Advertisement

Advertisement

Sum

**Base year weights (W) and current year price relatives (I) are given in Problem. Calculate the cost of living index in:**

Find y if the cost of living index is 200.

Group |
Food |
Clothing |
Fuel & Lighting |
House Rent |
Miscellaneous |

I | 180 | 120 | 160 | 300 | 200 |

W | 4 | 5 | 3 | y | 2 |

Advertisement

#### Solution

Group |
I |
W |
IW |

Food | 180 | 4 | 720 |

Clothing | 120 | 5 | 600 |

Fuel & Lighting | 160 | 33 | 480 |

House Rent | 300 | y | 300y |

Miscellaneous | 200 | 2 | 400 |

Total |
– |
y + 14 |
300y + 2200 |

From the table,

`sum"W" = y + 14, sum"IW" = 300y + 2200`

Now, by Family Budget Method,

CLI = `(sum"IW")/(sum"W")`

∴ 200 = `(300y + 2200)/(y + 14)` ...[∵ CLI = 150]

∴ 200y + 2800 = 300 +2200

∴ 300y – 200y = 2800 – 2200

∴ 100y = 600

∴ y = `(600)/(100)`

∴ y = 6.

Concept: Method of Constructing Cost of Living Index Numbers - Family Budget Method

Is there an error in this question or solution?