Chapter 6
Index Numbers
Sr. No. | Name of Chapter |
Q. 1. Choose the correct option :
1) Statements that are incorrect in relation to index numbers.
a) Index number is a geographical tool.
b) Index numbers measure changes in the air pressure.
c) Index numbers measure relative changes in an economic variable.
d) Index numbers are specialized averages.
Options :1) c and d
2) a and b
3) b and c
4) a and d
Ans: 1) c and d
2) Statements that highlight the significance of index numbers.
a) Index numbers are useful for making future predictions.
b) Index numbers help in the measurement of inflation.
c) Index numbers help to frame suitable policies.
d) Index numbers can be misused.
Options :1) b, c and d
2) a, c and d
3) a, b and d
4) a, b and c
Ans: 3) a, b and d
3) Statements that apply to weighted index numbers.
a) Every commodity is given equal importance.
b) It assigns suitable 'weights' to various commodities.
c) In most of the cases, quantities are used as weights.
d) Laaspeyre's and Paasche's method is used in the calculation of weighted index numbers.
Options :1) b, c and d
2) a, c and d
3) a, b and d
4) a, b, c and d
Ans: 1) b, c and d
4) Statements related to limitations of index numbers.
a) Index numbers are not completely reliable.
b) There may be a bias in the data collected.
c) Every formula has some kind of defect.
d) Index numbers ignore changes in the qualities of products.
Options :1) a, c and d
2) a, b, c and d
3) a, b and d
4) b, c and d
Ans: 2) a, b, c and d
|
Group A |
Group B |
|
1.
Price Index |
a = ⅀p1q1
/ ⅀p0q0 x 100 |
|
2.
Value Index |
b = ⅀q1
/ ⅀q0 x 100 |
|
3.
Quantity Index |
c = ⅀
p1q1 / ⅀p0q1 x 100 |
|
4.
Paasche’s Index |
d = ⅀
P1 / ⅀P0 x 100 |
Option : (1) 1-d, 2-c, 3-a, 4-b
(1) 1-d, 2-a, 3-b, 4-c
(1) 1-b, 2-c, 3-d, 4-a
(1) 1-c, 2-d, 3-a, 4-b
Q. 2. Complete the Correlation :
1) Price Index : Inflation :: Agricultural productivity Index : Agricultural production
2) P0 : Base year prices :: p1 : Current year prices
3) Laaspeyre's index : Base year Quantities :: Paasche's index : Current year quantities
4) Univariate Index: Single variable :: Composite index : Group of variables
Q. 3. Solve the following :
1) Calculate Price Index number from the given data :
|
Commodity |
A |
B |
C |
D |
|
Price
in 2005 (Rs.) |
6 |
16 |
24 |
4 |
|
Price
in 2010 (Rs.) |
8 |
18 |
28 |
6 |
Ans:
|
Commodity |
A |
B |
C |
D |
Total |
|
Price
in 2005 (Rs.) |
6 |
16 |
24 |
4 |
⅀P0
= 50 |
|
Price
in 2010 (Rs.) |
8 |
18 |
28 |
6 |
⅀ P1
= 60 |
Price Index = ⅀ P1 / ⅀P0 x 100
= 60 / 50 x 100
=
120
Therefore, Price Index Number = 120
Q.2 Calculate Quantity Index number from the
given data:
|
Commodity |
P |
Q |
R |
S |
T |
|
Base
Year Quantities |
170 |
150 |
100 |
195 |
205 |
|
Current
Year Quantities |
90 |
70 |
75 |
150 |
95 |
Ans:
|
Commodity |
Base Year Quantities |
Current Year Quantities |
|
P |
170 |
90 |
|
Q |
150 |
70 |
|
R |
100 |
75 |
|
S |
195 |
150 |
|
T |
205 |
95 |
|
|
⅀q0
= 820 |
⅀q1 =
480 |
Quantity Index = ⅀q1 / ⅀q0 x 100
=
24 / 41 x 100
=
58.536
Therefore, Quantity Index Number = 58.54
|
Commodity |
Base Year |
Current Year |
||
|
Price |
Quantity |
Price |
Quantity |
|
|
A |
8 |
30 |
12 |
25 |
|
B |
10 |
42 |
20 |
16 |
Ans:
|
Commodity |
Base Year |
Current Year |
P1q0 |
P0q0 |
||
|
Price |
Quantity |
Price |
Quantity |
|||
|
A |
8 |
30 |
12 |
25 |
360 |
240 |
|
B |
10 |
42 |
20 |
16 |
840 |
420 |
|
Total |
|
|
|
|
1200 |
660 |
Laaspeyre’s Index number
= ⅀p1q1 / ⅀p0q0 x 100
= 1200 / 660 x 100
= 60 / 33 x 100
= 181. 818
Laaspeyre’s Index Number = 181. 82
Q. 4. Distinguish between :
1) Simple Index Numbers and Weighted Index Numbers.
2) Price Index and Quantity Index.
3) Laaspeyre's Index and Paasche's Index.
Q. 5. State with resons whether you agree or disagree with the following statements :
1) Index numbers measure changes in the price level only.
Ans: Diagree
(a) Index numbers measure changes in the price level as well as change in the stock market price, cost of living, Industrial and agricultural production, export and import, etc.
(b) For Example, Labor productivity index number measures the general changes in the labor productivity over a period of time.
(c) Consumer Price Index Number, Wholesale Price Index Number, Index Service Production, Human Development Index Number, etc. are the special purpose index number measuring the changes in various economic various over a given period of time.
Thus, Index numbers do not measure changes in the price level only, but also measure changes in many other economic variable.
2) Index numbers are free from limitations.
Ans: Disagree
Index numbers are generally base on samples, we cannot include all the items in the construction of the index numbers. Hence they are not free from sampling errors.
3) Index numbers can be constructed without the base year.
Ans: Disagree
Q. 6. Answer the following :
1) Explain the features of index numbers.
Ans:
Croxton and Cowden : “Index Numbers are devices for measuring differences in the magnitude of a group of related variables.”
Features of Index Numbers :
1) Index numbers are statistical devices.
2) Index numbers are specialized averages which are capable of being expressed in percentages.
3) Index numbers measure the net change in one or more related variables over a period of time or between two different time periods or two different localities.
4) Index number which is computed from a single variable is called a ‘univariate index’, whereas an index which is constructed from a group of variables is called a ‘composite index’.
5) The year for which the index number is prepared is the current year.
6) The year with which the changes are measured is called the base year.
7) The base year’s index is assumed as 100 and accordingly the value of the current year is calculated.
8) Index numbers are also referred to as ‘barometers of economic activity’, since it is used to measure the trends and changes in the economy.
2) Explain the significance of index numbers in economics.
Ans:
Significance of Index Numbers in Economics :
Index numbers are indispensable tools of economic analysis. Following points explain the significance of index numbers :
1) Framing suitable policies : Index numbers provide guidelines to policy makers in framing suitable economic policies such as agricultural policy, industrial policy, fixation of wages and dearness allowances in accordance with the cost of living etc.
2) Studies trends and tendencies : Index numbers are widely used to measure changes in economic variables such as production, prices, exports, imports etc. over a period of time. For example, by examining the index of industrial production for the last five years, we can draw important conclusions about the trend of industrial production whether it shows an upward tendency or a downward tendency.
3) Forecasting about future economic activity : Index numbers are useful for making predictions for the future based on the analysis of the past and present trends in the economic activities. For example, based on the available data pertaining to imports and exports, future predictions can be made. Thus, forecasting guides in proper decision making.
4) Measurement of inflation : Index numbers are also used to measure changes in the price level from time to time. It enables the government to undertake appropriate anti-inflationary measures. There is a legal provision to pay the D.A. (dearness allowance) to the employees in organized sector on the basis of changes in Dearness Index.
5) Useful to present financial data in real terms : Deflating means to make adjustments in the original data. Index numbers are used to adjust price changes, wage changes etc. Thus, deflating helps to present financial data in real terms (at constant prices).
Q. 7. Answer in detail :
1) Explain the steps involved in the construction of index numbers.
Ans:
Construction of Index Numbers :
Following steps are involved in the construction of index numbers :
1) Purpose of index number : The purpose for constructing the index number, its scope as well as which variable is intended to be measured should be clearly decided to achieve fruitful results.
2) Selection of the base year : Base year is also called the reference year. It is the year against which comparisons are made. The base year should be normal i.e. it should be free from natural calamities. It should not be too distant in the past.
3) Selection of items : It is necessary to select a sample of the number of items to be included in the construction of a particular index number. For example, in the construction of price index numbers it is impossible to include each and every commodity. The commodities to be selected should represent the tastes, habits and customs of the people. Besides this, only standardized or graded items should be included to give better results.
4) Selection of price quotations : Prices of the selected commodities may vary from place to place and shop to shop in the same market. Therefore, it is desirable that price quotations should be obtained from an unbiased price reporting agency. To achieve accuracy, proper selection of representative places and persons is required.
5) Choice of a suitable average : Construction of index numbers requires choice of a suitable average. Generally, Arithmetic mean is used in the construction of index numbers because it is simple to compute compared to other averages.
6) Assigning proper weights : Weight refers to the relative importance of the different items in the construction of an index number. Weights are of two types i.e. quantity weights (q) and value weights (p x q). Since all items are not of equal importance, by assigning specific weights, better results can be achieved.
7) Selection of an appropriate formula : Various formulae are devised for the construction of index numbers. Choice of a suitable formula depends upon the purpose of index number and availability of data
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