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प्रश्न
Compute (i) Laspeyre’s (ii) Paasche’s (iii) Fisher’s Index numbers for the 2010 from the following data.
| Commodity | Price | Quantity | ||
| 2000 | 2010 | 2000 | 2010 | |
| A | 12 | 14 | 18 | 16 |
| B | 15 | 16 | 20 | 15 |
| C | 14 | 15 | 24 | 20 |
| D | 12 | 12 | 29 | 23 |
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उत्तर
| Commodity | 2000 (Base year) |
2010 (Current year) |
p0q0 | p0q1 | p1q0 | p1q1 | ||
| p0 | q0 | p1 | q1 | |||||
| A | 12 | 14 | 18 | 16 | 216 | 192 | 252 | 224 |
| B | 15 | 16 | 20 | 15 | 300 | 225 | 320 | 240 |
| C | 14 | 15 | 24 | 20 | 336 | 280 | 360 | 300 |
| D | 12 | 12 | 29 | 23 | 348 | 276 | 348 | 276 |
| Total | `sum"p"_0"q"_0` = 1200 | `sum"p"_0"q"_1` = 973 | `sum"p"_1"q"_0` = 1280 | `sum"p"_1"q"_1` = 1040 | ||||
(i) Laspeyre's Price Index
`"P"_01^"L" = (sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx 100`
= `1280/1200 xx 100`
= 106.6
(ii) Paasche's Price Index
`"P"_01^"P" = (sum"P"_1"q"_1)/(sum"p"_0"q"_1) xx 100`
= `1040/973 xx 100`
= 106.8
(iii) Fisher’s price index number
`"P"_01^"F" = sqrt((sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx (sum"p"_1"q"_1)/(sum"p"_0"q"_1)) xx 100`
= `sqrt(1280/1200 xx 1040/973) xx 100`
= `sqrt((13,31,200)/(11,67,600)) xx 100`
= `sqrt(1.14) xx 100`
= 106.7
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संबंधित प्रश्न
Features of index numbers:
- It is useful in framing suitable economic policies.
- It is useful to present financial data in real terms
- Index numbers are statistical devices.
- Index numbers are specialized averages.
Device that measures changes in an economic variable or a group of variables over a period of time –
Define Index Number
State the test of adequacy of index number
Define family budget method
Calculate by a suitable method, the index number of price from the following data:
| Commodity | 2002 | 2012 | ||
| Price | Quantity | Price | Quantity | |
| A | 10 | 20 | 16 | 10 |
| B | 12 | 34 | 18 | 42 |
| C | 15 | 30 | 20 | 26 |
An Enquiry was made into the budgets of the middle class families in a city gave the following information.
| Expenditure | Food | Rent | Clothing | Fuel | Rice |
| Price(2010) | 150 | 50 | 100 | 20 | 60 |
| Price(2011) | 174 | 60 | 125 | 25 | 90 |
| Weights | 35 | 15 | 20 | 10 | 20 |
What changes in the cost of living have taken place in the middle class families of a city?
Assertion and reasoning question:
- Assertion (A): The index number considers all factors.
- Reasoning (R): The index number is based on samples.
Explain the meaning of index number.
Read the given passage and answer the questions:
|
Index Number is a technique of measuring changes in a variable or group of related variables with reference to time, geographical location and other characteristics. Index Number is very useful for economists, farmers, traders, government, educationalists and trade union leaders for planning and implementing the plans according to their sector. The scope of index number is not limited to only one subject but it extends to many subjects such as Economics, Educational science, Psychology, History, Sociology, Geography etc. While framing index number its objective must be determined. To attain the objective the information is collected in various ways and this information is used for comparing two different time periods. For this purpose, the base year’s index is assumed as 100 and accordingly the value of the current year is calculated. Laspeyre, Paasche and Fisher have suggested different methods for constructing index numbers. |
- Explain the meaning of Index Number.
- To whom the Index Number is useful?
- Express your opinion about the given passage.
