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An index number is a statistical measure designed to show an average change in a variable or group.of related variables with respect to Time, Geographical location or Income group etc.

Geometric mean.

Base year prices (P₀).

A.M or GM. Is used because AM us very easy to calculate where as geometric mean is considered as most appropriate and better method for averaging the ratios.

The other name of the Consumer Price index is the cost of living index.

Equivalent of a rupees. It means that the rupee in Jan 2005 was worth 19 paise in 1982. In other worths 19 paise in 1982 in worth Rs. 1 in 2005 That is 526 times.

Here the specific class consumers means group of consumers who are having similar pattern of consumption. Generally those of factory workers, government employees, and the consumers who belonging to a particular community etc.

1993  –  1994

In general inflation is calculated by using the wholesale price index.

Yes, the CPI number for urban non – manual employees represents the changes in the cost of living of the president of India, Because he is also non – manual employee.

1.  Simple aggregative method.

2.  simple average of price relative method

3.  Weighted Aggregative method 

4.  Weighted average of Price relative method.

Index numbers are useful to governments in formulating Economic policies, such as Taxation, imports, exports, granting of licenses to new firms, fixation of Bank rates, salary and grants to employees. Also, in comparing variations in production, prices, shares, Demand, supply, and measurement of real Rupee.

Uses of the Wholesale Price Index numbers: 

1. The time series of wholesale Price index numbers can be used to forecast future prices.

2. With the help of wholesale price index number, we can estimate the future demand and supply situation.

3. It is used to measure the rate of inflation.

4. It can be used to eliminate the effect of change in price on aggregates such as national income, capital formation etc.

Option : (4) a, b and c

Steps involved in the construction of index numbers are as follows:

• Purpose of an Index Number : Before constructing an index number, one must know the purpose for which the index number is constructed. E.g. for the whole c sale price or retail price or for agricultural output, etc.
• Selection of a Base Year : It is important to select a base year against which comparisons are made. So base year or reference year should be a recent year and not a distant past. it should be normal and free from natural calamities, war, etc.
• Selection of Commodities: When the cost c of living index number of the middle class families is to be constructed, the items that are used by middle class families in everyday life should be included and items like big cars, AC’s, etc. should not be included.
• Selection of Prices : Prices differ from city ‘I to city and even from shop to shop in the same city. Hence, we should take a few standard shops from where middle class families buy goods and take the average of the prices of goods sold by them. Otherwise index number constructed may be misleading.
• Selection of suitable Average : An ; index number is a special kind of average, Generally arithmetic mean is commonly ? used for construction of index number as it is simple to calculate.
• Selection of Formula : Number of formulae can be used for construction, of index numbers. Economists have to decide which formula to use for the construction of a particular index number.
• Assigning proper Weights : Weights refer to the relative importance of different items in the construction of an index number. Weights may either be quantity weights (q) or value weights (p). All weights may not be equally important. Therefore, by s assigning specific weights better result can be obtained.

Features of Index Numbers:

• Index numbers are a specialised form of averages.
• They are expressed in percentage form without using a percentage sign.
• The year for which index number is being prepared is the current year.
• The year from which index number is being prepared is called the base year which is always taken as 100.
• They are used in measuring the changes in magnitudes which cannot be measured directly.
• The formula used for Price Index Number = \(\cfrac{Total\, Price\, of\, the\, Current\, year}{Total\, Price\, of\, the\, base\, year} \times 100\)

•  They are considered as barometer of economic activity.

  Index number which is calculated from a single variable is called “univariate • index” and which is constructed from a group of variables is called a “composite index”.

No, I do not agree with this statement. 

Index numbers can be constructed without the base year because :

• Index Numbers are the tools for measuring the changes in the magnitude of a variable or a group of variables over time with respect to a chosen year.
• Prices of some goods may increase and of other may decrease during the two periods. Index numbers solves this problem by taking the average change.
• For example, to know cost of living of people in general in India, Government chooses a base year 2010 which is taken as 100. Then cost of living is calculated in 2019 which may be 140.
• This difference of 40(140-100) shows that cost of living in India has increased by 40% since 2010.

Hence, Index Numbers cannot be constructed – without the base year.

Index numbers are significant tools of economic analysis in the following ways: 

(1) Help in formulating Policies : Index numbers help the government and business organisations in framing their suitable economic policies for agriculture and industrial sector, wage and dearness allowance policies, etc.

(2) Help in the study of Trends and Tendencies : Index numbers study the relative changes in the level of phenomenon of different periods of time, so they can be used to predict future events. The economists can study the general trends of changes in price levels, agricultural and industrial production, export, imports, etc.

(3) Economic Barometer : Just as barometer is used to measure atmospheric pressure, index numbers measure the level of economic and business behaviour. They are very important for an economist, businessman, planners, policy makers, etc.

(4) Helps in Measurement of Inflation : It helps the government to take measures against inflation by giving additional D.A. to the employees on the basis of Dearness Index.

(5) Help to adjust National Income : By comparing current year’s national product prices with the base year’s prices, the Domestic Product (GDP) produced. Hence, this shows changes in real national income.

(6) To present Financial Data in Real Income : Index numbers are used to adjust price change, wage change, etc. Thus deflating helps to present the financial data at constant prices.

(Note: Deflating means to make adjustments / in the original data)

(7) Helps in determining Depreciation Cost: The price index helps in determining the depreciation cost of durable goods. At the time of inflation, it is useful to know the ) original cost of the commodities.

 Price Index P₀₁  = x 100

\(\cfrac{42}{40} \times 100\)

= 105

Hence, P₀₁ = 105

Q₀₁= \(\frac{Σq_1p_0}{Σq_0p_0} \) = \(\frac{180}{150}\) = 120.

l₀₁ = \(\frac{Σpω}{Σω}\) = (110 × 3 + 120 × 8 + 112 × 4 + 108 × 6 + 105 × 9)/(3 + 8 + 4 + 6 + 9) 

= 104.466.

I₀₁ = \(\frac{Σpω}{Σω}\) = [100 × 1 + 120 X 3 + 130 × 4 + 110 × 2]/[1 + 3 + 4 + 2] 

= \(\frac{1200}{10}\)

= 120.

The index number for the year 2000 is ‘100’.

This test requires that the index number used should be independent of the units of measurement.

This requires that the index number is to work in a circular manner and this property enables us to find the index numbers from period to period without referring back to the original base each time. For 3 years 0(1998), 1(2005) and 2(2010):

Circular test is said to be satisfied if: P₀₁ × P₁₂ × P₂₀ = 1.

Simple Aggregative Index number p₀₁ = \(\frac{∑p_1}{∑p_0}\) × 1000

Here P₀ – Price in in 1990

P₁– Price in 2000

Σ p₀ = 70, Σ p₁ = 76, p₀₁

= \(\frac{76}{70}\) × 100 

= 108.57.

In weighted index numbers due weightage is given to different items in a relative way i.e., equal importance is not given to all items, where as in unweighted index numbers weights used are all uniform.

Price Relative is the price in the current year expressed as percentage of the price in the base P = \(\frac{p_1}{p_o}\) × 100.

Importance of Index Numbers:

Index Numbers have a great importance in Statistics.
They are used in the various fields of economics. Such as production, consumption, Price etc

With the help of Statistics, economic conditions can be studied and forecast can be made. They are called the “Economic Barometer” Their importance can be judged with the following facts.

1. Calculation of Price levels:
Index Numbers help in calculating levels of various items.

2. Helpful in taking decisions:
Index numbers are very helpful of Government in taking important decisions, such as granting dearness allowances to the employees.

3. Helpful in comparative Study:
They also help us in making comparative study of the changes occurring in the economy.

4. Helpful do insurance companies and Banking Institution. Index numbers help the insurance companies and banking institutions in determining of Premium – rates and interests respectively.

5. Helpful in assesing the development of an economy with the help of statistics, the development of an economy can be assessed.

An independent variable is that variable which is not dependent on any other values. Its value is free.

A dependent variable is that variable whose value depends on the value of an independent values.

Index number is a statistical measure showing percentage or relative changes in variables like prices, production, exports etc.

According to Spiegel:

An Index number is a statistical measure designed to show changes in a variable or group of related variables with respect to time, geographic location or other characteristics.

Basic consideration underlying the choice of base period.

1. The base period should be a normal period. Abnormal periods like period of war or floods etc. should not be selected as a base year.

2. The base period should be neither too short nor too long.

3. It should not be the period for which actual data are not available.

4. It should not be the too far back in the past.

Utility of index numbers

1. Index numbers are helpful to policymakers.

2. Index numbers simplify the facts.

3. Comparative study become easy.

4. Index number help us to study the general trend. 

5. They are helpful in determination of real change in income.

Time Reversal Test/Yes.

1. Many formulae are used and they give different answers for the index. 

2. As the customs and habits change from time to time, the uses of commodities also vary. 

3. There is ample scope for bias in the construction of Index numbers.

In the construction of index numbers, there are some practical difficulties and theoretical limitations.

1. Index numbers are not fully true. They simply indicate arithmetical tendency of the temporal change in the variable.

2. Index numbers do not help in international comparison.

3. Index numbers are prepared with certain specific objective.

4. It is difficult to collect retail prices so index numbers based on wholesale prices may be misleading.

Consumer price index measures the average changes in retail prices at which the consumers buy goods and services in the market at a given price.

1. Index numbers are expressed in percentage.

2. They are specialised type of average.

The other name of the consumer price index is price deflater of income.

1. Industrial workers.

2. Urban – non manual employees.

3. Agricultural labourers.

1. Consumer price index or cost of living index number.

2. Wholesale price index number.

Price index number is that number which measures and permits comparison of the price of certain goods.

The base year should be the year of economics stability. It should not to be too distant from the current year.

In the simple index number all items of the series are treated as of equal importance. In the weighted index, weights are accorded to different items-depending on their relative importance.

An index number is a statistical measure designed to show change in a variable or group of related variables with respect to time, geographic location or other characteristics.

Suppose the Percentage of weight given to food = x In this case Percentage of weight given to other items would be = (100 – x)

Hence,

125 = \(\frac{(X+120)+(100 - x)\times135}{100}\)

or 12,500 = 12x + 13,500 – 135x

or 15x = 13,500 – 12,500 = 1,000

X = \(\frac{1,000}{15}\)  = 66.66%

Hence, Percentage of the total weight given to food = 66.66.

The students are advised that they should enquire their parents about the daily expenditure. Quantities bought and Prices paid per unit of daily purchase of their family for two weeks, they will come to know that the rising prices of goods have effected that family very much.

Many Problems are faced while constructing an index number.

Two of them are as follows:

1. Selection of base year: 

The first problem which arises while preparing Index number is the section of base year. Which year should be selected as a base? While selecting a base year, we should remember that it should be a normal period. It should not be either too short or too long. It should be free from all sorts of abnormalities or irregular fluctuations.

2. Selection of items:

We should also be careful in selecting the items to be included in the index number. Items selected should be relevant to the purpose of the index. The items should be standardized which are easy to describe and understand. Moreover, the total number of commodities selected for the index should be neither too small nor too large.

1. It is helpful in wage negotiation.

2. It is helpful in the formation of income Policy, Price Policy taxation and general economic policy formulation.

3. It is used in calculating the purchasing power of money.

4. With the help of CPI, we can calculate the real wages.