price index, retail price index and link and chain index

1. INDEX NUMBERS
Jyothi .S
Assistant Professor,
Gfgcw,
Holenarasipura
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2. contents
□ Price index
□ Retail price index
□ Quantity index
□ Link and chain index
□ Simple and aggregate index numbers
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3. Price index
□ A price index is shown as a single number which indicates the
price change in a number of different goods. This
is calculated by comparing the price of goods to the base year.
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4. Retail price index/CPI
□ Retail Price Index(RPI) and Consumer Price
index(CPI) are both used to measure inflation.
□ These indices measure the change of average
prices over a certain amount of time. The
measurements are made by recording the
essential goods and services people are
expected to buy, putting them into an imaginary
shopping basket called the "Basket of Goods".
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5. A basket of goods
□ The imaginary shopping basket for a typical
family contains, for example, milk, bottled water,
sugar, tea, meat, cooking fuel, school books and
mobile phone charges.
□ The contents included in the basket are fixed in
the short term, but the prices of individual goods
change.
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6. □ Formula
RPI/CPI =
𝒄𝒐𝒔𝒕 𝒐𝒇 𝒎𝒂𝒓𝒌𝒆𝒕 𝒃𝒂𝒔𝒌𝒆𝒕 𝒊𝒏 𝒂 𝒈𝒊𝒗𝒆𝒏 𝒑𝒆𝒓𝒊𝒐𝒅
𝒄𝒐𝒔𝒕 𝒐𝒇 𝒎𝒂𝒓𝒌𝒆𝒕 𝒃𝒂𝒔𝒌𝒆𝒕 𝒂𝒕 𝒃𝒂𝒔𝒆
× 100
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7. A country had four items on its CPI index viz. Food, Clothes, Education, Fuel. The Country has year 2000 as the
base year for measuring CPI and the government in the year 2005 wants to see if the purchasing power of the
people of the Country has improved or deteriorated. The price of each item is as below.
Item Quantity Base year
2000
Current Year
2005
Food 30 38 42
Clothes 20 43 40
Education 30 35 38
Fuel 20 60 55
Market Basket Base year - 2000 4250
Market Basket Current year - 2005 4300
Consumer Price Index (CPI) 101.18
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8. Difference between RPI AND CPI
Basis of
Comparison
between CPI
vs RPI
Consumer Price Index (CPI) Retail Price Index (RPI)
Definition
CPI measures the weighted average
prices of the basket of goods and
services consumed by households.
RPI is a measure of consumer
inflation which considers the
changes in the retail prices of
a basket of goods and
services.
Components
The market basket involves Food
Beverages and Tobacco, Fuel and
Light, Housing, Clothing bedding, and
footwear, miscellaneous. The
dearness allowance of government
employees and wage contracts is also
included.
RPI calculates the variations in
the cost of the basket of retail
goods and services. RPI also
accounts for housing costs
such as mortgage interest
payments etc.
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9. Date of
Introduction
The introduction of the CPI was
after the First World War period
when there was a significant rise
in the prices.
RPI had been introduced
in the UK and was first
calculated in 1947.
Housing
Cost
The cost of housing is not
included while computing the
index.
Housing cost such as
mortgage interest
payments, insurance of
the building etc is
included.
Use of Mean The geometric mean is used Arithmetic mean is used
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10. Macroecono
mic
Relevance
CPI acts as a significant tool for
monitoring price stability and is
used extensively as a barometer
of inflation.
RPI is not used for
measuring the inflation
target by the Monetary
Policy Committee of the
Bank of England.
Size of the
Population
The population size considered
is large.
The population size
considered is
comparatively lower than
CPI.
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11. Quantity Index numbers
□ Quantity index numbers measure the change in
the quantity or volume of goods sold, consumed or
produced during a given time period.
□ Formula
Q01 =
∑Q1
∑Q0
× 100
where, Q1 is the quantity of the current year,
and Q0 is the quantity of the previous year,
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12. Link and Chain Index Numbers
□ Under this method, firstly we express the figures for
each year as a percentage of the preceding year.
These are known as Link Relatives. We then need to
chain them together by successive multiplication to form
a chain index.
□ Thus, unlike fixed base methods, in this method, the
base year changes every year. Hence, for the year
2001, it will be 2000, for 2002 it will be 2001, and so on.
Let us now study this method step by step.
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13. Steps in the construction of Chain Index
Numbers
□ Calculate the link relatives by expressing the figures as
the percentage of the preceding year. Thus,
Link Relatives of current year =
𝑷𝒓𝒊𝒄𝒆 𝒐𝒇 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝒚𝒆𝒂𝒓
𝒑𝒓𝒊𝒄𝒆 𝒐𝒇 𝒑𝒓𝒆𝒗𝒊𝒐𝒖𝒔 𝒚𝒆𝒂𝒓
× 100
□ Calculate the chain index by applying the following
formula:
Chain Index =
𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝒚𝒆𝒂𝒓 𝒓𝒆𝒍𝒂𝒕𝒊𝒗𝒆 ×𝒑𝒓𝒆𝒗𝒊𝒐𝒖𝒔 𝒚𝒆𝒂𝒓 𝒍𝒊𝒏𝒌 𝒓𝒆𝒍𝒂𝒕𝒊𝒗𝒆
100
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14. Solved Example on Chain Index Numbers
Year 2011 2012 2013 2014 2015 2016 2017 2018
Prices 120 124 130 144 150 160 164 170
Q. From the following data calculate the index numbers using the Chain
Index Numbers method.
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15. Solution
Year Price Link Relatives Chain indices
2011 120 100 100
2012 124 124/120 x 100 = 103.33 103.33×100/100 = 103.33
2013 130 130/124 x 100 = 104.83 104.83×103.33/100 = 108.32
2014 144 144/130 x 100 = 110.76 110.76×108.32/100 = 119.98
2015 150 150/144 x 100 = 104.16 104.16×119.98/100 = 124.97
2016 160 160/150 x 100 = 106.66 106.66×124.97/100 = 133.29
2017 164 164/160 x 100 = 102.5 102.5×133.29/100 = 136.62
2018 170 170/164 x 100 = 103.65 103.65×136.62/100 = 141.61
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