NM Shah (2017) Solutions for Class 11 Science Economics Chapter 9 Introduction To Index Numbers are provided here with simple step-by-step explanations. These solutions for Introduction To Index Numbers are extremely popular among class 11 Science students for Economics Introduction To Index Numbers Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the NM Shah (2017) Book of class 11 Science Economics Chapter 9 are provided here for you for free. You will also love the ad-free experience on Meritnation’s NM Shah (2017) Solutions. All NM Shah (2017) Solutions for class 11 Science Economics are prepared by experts and are 100% accurate.
Page No 350:
Question 1:
Construct the Index Number for 2011 with 2015 as base from the following prices of commodities by simple (Unweighted) aggregative method.
Commodities | : | A | B | C | D | E |
Prices in â¹(2015) | : | 50 | 40 | 10 | 5 | 2 |
Prices in â¹(2011) | : | 80 | 60 | 20 | 10 | 6 |
Answer:
Commodity | Prices in 2015 (p0) |
Prices in 2011 (p1) |
A B C D E |
50 40 10 5 2 |
80 60 20 10 6 |
∑ p0 = 107 | ∑ p1 = 176 |
Thus, price index is 164.48.
Page No 350:
Question 2:
Using the following data and 2008 as the base period, compute simple aggregative price indices for the two fuels.
Item | Producer's Price (in â¹) | ||
2008 | 2009 | 2010 | |
Coal ( â¹) | 5 | 3 | 4 |
Crude oil ( â¹) | 2 | 3 | 4 |
Answer:
Item | Prices in 2008 (p0) |
Prices in 2009 (p1) |
Prices in 2010 (p2) |
Coal Crude oil |
5 2 |
3 3 |
4 4 |
∑ p0 = 7 | ∑ p1 = 6 | ∑ p2 = 8 |
Thus, index number for 2009 is 85.71 and index number for 2010 is 114.28
Page No 350:
Question 3:
Calculate the index number for 2014 with 2013 as base from the following prices of the commodities by simple (unweighted) aggregative method.
Commodity and unit | Price ( â¹) (2013) |
Price ( â¹) (2014) |
Butter per kg | 20.00 | 22.00 |
Milk per litre | 3.00 | 4.50 |
Cheese per Tin | 18.00 | 19.80 |
Bread per Kg | 2.00 | 3.80 |
Eggs per Dozen | 4.00 | 4.50 |
Answer:
Commodity | Prices in 2013 (p0) |
Prices in 2014 (p1) |
Butter Milk Cheese Bread Eggs |
20 3 18 2 4 |
22 4.5 19.80 3.80 4.50 |
∑ p0 = 47 | ∑ p1 = 54.6 |
Thus, index number is 116.17.
Page No 350:
Question 4:
Calculate Quantity Index Numbers from the following data by simple aggregative method taking quantity of 2011 as base.
Commodity | Quantity (in tons) | ||||
2011 | 2012 | 2013 | 2014 | 2015 | |
A | 0.30 | 0.33 | 0.36 | 0.36 | 0.39 |
B | 0.25 | 0.24 | 0.30 | 0.32 | 0.30 |
C | 0.20 | 0.25 | 0.28 | 0.32 | 0.30 |
D | 2.00 | 2.40 | 2.50 | 2.50 | 2.60 |
[Quantity Index No. : 2012 = 117.1; 2013 = 125.1; 2014 = 127.3 ; 2015 = 130.5]
Answer:
Commodity | Quantity in 2011 (q0) |
Quantity in 2012 (q1) |
Quantity in 2013 (q2) |
Quantity in 2014 (q3) |
Quantity in 2015 (q4) |
A B C D |
0.30 0.25 0.20 2.00 |
0.33 0.24 0.25 2.4 |
0.36 0.30 0.28 2.50 |
0.36 0.32 0.32 2.50 |
0.39 0.30 0.30 2.60 |
∑ q0= 2.75 | ∑ q1 = 3.22 | ∑ q2= 3.44 | ∑ q3 = 3.5 | ∑ q4 = 3.59 |
Thus, quantity index for 2012 is 117.1.
Thus, quantity index for 2013 is 125.1.
Thus, quantity index for 2014 is 127.3.
Thus, quantity index for 2015 is 130.5.
Page No 350:
Question 5:
Calcualte index number for 2017 on the base prices for 2013 from the following by average of price relative method.
Items | : | Bricks | Timber | Plaster Board | Sand | Cement |
Price in â¹ (2013) | : | 10 | 20 | 5 | 2 | 7 |
Price in â¹ (2017) | : | 16 | 21 | 6 | 3 | 14 |
Answer:
Item | Prices in 2013 (p0) |
Prices in 2017 (p1) |
Price relatives of 2017 in relation to 2013 |
Brick | 10 | 16 | |
Timber | 20 | 21 | |
Plaster Board | 5 | 6 | |
Sand | 2 | 3 | |
Cement | 7 | 14 | |
Thus, index number is 147.
Page No 350:
Question 6:
Construct the index number for 2016 taking 2006 as base by price relative method using arithmetic mean.
Commodities | : | A | B | C | D |
Price in â¹ (2006) | : | 10 | 20 | 30 | 40 |
Price in â¹ (2016) | : | 13 | 17 | 60 | 70 |
Answer:
Items | : | Bricks | Timber | Plaster Board | Sand | Cement |
Price in â¹ (2013) | : | 10 | 20 | 5 | 2 | 7 |
Price in â¹ (2017) | : | 16 | 21 | 6 | 3 | 14 |
Commodities | Prices in 2006 (p0) |
Prices in 2016 (p1) |
|
A | 10 | 13 | |
B | 20 | 17 | |
C | 30 | 60 | |
D | 40 | 70 | |
Thus, index number is 147.5
Page No 351:
Question 7:
Construct Index Number for each year from the following average annual wholesale prices of cotton with 2001 as base .
Year | Wholesale Prices (in â¹) |
Year | Wholesale Prices (in â¹) |
2001 | 75 | 2006 | 70 |
2002 | 50 | 2007 | 69 |
2003 | 65 | 2008 | 75 |
2004 | 60 | 2009 | 84 |
2005 | 72 | 2010 | 80 |
Answer:
Prices in 2001 (p0) |
Prices in 2002 (p1) |
Prices in 2003 (p2) |
Prices in 2004 (p3) |
Prices in 2005 (p4) |
Prices in 2006 (p5) |
Prices in 2007 (p6) |
Prices in 2008 (p7) |
Prices in 2009 (p8) |
Prices in 2010 (p9) |
75 | 50 | 65 | 60 | 72 | 70 | 69 | 75 | 84 | 80 |
Page No 351:
Question 8:
The group indices of prices of commodities for second week of Sept. 2017 and the group weights are given below. Compute the index number by family budget method.
Group | Weights | Index |
Food Article | 31 | 473.6 |
Manufactures | 30 | 390.2 |
Industrial Raw Material | 18 | 510.2 |
Semi-Manufactures | 17 | 403.3 |
Miscellaneous | 4 | 624.4 |
Answer:
Group | Weights (w) |
Index (x) |
wx |
Food Article Manufactures Industrial Raw Material Semi-Manufactures Miscellaneous |
31 30 18 17 4 |
473.6 390.2 510.2 403.3 624.4 |
14681.6 11706 9183.6 6856.1 2497.6 |
∑w = 100 | ∑wx = 44924.9 |
Thus, the index of wholesale prices is 449.29.
Page No 351:
Question 9:
Calculate price index number for 2016 of following data by weighted aggregative method using (a) Laspeyre's method, (b) Paasche's method, (c) Fisher's method.
Commodity | Price (2012) |
Quantity (2012) |
Price (2016) |
Quantity (2016) |
A | 4 | 20 | 6 | 10 |
B | 3 | 15 | 5 | 23 |
C | 2 | 25 | 3 | 15 |
D | 5 | 10 | 4 | 15 |
Answer:
Commodity | Base Year | Current Year | ||||||
Prices p0 |
Quantity q0 |
Prices p1 |
Quantity q1 |
p0q0 | p0q1 | p1q0 | p1q1 | |
A B C D |
4 3 2 5 |
20 15 25 10 |
6 5 3 4 |
10 23 15 40 |
80 45 50 50 |
40 69 30 200 |
120 75 75 40 |
60 115 45 160 |
∑p0q0 = 225 | ∑p0q1 = 339 | ∑p1q0 = 310 | ∑p1q1 = 380 |
(a)
(b)
(c)
Note: As per the textbook, the price index using Paasche's method is 158.99 and Fisher's method is 148.1. However, as per the above solution the price index using Paasche's method should be 112.09 and Fisher's method should be 124.26.
Page No 351:
Question 10:
From the data given below , construct Laspeyre's , Paasche's and Fisher's price index and quantity index numbers with base 2015 and interpret.â
Commodity | 2015 | 2016 | ||
Price (â¹) |
Quantity (Kg) |
Price (â¹) |
Quantity (Kg) |
|
A B C |
4 3 8 |
2 5 2 |
6 2 4 |
3 1 6 |
Answer:
Commodity | Base Year | Current Year | ||||||
Price p0 |
Quantity q0 |
Price p1 |
Quantity q1 |
p0q0 | p0q1 | p1q0 | p1q1 | |
A B C |
4 3 8 |
2 5 2 |
6 2 4 |
3 1 6 |
8 15 16 |
12 3 48 |
12 10 8 |
18 2 24 |
∑p0q0 = 39 | ∑p0q1 = 63 | ∑p1q0 = 30 | ∑p1q1 = 44 |
Laspeyre's Price index =
Laspeyre's Quantity index =
Paasche's Price index =
Paasche's Quantity index =
Fisher's Price index =
Fisher's Quantity index =
Note: As per the textbook, the quantity indices using Laspeyre's and Paasche's methods are 143.18 and 130. However, as per the above solution the quantity indices using Laspeyre's and Paasche's methods should be 161.53 and 146.67.
Page No 351:
Question 11:
Calculate weighted aggregative of actual price index number and quantity index number from the following data using (i) Laspeyre's Method , and (ii) Paasche's Method and (iii) Fisher's Method and interpret them.
Commodity | Base year | Current Year | ||
Quantity lbs. |
Price per lb. |
Quantity lbs. |
Price âper lb. |
|
Bread | 6 | 40 paise | 7 | 30 paise |
Meat | 4 | 45 paise | 5 | 50 paise |
Tea | 0.5 | 90 paise | 1.5 | 40 pAise |
Answer:
Base Year | Current Year | |||||||
Quantity q0 |
Price p0 |
Quantity q1 |
Price p1 |
p0q0 | p1q1 | p1q0 | p0q1 | |
Bread Meat Tea |
6 4 0.5 |
40 45 90 |
7 5 1.5 |
30 50 40 |
240 180 45 |
210 250 60 |
180 200 20 |
280 225 135 |
∑p0q0= 465 | ∑p1q1= 520 | ∑p1q0= 400 | ∑p0q1 = 640 |
(i) Price Index number
(a) Laspeyre's
(b) Paasche's
(c) Fisher's
(ii) Quantity Index number
(a) Laspeyre's
(b) Paasche's
(c) Fisher's
The price index number for current year is 86.02 and 81.25 as per Laspeyres's method and Paasche's method respectively. This implies that there is net decrease in the prices in current year by 13.98% and 18.75% from the base year as per Laspeyres's method and Paasche's method respectively.
The quantity index number for current year is 137.63 and 130 as per Laspeyres's method and Paasche's method respectively. This implies that there is net increase in the quantity demanded by 37.63% and 30% from the base year as per Laspeyres's method and Paasche's method respectively.
Page No 352:
Question 12:
Calculate price index number by weighted average of price relative method.
Commodity | Price Base Year (in â¹) |
Price current year ( in â¹) |
Quantity Base year (in Kg) |
A | 6.0 | 8.0 | 40 |
B | 3.0 | 3.2 | 80 |
C | 2.0 | 3.0 | 2 |
Answer:
Commodity | Price in Base Year (p0) |
Price in Quantity Year (p1) |
Quantity in Base Year (q0) |
V (p0q0) |
RV | |
A B C |
6 3 2 |
8 3.2 3 |
40 80 20 |
133.33 106.67 150 |
240 240 40 |
31999.2 25600.8 6000 |
∑V = 520 | ∑RV = 63600 |
Weighted Average of Price Relative Method
Thus, price index number is 122.30.
Page No 352:
Question 13:
Prepare consumer price index numbers from the following data for 2014 and 2013 taking 2012 as base.
Group | Price (in â¹) |
||
2012 | 2013 | 2014 | |
A | 20.00 | 24.00 | 21.00 |
B | 1.25 | 1.50 | 1.00 |
C | 5.00 | 8.00 | 8.00 |
D | 2.00 | 2.25 | 2.12 |
Give weights to four groups as 4, 3, 2 and 1 respectively.
Answer:
Price Index for 2013
Group | p0 (2012) |
p1 (2013) |
W | WR | |
A B C D |
20 1.25 5 2 |
24 1.5 8 2.25 |
4 3 2 1 |
120 120 160 112.5 |
480 360 320 112.5 |
∑W= 10 | ∑WR=1272.5 |
Thus, consumer price index for 2013 is 127.25.
Price Index number for 2014
Group | p0 (2012) |
p1 (2014) |
W | WR | |
A B C D |
20 1.25 5 2 |
21 1 8 2.12 |
4 3 2 1 |
105 80 160 106 |
420 240 320 106 |
∑W= 10 | ∑WR=1086 |
Thus, consumer price index for 2014 is 108.6.
Note: As per textbook, consumer index for 2014 is 109.78. However, as per the above solution, consumer index for 2014 should be 108.6.
Page No 352:
Question 14:
From the data given below construct the consumer price index number:
Commodity | Price Relatives | Weights |
Food | 250 | 45 |
Rent | 150 | 15 |
Clothing | 320 | 20 |
Fuel and Lighting | 190 | 5 |
Miscellaneous | 300 | 15 |
Answer:
Commodity | Price relatives (R) |
Weights (W) |
WR |
Food Rent Clothing Fuel Miscellaneous |
250 150 320 190 300 |
45 15 20 5 15 |
11250 2250 6400 950 4500 |
∑W = 100 | ∑WR = 25350 |
Thus, the consumer price index number is 253.5.
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