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The number showing the percentage of relative changes in the cost of living of the people of a certain section of the society in the current year as compared to the base year is called the cost of living index number.

The cost of living index number is used in India to find the rate of dearness allowance.

The main difference between fixed base method and chain base method is that ‘in fixed base method the base year remains constant throughout the period of comparison while in chain base method at any given time the preceding year is taken as the base year.

The main differences between explicit weight and implicit weight are as follows:

The uses of cost of living index number are as follows :

• Cost of living Index number provides a realistic picture of the economic position of different class of people. Hence, it is useful to decide wages, dearness allowance, bonus as well as to suggest changes in other allowances to be paid to that class of people.
• It provides the guidance to the government for deciding on which items, control should levied and which items should be kept free.
• It helps the government in divising the taxation policy. If tax is levied on any item then this index number enables the government to infer about its possible impact on the standard of living of the different class of people.
• It is used to measure the changes in purchasing power of money and to know the real earning ability of the earning person.
• It is useful to the government and other public institutions to determine about the type of facilities and incentives to be given to different classes of people to raise their standard of living.

The Fisher’s index number is called an ideal index number due to the following reasons:

• Fisher’s index number considers and quantities of both the years, base year and current year in the construction of the index number.
• It satisfies both the important fundamental tests, time reversal and factor reversal tests, of index number.
• The geometric mean is used to calculate this index number which is the best average for the construction of index number.
• It balances the demerits of Laspeyre’s and Paasche’s index numbers.

Meaning of cost of living index number: The number showing the percentage of relative changes in the cost of living of the people of a certain section of the society in the current year as composed to the base year is called the cost of living index number.

The following points should be taken into account while constructing the cost of living index number:

1. Purpose of construction: While constructing the cost of living index number, first of all its purpose should be defined. It should be made clear about the class of people for whom this index number is to be constructed. The decision regarding selection of commodities, their numbers, their quantities, etc. can be taken after knowing the requirements of different classes of people. This means that it is absolutely necessary to clarify the purpose for which the cost of living index number is to be constructed.

2. Family budget inquiry: For family budget inquiry, a random sample for specified class of people is selected for whom the cost of living Index number is to be constructed.

3. Classification of commodities: Generally, the list of commodities obtained by family budget inquiry can be classified into five heads :

1. Food items,
2. Clothing,
3. House rent,
4. Fuel and Light,
5. Miscellaneous expenditure

4. Availability of prices of items : The retail prices of items of consumption by families are collected from the government recognised or approved shops located in the area where the families of that class of people reside. Sometimes the simple average of retail prices obtained from different shops at different times are taken into consideration. To obtain retail prices of commodities unit of quantity is taken as base unit.
For example, price is obtained as ₹ 10 per kg and not as ₹ 1 per 100 gm. This type of retail prices are obtained according to the requirements of index numbers as weekly, fortnightly, monthly or yearly basis.

5. Selection of base year: The year with normal events should be selected as the base year and price relatives of all the selected items are obtained as follows:
Price relative (I) \(= \cfrac{Retail\, price\, of\, the\, current \,year}  {Retail\, price\, of\, the\, base\, year}  × 100\)

6. Selection of average : For obtaining common price relative from different price relatives of different commodities, appropriate average should be used. Theoretically, the Geometric mean is an ideal average for construction of Index number, but it’s computation is difficult. Hence, weighted average is used in the practice.

7. Selection of weighted method: In the context of total expenditure, importance (weight) of each group and each item is determined and by the following two methods cost of living index number is constructed :

1. Total expenditure method and
2. Family budget method.

The number of items selected in the construction of an index number, the importance of every item is generally not same. So a number assigned to each item according to its importance is called weight of the item.

The weights assigned to the items are of two types:

1. Implicit weight and
2. Explicit weight.

The weighted average is the appropriate average for the construction of index number.

Correct option is (d) Cost of living index number

Correct option is (d) Geometric mean

Correct option is (c) 550

Suppose the production of base year = 1

∴ The production in the year 2016

= 1 + \((1\times\frac{9}{5}=1+\frac{9}{5})\) = \(\frac{14}{5}\)

∴ The index number of production for the year 2016

= \(\cfrac{\frac{14}{5}}{1}\times100\)

= \(\frac{14}{5}\times100=280\)

Correct option is (c) Expenditure of base year

Correct option is (c) 133.33

Correct option is (c) Purchasing power of money is. ₹ 0.5.

Wholesale price index number for the year 2014 = 177.6 and

Wholesale price index number for the year 2015 = 181.2

Rate of inflation =

\(=\frac{(Wholesale\, price\, index \, number\, for\, the\, year \,2015)-( Wholesale \,price\, index\, number\, for\,the\, year\, 2014)}{Wholesale\, price\, index\, number \,for\, the\, year\, 2014} \times 100\)

\(=\frac{181.2-177.6}{177.6} \times 100\)

\(=\frac{3.6}{177.6} \times 100\)

= \(0.0203\,\times 100\)

= 2.03 %

Correct option is (a) ₹ 26000

The average disposable income of family of a class = ₹ 25000 in the year 2014.

Base year is 2014. So the cost of living index number for the year 2014 = 100.

Cost of living index number for the year 2016 = 120.

Now, if the index number is 100, then the average disposable income is = ₹ 25000.

∴ If the index number is 120,

then the average disposable income = \(\frac{25000×120}{100}= ₹ 30000\)

\(I = \frac{Σ\left(\frac{p_{1i}}{p_0}\right)}{n} × 100\)

Real wage = \(\frac{ Wage}{  cost \,of \,living \,index \,number}\)  × 100

‘Inflation’ refers to increase in prices and ‘deflation’ refers to decrease in prices.

The merits and limitations of fixed base method are as follows:

Merits :

• The base year is constant throughout the period of comparison.
• As the base year remains constant, uniformity is maintained in the comparison of the relative changes in the values of variable.
• This method is useful to compare the long term changes in the values of the variable.
• It is easy to understand and simple to compute.

Limitations:

• With change in time the taste, habits and fashion of consumers also changed and the items used by consumers will be changed. In this method the items which are not of much usage cannot be removed and the new items of usage cannot be considered.
• It is not always possible to have a standard year with normal conditions as the base year. So the selection of base year is difficult.
• If the base year is not selected appropriately, the reliability of the index number reduces.
• It is not suitable to compare short term changes in the value of the variable.
• It is not possible to make necessary change in determining weights of the items due to change in the quality of the items.
• If the base year is a year of very remote past, the comparison of relative changes in the value of the variable cannot be considered appropriate.

The merits and limitations of chain base method are as follows:

Merits:

• In this method the problem of selecting the base year does not arise.
• In this method at any given time the preceeding year is taken as the base year.
• As the comparison is being done with the preceeding year, new item can be included according to taste and choice of the consumers and it is possible to remove the items not in use,
• As the value of the variable in the current period is compared with the period in the recent past, this method is useful in the fields of economics, trade and commerce.
• The index number of production and sales obtained by this method are mainly free from seasonal and cyclical fluctuations.
• Short term changes in the prices and production of the commodities can be compared by the index number obtained by this method.

Limitations :

• This method is not very convenient for long term comparison.
• If there is an error in the calculation of index number by this method then the effect of that error continues in the interpretation of the index number of the succeeding year.
• There is no uniformity in the comparison of the index numbers obtained by this method.
• If the information for a year is not available, then the index number for the next year cannot be obtained.