Construct Fisher ideal index for the following data taking 2014 as base year Items year 2014 year 2015 Price Quantity Price Quantity A 6 50 10 56 B 2 100 2 120 C 4 60 6 60 D 10 30 12 24 E 8 40 12 36

Given that, Items year 2014 year 2015 Price Quantity Price Quantity A 6 50 10 56 B 2 100 2 120 C 4 60 6 60 D 10 30 12 24 E 8 40 12 36 Let p 0 , q 0 are prices and quantities of items of base year 2014 and p 1 , q 1 are prices and quantities of items of current year 2015 . Tabular form: Items year 2014 year 2015 Price p 0 Quantity q 0 Price p 1 Quantity q 1 p 0 q 0 p 1 q 0 p 0 q 1 p 1 q 1 A 6 50 10 56 300 500 336 560 B 2 100 2 120 200 200 240 240 C 4 60 6 60 240 360 240 360 D 10 30 12 24 300 360 240 288 E 8 40 12 36 320 480 288 432 ∑ p 0 q 0 = 1360 ∑ p 1 q 0 = 1900 ∑ p 0 q 1 = 1344 ∑ p 1 q 1 = 1880 We know that, Fisher’s ideal index formula is P 01 F = ∑ p 1 q 0 ∑ p 0 q 0 × ∑ p 1 q 1 ∑ p 0 q 1 Now, P 01 F = 1900 1360 × 1880 1344 = 139 . 7 × 139 . 7 = 139 . 7 . ∴ P 01 F = 139 . 7 , is Fisher ideal index number.

Construct Paasche’s index for the following data taking 2014 as base year Items year 2014 year 2015 Price Quantity Price Quantity A 6 50 10 56 B 2 100 2 120 C 4 60 6 60 D 10 30 12 24 E 8 40 12 36

Given that, Items year 2014 year 2015 Price Quantity Price Quantity A 6 50 10 56 B 2 100 2 120 C 4 60 6 60 D 10 30 12 24 E 8 40 12 36 Let p 0 , q 0 are prices and quantities of items of base year 2014 and p 1 , q 1 are prices and quantities of items of current year 2015 . Tabular form: Items year 2014 year 2015 Price p 0 Quantity q 0 Price p 1 Quantity q 1 p 0 q 0 p 1 q 0 p 0 q 1 p 1 q 1 A 6 50 10 56 300 500 336 560 B 2 100 2 120 200 200 240 240 C 4 60 6 60 240 360 240 360 D 10 30 12 24 300 360 240 288 E 8 40 12 36 320 480 288 432 ∑ p 0 q 0 = 1360 ∑ p 1 q 0 = 1900 ∑ p 0 q 1 = 1344 ∑ p 1 q 1 = 1880 We know that, Paasche’s index price method formula P 01 P = ∑ p 1 q 1 ∑ p 0 q 1 × 100 Now, P 01 P = 1880 1344 × 100 = 139 . 7 ∴ P 01 P = 139 . 7 , is Paasche’s index number.

Construct Laspeyre’s index for the following data taking 2014 as base year Items year 2014 year 2015 Price Quantity Price Quantity A 6 50 10 56 B 2 100 2 120 C 4 60 6 60 D 10 30 12 24 E 8 40 12 36

Given that, Items year 2014 year 2015 Price Quantity Price Quantity A 6 50 10 56 B 2 100 2 120 C 4 60 6 60 D 10 30 12 24 E 8 40 12 36 Let p 0 , q 0 are prices and quantities of items of base year 2014 and p 1 , q 1 are prices and quantities of items of current year 2015 . Tabular form: Items year 2014 year 2015 Price p 0 Quantity q 0 Price p 1 Quantity q 1 p 0 q 0 p 1 q 0 p 0 q 1 p 1 q 1 A 6 50 10 56 300 500 336 560 B 2 100 2 120 200 200 240 240 C 4 60 6 60 240 360 240 360 D 10 30 12 24 300 360 240 288 E 8 40 12 36 320 480 288 432 ∑ p 0 q 0 = 1360 ∑ p 1 q 0 = 1900 ∑ p 0 q 1 = 1344 ∑ p 1 q 1 = 1880 Formula of Laspeyre’s index numder is P 01 L = ∑ p 1 q 0 ∑ p 0 q 0 × 100 ⇒ 1900 1360 × 100 = 139 . 7 ∴ Laspeyre’s index number is P 01 L = 139 . 7 .

Calculate Fisher’s ideal index method for the following data Commodity 2000 2001 Price Quantity Price Quantity A 2 7 3 5 B 5 11 6 10 C 3 14 5 11 D 4 16 4 18

Given that, Commodity 2000 2001 Price Quantity Price Quantity A 2 7 3 5 B 5 11 6 10 C 3 14 5 11 D 4 16 4 18 Let p 0 , p 1 are the prices of the commodities and q 0 , q 1 are the quantities of commodities Tabular form: Commodity 2000 2001 Price ( p 0 ) Quantity ( q 0 ) Price ( p 1 ) Quantity ( q 1 ) p 0 q 0 p 1 q 0 p 0 q 1 p 1 q 1 A 2 7 3 5 14 21 10 15 B 5 11 6 10 55 66 50 60 C 3 14 5 11 42 70 33 55 D 4 16 4 18 64 64 72 72 Σ p 0 q 0 = 175 Σ p 1 q 0 = 221 Σ p 0 q 1 = 165 Σ p 1 q 1 = 202 We know that, P F 01 = P 01 L × P 01 P = ∑ p 1 q 0 ∑ p 0 q 0 × ∑ p 1 q 1 ∑ p 0 q 1 = 221 175 × 202 165 × 100 = 44642 28875 = 124 . 33 . ∴ p F 01 = 124 . 33 is index number.

Construct Marshall-Edgeworth index for the following data taking 2014 as base year Items year 2014 year 2015 Price Quantity Price Quantity A 6 50 10 56 B 2 100 2 120 C 4 60 6 60 D 10 30 12 24 E 8 40 12 36

Given that, Items year 2014 year 2015 Price Quantity Price Quantity A 6 50 10 56 B 2 100 2 120 C 4 60 6 60 D 10 30 12 24 E 8 40 12 36 Let p 0 , q 0 are prices and quantities of items of base year 2014 and p 1 , q 1 are prices and quantities of items of current year 2015 . Tabular form: Items year 2014 year 2015 Price p 0 Quantity q 0 Price p 1 Quantity q 1 p 0 q 0 p 1 q 0 p 0 q 1 p 1 q 1 A 6 50 10 56 300 500 336 560 B 2 100 2 120 200 200 240 240 C 4 60 6 60 240 360 240 360 D 10 30 12 24 300 360 240 288 E 8 40 12 36 320 480 288 432 ∑ p 0 q 0 = 1360 ∑ p 1 q 0 = 1900 ∑ p 0 q 1 = 1344 ∑ p 1 q 1 = 1880 We know that, Marshall-Edgeworth index P 01 M = ∑ p 1 q 0 + ∑ p 1 q 1 ∑ p 0 q 0 + ∑ p 0 q 1 × 100 Now, P 01 M = 1900 + 1880 1360 + 1344 × 100 = 3780 2704 = 139 . 8 ∴ P 01 M = 139 . 8 , is Marshall-Edgeworth index number.

The DorbishBowleys price index is the

MEDIUM

Mathematics>Statistics>Index Numbers>Weighted Index Numbers

The weighted aggregative price index numbers for $2001$ with $2000$ as the base year using Paasche's Index Number is:

Commodity	Price (in $₹$ )		Quantities
	$2000$	$2001$	$2000$	$2001$
$A$	$10$	$12$	$20$	$22$
$B$	$8$	$8$	$16$	$18$
$C$	$5$	$6$	$10$	$11$
$D$	$4$	$4$	$7$	$8$

EASY

Mathematics>Statistics>Index Numbers>Weighted Index Numbers

If Laspeyre’s index number is

110

and Fisher’s ideal index number is

109

. Then Paasche’s Index number is

EASY

Mathematics>Statistics>Index Numbers>Weighted Index Numbers

Fisher’s ideal index does not satisfy ______ test

MEDIUM

Mathematics>Statistics>Index Numbers>Weighted Index Numbers

The weighted aggregative price index numbers for $2001$ with $2000$ as the base year using Marshal - Edgeworth Index Number is:

Commodity	Price (in $₹$ )		Quantities
	$2000$	$2001$	$2000$	$2001$
$A$	$10$	$12$	$20$	$22$
$B$	$8$	$8$	$16$	$18$
$C$	$5$	$6$	$10$	$11$
$D$	$4$	$4$	$7$	$8$

MEDIUM

Mathematics>Statistics>Index Numbers>Weighted Index Numbers

The value of the base time period serves as a standard point of comparison:

MEDIUM

Mathematics>Statistics>Index Numbers>Weighted Index Numbers

The weighted aggregative price index hymbers for $2001$ with $2000$ as the base year using Fisher's Index Number is

Commodity	Price (in $₹$ )		Quantities
	$2000$	$2001$	$2000$	$2001$
$A$	$10$	$12$	$20$	$22$
$B$	$8$	$8$	$16$	$18$
$C$	$5$	$6$	$10$	$11$
$D$	$4$	$4$	$7$	$8$