हिंदी
तमिलनाडु बोर्ड ऑफ सेकेंडरी एज्युकेशनएचएससी वाणिज्य कक्षा १२

Calculate the Laspeyre’s, Paasche’s and Fisher’s price index number for the following data. Interpret on the data. Commodities Base Year Current Year Price Quantity Price Quantity A 170 562 72 632

Advertisements
Advertisements

प्रश्न

Calculate the Laspeyre’s, Paasche’s and Fisher’s price index number for the following data. Interpret on the data.

Commodities Base Year Current Year
Price Quantity Price  Quantity
A 170 562 72 632
B 192 535 70 756
C 195 639 95 926
D 1987 128 92 255
E 1985 542 92 632
F 150 217 180 314
7 12.6 12.7 12.5 12.8
8 12.4 12.3 12.6 12.5
9 12.6 12.5 12.3 12.6
10 12.1 12.7 12.5 12.8
सारिणी
योग
Advertisements

उत्तर

Commodities Base Year Current Year p0q0 p0q1 p1q0 p1q1
p0 q0 p1  q1
A 170 562 72 632 95540 107440 40464 45504
B 192 535 70 756 102720 145152 37450 52920
C 195 639 95 926 124605 180570 60705 87970
D 1987 128 92 255 23936 47685 11776 23460
E 1985 542 92 632 100270 116920 49864 58144
F 150 217 180 314 32550 47100 39060 56520
7 12.6 12.7 12.5 12.8 160.02 161.28 158.75 160
8 12.4 12.3 12.6 12.5 152.52 155 154.98 157.5
9 12.6 12.5 12.3 12.6 157.50 158.80 153.75 155
10 12.1 12.7 12.5 12.8 153.67 154.90 158.75 160
Total 480244.71 645496.98 239945.23 325150.5

Lasperyre’s price Index number

`"P"_01^"L" = (sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx 100`

= `239945.23/480244.71 xx 100`

= 49.96

Passhe's price index number

`"P"_01^"p" = (sum"p"_1"q"_1)/(sum"p"_0"q"_1) xx 100`

= `325150.5/645496.98 xx 100`

= 50.37

Fisher's price index number

`"P"_01^"F" = [sqrt((sum"p"_1"q"_0 xx sum"p"_1"q"_1)/(sum"p"_0"q"_0 xx sum"p"_0"q"_1))] xx 100`

= `[sqrt((239945.23 xx 325150.5)/(480224.71 xx 645496.98))] xx 100`

= `sqrt((3572000)/(1827840)) xx 100`

= `sqrt(1.9542) xx 100`

= `1.3979 xx 100`

= 139.79

= 139.8

Time reversal test

Test is satisfied when `"P"_01 xx "P"_10` = 1

`"P"_01 = sqrt((sum"p"_1"q"_0 xx sum"p"_1"q"_1)/(sum"p"_0"q"_0 xx sum"p"_0"q"_1))`

= `sqrt((1900 xx 1880)/(1360 xx 1344))`

`"P"_10 = sqrt((sum"p"_0"q"_1 xx sum"p"_0"q"_0)/(sum"p"_1"q"_1 xx sum"p"_1"q"_0))`

= `sqrt((1344 xx 1360)/(1880 xx 1900))`

`"P"_01 xx "P"_10 = sqrt((1900 xx 1880 xx 1344 xx 1360)/(1360 xx 1344 xx 1880 xx 1900))`

= `sqrt(1)`

Hence Fisher’s Ideal Index satisfies Time reversal test

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 9: Applied Statistics - Miscellaneous problems [पृष्ठ २३१]

APPEARS IN

सामाचीर कलवी Business Mathematics and Statistics [English] Class 12 TN Board
अध्याय 9 Applied Statistics
Miscellaneous problems | Q 4 | पृष्ठ २३१

संबंधित प्रश्न

______ : Base year prices :: P1 : Current year prices.


Complete the Correlation:

__________ : Single variable :: Composite index : Group of variables


Assertion (A): Index numbers are statistical devices.

Reasoning (R): Index numbers measure only changes in the price level over a period of time.


Identify & explain the concept from the given illustration.

Agricultural Research Institute constructed an index number to measure changes in the production of raw cotton in Maharashtra during the period 2015-2020.


Explain factor reversal test


Calculate price index number for 2005 by (a) Laspeyre’s (b) Paasche’s method

Commodity 1995 2005
Price Quantity Price  Quantity
A 5 60 15 70
B 4 20 8 35
C 3 15 6 20

Using the following data, construct Fisher’s Ideal index and show how it satisfies Factor Reversal Test and Time Reversal Test?

Commodity Price in Rupees per unit Number of units
Basic year Current year Base year Current year
A 6 10 50 56
B 2 2 100 120
C 4 6 60 60
D 10 12 50 24
E 8 12 40 36

Calculate the cost of living index by aggregate expenditure method:

Commodity Weight
2010
Price (Rs.)
2010 2015
P 80 22 25
Q 30 30 45
R 25 42 50
S 40 25 35
T 50 36 52

Choose the correct alternative:

Cost of living at two different cities can be compared with the help of


Read the given passage and answer the questions:

Index Number is a technique of measuring changes in a variable or group of related variables with reference to time, geographical location and other characteristics.

Index Number is very useful for economists, farmers, traders, government, educationalists and trade union leaders for planning and implementing the plans according to their sector.

The scope of index number is not limited to only one subject but it extends to many subjects such as Economics, Educational science, Psychology, History, Sociology, Geography etc.

While framing index number its objective must be determined. To attain the objective the information is collected in various ways and this information is used for comparing two different time periods. For this purpose, the base year’s index is assumed as 100 and accordingly the value of the current year is calculated.

Laspeyre, Paasche and Fisher have suggested different methods for constructing index numbers.

  1. Explain the meaning of Index Number.
  2. To whom the Index Number is useful?
  3. Express your opinion about the given passage.

Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×