Unit 4
Index Numbers
Q1) A family budget survey of middle class families gives the following data:
Calculate cost of living index number for the year 2019 by taking 2018 as base year.
A1)
Q2) Calculate Cost of Living Index Number for the following data:
Q3) Cost of living index number of the following data is known to be 126.2. Obtain the missing weight.
A3) Suppose the missing weight is x. We calculate cost of living index number as usual and equate to given value 126.2.
Q4) Calculate price index number for the following data for the year 2020 taking 2015 as a base year by using Lasperys, Paasche’s and Fishers price index number
A4)
Q5) Construct the cost of living index for the year 1982 (Base 1980 = 100).
A5)
Q6) Calculate weighted average of relative method
Commodity | Base price year | current price year | Weight |
X | 3 | 4 | 7 |
Y | 1.5 | 1.6 | 8 |
Z | 1 | 1.5 | 9 |
A6)
Commodity | Base price year | current price year | Weight | price relatives | RW |
X | 3 | 4 | 7 | 133.3 | 933.33 |
Y | 1.5 | 1.6 | 8 | 106.7 | 853.33 |
Z | 1 | 1.5 | 9 | 150.0 | 1350 |
|
|
| 24 |
| 3136.66 |
P01 = 3136.66/24 = 130.67
Q7) Calculate the price indices from the following data by applying (1) Laspeyre’s method (2) Paasche’s method and (3) Fisher ideal number by taking 2010 as the base year.
Commodity | 2010 | 2011 | ||
PO | QO | P1 | Q1 | |
A | 20 | 10 | 25 | 13 |
B | 50 | 8 | 60 | 7 |
C | 35 | 7 | 40 | 6 |
D | 25 | 5 | 35 | 4 |
A7)
Commodity | 2010 | 2011 |
|
|
|
| ||
PO | QO | P1 | Q1 | Poqo | P1qo | Poq1 | P1q1 | |
A | 20 | 10 | 25 | 13 | 200 | 250 | 260 | 325 |
B | 50 | 8 | 60 | 7 | 400 | 480 | 350 | 420 |
C | 35 | 7 | 40 | 6 | 245 | 280 | 210 | 240 |
D | 25 | 5 | 35 | 4 | 125 | 175 | 100 | 140 |
|
|
|
|
| 970 | 1185 | 920 | 1125 |
P 01 = (1185/970)*100 = 122.16
P 01 = (1125/920)*100 = 122.28
P 01 = √ = ((1185/970) + (1125/920)) *100 = 120.55
Q8) Explain the problems in construction of index number
A8) The construction of the price index involves the following problems
- Fixed base method in which the base year remains fixed
- Chain base method in which base year goes on changing. Ex -2000 base year for 2001, 2001 base year for 2002, and so on
2. Selection of commodities – selection of commodities is one of the problems in constructing index number. As all commodities are not included, only representative commodities are selected keeping in mind the purpose and type of index number.
The following points are considered while selecting commodities
3. Collection of prices – the next problem is the collection of prices. Problems are from where the prices to be collected, which price to select wholesale or retail, whether to include taxes in the price. the following points should be considered while collecting prices
4. Selection of averages – Fourth problem is to choose a suitable average. Theoretically, geometric mean is the best for this purpose. But, in practice, arithmetic mean is used because it is easier to follow.
5. Selection of weights – commodities included in the calculation of index numbers are not of equal importance. Therefore proper weight should be assigned to the commodities for accurate index numbers. Weight should be unbiased and be rationale. For ex – price of books should be given more weightage while preparing index numbers for teachers rather than for workers.
6. Purpose of index numbers – the important point in the construction of index numbers is the objective of index numbers. Before preparing index numbers, it is important to be clear about the purpose of the index numbers. Different index numbers are prepared with a specific purpose.
Q9) Explain methods of construction
A9) Aggregate Expenditure Method
In this method, the quantities of commodities consumed by the particular group in the base year are estimated and these figures or their proportions are used as weights. Then the total expenditure of each commodity for each year is calculated. The price of the current year is multiplied by the quantity or weight of the base year. These products are added. Similarly, for the base year the total expenditure of each commodity is calculated by multiplying the quantity consumed by its price in the base year. These products are also added. The total expenditure of the current year is divided by the total expenditure of the base year and the resulting figure is multiplied by 100 to get the required index numbers. In this method, the current period quantities are not used as weights because these quantities change from year to year.
Here,
Pn Represent the price of the current year,
Po Represents the price of the base year and
qo Represents the quantities consumed in the base year.
Family Budget Method
In this method, the family budgets of a large number of people are carefully studied and the aggregate expenditure of the average family for various items is estimated. These values are used as weights. The current year’s prices are converted into price relatives on the basis of the base year’s prices, and these price relatives are multiplied by the respective values of the commodities in the base year. The total of these products is divided by the sum of the weights and the resulting figure is the required index numbers.
Here, I=Pn/P0×100 and W=Poqo
Q10) Construct the consumer price index number for 1988 on the basis of 1987 from the following data using: (1) Aggregate Expenditure Method (2) Family Budget Method.
Commodities | Quantity consumed in 1987 | Unit | Prices | |
1987 | 1988 | |||
AA | 6 quintal | quintal | 315.75 | 316 |
BB | 6 quintal | quintal | 305 | 308 |
CC | 1 quintal | quintal | 416 | 419 |
DD | 6 quintal | quintal | 528 | 610 |
EE | 4 kg | kg | 12 | 11.5 |
FF | 1 quintal | quintal | 1020 | 1015 |
A10)
The consumer price index number of 1988 by Aggregate Expenditure Method:
2. The consumer price index number of 1988 by Family Budget Method: