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Index Numbers
Index numbers
Index numbers measure the magnitude of economic changes over time. They express these
changes as percentages of a predetermined period (usually a particular year, known as the
base year). The Index of Retail Prices, which attempts to measure the change in price of the
goods and services we buy, is one of the most important indexes because
 It measures the cost of living, inflation
 It enables governments to monitor inflation
 It is used in pay determination and in wage negotiations
 It is linked to increases in social welfare and pensions.
Price Relative
This is a simple index that shows the price of a single item over a period of time as a
percentage of the price in the base year.
Example: The price of Product A over 3 years is as follows:
2003 €4.50
2004 €4.70
2005 €4.89
The price relatives, using 2003 as base year, are
2003
= 100
2004 (4.70/4.50)x100 = 104.4
2005 (4.89/4.50)x100 = 108.7
This index tells us that the price of Product A rose by 4.4% between 2003 and 2004 and by a
further 4.3% between 2004 and 2005.
Laspeyre’s Index
The Laspeyre Index uses the quantities of the base year to give relative importance to the
different products. This is known as weighting. The index is calculated by the formula:
Laspeyre Index =
 Pn Qo *100
 P0Q0
Laspeyre Advantages
1. Weights (the quantities) are only
needed for one year, the base year
2. Because of this it is cheaper to
construct
3. The indexes for each year can be
compared directly
Pn is the price in the year for
which the index is being calculated
and P0 and Q0 are the price and
quantities in the base Year
Laspeyre Disadvantages
1. Tends to overstate price increases
2. Does not take account of changes in
demand.
The Laspeyre Index tells us what we would have paid in year n for a collection of goods
assuming we bought the base year quantities.
Walter Fleming
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Index Numbers
Paasche Index
This calculates an index using the quantities of the year for which the index is being
calculated. This index takes changes in consumption into account.
 Pn Qn *100
Paasche Index =
Qn are the Quantities
 P0Qn
in the year in which
the index is being
calculated
Paasche’s Advantages
1. Uses current quantities (weights) and 1.
so takes changes in consumption patterns
into account.
2. Does not overstate price increases
Paasche’s Disadvantages
1. Not a pure index as price and
quantities change
2. Long and expensive to update weights
3. The indexes for each year cannot be
compared directly since the quantities
change
4. Tends to understate price changes
The Paasche tells us what we would pay in the base year for the amount of goods we bought
in the current year.
Limitations of Laspeyre and Paasche indexes
The Laspeyre Index tends to overstate price increases, whereas the Paasche Index tends to
understate increases.
Indices give only a general indication of change over a wide geographical area.
The choice of base year can affect the indices. The base year should not be too far in the
past. It should also be a fairly unexceptional period, not one of say very high or very low
inflation.
Fisher’s Index
As said above, the Laspeyre Index tends to overstate the changes in price while the Paasche
Index tends to understate price changes. The Fisher Index attempts to correct this.
Fisher’s index =
(Laspeyre's Ιndex) x (Paasche's Index)
Fisher’s index lies between the other two indexes. It is referred to as an “ideal” index
because it correctly predicts the expenditure index.
Walter Fleming
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Index Numbers
Example:
2003
Product
A
B
C
2005
Price
1.15
0.80
2.50
Quantity
20
90
10
Price
1.30
1.04
2.90
Laspeyre Index for 2005
using 2003 as base year
Paasche Index for 2005
Σpnq0
1.30 x 20 = 26.00
1.04 x 90 = 93.60
2.90 x 10 = 29.00
Total
= 148.60
Σpnqn
1.30 x 50 = 65.00
1.04 x 60 = 60.24
2.90 x 15 = 43.50
= 168.74
Σp0q0
1.15 x 20 = 23.00
0.80 x 90 = 72.00
2.50 x 10 = 25.00
= 120.00
Index for 2005 = 148.60/120.00 = 124
Fisher’s index =
Quantity
50
60
15
Σp0qn
1.15 x 50 = 57.50
0.80 x 60 = 48.00
2.50 x 15 = 37.50
= 143.00
Paasche Index for 2005
= 168.74/143.00 = 118
(124) x(118)  120.96
The Consumer (Retail) Price Index
The Consumer Price index (CPI) is designed to measure the change in the level of prices paid
for consumer goods and services. It measures inflation.
The Central Statistics Office (CSO) collects the prices of a fixed representative group of
goods and services every month. Over 50,000 prices are collected from shops, supermarkets,
petrol stations, service outlets, etc as well as from utilities, transport companies, doctors,
dentists, etc. The prices are combined into a single index measuring the overall level of
prices.
Not all goods and services are treated equally. The CSO decides what weight to apply to a
product by determining the average weekly expenditure of an average household on the
product or service. This information is got through the Household Budget Survey, which is
carried out every 5 years. This survey also determines which goods and services should be
included or dropped. The survey involves over 7000 households chosen at random from all
private households in the state.
STAGES INVOLVED IN THE CONSTRUCTION OF THE CPI
Selection of Component Commodities:
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Index Numbers
The commodities and services purchased by the great majority of households should be
used, e.g. food, housing, transport and vehicles, etc.
Selection of Weights:
Each component group should be weighted “annually” according to the expenditure of
a typical family.
Collection of Data:
Usually involves continuous investigation to find prices and weights for commodities.
Selection of a Base Time Period:
A base period should be chosen which is not too far in the past.
USES OF CONSUMER PRICE INDEX
1. To measure the rate of inflation
2. Wage negotiations
3. Widening of the tax bands - used by Government as the yardstick by which tax
bands are widened in the annual budget.
4. Maintaining the real value of social welfare payments.
5. To maintain the real value of savings
6. International competitiveness - a comparison of our inflation rate with those of our
trading partners indicates whether our international competitiveness is improving or
worsening.
Other uses of the CPI
1. To find "Real" wages
The "real" wage is an indication of how much purchasing value wage increases give us.
If for example, my wage was €200 in 1998 and it was €400 in 2001, it would appear my
wages had doubled. However if the CPI had increased from 100 in 1998 to 110 in 2001
then my real wage in 2001 would be €363.63, that is it took €400 in 2001 to buy the same
goods that cost €363.63 in 1998.
To find real wages:
(Wage divided by Index Number) * 100
Walter Fleming
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Index Numbers
2. Changing the base year of an index
From time to time it is necessary to change the base year to prevent the index becoming
too unwieldy. We need to be able to change from "old" index numbers to "new" index
numbers.
Example:
Year
1979
1980
1981
Index (Base 1968 =100)
340
346
351
If the Base Year is changed to 1980 = 100 what is the new index for 1981?
New Index =(Index for required year) divided by ( index of New Base Year) *100
New index for 1981 = 351/346 * 100 = 101.4
OTHER COMMONLY USED INDICES
1. The agricultural output price index
2. The wholesale price index
3. Industrial production index
4. Import price index
5. Export price index
6. Shares Indices e.g. Financial Times Share index.
LIMITATIONS OF INDEX NUMBERS
1. Index numbers give only general indications of changes therefore they will not
cater for minority groups generally.
2. Weights become out of date.
3. The information used might be biased.
4. Open to misinterpretation.
Walter Fleming
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