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Economics 6 Marks Question

Index Numbers · CBSE STD 11 Commerce (CBSE - English Medium). 39 questions.

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Question 16 Marks
Explain the various steps involved in the construction of index number on industrial production.
Answer
Following are the steps involved in the construction of index number on industrial production:
  1. Classification of Industries: Major industries are grouped under the following heads:
  1. Mining.
  2. Manufacturing.
  3. Electricity.
  1. Choice of the Base Year: The base year should be the year of economic stability. It should not be at much distance from the current year.
  2. Data Related to Industrial Production: The data relating to the production of different industries are collected.
  3. Assigning Weights: Weights are assigned on the basis of the relative importance of different industries. The weights are based on the values of net output of different industries, capital invested and their contribution to national income.
  4. Formula Index number on industrial production is calculated by using the following formula:
$\text{Index Number}=\frac{\Sigma\bigg[\frac{\text{q}_1}{\text{q}_0}\times100\bigg]\text{W}}{\Sigma\text{W}}$
Here, $q_1$ = Current year's quantity, $q_0$ = Base year's quantity, W = Weights.
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Question 26 Marks
Why do we need an index number?
Answer
An index number is a statistical device that is used to measure the changes in the related variables. Its importance is explained in the following points:
  1. To measure change in the price level: Index numbers measure and compare prices of different commodities with the help of Wholesale Price Index (WPI). It is widely used to measure the level of inflation in an economy.
  2. To study a change in the standard of living: Index numbers help to assess the living standard of people. Cost of living index measures the relative cost of living over time. If the index number has a low value, then it implies that people have low standard of living and vice-versa.
  3. Useful in planning and decision making: Index numbers serve as the most important tool for business communities for drafting various plans and designing various policies. It is useful for the government and the planners to work out inflation rate with the help of consumer price index.
  4. To determine the level of production: Index number of Industrial Production measures changes in the physical volume of production. Also, the production index is an important indicator to ascertain the output level.
  5. To help the government in framing policy: Index numbers are of great help to the government to frame fiscal and monetary policies. The government formulates policies regarding inflation, trade, income, salaries and allowances.
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Question 36 Marks
Explain briefly the various characteristics or features of index numbers.
Answer
The characteristics of index numbers are as follows:
  1. Specialised Averages: Index numbers are specialised averages as they are helpful in computing combined averages of goods and services expressed in different units. Unlike the measures of central tendency, which can compute averages of variables expressed in one unit only, index numbers can measure the averages of variables with diverse units.
  2. Measure the Relative Changes: Index numbers Measure the relative change in the value of the variable under study. Because of this, index numbers are expressed in terms of percentages which are independent of the units of measurement.
  3. Measure the Net Changes: Index numbers measure net changes in a variable or group of variables. They describe net change in a single number. This facilitates the comparisons of two or more index numbers.
  4. Measure the Change not Capable of Direct Measurement: Index numbers are meant to study the changes in the effects of such factors which cannot be measured directly. For example, changes in business activity in a country are not capable of direct measurement but it is possible to study relative changes in business activity with the help of index number.
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Question 46 Marks
The consumer price index for June, $2005$ was $125$. The food index was $120$ and that of other items $135$. What is the percentage of the total weight given to food?
Answer
The price index for June 2005 = 125 Food index = 120 Index for other items = 135 Assume weight assign to food is $W_1$​​​​​​​ and to other items is $W_2​​​​​​​$​​​​​​​ We know the sum of total weights is 100 i.e. $W_1+ W_2 = 100$
Items Index, I Weights, W WI
Food $120$ $W_1$ $120W_1$
Other items $135$ $W_2​​​​​​​$ $135W_2​​​​​​​$
    $W_1 + W_2 = 100$ $120W_1 + 135W_2​​​​​​​$
$\text{CPI}=\frac{\sum\text{WI}}{\sum\text{W}}$
$125=\frac{120\text{W}_1\ +\ 135\text{W}_2}{\text{W}_1\ +\ \text{W}_2}$
$125\text{W}_1+125\text{W}_2=120\text{W}_1+135\text{W}_2$
$125\text{W}_1-120\text{W}_1=135\text{W}_2-125\text{W}_2$
$5\text{W}_1=10\text{W}_2$
$\text{W}_1=2\text{W}_2\ .....(\text{i})$
$\text{W}_1+\text{W}_2=100\ ....(\text{ii})$
By putting the value of W1 the equations (ii), we get$2\text{W}_2+\text{W}_2=100$
$3\text{W}_2=100$
$\text{W}_2=\frac{100}{3}=33.33$
$\text{W}_1=2\times\Big(\frac{100}{3}\Big)=66.67$
Thus, the weights assign to food is 66.67 and to other items are 33.33
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Question 56 Marks
What does a consumer price index for industrial workers measure?
Answer
A Consumer Price Index for Industrial Workers measures the impact of changes in the retail prices on the cost of living of industrial workers. In a country like India, CPI for industrial workers is estimated and published by the Labour Bureau, Shimla taking 1982 as the base year for the current series. In India, CPI for industrial workers is the most popular index and is used by the government to regulate Dearness Allowance (D.A.) to compensate its employees against the price rise.
The weight schemes in CPI for Industrial Workers include food, pan, supari, tobacco, fuel and lighting, housing, clothing, and miscellaneous expenses. Food being the most important component has the highest weight. Thus, it implies that the food price changes have a significant impact on the CPI.
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Question 66 Marks
Explain fisher's ideal index number and His discuss how far it is ideal?
Answer
The Fisher's index number is called ideal index number due to the following characteristics.
  1. It is based on the GEOMETRIC MEAN which is theoretically considered as the best average of constructing index numbers.
  2. It takes into account both current and base year prices as quantities.
  3. It satisfies both time reversal and factor reversal test which are suggested by Fisher.
  4. The upward bias of Lasperey's index number and downward bias of Paasche's index number are balanced to a great extent.
  5. Irving Fisher has considered two important properties which an index number should satisfy. These are tests of reversibility.
Time reversal test.

Factor reversal test.

If an index number satisfies these two tests it is said to be an ideal index number. Fisher's formula satisfies both these tests. (You will read about these tests in detail in higher classes.)
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Question 76 Marks
Is the change in any price reflected in a price index number?
Answer
The change in any price may or may not be reflected in a price index number. An index number shows changes in terms of average. For example, when it is said that index number in 2012-13 has risen to 110, it means that prices of all goods and services have increased by 10% on average. However, it does not mean that prices of all goods and services have uniformly risen by 10%. The price of a particular good might have risen by more than 10% or less than 10% or even might have not change. Whether the change in price will be reflected in a price index number or not depends on the weight associated with the item. Lower or negligible weight reflects lower or negligible change in the index number and higher weight reflects higher change in the index number.
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Question 86 Marks
Index numbers are constructed with certain specific objectives. So, their use is limited. In the context of this statement, discuss any four limitations of index numbers.
Answer
The limitations of index numbers are:
  1. Limited Applicability: Each and every index number is constructed for a specific purpose. If it is used for some other purpose, then it might give misleading results. So, index number has limited applicability.
  2. International Comparison is not possible: Due to difference in the unit of currency and also difference in the composition of production and consumption across different countries, index numbers fail to facilitate international comparison.
  3. Limited Coverage: Index numbers are generally based on sample items, as it is practically impossible to include all the commodities. If the selected items are not able to represent the entire universe, then index numbers will not present a clear picture.
  4. Difficulties in the Construction of Index Numbers: The construction of index numbers involves several problems such as selection of base year, selection of commodities, selection of average, selection of source of data, etc.
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Question 96 Marks
What do you understand by absolute change, relative change and net change?
Answer
Absolute Change: is the actual difference between the prices of a good/service in current year as compared to base year. For example, the price of sugar in 2010 was ₹ 15 per kg and in 2016 is ₹ 42 per kg. So, absolute change in price is ₹ 27 per kg (42-15). Relative Change: is the percentage increase or decrease between the price of a good/service in current year as compared to base year. In case of the example discussed above, the relative change in the price of sugar will be 180%, which is computed with the help of given formula,$\text{Relative change}=\frac{\text{Change in Price}}{\text{Price in BaseYear}}\times100$
$=\frac{27}{15}\times100=180\%$
Net Change: is the average of the percentage change in the prices of goods or services in the current year as compared to a base year. For example, price of sugar increases by 180% and price of oil increases by 40%. So, on a whole, the net change in prices is 110% $\bigg[\frac{180+40}{2}\bigg].$
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Question 106 Marks
An enquiry into the budgets of the middle class families in a certain city gave the following information:
Expenses on items Food 35% Fuel 10% Clothing 20% Rent 15% Misc. 20%
Price (in ₹) in 2004 1500 250 750 300 400
Price (in ₹) in 1995 1400 200 500 200 250
What is the cost of living index during the year 2004 as compared with 1995?
Answer
Items Weight W Price in 1995 $P_0$ Price in 2004 $P_1$ $\text{R}=\frac{\text{P}_1}{\text{P}_0}\times100$ WR
Food 35 1400 1500 $\frac{1500}{1400}\times100=107.14$ 3,749.90
Fuel 10 200 250 $\frac{250}{200}\times100=125$ 1,250
Clothing 20 500 750 $\frac{750}{500}\times100=150$ 3,000
Rent 15 200 300 $\frac{300}{200}\times100=150$ 2,250
Misc. 20 250 400 $\frac{400}{250}\times100=160$ 3,200
  $\sum\text{W}=100$       $\sum\text{WR}=13,449.9$
$\text{CPI}=\frac{\sum\text{WR}}{\sum\text{W}}$
$=\frac{13449.9}{100}=134.49$
Cost of Living Index = 134.50
Thus, the prices rose by 34.50% during 1995 and 2004
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Question 116 Marks
What is the difference between a price index and a quantity index?
Answer
 
Price Index
Quantity Index
1.
It measures general changes in prices between current year and base year.
It measures average change in quantities and assists to compare changes in physical quantity of commodities produced and consumed.
2.
Two methods to calculate Price Index Number are:
  • Simple aggregative method.
  • Simple average of price relative method.
Two methods to calculate Quantity Index Number are:
  • Weighted average of price relative method.
  • Weighted aggregative method.
3.
It is also known as unweighted index number.
It is also known as weighted index number.
4.
It considers the prices of the commodity of both base year and current year.
It considers the weights of commodity assigned according to the quantity.
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Question 126 Marks
The monthly per capita expenditure incurred by workers for an industrial centre during 1980 and 2005 on the following items are given below. The weights of these items are 75, 10, 5, 6 and 4 respectively. Prepare a weighted index number for cost of living for 2005 with 1980 as the base.
Items Price in 1980 Price in 2005
Food 100 200
Clothing 20 25
Fuel & lighting 15 20
House rent 30 40
Misc 35 65
Answer
Calculation of cost of living index for 2005 with 1980 as base year:
Commodity Price in 1980 $(P_0)$ Price in 2005 $(P_1)$ Weight Price relatives (R)$\text{R}=\frac{\text{P}_1}{\text{P}_0}\times100$ RW
Food 100 200 75 $\frac{200}{100}\times100=200$ 15,000
Clothing 20 15 10 $\frac{25}{20}\times100=125$ 1,250
Fuel and Lighting 15 20 5 $\frac{20}{15}\times100=133.33$ 666.65
House Rent 30 40 6 $\frac{40}{30}\times100=133.33$ 799.98
Miscellaneous 35 65 4 $\frac{65}{35}\times100=185.71$ 742.84
      $\sum\text{W}=100$   $\sum\text{RW}=18,459.47$
Cost of Living (CPI) $=\frac{\sum\text{RW}}{\sum\text{W}}$$=\frac{18459.47}{100}=184.59$
Therefore, the cost of living index (CPI) in the current year (2005) has increased by 84.59% as compared to the base year (1980).
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Question 136 Marks
Define cost of living index numbers. Give its formulae.
Answer
The cost of living index numbers measures the changes in the level of prices of commodities which directly affects the cost of living of a specified group of persons at a specified place. The general index numbers fails to give an idea on cost of living of different classes of people at different places. Different classes of people consume different types of commodities, people's consumption habit is also vary from man to man, place to place and class to class i.e. richer class, middle class and poor class. For example the cost of living of rickshaw pullers at BBSR is different from the rickshaw pullers at Kolkata. The consumer price index helps us in determining the effect of rise and fall in prices on different classes of consumers living in different areas.
  1. Aggregate expenditure method or weighted aggregative method: In this method the quantities of commodities consumed by the particular group in the base year are taken as weights. The formula is given by:
Consumer price index = $\frac{\sum\text{p}_\text{1}\text{q}_\text{0}}{\sum\text{p}_\text{0}\text{q}_0}\times100$
  1. Family budget method or the method of weighted relatives: In this method cost of living index is obtained on taking the weighted average of price relatives, the weights are the values of quantities consumed in the base year i.e. $v = p_0g_0$. Thus the consumer price index number is given by:
Consumer price index = $\frac{\sum\text{p}_\text{1}\text{q}_\text{0}}{\sum\text{p}_0\text{q}_\text{0}}\times100$ Where $\frac{\sum\text{p}\upsilon}{\sum\upsilon}$ for each item
$\upsilon=\text{p}_0\text{q}_0$ value on the base year.
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Question 146 Marks
Calculate weighted index number for 2018 by Weighted Aggregative Method and Weighted Average of Relative Method for the following data:
Item Weight Prices in 2017 Prices in 2018
A 10 100 161
B 7 200 210
C 15 50 60
D 9 20 30
E 10 10 14
Answer
Item Weight $p_0$ $p_1$ $p_0W$ $p_1W$ $\text{R}=\frac{\text{p}_1}{\text{p}_0}\times100$ WR
A 10 100 161 1000 1610 161 1610
B 7 200 210 1400 1470 105 735
C 15 50 60 750 900 120 1800
D 9 20 30 180 270 150 1350
E 10 10 14 100 140 140 1400
  $\Sigma\text{W}=51$     $\Sigma\text{p}_0\text{W}=3430$ $\Sigma\text{p}_1\text{W}=4390$   $\Sigma\text{WR}=6895$
Weighted Aggregative Methode:
$\text{P}_{01}=\frac{\Sigma\text{p}_1\text{W}}{\Sigma\text{p}_0\text{W}}\times100=\frac{4390}{3430}\times100=127.98$
Weighted Average of Price Method:
$\text{p}_{01}=\frac{\Sigma\text{WR}}{\Sigma\text{W}}=\frac{6895}{51}=135.19$
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Question 156 Marks
Write a short note on Index for Industrial Production.
Answer
The index number of industrial production aims to measure the change in the level of industrial production in a given period as compared to some other time period which is called base year. It measures changes in the quantity of output instead of change in its money value. In India these statistics are compiled by official and non official agencies. The general index of industrial production is most popular among these. In India, index of industrial production is published by Central Statistical Organization (CSO), Industrial Statistics Wing. In computing an index of industrial production as a whole the area which is to be covered needs to be defined properly. These indices are limited to secondary sector activities. Building and construction are also taken as doubtful items at times. A more difficult problem arises in case of repair work. Some repair work is clearly a part of secondary sector like repairs in ship building or railways but sometimes repair is a part of servie sector like automobile repairs, shoe repairs, cloth repairs etc. Another problem arises in selection of weights: some use quantity as weights while others use value as weights.Usually, important data about production are collected under the following major heads:
  1. Mining Industries-Coal: Iron Ore, Copper, Aluminium, Petroleum etc.
  2. Metallurgical Industries: Iron and Steel, Steel Industry etc.
  3. Mechanical Industries: Locomotives, ships, aero planes etc.
  4. Textile Industries-Cotton: Woolen, Jute, Silk etc.
  5. Industries subject to Excise Duty: Sugar, tobacco,, Breweries, Tobacco etc.
  6. Miscellaneous: Cement, Glass, Soap, Chemical etc.
The table given below shows broad industrial groupings and their weights:
S. No.
Broad Groupings
Weight in %
1.
Mining and Quarrying
10.47
2.
Manufacturing
79.36
3.
Electricity
10.17
Usually eights in a index number of industrial production are based on the net output of various industries. The weighted arithmetic mean or geometric mean of the relatives gives the index number of industrial production. Such index numbers can be constructed for gross output as well as net output. Index Number of Industrial Production.
$\text{IIP}=\frac{\sum\bigg(\frac{\text{q}_1}{\text{q}_0}\bigg)\text{W}}{\sum\text{W}}$
Where $q_1 $= Current Year QuantityProduced $q_0 $= Base Year Quantity
Produced W = Relative importance of different outputs.
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Question 166 Marks
Discuss the general method of constructing an index number.
Answer
The general method of constructing an index number is the calculation by simple index number.
In simple index number, all items are given equal weightage.There are two unweighted methods for it.
  1. Simple Aggregative Index.
  2. Simple Average of Price Relatives.
  1. Simple Aggregative Method: In this method, the average price of all items in the current year is expressed as a percentage of the same in the base year. Index Number is determined by using the formula:
$\text{P}_{01}=\frac{\Sigma\text{p}_1}{\Sigma\text{p}_0}\times100.$
Here, ‘O'stands for the base year and 'l' stands for the current year.
$Ep_1$ = Sum of prices of different commodities for the current year.
$Ep_0$ = Sum of prices of different commodities for the base year.
  1. Simple Average of Price Relative Method: In this method, price relatives are calculated as below:
$\text{P}_{01}=\frac{\Sigma\Big(\frac{\text{p}_1}{\text{p}_0}\times100\Big)}{\text{N}}$
Here, N = Number of commodities
$P_1$ = Price of current year
$P_0$ = Price of base year Average of price relatives is obtained by the formula:
$\frac{\text{p}_1}{\text{p}_0}\times100$ = Price relative.
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Question 176 Marks
Calculate the weighted average of price relative index for 2016 on the basis of 2012 from the following data:
Commodity W $P_0$ $P_1$
2012 2016
A
10
15
20
B
8
10
12
C
6
5
8
D
6
10
13
E
4
4
5
Answer
Consturction of Index Number:
Commodity W Price in 2012 (₹)$(p_0)$ Price in 2016 (₹) ($P_1)$ $\text{I}\bigg(\frac{\text{p}_1}{\text{p}_0}\times100\bigg)$` IW
A 10 125 20 133.33 1333
B 8 10 12 120 960
C 6 5 8 160.0 960
D 6 10 13 130.00 780
E 4 4 5 125.00 500
  $\Sigma\text{W}=34$       $\Sigma\text{IW}=4533$
$\text{P}_{01}=\frac{\Sigma\text{IW}}{\Sigma\text{W}}=\frac{4533}{33}=133.3$
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Question 186 Marks
State the major steps involved in the construction of wholesale price index numbers.
Answer
Index numbers are the best indicators of the economic progress of a community, a nation and the world as a whole. Wholesale price index numbers can also be constructed for different economic activities such as Indices of Agricultural production, Indices of Industrial production, Indices of Foreign Trade etc. Besides some International organizations like the United Nations Organization, the F.A.O. of the U.N., the World Bank and International Labour Organization, there are a number of organizations in the country who publish index numbers on different aspects. These are (a) Ministry of Food and Agriculture, (b) Reserve Bank of India, (c) Central Statistical Organization, (d) Department of Commercial Intelligence and Statistics, (e) Labour Bureau, (f) Eastern Economist. The Central Statistical Organization of the Government of India publishes a Monthly Abstract of' Statistics which contains All India index numbers of Wholesale Prices (Revised series : Base year 1981-82) both commodity-wise and also for the aggregate.
  1. Purpose or object of index numbers: A wholesale price index number which is properly designed for a purpose can be most useful and powerful tool. Thus the first and the foremost problem are to determine the purpose of index numbers. If we know the purpose of the index numbers we can settle some related problems.
  2. Selection of commodities: Representative items should be taken into consideration. The items may be grouped into relatively homogeneous heads to make the calculation. The construction of WPI of a region or country we may group the commodities as Primary Articles – (a) Food Articles (b) Non-food Articles (c) Minerals (ii) Fuel. Power, Light and Lubricants (iii) Manufactured Products (iv) Chemicals and Chemical Products (v) Machinery and Machine Equipments (vi) Other Miscellaneous Manufacturing Industries.
  3. Selection of base period:
  1. The base period must be a normal period i.e. a period frees from all sorts of abnormalities or random fluctuations such as labor strikes, wars, floods, earthquakes etc.
  2. The base period should not be too distant from the given period. Since index numbers are essential tools in business planning and economic policies the base period should not be too far from the current period. For example for deciding increase in dearness allowance at present there is no advantage in taking 1950 or 1960 as the base, the comparison should be with the preceding year after which the DA has not been increased.
  3. Fixed base or chain base .While selecting the base a decision has to be made as to whether the base shall remain fixing or not i.e. whether we have fixed base or chain base. In the fixed base method the year to which the other years are compared is constant.
On the other hand, in chain base method the prices of a year are linked with those of the preceding year. The chain base method gives a better picture than what is obtained by the fixed base method.
  1. Data for index numbers: The data, usually the set of prices and of quantities consumed of the selected commodities for different periods, places etc. constitute the raw material for the construction of wholesale rice index numbers. The data should be collected from reliable sources such as standard trade journals, official publications etc.
  2. Selection of appropriate weights: A decision as to the choice of weights is an important aspect of the construction of index numbers. The problem arises because all items included in the construction are not of equal importance. So proper weights should be attached to them to take into account their relative importance. Thus there are two type of indices. Un weighted indices- in which no specific weights are attached Weighted indices- in which appropriate weights are assigned to various items.
  3. Choice of average: Since index numbers are specialized averages, a choice of average to be used in their construction is of great importance.
  4. Choice of formula: The selection of a formula along with a method of averaging depends on data at hand and purpose for which it is used. Different formulae developed for the purpose have already been discussed in earlier sections.
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Question 196 Marks
Explain the need of weights in index numbers. Explain commonly used weighting schemes.
Answer
The term weight refers to the relative importance of the different items in the construction of the index. Generally various items say wheat, rice, kerosene, clothing etc. included in the index are not of equal importance, proper weights should be attached to them to take into their relative importance.Thus there are two types of indices:
  1. Unweighted indices-in which no specific weights are attached to various commodities.
  2. Weighted indices-in which appropriate weights are assigned to various commodities.
The Unweighted indices can be interpreted as weighted indices by assuming the corresponding weight for each commodity being unity. But actually the commodities included in the index are all not of equal importance. Therefore it is necessary to adopt some suitable method of weighting, so that arbitrary and haphazard weights may not affect the results.There are two methods of assigning weights:
  1. Implicit weighting.
  2. Explicit weighting.
In implicit weighting, a commodity or its variety is included in the index a number of times. For example if wheat is to be given in an index twice as much times as rice then the weight of wheat is two whereas in explicit weighting two types of weights can be assigned. i.e. quantity weights or value weights. A quantity weight symbolized by q means the amount of commodity produced, distributed or consumed in some time period. A value weight in the other hand combines price with quantity produced, distributed or consumed and is denoted by v = pq. For example quantity weights are used in the method of weighted aggregative like Lasperey's, Paasche's index numbers and value weights are used in the method of weighted average of price relatives.
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Question 206 Marks
What are the limitations of index numbers?
Answer
Although index numbers are indispensable tools in economics, business, management etc, they have their limitations and proper care should be taken while interpreting them. Some of the limitations of index numbers are as given below:
  1. Not based on all items: Since index numbers are generally based on a sample, it is not possible to take into account each and every item in the construction of index.
  2. Not free from Error: At each stage of the construction of index numbers, starting from selection of commodities to the choice of formulae there is a chance of the error being introduced. Index numbers are also special type of averages, since the various averages like mean, median, GEOMETRIC MEAN have their relative limitations, their use may also introduce some error. None of the formulae for the construction of index numbers is exact and contains the so called formula error. For example Laspayer's index number has an upward bias while Paasche's index has a downward bias.
  3. Meant for Particular Purpose: An index number is used to measure the change for a particular purpose only. Its misuse for other purpose would lead to unreliable conclusions.
  4. Difference of Time: With the passage of time, it is difficult to make comparisons of index numbers. Over time a person's habit, taste etc. Also undergo change. Consequently, index numbers constructed on the basis of old consumption pattern and hence it becomes obsolete over time. In the construction of price or quantity index numbers it may not be possible to retain the uniform quality of commodities during the period of investigation.
  5. Difficulty in getting data on retail prices: Retail prices vary a great deal from place to place. Most of the index numbers are prepared on the basis of whole sale prices.
  6. International Comparison is not Possible: Different countries develop their indices different years as base years and hence inter-country comparison is not possible by using international comparison.
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Question 216 Marks
Construct index number of price for the year price of 2016 from the following data by:
  1. Laspeyre's Method.
  2. Paasche's Method.
  3. Fisher's Method.
Commodity 2008 2016
Price Quantity Price Quantity
A 10 30 12 35
B 9 10 11 15
C 8 20 7 25
D 6 20 7 25
Answer
Construction of Index number:
Commodity 2008 (Base Year) 2016 (Current Year) $p_0q_0$ $p_0q_1$ $p_1q_1$ $p_1q_1$
$p_0$ $q_0$ $p_1$ $q_1$
A 10 30 12 35 300 350 360 420
B 9 10 11 15 90 135 110 165
C 8 15 10 20 120 160 150 200
D 6 20 7 25 120 150 140 175
          $\Sigma\text{p}_0\text{q}_0=630$ $\Sigma\text{p}_0\text{q}_1=795$ $\Sigma\text{p}_1\text{q}_0=760$ $\Sigma\text{p}_1\text{q}_1=960$
  1. Laspyer's Methode: $\text{P}_{01}=\frac{\Sigma\text{p}_1\text{q}_0}{\Sigma\text{p}_0\text{q}_0}\times100=\frac{760}{630}\times100=120.63$
  2. Paasche's Mrthode: $\text{P}_{01}=\frac{\Sigma\text{p}_1\text{q}_1}{\Sigma\text{p}_0\text{q}_1}\times100=\frac{960}{795}\times100=120.75$
  3. Fisher's Methode: $\text{P}_{01}=\sqrt{\frac{\Sigma\text{p}_1\text{q}_0}{\Sigma\text{p}_0\text{q}_0}\times\frac{\Sigma\text{p}_1\text{q}_1}{\Sigma\text{p}_0\text{q}_1}}\times100$
$=\sqrt{\frac{760}{630}\times\frac{960}{795}}\times100=\sqrt{1.206\times1.207}\times100$
$=\sqrt{1.455\times100}=1.2065\times100=120.65.$
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Question 226 Marks
Define wholesale price index numbers. Give its uses.
Answer
The Wholesale price Index measures the relative changes in the prices of commodities traded in the wholesale markets. These are constructed on weekly basis. These are published every week by the office of Economic Advisor, ministry of Industry, Government of India. First, such index number was constructed in 1947 and thereafter in 1952-53 as base year in 1956. In India, 2004-05 is used as base year for constructing index numbers. In India all commodities which are used in construction of Wholesale Price Index have been grouped into three categories.
  1. Primary Articles: It includes 98 commodities like rice, fruits, pulses, vegetables and non food articles like cotton, jute, metals, non metals etc. it weightage has been 22.02.
  2. Fuel, Power, Light and Lubricants: It includes 19 items like Coal, Petroleum Products, Electricity, Lubricants, etc. It weightage has been 14.23.
  3. Manufacturing: It includes 318 items like Textiles, Sugar, Paper, Machinery, Chemicals, Fertilizers, Leather, etc. Its weightage has been 63.74.
Uses of Wholesale Price Index:
  1. Forecasting Demand and Supply: The wholesale price indices are often used to forecast demand and supply situation in the economy. By considering present demand and supply situation, we can have an idea of demand and supply in the future.
  2. Forecasting Future prices: By looking at WPI statistics of an economy or a state, one can have an idea of expected price rise in the future.
  3. Determination of Real Changes in Aggregates: The wholesale price index enables us to find out the real changes in aggregates like national income and national expenditure. It can be understood by looking at the formula of estimating real national income from nominal national income.
Real Change in National Income = () × Wholesale price of Base Year

It is clear from above that given Wholesale price index we can convert nominal aggregates into real aggregates which are free from the effect of price changes.
  1. Indicator of Rate of Inflation: Te wholesale price index is also used to find the rate of inflation in an economy in a financial year or other time period.
$=\frac{\text{Currrent year WPI-Previous year WPI}}{\text{Previous Year WPI}}\times100$

Wholesale price index is prepared every week. If suppose WPI for week 1 is 400 and for week 2 it is 450 then rate of inflation will be equal to:

$\text{Rate of infaltion}=\frac{450-400}{400}\times100$
  1. Useful in Planning: Government launches many plans which require huge amount of expenditure and take a long time in their completion. It is difficult to estimate the cost of their construction without availability of WPI. Government needs to make provision for these in its five year plans. It is useful in finding the real cost of producing these goods and services. Government also needs to know rate of inflation for making efficient plans and to allocate resources amongst different schemes and sectors of the economy.
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Question 236 Marks
Construct the following indices by taking 2014 as the base year
  1. Simple Aggregative Price Index.
  2. Index of Average of Price Relative.
Item
A
B
C
D
E
Price in 2014 (₹)
6
2
4
10
8
Price in 2015 (₹)
10
2
6
12
12
Price in 2016 (₹)
15
3
8
14
 16
Answer
Construction of Index number:
Item
Price in 2014 (₹)
Price in 2015 (₹)
Price in 2016 (₹)
$\text{I}\bigg(\frac{\text{p}_1}{\text{p}_0}\times100\bigg)$
$\text{I}_2\bigg(\frac{\text{p}_2}{\text{p}_0}\times100\bigg)$
A
6
10
15
166.67
250
B
2
2
3
100.00
150
C
4
6
8
150.00
200
D
10
12
12
120.00
140
E
8
12
16
150.00
200
n = 5
$\Sigma\text{p}_0=30$
$\Sigma\text{p}_1=42$
$\Sigma\text{p}_2=56$
$\Sigma\text{I} _1=686.67$
$\Sigma\text{I}_2=940$
  1. Simple Aggregative Price Index:
$\text{P}_{01}=\frac{\Sigma\text{p}_1}{\Sigma\text{p}_0}\times100=\frac{42}{30}\times100=140(\text{for 2015}),$

$\text{p}_{02}=\frac{\Sigma\text{p}_2}{\Sigma\text{p}_0}\times100=\frac{56}{30}\times100=186.67(\text{for 2016})$
  1. Index of Avrege of Price Relative:
$\text{p}_{01}=\frac{\Sigma\text{I}_1}{\text{n}} =\frac{686.67}{5}=137.34(\text{for 2015}),$

$\text{p}_{02}=\frac{\Sigma\text{I}_2}{\text{n}}=\frac{940}{5}=188(\text{for 2016})$
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Question 246 Marks
Explain the various steps in the construction of $CPI$.
Answer
The construction of consumer price index involves the following steps:
  1. Decision about the class of people: First of all, it should be made clear for which class of consumers, the index number is to be constructed, i.e., whether the index is related to industrial workers, agricultural workers, urban non-manual workers etc. At the same time, the scope of the index should also be defined.
  2. Conducting a family budget survey: A family budget enquiry is to be conducted from a sample of families in order to collect the data about the items of income-expenditure, quantities of commodities etc. Items of consumption are mainly divided into five categories, i.e., food, clothing, fuel and lighting, house rent and miscellaneous.
  3. Price quotations: After selecting the commodities, their retail prices are obtained Retail prices of the selected commodities are collected from the reliable sources and from those places where the most of the consumers buy their goods.
  4. To decide weight: To indicate the relative importance of the items of consumption, weights are assigned to them. Weights can be given in two ways, i.e., quantity weights (either $q_0$ or $q_1$) and weights in the proportion of expenditure made on each commodity in the base year.
  5. Methods of construction: There are two methods of constructing consumer price index. These are:
  1. Aggregate Expenditure Methode:
$\text{P}_{01}=\frac{\Sigma\text{p}_1\text{q}_0}{\Sigma\text{p}_0\text{q}_0}\times100.$
  1. Family Budget Methode:
$\text{P}_{01}=\frac{\Sigma\text{RW}}{\Sigma\text{W}}$
Where $\text{R}=\frac{\text{p}_1}{\text{p}_0}\times100$
W = Weight
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Question 256 Marks
Calculate weighted aggregative price index from the following data using Fisher's method.
Commodity Base Year Current Year
Price (₹) Quantity Price (₹) Quantity
A 2 10 4 5
B 5 12 6 10
C 4 20 5 15
D 2 15 3 10
Answer
Consturction of Index Number:
Commodity
Base Year
Current Year
$p_0q_0$
$p_1q_0$
$p_0q_1$
$p_1q_1$
$p_0$
$q_0$
$p_1$
$q_1$
A
2
10
4
5
20
40
10
20
B
5
12
6
10
60
72
50
60
C
4
20
5
15
80
100
60
75
D
2
15
3
10
30
45
20
30
          $\Sigma\text{p}_0\text{q}_0=190$ $\Sigma\text{p}_0\text{q}_1=257$ $\Sigma\text{p}_0\text{q}_1=140$ $\Sigma\text{p}_1\text{q}_1=185$
Fisher's Price Index Number $\text{P}_{01}=\sqrt{\frac{\Sigma\text{p}_1\text{q}_0}{\Sigma\text{p}_0\text{q}_0}\times\frac{\Sigma\text{p}_1\text{q}_1}{\Sigma\text{p}_0\text{q}_1}}\times100$$=\sqrt{\frac{185}{140}\times\frac{257}{190}}\times100=\sqrt{1.32\times1.35}\times100$
$=1.3335\times100$
$\text{P}_{01}=133.5$
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Question 266 Marks
Record the daily expenditure, quantities bought and prices paid per unit of the daily purchases of your family for two weeks. How has the price change affected your family?
Answer
Week 1
Days
Bread
 
Milk
 
Price per loaf
Quantity
Total expense
Price per litre
Quantity
Total expense
Monday
25
2
50
40
1
40
Tuesday
24
1
24
39
2
78
Wednesday
24
1.5
36
38
1.5
57
Thursday
23
2
46
40
1
40
Friday
24
1
24
39
2
78
Saturday
22
2.5
55
37
1
37
Sunday
24
2
48
39
1.5
58.5
 
 
 
283
 
 
388.5
Week 2
Days
Bread
 
Milk
 
Price per loaf
Quantity
Total expense
Price per litre
Quantity
Total expense
Monday
26
2
52
42
1
42
Tuesday
23
2
46
40
2
80
Wednesday
24
1.5
36
39
2
78
Thursday
25
2
50
39
1
39
Friday
26
1
26
40
2
80
Saturday
22
2.5
55
39
1
39
Sunday
23
2
46
39
1.5
58.5
 
 
 
311
 
 
 416.5
The household expense on the first day of the week for bread was ₹ 50 and the expense on the first day of the second week has increased to ₹ 52 and the price of milk expenses increased from ₹ 40 to ₹ 42. Hence, the total expenditure has been increased from ₹ 90 (50 + 40) to ₹ 94 (52 + 42). Therefore, the increase in the price will lead to an increase in the household expense of a family.
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Question 276 Marks
Discuss in brief, the methods of constructing weighted index numbers.
Answer
Weighted index numbers are the index number in which different items of the series are accorded different weightage, depending upon their relative importance.There are two methods of constructing weighted index numbers:
  1. Weighted Average of Price Relative Method: According to this method, weighted index number is simply the weighted arithmetic mean of price relative. In this method, weighted sum of the price relative is divided by the sum total of the weights.
$\text{Thus,}\ \text{P}_{01}=\frac{\Sigma\text{IW}}{\Sigma\text{W}}$
  1. Weighted Aggregative Method: Under this method, weights are assigned to various items and instead of finding the simple aggregate of price, the weighted aggregate of the price are obtained. The different methods to compute weighted aggregative index numbers are:
Laspeyre's Method: This method uses the base year quantities as weights. The following formula is used to calculate index number
$\text{P}_{01}=\frac{\Sigma\text{p}_1\text{q}_0}{\text{p}_0\text{q}_0}\times100$
Paasche's Method: This method uses the current year quantities as weights The following formula is used to calculate index number
$\text{P}_{01}=\frac{\Sigma\text{p}_1\text{q}_1}{\text{p}_0\text{q}_1}\times100$
Fisher's Method: This method combines the techniques of Laspeyre's method and Paasche's method and uses both base year as well as current year quantities $(q_0, q_1)$ as weight.
The formula to construct index number is:
$\text{P}_{01}=\sqrt{\frac{\Sigma\text{p}_1\text{q}_0}{\Sigma\text{p}_0\text{q}_0}\times\frac{\Sigma\text{p}_1\text{q}_1}{\Sigma\text{p}_0\text{q}_1}}\times100$
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Question 286 Marks
Write the formulae for Lasperey's, Paasche's and fisher's quantity index numbers.
Answer
Lasperey's method: This method is devised by Laspeyre in year 1871.It is the most important of all the types of index numbers. In this method the base year quantities are taken weights. The formula for constructing Lasperey's price index number is $\text{P}_\text{01La}=\frac{\sum\text{p}_1}{\sum\text{p}_0}\times100$ Paasche's method: It was determined by a German Statistician in 1874 in which he took the quantities of current year as weights. In this method the formula is given by$\text{P}^\text{Pa}_\text{01}=\frac{\sum\text{p}_1\text{q}_0}{\text{p}_0\text{q}_0}\times100$
Fisher's ideal method: Fishers price index number is given by root of the multiplication of the Laspeyer's and Paasche's index numbers. It is called ideal index.$\text{P}^\text{F}_{01}=\sqrt{\text{P}^\text{La}_{01}\text{P}^\text{Pa}_{01}}$
$=\sqrt{\frac{\sum\text{p}_1\text{q}_0}{\text{p}_0\text{q}_0}\times100\frac{\sum\text{p}_\text{i}\text{q}_1}{\sum\text{p}_0\text{q}_1}\times100}$
$=\sqrt{\frac{\sum\text{p}_\text{1}\text{q}_0\sum\text{p}_\text{1}\text{q}_1}{\sum\text{p}_\text{0}\text{q}_0\sum\text{p}_\text{0}\text{q}_1}}\times100$
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Question 296 Marks
Calculate the cost of living index number using family budget method.
Commodity
Wheat
Rice
Pulses
Ghee
Sugar
Oil
Fuel
Clothes
Unit Consumed In Base Year
200
50
56
20
40
50
60
40
Price in ₹ (Base Year)
1.0
3.0
4.0
20.0
2.5
10.0
2.0
15.0
Price in ₹ (Current Year)
1.2
3.5
5.0
30.0
5.0
15.5
2.5
18.0
Answer
Construction of Index number:
Commodity
Unit Consumed In Base Year
Price in ₹ (Base Year)
Price in ₹ (Current Year)
$\text{I}\bigg(\frac{\text{p}_1}{\text{p}_0}\times100\bigg)$
$W (p_0-q_0)$
IW
Wheat
200
1.0
1.2
120.00
200
24000
Rice
50
3.0
3.5
116.67
150
17500.5
Pulses
56
4.0
5.0
125.00
224
28000
Ghee
20
20.0
30.0
150.00
400
60000
Suger
40
2.2
5.0
200.00
100
20000
Oil
50
10.0
15.5
155.5
500
77500
Fuel
60
2.0
2.5
125.00
120
15000
Clothes
40
15.0
18.0
120.00
600
72000
 
 
 
 
 
$\Sigma\text{W}=2294$
$\Sigma\text{IW}=314000.5$
$\text{CPI}=\frac{\Sigma\text{IW}}{\Sigma\text{W}}=\frac{314000.5}{2294}=136.88$
This result indicates that CPI in the current year has increased by 36.88% as compared to the base period.
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Question 306 Marks
State any four uses of different types of Index Numbers.
Answer
All index numbers are used in policy-making. The main uses of various index numbers are:
  1. Consumer Price Index (CPI): Is helpful in the wage negotiations, formulation of income policy, price policy, rent control, taxation and general economic policy formulation. It is also used in calculating the purchasing power of money and real wages.
  2. Wholesale Price Index (WPI): Is used to eliminate the effect of changes in general price level on aggregates such as national income, capital formation etc. It is widely used to measure the rate of inflation. If the WPI rises, the inflation rate rises.
  3. Index of Industrial Production (IIP): Gives us a quantitative figure about the changes in the production in the industrial sector.
  4. Agricultural Production Index (API): Provides us a ready reckoner over the performance of agricultural sector.
  5. Sensex: Is a useful guide for investors in the stock market. If the sensex is rising, investors are optimistic of the future performance of the economy.
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Question 316 Marks
Calculate the index number for the period year 2008 to 2015, taking 2008 as base year:
Year (₹) 2008 2009 2010 2011 2012 2013 2014 2015
Price (₹) 75 50 65 60 72 90 75 70
Answer
Consturction of Index Number:
Year Price (₹) Index Numbers (Base Year 2018 = 100)
2008 75 100
2009 50 $\frac{50}{75}\times100=66.67$
2010 65 $\frac{65}{75}\times100=86.67$
2011 60 $\frac{60}{75}\times100=80.0$
2012 72 $\frac{72}{75}\times100=96.0$
2013 90 $\frac{90}{75}\times100=120$
2014 75 $\frac{75}{75}\times100=100$
2015 70 $\frac{70}{75}\times100=93.33$
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Question 326 Marks
State any four difficulties in constructing index numbers.
Answer
The problems/ difficulties faced while constructing an index number are:
  1. Purpose of the index: Calculation of a volume index will be appropriate when one needs a value index. The selection of items, their prices etc. depend on the purpose of index numbers which should be clear.
  2. Selection of the items: The total number of items selected for the index should be neither too small nor too large. Items should be relevant to the purpose of the index. The items should be standardised and representative of the whole group for which index number is to be constructed.
  3. Price quotation: We know that price of many commodities vary from place to place and even from shop to shop in the same market. A selection must also be made as to whether the wholesale price or retail price are required. The choice would depend upon the purpose of index number.
  4. Selection of base year: Base year is the reference year from which comparisons are made. The base year should be a normal year. It should be free from abnormalities like wars, earthquakes etc. Moreover, it should not be from distant past. It should be a year of recent past. It should neither be too far nor too near.
  5. Selection of weights: In fact, all commodities included do not have equal importance. Therefore, to have accurate results, commodities are assigned weights according to their importance. There are two ways of assigning weights, i.e., quantity weights and value weights.
  6. Choice of an average: Mostly choice is to be made between arithmetic mean and geometric mean. Though geometric mean is considered best in theory as this is the most suitable average for measuring relative changes, yet arithmetic mean is more popularly used while constructing index numbers.
  7. Choice of an appropriate formula: Various formulae can be used in the construction of index numbers but it is very essential to select the most suitable out of them. The selection of the formulae depends upon the purpose of index number and availability of data.
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Question 336 Marks
Construct index number of 2015 from the given data by the simple aggregative method and the simple average of relative method.
Commodity
A
B
C
D
E
F
Price In 2015 (₹)
10
18
16
14
12
17
Price in 2010 (₹)
8
15
12
10
8
12.5
Answer
Consturction of Index Number:
Commodity
Price in 2010 (₹)($p_0$​​​​​​​)
Price in 2015 (₹)$(P_1)$
$\text{I}\bigg(\frac{\text{p}_1}{\text{p}_0}\times100\bigg)$
A
8
10
125
B
154
18
120
C
12
16
133.3
D
10
14
140
E
8
12
150
F
12.5
17
136
n = 6
$\Sigma\text{p}_0=65.5$
$\Sigma\text{p}_1=87$
$\Sigma\text{I}=804.3$
  1. Simple Aggretive Methode:
$\text{P}_{01}=\frac{\Sigma\text{p}_1}{\Sigma\text{q}_0}\times100=\frac{87}{65.5}\times100=132.8$
  1. Simple Avrage of Relative Methode:
$\text{P}_{01}=\frac{\Sigma\text{I}}{\text{n}}=\frac{804.3}{6}=134.05$
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Question 346 Marks
Construct the following indices by taking 2015 as the base:
  1. Simple Aggregative Price Index.
  2. Index of Average of Price Relatives.
Items
A
B
C
D
E
Prices ₹ (2015)
6
2
4
10
8
Prices ₹ (2016)
10
2
6
12
12
Prices ₹ (2017)
15
3
8
14
16
Answer
Items
$p_0$
$p_1$
$p_2$
$\frac{\text{p}_1}{\text{p}_0}\times100$
$\frac{\text{p}_2}{\text{p}_0}\times100$
A
6
10
15
166.66
250
B
2
2
3
1000.00
150
C
4
6
8
150.00
200
D
10
12
14
120.00
140
E
8
12
16
150.00
200
 
$\Sigma\text{p}_0=30$
$\Sigma\text{p}_1=42$
$\Sigma\text{p}_2=56$
$\Sigma\Big(\frac{\text{p}_1}{\text{p}_0}\times100\Big)=686.66$
$\Sigma\Big(\frac{\text{p}_2}{\text{p}_0}\times100\Big)=940$
  1. Simple Aggregative Price Index:
$\text{p}_{01}=\frac{\Sigma\text{p}_1}{\Sigma\text{p}_0}\times100$

$=\frac{42}{30}\times100=140$ (For 2016)

$\text{p}_{02}=\frac{\Sigma\text{p}_2}{\Sigma\text{p}_0}\times100$

$=\frac{56}{30}\times100=186.66$ (For 2017)
  1. Index of Average of price Relatives:
$\text{P}_{01}=\frac{\Sigma\Big(\frac{\text{p}_1}{\text{p}_0}\times100\Big)}{\text{N}}=\frac{686.66}{5}=137.33$

$\text{P}_{02}=\frac{\Sigma\Big(\frac{\text{p}_2}{\text{p}_0}\times100\Big)}{\text{N}}=\frac{940}{5}=188$
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Question 356 Marks
Explain the concept and uses of index numbers.
Answer
'Index numbers are devices for measuring differences in the magnitude of a group of related variables.- Croxton & Cowden
Index numbers are indispensable tools of economics and business analysis. Following are the main uses of index numbers:
  1. Index numbers helps in formulating suitable economic policies and planning: Many of the economic and business policies are guided by index numbers. For example while deciding the increase of DA of the employees; the employer's have to depend primarily on the cost of living index. If salaries or wages are not increased according to the cost of living it leads to strikes, lock outs etc. The index numbers provide some guide lines that one can use in making decisions.
  2. They are used in studying trends and tendencies: Since index numbers are most widely used for measuring changes over a period of time, the time series so formed enable us to study the general trend of the phenomenon under study. For example for last 8 to 10 years we can say that imports are showing upward tendency.
  3. Useful to Business Community: Businessmen need to know the trends in the market to take decisions about wage rates, prices of the product, prices of raw materials etc. Therefore, index numbers are very useful for them.
  4. Information Regarding Foreign Trade: Index of Exports and Imports provides relevant information regarding foreign trade and accordingly government can formulate its export-import policy, business men who are engaged in foreign trade can take their decisions and one can predict changes in inflow or outflow of foreign exchange.
  5. They are useful in forecasting future economic activity: Index numbers are used not only in studying the past and present workings of our economy but also important in forecasting future economic activity. Index numbers measure the purchasing power of money.
  6. The cost of living index numbers determine whether the real wages are rising or falling or remain constant: The real wages can be obtained by dividing the money wages by the corresponding price index and multiplied by 100. Real wages helps us in determining the purchasing power of money. Index numbers are used in deflating. Index numbers are highly useful in deflating i.e. they are used to adjust the wages for cost of living changes and thus transform nominal wages into real wages, nominal income to real income, nominal sales to real sales etc. through appropriate index numbers.
  7. Used in Deflating: Deflating means correcting or adjusting a value which has inflated. It makes allowances for the effect of price changes. When prices rise, the purchasing power of money declines. If the money incomes of people remain constant between two periods and prices of commodities are doubled the purchasing power of money is reduced to half. For example if there is an increase in the price of rice from ₹ 10/ kg in the year 1980 to ₹ 20/kg in the year 1982. then a person can buy only half kilo of rice with ₹ 10. so the purchasing power of a rupee is only 50 paise in 1982 as compared to 1980.
Thus the purchasing power of money

$=\frac{1}{\text{ Price Index}}$

In times of rising prices the money wages should be deflated by the price index to get the figure of real wages. The real wages alone tells whether a wage earner is in better position or in worst position.

For calculating real wage, the money wages or income is divided by the corresponding price index and multiplied by 100.

$\text{i.e. Real wages}=\frac{\text{Money wages}}{\text{Price Index}}\times100$

$\text{Thus Real wages Index}=\frac{\text{Real wage of current year }}{\text{Real wage of base year}}\times100.$
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Question 366 Marks
Calculate Laspeyre’s and Paasche's price index numbers on the basis of the following data:
Commodity
A
B
C
D
E
Base Year Price ($p_0)$
10
25
30
15
20
Current Year Price ($p_1)$
15
40
45
30
25
Base Year Quantity $(q_0)$
6
10
15
20
8
Current Year Quantity $(q_1)$
8
20
12
15
6
Answer
Commodity $p_0$ $q_0$ $p_1$ $q_1$ $p_0q_0$ $p_1q_0$ $p_0q_1$ $p_1q_1$
A 10 6 15 8 60 90 80 120
B 25 10 40 20 250 400 500 800
C 30 15 45 12 450 675 360 540
D 15 20 30 15 300 600 225 450
E 20 8 25 6 160 200 120 150
          $\Sigma\text{p}_0\text{q}_0=1220$ $\Sigma\text{p}_1\text{q}_0=1965$ $\Sigma\text{p}_0\text{q}_1=1285$ $\Sigma\text{p}_1\text{q}_1=2060$
Lasepere's Price Index: $\text{P}_{01}=\frac{\Sigma\text{p}_1\text{q}_0}{\Sigma\text{p}_0\text{q}_0}\times100$
$=\frac{1965}{1220}\times100=161.60$
Paasche's Price Index: $\text{P}_{01}=\frac{\Sigma\text{p}_1\text{q}_1}{\Sigma\text{p}_0\text{q}_1}\times100.$
$=\frac{2060}{1285}\times100=160.31$
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Question 376 Marks
Given the following data:
Year CPI of industrial workers (1982 = 100) CPI of agricultural labourers (1986–87 = 100) WP (1993–94=100)
1995-96 313 234 121.6
1996-97 342 256 127.2
1997-98 366 264 132.8
1998-99 414 293 140.7
1999-00 428 306 145.3
2000–01 444 306 155.7
2001–02 463 309 161.3
2002–03 482 319 166.8
2003–04 500 331 175.9
Source: Economic Survey, 2004–2005, Government of India:
  1. Comment on the relative values of the index numbers.
  2. Are they comparable?
Answer
    1.  
Year CPI of Industrial Workers
(1982 = 100)		 Inflation Rate (in %)
$=\frac{\text{A}_2-\text{A}_1}{\text{A}_1}\times100$
1995–96 313 $\frac{313-100}{100}\times100=213$
1996–97 342 $\frac{342-100}{100}\times100=242$
1997–98 366 $\frac{366-100}{100}\times100=266$
1998–99 414 $\frac{414-100}{100}\times100=314$
1999–00 428 $\frac{428-100}{100}\times100=328$
2000–01 444 $\frac{444-100}{100}\times100=344$
2001–02 463 $\frac{463-100}{100}\times100=363$
2002–03 482 $\frac{482-100}{100}\times100=382$
2003–04 500 $\frac{500-100}{100}\times100=400$
  1.  
Year CPI of Non-manual Employees
(1984-85 =100)		 Inflation Rate (in %)
$=\frac{\text{A}_2-\text{A}_1}{\text{A}_1}\times100$
1995–96 257 $\frac{257-100}{100}\times100=157$
1996–97 283 $\frac{283-100}{100}\times100=183$
1997–98 302 $\frac{302-100}{100}\times100=202$
1998–99 337 $\frac{337-100}{100}\times100=237$
1999–00 352 $\frac{352-100}{100}\times100=252$
2000–01 352 $\frac{352-100}{100}\times100=252$
2001–02 390 $\frac{390-100}{100}\times100=290$
2002–03 405 $\frac{405-100}{100}\times100=305$
2003–04 420 $\frac{420-100}{100}\times100=320$
  1.  
Year CPI of Agricultural Labourers
(1986-87=100)		 Inflation Rate (in %)
$=\frac{\text{A}_2-\text{A}_1}{\text{A}_1}\times100$
1995–96 234 $\frac{234-100}{100}\times100=134$
1996–97 256 $\frac{256-100}{100}\times100=156$
1997–98 264 $\frac{264-100}{100}\times100=164$
1998–99 293 $\frac{293-100}{100}\times100=193$
1999–00 306 $\frac{306-100}{100}\times100=206$
2000–01 306 $\frac{306-100}{100}\times100=206$
2001–02 309 $\frac{309-100}{100}\times100=209$
2002–03 319 $\frac{319-100}{100}\times100=219$
2003–04 331 $\frac{331-100}{100}\times100=231$
  1.  
Year WPI
(1993-94 =100)		 Inflation Rate (in %)
$=\frac{\text{A}_2-\text{A}_1}{\text{A}_1}\times100$
1995–96 121.6 $\frac{121.6-100}{100}\times100=21.6$
1996–97 127.2 $\frac{127.2-100}{100}\times100=27.2$
1997–98 132.8 $\frac{132.8-100}{100}\times100=32.8$
1998–99 140.7 $\frac{140.7-100}{100}\times100=40.7$
1999–00 145.3 $\frac{145.3-100}{100}\times100=45.3$
2000–01 155.7 $\frac{155.7-100}{100}\times100=55.7$
2001–02 161.3 $\frac{161.3-100}{100}\times100=61.3$
2002–03 166.8 $\frac{166.8-100}{100}\times100=66.8$
2003–04 175.9 $\frac{175.9-100}{100}=75.9$
  1. The inflation rate for industrial worker with the base year 1982 is the highest and WPI with the base year 1993-94 has the least.
  2. No, the index numbers are not comparable because of the following reasons:
  • Base periods for CPI of industrial workers, urban non-manual workers, agricultural labourers and WPI are different.
  • Commodities and their weightage given to different index may vary from one index number to another.
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Question 386 Marks
Define a wholesale index number. What are its uses?
Answer
The Wholesale price Index measures the relative changes in the prices of commodities traded in the wholesale markets. These are constructed on weekly basis. These are published every week by the office of Economic Advisor, ministry of Industry, Government of India. First, such index number was constructed in 1947 and thereafter in 1952-53 as base year in 1956. In India, 2004-05 is used as base year for constructing index numbers.
  1. Forecasting Demand and Supply: The wholesale price indices are often used to forecast demand and supply situation in the economy. By considering present demand and supply situation, we can have an idea of demand and supply in the future.
  2. Forecasting Future prices: By looking at WPI statistics of an economy or a state, one can have an idea of expected price rise in the future.
  3. Determination of Real Changes in Aggregates: The wholesale price index enables us to find out the real changes in aggregates like national income and national expenditure. It can be understood by looking at the formula of estimating real national income from nominal national income.
Real Change in National Income = ()

It is clear from above that given Wholesale price index we can convert nominal aggregates into real aggregates which are free from the effect of price changes.
  1. Indicator of Rate of Inflation: Te wholesale price index is also used to find the rate of inflation in an economy in a financial year or other time period. Rate of Inflation $=\frac{\text{Currrent year WPI-Previous year WPI}}{\text{Previous Year WPI}}\times100$
  2. Useful in Planning: Government launches many plans which require huge amount of expenditure and take a long time in their completion. It is difficult to estimate the cost of their construction without availability of WPI. Government needs to make provision for these in its five year plans. It is useful in finding the real cost of producing these goods and services. Government also needs to know rate of inflation for making efficient plans and to allocate resources amongst different schemes and sectors of the economy.
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Question 396 Marks
Define index number. Discuss various problems in the construction of index numbers.
Answer
“In its simplest form an index number is the ratio of two index numbers expressed as a percent. An index number is a statistical measure-a measure designed to show changes in one variable or in a group of related variables over time, or with respect to geographic location, or in terms of some other characteristics."- Patternson "An index number is a statistical measure designed to show changes in a variable or a group of related variables with respect to time, geographic location or other characteristics such as income, profession, etc."Spiegel Before constructing index numbers the careful thought must be given into following problems:
  1. Purpose of index numbers: An index number which is properly designed for a purpose can be most useful and powerful tool. Thus the first and the foremost problem are to determine the purpose of index numbers. If we know the purpose of the index numbers we can settle some related problems. For example if the purpose of index number is to measure the changes in the production of steel, the problem of selection of items is automatically settled. But the problem is index which is constructed for one purpose cannot be used of another purpose. Therefore, every time we have to reconstruct it for different purposes. For example, retail prices are meaningful in construction of consumer price index while wholesale prices are used for wholesale price index.
  2. Selection of commodities: After defining the purpose of index numbers, select only those commodities which are related to that index. For example if the purpose of an index is to measure the cost of living of low income group we should select only those commodities or items which are consumed by persons belonging to this group and due care should be taken not to include the goods which are utilized by the middle income group or high income group i.e. the goods like cosmetics, other luxury goods like scooters, cars, refrigerators, television sets etc. Selection of items also get changes as soon as the purpose of index changes.
  3. Selection of base period: The period with which the comparisons of relative changes in the level of phenomenon are made is termed as base period. The index for this period is always taken as 100.
  4. Data for index numbers: The data, usually the set of prices and of quantities consumed of the selected commodities for different periods, places etc. constitute the raw material for the construction of index numbers. The data should be collected from reliable sources such as standard trade journals, official publications etc. for example for the construction of retail price index numbers, the price quotations for the commodities should be obtained from super bazaars, departmental stores etc. and not from wholesale dealers. Wherever we get data, e must ensure that it is reliable, accurate, adequate and comparable.
  5. Price Quotations: Prices of many commodities vary from place to place. It is practically not possible to collect price quotations from all places. Therefore, we can use such areas which are well known for those commodities. There are two ways in which prices may b quoted:
  • Money Prices: In this prices are quoted per unit of commodity like ₹ 30 per kg
  • Quantity prices: Quantity prices are quoted per unit of money. For example 50 ML milk per 1 rupee.
  1. Selection of appropriate weights: A decision as to the choice of weights is an important aspect of the construction of index numbers. The problem arises because all items included in the construction are not of equal importance. Therefore, proper weights should be attached to them to take into account their relative importance. Thus there are two types of indices.
  1. Unweighted indices: In which no specific weights are attached.
  2. Weighted indices: In which appropriate weights are assigned to various items.
  1. Choice of average: Since index numbers are specialized averages, a choice of average to be used in their construction is of great importance. Usually the following averages can be used.
  1. Arithmetic Mean.
  2. Geometric Mean.
  3. Median.
Among these averages Geometric Mean is the appropriate average to be used. But in practice Geometric Mean is not used as often as Arithmetic Mean because of its computational difficulties. Median has erratic difficulties.
  1. Choice of formula: A large variety of formulae are available to construct an index number. The problem very often is that of selecting the appropriate formula. The choice of the formula would depend not only on the purpose of the index but also on the data available.
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