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Question
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?
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Solution
| Expenditure | Base Year Price 2010 (p0) |
Current Year Price 2011 (p1) |
Weight (W) |
P = `"p"_1/"p"_0 xx 100`PW | PW |
| Food | 150 | 174 | 35 | 116 | 4060 |
| Rent | 50 | 60 | 15 | 120 | 1800 |
| Clothing | 100 | 125 | 20 | 125 | 2500 |
| Fuel | 20 | 25 | 10 | 125 | 1250 |
| Rice | 60 | 90 | 20 | 150 | 3000 |
| Total | 100 | 12610 | |||
Cost of living index number = `(sum"PW")/(sum"W")`
= `12610/100`
= 126.1
For the middle-class families of the city, the cost of living has increased up to 26.1 % in 2011 as compared to 2010.
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RELATED QUESTIONS
State with reason whether you agree or disagree with the following statement:
Index numbers measure changes in the price level only.
State with reasons whether you agree or disagree with the following statement:
Index numbers can be constructed without the base year.
Discuss about Cost of Living Index Number
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 |
Using the following data, construct Fisher’s Ideal index and show how it satisfies Factor Reversal Test and Time Reversal Test?
| Commodity | Price in Rupees per unit | Number of units | ||
| Basic year | Current year | Base year | Current year | |
| A | 6 | 10 | 50 | 56 |
| B | 2 | 2 | 100 | 120 |
| C | 4 | 6 | 60 | 60 |
| D | 10 | 12 | 50 | 24 |
| E | 8 | 12 | 40 | 36 |
The following are the group index numbers and the group weights of an average working class family’s budget. Construct the cost of living index number:
| Groups | Food | Fuel and Lighting |
Clothing | Rent | Miscellaneous |
| Index Number | 2450 | 1240 | 3250 | 3750 | 4190 |
| Weight | 48 | 20 | 12 | 15 | 10 |
Choose the correct alternative:
While computing a weighted index, the current period quantities are used in the:
Using the following data, construct Fisher’s Ideal Index Number and Show that it satisfies Factor Reversal Test and Time Reversal Test?
| Commodities | Price | Quantity | ||
| Base Year | Current Year | Base Year | Current Year | |
| Wheat | 6 | 10 | 50 | 56 |
| Ghee | 2 | 2 | 100 | 120 |
| Firewood | 4 | 6 | 60 | 60 |
| Sugar | 10 | 12 | 30 | 24 |
| Cloth | 8 | 12 | 40 | 36 |
Explain the meaning of index number.
The base year's index of a selected variable is assumed as ______.
