The monthly expenditure (Rs.) of a family on some important items and their Goods and Services Tax (GST) rates applicable to these items is as follows: Items Monthly Expense (Rs.) GST Rate % Cereals 1500 0 Eggs 250 0 Fish, Meat 250 0 Medicines 50 5 Biogas 50 5 Transport 100 5 Butter 50 12 Babool 10 12 Tomato Ketchup 40 12 Biscuits 75 18 Cakes, Pastrics 25 18 Branded Garments 100 18 Vacuum Cleaner, Car 1000 28 Calculate the average tax rate as far as family is concerned.

Category Expenditure (W) GST Rate(X) WX Category 1 2000 0 0 Category 2 200 0 . 05 10 Category 3 100 0 . 12 12 Category 4 200 0 . 18 36 Category 5 1000 0 . 28 280 3500 338 The mean GST rate as far as this family is concerned is = ∑ WX ∑ W = 338 3500 = 0 . 0966 %

An enquiry into the budgets of the middle class families in a certain city gave the following information; Expenses on items Food 35 % Fuel 10 % Clothing 20 % Rent 15 % Misc. 20 % Price (in ₹ ) in 2004 1500 250 750 300 400 Price (in ₹ ) in 1995 1400 200 500 200 250 What is the cost of living index during the year 2004 as compared with 1995 ?

Items Weight W Price in 1995 P 0 Price in 2004 P 1 R = P 1 P 0 × 100 W R Food 35 1 , 400 1 , 500 1 , 500 1 , 400 × 100 = 107 . 14 3 , 749 . 90 Fuel 10 200 250 250 200 × 100 = 125 1 , 250 Clothing 20 500 750 750 500 × 100 = 150 3 , 000 Rent 15 200 300 300 200 × 100 = 150 2 , 250 Miscellaneous 20 250 400 400 250 × 100 = 160 3 , 200 Σ W = 100 Σ W R = 13 , 449 . 9 CPI = Σ W R Σ W = 13449 . 9 100 = 134 . 49 Cost of Living Index = 134 . 50 Thus, the price rose by 34 . 50 % during 1995 and 2004 .

Given the following data- Year CPI of industrial workers ( 1982 = 100 ) CPI of agricultural labourers ( 1986 = 100 ) WPI ( 1993 - 94 = 100 ) 1995 - 96 313 234 121 . 6 1996 - 97 342 256 127 . 2 1997 - 98 366 264 132 . 8 1998 - 99 414 293 140 . 7 1999 - 00 428 306 145 . 3 2000 - 01 444 306 155 . 7 2001 - 02 463 309 161 . 3 2002 - 03 482 319 166 . 8 2003 - 04 500 331 175 . 9 Are they comparable?

Given the following data- Year CPI of industrial workers ( 1982 = 100 ) CPI of agricultural labourers ( 1986 = 100 ) WPI ( 1993 - 94 = 100 ) 1995 - 96 313 234 121 . 6 1996 - 97 342 256 127 . 2 1997 - 98 366 264 132 . 8 1998 - 99 414 293 140 . 7 1999 - 00 428 306 145 . 3 2000 - 01 444 306 155 . 7 2001 - 02 463 309 161 . 3 2002 - 03 482 319 166 . 8 2003 - 04 500 331 175 . 9 No, the index number is not comparable because of the following reasons: Base periods for CPI of industrial workers, urban non-manual workers, agricultural labourers and WPI are different. Commodities and their weightage in different index numbers may be different.

Given the following data- Year CPI of industrial workers ( 1982 = 100 ) CPI of agricultural labourers ( 1986 = 100 ) WPI ( 1993 - 94 = 100 ) 1995 - 96 313 234 121 . 6 1996 - 97 342 256 127 . 2 1997 - 98 366 264 132 . 8 1998 - 99 414 293 140 . 7 1999 - 00 428 306 145 . 3 2000 - 01 444 306 155 . 7 2001 - 02 463 309 161 . 3 2002 - 03 482 319 166 . 8 2003 - 04 500 331 175 . 9 Comment on the relative values of the index numbers.

(a) Inflation using CPI of Industrial Workers Year CPI of industrial workers ( 1982 = 100 ) Inflation Rate (in % ) = A 2 - A 1 A 1 × 100 1995 - 96 313 313 - 100 100 × 100 = 213 1996 - 97 342 342 - 100 100 × 100 = 242 1997 - 98 366 366 - 100 100 × 100 = 266 1998 - 99 414 414 - 100 100 × 100 = 314 1999 - 00 428 428 - 100 100 × 100 = 328 2000 - 01 444 444 - 100 100 × 100 = 344 2001 - 02 463 463 - 100 100 × 100 = 363 2002 - 03 482 482 - 100 100 × 100 = 382 2003 - 04 500 500 - 100 100 × 100 = 400 (b) Inflation using CPI of Non-maunal Employees Year CPI of Non-manual Employees ( 1984 - 85 = 100 ) Inflation Rate (in % ) = A 2 - A 1 A 1 × 100 1995 - 96 257 257 - 100 100 × 100 = 157 1996 - 97 283 283 - 100 100 × 100 = 183 1997 - 98 302 302 - 100 100 × 100 = 202 1998 - 99 337 337 - 100 100 × 100 = 237 1999 - 00 352 352 - 100 100 × 100 = 252 2000 - 01 352 352 - 100 100 × 100 = 252 2001 - 02 390 390 - 100 100 × 100 = 290 2002 - 03 405 405 - 100 100 × 100 = 305 2003 - 04 420 420 - 100 100 × 100 = 320 (c) Inflation using CPI of Agricultural Labourers Year CPI of Agricultural Labourers ( 1986 - 87 = 100 ) Inflation Rate (in % ) = A 2 - A 1 A 1 × 100 1995 - 96 234 234 - 100 100 × 100 = 134 1996 - 97 256 256 - 100 100 × 100 = 156 1997 - 98 264 264 - 100 100 × 100 = 164 1998 - 99 393 293 - 100 100 × 100 = 193 1999 - 00 306 306 - 100 100 × 100 = 206 2000 - 01 306 306 - 100 100 × 100 = 206 2001 - 02 309 309 - 100 100 × 100 = 209 2002 - 03 319 319 - 100 100 × 100 = 219 2003 - 04 331 331 - 100 100 × 100 = 231 (d) Inflation using WPI Year WPI ( 1993 - 94 = 100 ) Inflation Rate (in % ) = A 2 - A 1 A 1 × 100 1995 - 96 121 . 6 121 . 6 - 100 100 × 100 = 21 . 6 1996 - 97 127 . 2 127 . 2 - 100 100 × 100 = 27 . 2 1997 - 98 132 . 8 132 . 8 - 100 100 × 100 = 32 . 8 1998 - 99 140 . 7 140 . 7 - 100 100 × 100 = 40 . 7 1999 - 00 145 . 3 145 . 3 - 100 100 × 100 = 45 . 3 2000 - 01 155 . 7 155 . 7 - 100 100 × 100 = 55 . 7 2001 - 02 161 . 3 161 . 3 - 100 100 × 100 = 61 . 3 2002 - 03 166 . 8 166 . 8 - 100 100 × 100 = 66 . 8 2003 - 04 175 . 9 175 . 9 - 100 100 × 100 = 75 . 9 The inflation rate calculated using CPI industrial worker with the base year 1982 is the highest and inflation rate calculated using WPI with the base year 1993 - 94 is the least.

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The price relative is a price index that is determined by:

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Important Questions on Index Numbers

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Economics>Statistics in Economics>Index Numbers>Index Numbers and their Construction

In most of the weighted index numbers, the weight pertains to

MEDIUM

Economics>Statistics in Economics>Index Numbers>Index Numbers and their Construction

Why do we need an index number?

HARD

Economics>Statistics in Economics>Index Numbers>Index Numbers and their Construction

The monthly expenditure (Rs.) of a family on some important items and their Goods and Services Tax (GST) rates applicable to these items is as follows:

Items	Monthly Expense (Rs.)	GST Rate %
Cereals	$1500$	$0$
Eggs	$250$	$0$
Fish, Meat	$250$	$0$
Medicines	$50$	$5$
Biogas	$50$	$5$
Transport	$100$	$5$
Butter	$50$	$12$
Babool	$10$	$12$
Tomato Ketchup	$40$	$12$
Biscuits	$75$	$18$
Cakes, Pastrics	$25$	$18$
Branded Garments	$100$	$18$
Vacuum Cleaner, Car	$1000$	$28$

Calculate the average tax rate as far as family is concerned.

EASY

Economics>Statistics in Economics>Index Numbers>Index Numbers and their Construction

What does a consumer price index for industrial workers measure?

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Economics>Statistics in Economics>Index Numbers>Index Numbers and their Construction

Why is it essential to have different CPI for different categories of consumers?

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Economics>Statistics in Economics>Index Numbers>Index Numbers and their Construction

An enquiry into the budgets of the middle class families in a certain city gave the following information;

Expenses on items	Food $35 %$	Fuel $10 %$	Clothing $20 %$	Rent $15 %$	Misc. $20 %$
Price (in $₹$ ) in $2004$	$1500$	$250$	$750$	$300$	$400$
Price (in $₹$ ) in $1995$	$1400$	$200$	$500$	$200$	$250$

What is the cost of living index during the year $2004$ as compared with $1995$ ?

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Economics>Statistics in Economics>Index Numbers>Index Numbers and their Construction

The impact of change in the price of a commodity with little weight in the index will be:

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Economics>Statistics in Economics>Index Numbers>Index Numbers and their Construction

Record the daily expenditure, quantities bought and prices paid per unit of the daily purchases of your family for two weeks. How has the price change affected your family?

HARD

Economics>Statistics in Economics>Index Numbers>Index Numbers and their Construction

Commodity	Base Year price P₀	Base year Quantity Q₀	Current year price P₁	Current year Quantity Q₁
A	$4$	$5$	$2$	$10$
B	$6$	$10$	$5$	$12$
C	$5$	$15$	$4$	$20$
D	$3$	$10$	$2$	$15$

Calculate the price index using Laspeyre's, and Paasche's formula.

Interchange the current period values with the base period values. Calculate the price index using Laspeyre's, and Paasche's formula. What difference do you observe from the earlier illustration?

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Economics>Statistics in Economics>Index Numbers>Index Numbers and their Construction

Can the CPI for urban non-manual employees represent the changes in the cost of living of the President of India?

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Economics>Statistics in Economics>Index Numbers>Index Numbers and their Construction

What is the difference between a price index and a quantity index?

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Economics>Statistics in Economics>Index Numbers>Index Numbers and their Construction

What are the desirable properties of the base period?

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Economics>Statistics in Economics>Index Numbers>Index Numbers and their Construction

Given the following data-

Year	CPI of industrial workers $(1982 = 100)$	CPI of agricultural labourers $(1986 = 100)$	WPI $(1993 - 94 = 100)$
$1995 - 96$	$313$	$234$	$121.6$
$1996 - 97$	$342$	$256$	$127.2$
$1997 - 98$	$366$	$264$	$132.8$
$1998 - 99$	$414$	$293$	$140.7$
$1999 - 00$	$428$	$306$	$145.3$
$2000 - 01$	$444$	$306$	$155.7$
$2001 - 02$	$463$	$309$	$161.3$
$2002 - 03$	$482$	$319$	$166.8$
$2003 - 04$	$500$	$331$	$175.9$

Are they comparable?

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Economics>Statistics in Economics>Index Numbers>Index Numbers and their Construction

A consumer price index measures changes in

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Economics>Statistics in Economics>Index Numbers>Index Numbers and their Construction

The consumer price index for June,

2005

was

125

. The food index was

120

and that of other items

135

. What is the percentage of the total weight given to food?

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Economics>Statistics in Economics>Index Numbers>Index Numbers and their Construction

Try to list the important items of consumption in your family.

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Economics>Statistics in Economics>Index Numbers>Index Numbers and their Construction

If the salary of a person in the base year is Rs.

4000

per annum and the current year salary is Rs.

6000

, by how much should his salary be raised to maintain the same standard of living if the CPI is

400

HARD

Economics>Statistics in Economics>Index Numbers>Index Numbers and their Construction

Given the following data-

Year	CPI of industrial workers $(1982 = 100)$	CPI of agricultural labourers $(1986 = 100)$	WPI $(1993 - 94 = 100)$
$1995 - 96$	$313$	$234$	$121.6$
$1996 - 97$	$342$	$256$	$127.2$
$1997 - 98$	$366$	$264$	$132.8$
$1998 - 99$	$414$	$293$	$140.7$
$1999 - 00$	$428$	$306$	$145.3$
$2000 - 01$	$444$	$306$	$155.7$
$2001 - 02$	$463$	$309$	$161.3$
$2002 - 03$	$482$	$319$	$166.8$
$2003 - 04$	$500$	$331$	$175.9$

Comment on the relative values of the index numbers.

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Economics>Statistics in Economics>Index Numbers>Index Numbers and their Construction

The monthly per capita expenditure incurred by workers for an Industrial centre during $1980$ and $2005$ on the following items are given below. The weights of these items are $75, 10, 5, 6$ and $4$ respectively. Prepare a weighted index number for cost of living for $2005$ with $1980$ as the base.

Items	Price in $1980$	Price in $2005$
Food	$100$	$200$
Clothing	$20$	$25$
Fuel & lighting	$15$	$20$
House rent	$30$	$40$
Misc	$35$	$65$

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Economics>Statistics in Economics>Index Numbers>Index Numbers and their Construction

Is the change in any price reflected in a price index number?

The price relative is a price index that is determined by:

Important Questions on Index Numbers

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