Chapter 6 -INDEX NUMBERS.

09 Nov 2020 7:43 pm

Balbharati, solutions, for, Economics, HSC, 12th, Standard, Maharashtra, State, Board, Chapter 6, INDEX NUMBERS, WITH SOLUTIONS,

1.Choose the correct pair:

Group AGroup B
1) Price Indexa) ∑p1q1/∑p0q0×100
2) Value Indexb) ∑q1/∑q0×100
3) Quantity Indexc) ∑p1q1/∑p0q1×100
4) Paasche’s Indexd) ∑p1/∑p0×100
Options

1-d, 2-c, 3-a, 4-b

1-d, 2-a, 3-b, 4-c

1-b, 2-c, 3-d, 4-a

1-c, 2-d, 3-a, 4-b


2. Choose the correct pair:

Group AGroup B
1) Price Indexa) ∑p1q1/∑p0q0×100
2) Value Indexb) ∑q1/∑q0×100
3) Quantity Indexc) ∑p1q1/∑p0q1×100
4) Paasche’s Indexd) ∑p1/∑p0×100
Options

1-d, 2-c, 3-a, 4-b

1-d, 2-a, 3-b, 4-c

1-b, 2-c, 3-d, 4-a

1-c, 2-d, 3-a, 4-b

Q.2. Complete the Correlation:

1. Price Index : Inflation :: Quantity Index : Agricultural production.

2. Po: 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:

CommodityABCD
Price in 2005 (₹)616244
Price in 2010 (₹)818286

SOLUTION:- 

CommodityPrice in 2005 (₹) P0Price in 2010 (₹) P1
A68
B1618
C2428
D46
Total∑P0 = 50∑P1 = 60

⇒ Here, ∑P0 = 50 and ∑P1 = 60

Using Simple Aggregate Price Index formula

∴ Simple Aggregate Price Index = P1/P0 * 100

60/50 * 100

=120

2. Calculate Quantity Index number from the given data:

CommodityPQRST
Base year quantities170150100195205
Current year quantities90707515095

SOLUTION: –

CommodityBase year quantities q0Current year quantities q1
P17090
Q15070
R10075
S195150
T20595
Total∑q0 = 820∑q1 = 480

Quantity Index Number = q1/q0 * 100

480/820 *100

= 58.54.

3. Calculate Value Index number from the given data:

CommodityBase yearCurrent year
PriceQuantityPriceQuantity
A40157020
B10126022
C50109018
D201410016
E30134015

Solution: –

CommodityBase yearCurrent year
 p0q0p0q0p1q1p1q1
A401560070201400
B101212060221320
C501050090181620
D2014280100161600
E30133904015600
Total∑p0q0 =1890∑p1q1 =6540

value Index Number = p1q1/p0q0 * 100

∑p1q1/∑p0q0×100

= 6540/1890×100

= 346.03

4. Calculate Laaspeyre’s index from the given data:

CommodityBase yearcurrent year
PriceQuantityPriceQuantity
X8301225
Y10422016

Solution: –

CommodityBase yearCurrent year  
p0q0p1q1p1q0p0q0
X8301225360240
Y10422016840420
Total    1200660

Laaspeyre’s index = p1q0/p0q0 * 100

∑p1q0/∑p0q0×100

= 1200/660×100

= 181.81

5. Calculate Paasche’s index from the given data:

CommodityBase yearcurrent year
PriceQuantityPriceQuantity
X8301225
Y10422016

Solution: –

CommodityBase yearCurrent year  
p0q0p1q1p1q1p0q1
X8301225300200
Y10422016320160
Total    620360

Paasche’s index = p1q1/p0q1

∑p1q1/∑p0q1×100

= 620/360×100

= 172.22

Q.4. Distinguish between:

1. Simple Index Numbers and Weighted Index Numbers

Simple Index NumbersWeighted Index Numbers
In this method, every commodity is given equal importance. It is the easiest method for constructing index numbers. In this method, suitable weights are assigned to various commodities. It gives relative importance to the commodity in the group. In most of the cases ‘quantities’ are used as weights.
This method can be applied to determine the Price Index Number, Quantity Index Number, and Value Index Number. There are various methods of constructing weighted index numbers such as Laaspeyre’s Price Index, Paasche’s Price Index, etc.

2. Price Index and Quantity Index.

Price IndexQuantity Index
1. Price Index Number is calculated by two methods, namelya. Simple Aggregative Methodb. Simple Average of Price Relative Method1. Quantity Index Number is calculated by two methods, namelya. Weighted Average of Price Relative Methodb. Weighted Aggregative Method
2. Price Index number is also known as the Unweighted Index Number.2. Quantity Index Number is also known as Weighted Index Number.
3. Price Index Number takes into account the prices of the commodity of the base year as well as of the current year.3. Quantity Index takes into consideration the weights of goods assigned according to the quantity.

3. Laaspeyre’s Index and Paasche’s Index.

Laaspeyre’s Index Paasche’s Index
1. In Laaspeyre’s index, base year quantities are taken as weights.1. In Paasche’s index, current year quantities are taken as weights.
2. Laaspeyre’s index can be calculated as Laaspeyre’s index = p1q0/p0q0 * 100∑p1q0/∑p0q0×1002. Paasche’s index can be calculated as Paasche’s index = p1q1/p0q1* 100∑p1q1/∑p0q1×100

Q.5. State with reason whether you agree or disagree with the following statement:

1. Index numbers measure changes in the price level only.

Options

Agree

Disagree

Reasons: –

No, I disagree with the above statement

1. Index numbers are also used to measure changes in the price level from time to time. 

2. It enables the government to undertake appropriate anti-inflationary measures.

2.  Index numbers are free from limitations.

Options

Agree

Disagree

Reasons: –

No, I disagree with the above statement

1. Index numbers are generally based on samples. 

2. 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.

 
Options

Agree

Disagree

Reasons: –

No, I disagree with the above statement

1. Index numbers can be misused. 

2. They compare a situation in the current year with a situation in the base year.

Q.6. Answer the following:

1. Explain the features of index numbers.

Following are the various feature of index number:

Measures of relative changes: Index number measures relative or percentage changes in the variable over time.

Quantitative expression: Index numbers offer a precise measurement of the quantitative change in the concerned variable over time.

Average: Index numbers show changes in terms of average.

2. Explain the significance of index numbers in economics.

Answer: –

Significance of Index Numbers in Economics:

Index numbers are indispensable tools of economic analysis. 

Following points explain the significance of index numbers:

Framing suitable policies: Index numbers provide guidelines to policymakers 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.

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.

Forecasting about the 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.

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 the organised sector on the basis of changes in the Dearness Index.

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).

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.

Answers: –

Following steps are involved in the construction of index numbers :

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.

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.

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.

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.

Choice of a suitable average: Construction of index numbers requires the choice of a suitable average. Generally, the Arithmetic mean is used in the construction of index numbers because it is simple to compute compared to other averages.

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.

Selection of an appropriate formula: Various formulae are devised for the construction of index numbers. The choice of a suitable formula depends upon the purpose of the index number and availability of data.

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