Index Numbers
1 Introduction
The purpose of index numbers is to show the rate of change of a variable from one specified time to another. The most common use is as a way of measuring the effect of inflation on prices.
2 Simple index numbers
Simple index numbers are based on a single item. There are two types: price relative and quantity relative.
A price relative index number shows changes in the price of an item over time.
A quantity relative index number shows changes in quantity over time.
Simple price index = | P1 | × 100 |
P0 |
Simple quantity index = | q1 | × 100 |
q0 |
The price of coffee was $2.40 in 2006, $2.50 in 2007, and $2.60 in 2008
Calculate the price index for 2007 and 2008 using 2006 as base year.
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Sales of tea were 8,200 packets in 2008, 9,000 packets in 2009 and 9,400 packets in 2010.
Calculate the quantity index for 2009 and 2010 using 2008 as a base year.
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3 Laspeyre and Paasche index numbers
In order, for example, to measure the overall effect of inflation, it is more sensible to consider the change in price of a typical ‘shopping basket’ of goods rather than looking at just one item.
To make sure that we are only measuring the effect of price inflation, it is important to compare the same shopping basket in terms of quantities.
The Laspeyre price index uses base period quantities, whereas the Paasche price index uses current period quantities.
Below are stated the quantities and unit prices for a typical ‘shopping basket’ in each of the year 2008, 2009, and 2010.
2008 | 2009 | 2010 | ||||
quantity | price p.u. | quantity | price p.u. | quantity | price p.u. | |
Coffee | 20 | $4.00 | 15 | $4.50 | 15 | $4.80 |
Sugar | 15 | $0.60 | 18 | $0.70 | 20 | $1.00 |
Bread | 30 | $0.80 | 35 | $1.00 | 40 | $1.10 |
Calculate price index numbers for 2009 and 2010, with 2008 as a base year, using:
Laspeyre
Paasche
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4 Advantages and disadvantages
Laspeyre price index
Paasche price index
Index Numbers
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