40

= 150

This indicates the price of the commodity increased by 50% between 1990 and 1995. The percentage sign is always omitted

Quantity / Volume relative

Instead of comparing the price of a commodity we can compare the quantity or volume produced or the quantity consumed

Example

The quantity of sugar produced by Kakira Sugar Works in 2004 was 1800 tonnes. In 2009 the quantity produced was 2300 tones. Using 2004 as base year calculate the quantity relative for 2009.

Quantity relative for 2009

= quantity produced in 2009 x 100

quantity produced in 2004

= 2300 x 100

1800

= 128

Thus 28% more sugar was produced in 2009 than in 2004

Simple aggregate price index

Sometimes we calculate the total price of a group of items as a ratio of the total price of the same group of items in the base year to give simple aggregate price index

Simple aggregate price index

=

Simple aggregate price index =

Simple aggregate price index

P0Pn

ITEM20042009

A 20004000

B 25003000

C 4500040500

ΣPn = 47500/=

Σpo = 49500/=

Simple aggregate price index

= (47500)/ 49500 x 100 = 96

Simple aggregate price index

This type of index has a number of disadvantages. It ignores importance of each item and the units to which the prices refer. Average simple price index

Σ (Pn/P0)x100

n

Where n is the number of items

It shows the overall increase in prices

Weighted indices

For a price index to be realistic, it should take into account the relative importance of the commodities. Base year weighted index = Cost of base period quantity at current prices Cost of base period quantities at base period prices

Base year weighted index

Base year weighted index assumes that the quantities purchased do not change from the base...