Weighted index numbers

Weighted index numbers

1. Weighted Index Numbers NADEEM UDDIN ASSOCIATE PROFESSOR OF STATISTICS

2. Weighted Index Numbers : There are two methods of calculating weighted index numbers. 1- Weighted aggregative price index numbers. 2- Weighted average of relatives price index numbers.   Weighted Aggregative Price Index Numbers: In this we calculate the total expenditure of the current year and the base year. Price of each commodity is multiplied with the weight of the commodity which is usually the quantity consumed or quantity produced. The quantity of the base year or current year can be used as weight. The current period expenditure is compared with the base period expenditure.

3.   The general formula for computing a weighted aggregates price index is OR

4. Example-1: For the following data calculate weighted aggregative price index number Weight Price 2004 Price 2005 32 2.20 2.60 119 2.60 2.90 75 3.10 3.20 16 3.30 3.35 W p o p n p nW p oW 32 2.20 2.60 83.2 70.4 119 2.60 2.90 345.1 309.4 75 3.10 3.20 240 232.5 16 3.30 3.35 53.6 52.8       721.9 665.1 Solution:

5. Items Price 2003 Price 2004 Price 2005 Average no.used A 1.25 1.50 2.00 900 B 6.50 7.00 6.25 50 C 5.25 5.90 6.40 175 D 0.50 0.80 1.00 200 Example-2: MR A is incharge of keeping in stock certain items that his company needs in repairing its machines ,he arranged the data in the following table. Calculate weighted aggregative price index. Solution: p o p n q p n q p o q 1.25 1.50 900 1350 1125 6.50 7.00 50 350 325 5.25 5.90 175 1032.5 918.75 0.50 0.80 200 160 100       2892.5 2468.75

6. p o p n q p n q p o q 1.25 2.00 900 1800 1125 6.50 6.25 50 312.5 325 5.25 6.40 175 1120 918.75 0.50 1.00 200 200 100       3432.5 2468.75

7. There are various kinds of weighted aggregative Price index numbers. Laspeyre’s Index: In Laspeyre`s method base year quantities are used as weights for price index number. This is also called base year quantity weighted method. Paasche’s Index : In Paasche`s method current year quantities are used as weights for price index number. This is also called current year quantity weighted method.

8. Marshall- Edgeworth price index : In Marshall – Edgeworth the weights are taken as an average of the respective quantities in the base period and in the given period.   Fisher’s Ideal Index : Fisher Index is the geometric means of the Laspeyre’s and Paasche’s Index. This index lies between Laspeyre’s and Paasche’s indices. OR

9. Example–3: Construct index number of prices from the following data by using Laspeyre’s method taking 2007 as base year. Commodities Price 2007 Quantity 2007 Price 2008 Quantity 2008 A 8 45 12 50 B 4 100 4 110 C 6 50 8 55 D 12 30 14 35 Commodities P o q o p n q n p n q o p o q o A 8 45 12 50 540 360 B 4 100 4 110 400 400 C 6 50 8 55 400 300 D 12 30 14 35 420 360           Solution:

10. Comments: The Prices increased by 23.94% in the year 2008 with respect to 2007.

11. Example-4: Construct index number of prices from the following data by using Paasche’s method for the year 2008. Commodities Price 2007 Quantity 2007 Price 2008 Quantity 2008 A 8 45 12 50 B 4 100 4 110 C 6 50 8 55 D 12 30 14 35 Commodities p o q o p n q n p n q n p o q n A 8 45 12 50 600 400 B 4 100 4 110 440 440 C 6 50 8 55 440 330 D 12 30 14 35 490 420           Solution:

12. Comments: The Prices increased by 23.90% in the year 2008 with respect to 2007.

13. Example–5: Construct index number of prices from the following data by using Fisher Ideal Index method. Commodities Price 2007 Quantity 2007 Price 2008 Quantity 2008 A 8 45 12 50 B 4 100 4 110 C 6 50 8 55 D 12 30 14 35 Solution:

14. Comments: The Prices increased by 23.91% in the year 2008 with respect to 2007.

15. Example–6: Construct index number of prices from the following data by using Marshall- Edgeworth price index. Commodities Price 2007 Quantity 2007 Price 2008 Quantity 2008 A 8 45 12 50 B 4 100 4 110 C 6 50 8 55 D 12 30 14 35 Solution: Commodities Price 2007 Quantity 2007( ) Price 2008( ) Quantity 2008( ) A 8 45 12 50 95 1140 760 B 4 100 4 110 210 840 840 C 6 50 8 55 105 840 630 D 12 30 14 35 65 910 780             3730 3010 Commodities A 8 45 12 50 95 1140 760 B 4 100 4 110 210 840 840 C 6 50 8 55 105 840 630 D 12 30 14 35 65 910 780            

16. Comments: The Prices increased by 23.92% in the year 2008 with respect to 2007.  

17. Example–7: Construct index number of prices from the following data by using alternative formula of Marshall- Edgeworth price index. Commodities Price 2007 Quantity 2007 Price 2008 Quantity 2008 A 8 45 12 50 B 4 100 4 110 C 6 50 8 55 D 12 30 14 35 Solution:

18. Comments: The Prices increased by 23.92% in the year 2008 with respect to 2007.