Sandeep Garg Class 11 Economics Solutions Economics Chapter 9 – Index Numbers are illustrated by the professional economic educator from the contemporary edition of Sandeep Garg Economics Class 11 textbook solutions.
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Sandeep Garg Solutions Class 11 – Chapter 9
Question 1
Arrange an index number for the year 2015 on the basis of 2010 using the simple aggregative method:
| Goods | Unit | Cost | |
| 2010 | 2015 | ||
| Potato | Kilo | 100 | 500 |
| Tomato | Kilo | 400 | 250 |
| Onion | Kilo | 200 | 400 |
| Oil | litre | 4 | 5 |
| Fabric | meter | 2 | 3 |
ANSWER:
| Goods | 2010 Price (P0) | 2015 Price (P1) |
| Potato Tomato Onion Oil Fabric | 100 400 200 4 2 | 500 250 400 5 3 |
| ΣP0 = 702 | ΣP1 = 928 |
P01 = (frac{sum P_{1}}{sum P_{0}}, X, 100)
P01 = (frac{928}{702}, X, 100)
P01 = 132
Question 2
Form an index number using 2010 price:
| Items | P | Q | R | S | T | U |
| Prices (2011) | 220 | 50 | 370 | 110 | 70 | 90 |
| Prices (2016) | 250 | 80 | 500 | 130 | 72 | 100 |
ANSWER:
| Items | Price in 2011 (P0) | Price in 2016 (P1) |
| P Q R S T U | 220 50 370 110 70 90 | 250 80 500 130 72 100 |
| ΣP0 = 910 | ΣP1 = 1152 |
P01 = (frac{sum P_{1}}{sum P_{0}}, X, 100)
P01 = (frac{1152}{910}, X, 100)
P01 = 126.59
Question 3
Prepare an index number for 2014 on the basis of 2010 from the below data using aggregate expenditure method.
| Particulars | Quantity (kg.) | Prices | |
| 2010 | 2014 | ||
| G | 9 | 21 | 25 |
| H | 6 | 20 | 22 |
| I | 4 | 19 | 23 |
| J | 3 | 9 | 10 |
| K | 3 | 5 | 9 |
Answer:
| Article | 2010 Price (P0) | 2014 Price (P1) | Quantity (Q0) | P0Q0 | P1Q0 |
| G H I J K | 21 20 19 9 5 | 25 22 23 10 9 | 9 6 4 3 3 | 189 120 76 27 15 | 225 132 92 30 27 |
| ΣP0Q0 = 427 | ΣP1Q0 = 506 |
The consumer price index for the year 2014 is
(frac{sum P_{1}Q_{0}}{sum P_{0}Q_{0}},, imes 100)
= (frac{506}{427}, X, 100)
= 118.50
Question 4
Calculate the consumer index number by using the family budget method.
| Items | Quantity | Base Price Year | Current Price Year |
| Rent | 45 | 200 | 225 |
| Food | 20 | 300 | 350 |
| Clothing | 8 | 150 | 175 |
| Fuel | 10 | 100 | 110 |
| Misc. | 17 | 200 | 250 |
Answer:
| Items | Base Price Year (P0) | Current Price Year (P1) | (I ,=, frac{P_{1}}{P_{0}} , imes , 100) | Quantity (Q0) | P0Q0 (W) | RW |
| Rent | 200 | 225 | 112.5 | 45 | 9000 | 1012500 |
| Food | 300 | 350 | 116.66 | 20 | 6000 | 699960 |
| Clothing | 150 | 175 | 116.66 | 8 | 1200 | 139992 |
| Fuel | 100 | 110 | 110 | 10 | 1000 | 110000 |
| Misc. | 200 | 250 | 125 | 17 | 3400 | 425000 |
| ΣW= 20600 | ΣWI = 2387452 |
The consumer price index for the current year as per family budget method is:
(frac{sum WI}{sum W} = frac{2387452}{20600} = 115.89)
Question 5
Arrange an index for 2015 taking 2010 using a simple aggregate and price relatives method
| Items | A | B | C | D |
| Year 2010 Price | 20 | 40 | 50 | 70 |
| Year 2015 Price | 30 | 50 | 70 | 90 |
Answer:
Simple Aggregate Method
| Items | 2010 Price (P0) | 2015 Price (P1) |
| A B C D | 20 40 50 70 | 30 50 70 90 |
| ΣP0 = 180 | ΣP1 = 240 |
= 240/180 × 100
= 133.33
Price Relative Method
| Items | Year 2010 Price (P0) | Year 2015 Price (P1) | (R ,=, frac{P_{1}}{P_{0}} , imes , 100) |
| A | 20 | 30 | 150 |
| B | 40 | 50 | 125 |
| C | 50 | 70 | 140 |
| D | 70 | 90 | 128.57 |
| N= 4 |  = 543.57 |
Simple Average of Price Relatives
P01 = 543.57/ 4
= 135.89
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