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Index Numbers

Important Index Numbers

The rate of inflation in December 2017 was 5.21 index points, which was the highest in last 17 months. We hear about the term inflation often and how it affects our price levels along with our currency’s power. As you might have noticed the unit for measurement of inflation is index point. In essence, inflation and index numbers are intimately connected to each other. So it is important for us economics students, to understand some important index numbers such as CPI and WPI.

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The Two Indices of Our Concern

Although there is an arsenal of index numbers, there are two indices that effectively display the change in prices and its effect on the cost of living of various sections of society. These two indices are- Wholesale Price Index (WPI) and Consumer Price Index (CPI).

Both of these indices are well-equipped to represent the effects on different classes of an economy whose consumption and production patterns vary drastically. Their reliability can be affirmed with the fact that the  Reserve Bank of India uses 1 WPI and 4 types of CPI to reflect the general price levels and its changes. Without further due let us study these two index numbers.

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Consumer Price Index Number

There exists a vast difference in the consumption patterns of the diverse divides of society. To point out, this pattern is governed by the prices paid by these sections to consumer goods and services. The general index numbers are unable to effectively depict the changes in such patterns triggered by the changes in price levels. Hence the consumer price index (CPI) came into the picture.

A consumer price index number measures the average change in prices paid by the specific type of consumer for consuming goods and services in the current year in comparison to a base year. It is also known as the cost of living index because a change in price levels affects the consumption patterns which in turn alters the cost of living. CPI is generally constructed for three groups- Industrial Workers, Urban Non-Manual Employees, Agricultural Labourers.

Significance of CPI

As noted above, CPI very well depicts how the changes in general price levels affect heterogeneous consumers. Effectively, it helps the government formulate the price policy, fiscal policy, taxation policies etc. In other words, these indices help the government to take calculated risks for development without drastically affecting the cost of living.

Additionally, the state also makes use of them to decide the wage contracts and agreements of workers along with the dearness allowances. Also, these indices are an accurate indicator of the power of an economy’s currency. This is again because of the fact that they quantify the changes in consumption triggered by price changes. Thus effectively displaying the goods and services that can be consumed using the currency.

Lastly, as national income can also be calculated using consumption expenditure because one man’s expenditure is other man’s income, the CPI acts as a national income deflator.

Arguments against CPI

In addition to the general limitations of index numbers, there are some difficulties extensively related to CPI too. The first problem relates to the fact that different classes of consumers have varying standards of living hence one CPI cannot represent the diversity.

In addition to this, price indices are constructed using the retail prices. However, retail prices can vary greatly from shops to shops, hence the choice of retail price tends to change the result. Thus a general retail price has to be chosen as a representative of all the retail prices prevailing in the market.

The last and the main difficulty corresponds to the factor of change in consumption. This means that even within a specific class of consumers, the consumption can differ to a large extent. Also, the consumption ratio of an individual consumer can change over a period of time. Due to this reason, the existence of a CPI that exhibits a change in the cost of living in its entirety is questionable.

Approaches to Construct a CPI

Taking cues from the two methods of assigning weights, there are two methods to construct a consumer price index number.

1. Aggregative Expenditure Method

This method is based on Laspeyres formula as can be seen below:

CPI = (∑P1Q0 ÷ ∑P0Q0) ×100

Here, ∑P1Q0= Summation of, prices of current year multiplied by respective quantities consumed in base year taken as weights

∑P0Q0= Summation of, prices of base year multiplied by respective quantities consumed in base year taken as weights

2. Family Budget Method

This method calculates CPI using price relatives method. Here, weight is defined as the product of price and quantity consumed of the commodity, both with respect to the base year. Price relative is the ratio of current year’s price to base year’s price multiplied by 100. The formula to calculate CPI is as follows:

CPI = ∑RW÷∑W

Here, ∑RW= Summation of the product of price relative (R) and weight(P0Q0) of the commodity

∑W= Summation of the weights(P0Q0) of all the commodities

Wholesale Price Index (WPI)

As the name suggests, WPI simply measures the temporal change in wholesale prices of commodities. Unlike CPI, which looks at the relative change in prices from the consumption perspective, WPI looks at the relative change in price from wholesale market’s perspective. Therefore it is an index of critical importance.

For the purpose of calculating WPI, commodities have been classified into the following three:

  1. Primary Articles- Includes eatables like rice, fruits, pulses etc. and non-food items like cotton, jute etc.
  2. Fuel and Power- Includes items like petroleum products, coal, electricity etc.
  3.  Manufactured Goods- Includes manufacturing items like paper, sugar, leather, chemicals etc.

Significance of WPI

The wholesale price index is an accurate measurement of predicting the demand and supply of commodities in the economy. For example, an increase is WPI indicates an increase in demand on an average. WPI can be used to calculate the real and monetary values of aggregates like national income.

Real value refers to the value of aggregate at base year prices. Monetary value refers to the value of aggregate at current year prices. The two values are tied by WPI through the following formula:

Real aggregate of the current year = monetary aggregate of current year × ( price index of base year ÷ price of current year)

Additionally, WPI is used to calculate the rate of inflation. It is calculated as under:

Rate of inflation = [(P2 – P1) ÷P1]×100

Here, P2= Current WPI and P1= Previous WPI

Note: The annual rate of inflation is calculated as the average of WPI for all weeks of the year.

Industrial Production Index(IPI)

Apart from the two major indices, WPI and CPI, there is a third index IPI which also holds critical importance. The index of industrial production measures the change of industrial production relative to a base year.

Unlike WPI and CPI, this index number focuses on production rather than price. It is a useful tool to measure the industrial growth of an economy. For calculating industrial production index, the industries are divided into mining, manufacturing and electricity.

Constructing an IPI

A difference between the construction of an IPI and other indices is the approach towards how weights are considered. For an IPI, weights are assigned according to the output of industries and their contribution to the national income. The following formula is used:

Index number of industrial production =  (∑RW÷∑W)×100

Here, R= Ratio of level of production in current year to the level of production in base year

W= Assigned weights

The Relation between Inflation and Index Numbers

The term inflation is among the most frequently occurring terms in economics. Inflation denotes the rise in the general price level in an economy over a long period of time. In simple words under conditions of inflation, a particular commodity remains unchanged but it’s price still rises.

Such a constant rise in general price levels, with money income remaining same, erodes the purchasing power of consumers. In addition to this, it also brings down the value of currency slowly.

As wholesale price index represents the temporal change in general price level, inflation and WPI are inter-related. The mathematical formula to find out inflation rate using WPI has already been mentioned.

Another point worth noting is that a fall in the rate of inflation does not mean fall in price levels. It simply indicates the fall in the incidence of inflation. In simpler words, it represents the fall in the pace of increase in general price levels, which still continue to rise.

Sensex

Sensex CPI

Sensex is the index that represents the changes in Indian stock market. Since it is not possible to take into account every company’s stocks, Sensex considers stocks of the 30 leading companies. These are assumed to represent the whole stock market.

Thus Sensex, a short form for Bombay Stock Exchange Sensitive Index, focuses on the principal industries of the economy. Note that an increase in Sensex represents expected earnings from investments in stocks, an overall increase in shares and a good performance of leading industries of the economy.

Solved Example for You

Q:  Construct the cost of living index for 2014 on the basis of 2004 from the following data and give your comments:

Item Prices in 2004 ( Rs.) Prices in 2014( Rs.)  Weights
Food  40 55 5
Fuel 8 12 2
Clothing 25 37 4
Rent 15 22 3
Miscellaneous 25 30 1

Ans:

Items P0 P1 R=(P1÷P0)×100 Weights(W) RW
Food 40 55 137.5 5 687.5
Fuel 8 12 150 2 300
Clothing 25 37 148 4 592
Rent 15 22 146.7 3 440.1
Miscellaneous 25 30 120 1 120
∑W= 15 ∑RW = 2139.6

Cost of living index number= ∑RW/∑W = 2139.6/15 = 142.64

As already mentioned, the index of the base year is generally taken to be 100. According to this assumption, the increase in the cost of living index is 42.64% in 2014 relative to 2004 taken as the base year.

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Chinmay Hegde
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Chinmay Hegde

This answer is wrong p1q0 is 855 . There is a mistake in 4th item they took p1q0 of that item as 100 but it is 500 . They took as 4*. It it is 20*25

Shanaya
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Shanaya

Illustration 2: For the data given below, calculate the Index Number by taking:
i) 2009 as the base year;
ii) 2016 as the base year; and
iii) 2009 to 2011 as a base period.

Can someone solve this?

Shanaya
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Shanaya

Year Price of Commodity ‘X’ Year Price of Commodity ‘X’ 2009 4 2014 10 2010 5 2015 9 2011 6 2016 10 2012 7 2017 11 2013 8

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