CIMA BA1 Syllabus A. Macroeconomic And Institutional Context Of Business - Index Numbers - Notes ^{14 / 17}

Basic Index Numbers

Index numbers help us compare values over time.....

1. A base year is given an index number of 100

2. Future years are given index numbers by comparing the values over two periods and multiplying by 100.

Illustration 1

A cup of milk was $2.00 in 20X0 
A cup of milk was $3.40 in 20X9

• Index Numbers

  20X0 = 100

  20X9 = 100 x 3.40 / 2.00  = 170

• You can now easily see prices have increased by 70% by looking at the index number rise from 100 to 170

Fixed Base And Chain Base Methods

There are 2 ways in which index numbers can be compared:

1. Fixed Base

   As above, a base year is selected (index 100), and all subsequent changes are measured against this base

2. Chain base

   Here changes are measured against the period immediately before

Illustration 2 - Chain Base and Fixed Base

Cup of Coffee 

$2.50 in 20X0
$3.00 in 20X1
$3.30 in 20X2

Price and Quantity Indices

• Price Indices

  Measures changes in the monetary value of a group of items over time. 

  Eg Consumer Prices Index (CPI) for inflation
  
  

• Quantity Indices

  Measures changes in the Non-monetary value of a group of items over time 

  Eg. Production volumes

Illustration 3

Using the CPI data below calculate the annual rate of inflation in 20X9 (to one decimal place).

Solution

• 111 / 115 x 100 =  96.5

  100 - 96.5 = - 3.5%

Base & Current Weighted Price Indices

Here we look at 2 ways of working out the change in price at a basket of goods

We take into account the quantity of the items in the baskets though too

So we use either:

1) The Base (start) Quantities 
2) The Current (latest) Quantities

• Using the base quantities is called the Base Weighted price index

• Using the current quantities is called the Current Weighted price index

Illustration 4

2 products are in our basket, milk and butter

We show you their quantities at the start (Base) and their quantities now (Current) 

We also show you the prices at the start (Base) and their quantities now (Current)

a) What is the overall price index For this 'basket' of goods, using a Base weighted approach?

b) What is the overall price index for this 'basket' of goods, using a Current weightings approach?

For this approach, we are using the base year quantity

The price rise is 43.8% using Base weighted approach

The price rise is 42.3% using current weightings approach

Using price indices to deflate a time series

Here, we will remove the effect of inflation on data (e.g Wage expenses)

One of the uses of a price index is to deflate data that includes inflation, often called ’nominal’ data, by stripping out the effect of inflation so that the data becomes ’real’ (ie not distorted by inflation).

Illustration 5

Average wages have increased between 20X5 and 20X9 from $10,000 per head to $19,000 in nominal terms.

CPI data is given below as a fixed index.

How much better off are workers in real terms?

This can be addressed by expressing wages in terms at base year (ie 20X5) prices.

• 20X5 wages are already in terms at 20X5 prices.

• 20X9 wages of $19,000 can be adjusted by dividing by 121/100 
  therefore: $19,000 / 1.21 = $15,702.

• So ‘real’ wages have risen by (15,702 / 10,000) - 1 = 57%