# Question-1

Construct the following indices by taking 1997 as the base :

(i) simple Aggregative price Index

(ii) Index of Average of price Relatives

 Items A B C D E Prices Rs. (1997) 6 2 4 10 8 Prices Rs. (1998) 10 2 6 12 12 Prices Rs. (1999) 15 3 8 14 16

Solution:
 Items A B C D E 6 2 4 10 8 10 2 6 12 12 15 3 8 14 16 166.67 100.00 150.00 120.00 150.00 250 150 200 140 200

Simple Aggregative Price Index :

Index of Average of Price Relatives :

# Question-2

From the following data construct price index of 1995 taking 1990 as base by using simple Average of price Relative Method :
 Commodity A B C D Prices in 1990 (Rs.) 60 45 80 25 Prices in 1995 (Rs.) 75 50 70 40

Solution:

 Commodity A B C D 60 45 80 25 75 50 70 40 125 111.11 87.50 16.00

# Question-3

Calculate the index numbers for different years taking 1984 as the base year :
 Year 1984 1985 1986 1987 1988 1989 Prices 80 90 100 110 140 160

Solution:
 Commodity A B C D E 10 25 30 15 20 6 10 15 20 8 15 40 45 30 25 8 20 12 15 6 60 250 450 300 160 90 400 675 600 200 80 500 360 225 120 120 800 540 450 150

Laspeyre's Price Index :

# Question-4

Calculate weighted aggregative price index from the following data using :

(i) Laspeyre's method and (ii) paasche's method

 Base Period Current Period Price Quantity Price Quantity A 2 10 4 5 B 5 12 6 10 C 4 20 5 15 D 2 15 3 10

Solution:
 Commodity A B C D 2 5 4 2 10 12 20 15 4 6 5 3 5 10 15 10 20 60 80 30 40 72 100 45 10 50 60 20 20 60 75 30

# Question-5

Calculate weighted aggregative price index number from the following data by using Passche's method :
 Commodity Base Year Current Period Price Quantity Price Quantity A 10 30 12 50 B 8 15 10 25 C 6 20 6 30 D 4 10 6 20

Solution:

 Commodity A B C D 10 8 6 4 30 15 20 10 12 10 6 6 50 25 30 20 500 200 180 80 600 250 180 120

.

# Question-6

Calculate Laspeyre's and passche's index for the following data :
 Commodity 1970 1990 Price Expenditure Price Expenditure A 8 100 10 90 B 10 60 11 66 C 5 100 5 100 D 3 30 2 24 E 2 8 4 20

Solution:
Since we are given the expenditure and price, we can obtain the quantity by dividing expenditure by the price for each commodity.
 Commodity A B C D E 8 10 5 3 2 12.50 6.0 20.0 10.0 4.0 10 11 5 2 4 9 6 20 12 5 100 60 100 30 8 125 66 100 20 16 72 60 100 36 10 90 66 100 24 20

# Question-7

Calculate weighted average of price relative index from the following data:
 Items Weight in % (Rs.) Base Year Price (Rs.) Current Year Price (Rs.) A 40 2 4 B 30 5 6 C 20 4 5 D 10 2 3

Solution:
 Items W RW A     B     C     D 40     30     20     10 2     5     4     2 4     6     5     3 8000     3600     2500     1500

# Question-8

The monthly per capita expenditure incurred by workers of 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 base.
 Items Price in 1980 Price in 2005 Food 100 200 Clothing 20 25 Fuel and Lighting 15 20 House Rent 30 40 Misc. 35 65

Solution:
 Item W RW Food Clothing Fuel and Lighting House Rent Misc. 75 10 5   6 4 100 20 15   30 35 200 25 20   40 65 200 125 133.33   133.33 185.71 15000 1250 666.65   799.98 742.84

# Question-9

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% Prices in 2004 (Rs.) 1500 250 750 300 400 Prices in 1995 (Rs.) 1400 200 500 200 250

Solution:
 Items W in % (1995) (2004) RW Food Fuel Clothing Rent Misc : 35 10 20 15 20 1400 200 500 200 250 1500 250 750 300 400 107.14 125.00 150.00 150.00 160.00 3750 1250 3000 2250 3200

CPI =

This result indicates that the CPI in the current year has increased by 34.5 per cent as compared to the base period.

# Question-10

Calculate the 'Cost of Living Index Number' using family budget method :
 Commodities Wheat Rice Pulses Ghee Sugar Oil Fuel Clothes Units consumed in base year 200 50 56 20 40 50 60 40 Price Rs. (In base year) 1.0 3.0 4.0 20.0 2.5 10.0 2.0 15.0 Price Rs. (In current year) 1.2 3.5 5.0 30.0 5.0 15.5 2.5 18.0

Solution:
 Commodities W= RW Wheat Rice Pulses Ghee Sugar Oil Fuel Clothes 200 50 56 20 40 50 60 40 1.0 3.0 4.0 20.0 2.5 10.0 2.0 15.0 1.2 3.5 5.0 30.0 5.0 15.5 2.5 18.0 120.00 116.67 125.00 150.00 200.00 155.00 125.00 120.00 200 150 224 400 100 500 120 600 24000 17500.5 28000 60000 20000 77500 15000 72000

CPI =

This result indicates that CPI in the current year has increased by 36.88 as compared to the base period.

# Question-11

If the salary of a person in the base year is Rs. 4,000 per annum and the current year salary is Rs. 6,000 by how much should his salary rise to maintain the same standard of living if the CPI of the current year is 400?

Solution:
Salary required in the current year to maintain the same standard of living of base year

Current year salary = Rs. 16,000

The increase in current salary required = 16000-6000=Rs.10,000.

# Question-12

A price index of two items of A and B is being estimated. If two items are assigned weights of 64 and 36 respectively, the price index becomes 279. Similarly, if they are assigned weights of 50 each, the price index turns out to be 265. Determine the individual price index numbers of items A and B.

Solution:
There are two situations in the given conditions. Let be the index for the first item and be the index for the second item.

First Situation : â€¦(i)

Second situation : â€¦(ii)

From (i) , â€¦(iii)

From (ii)m

Solving (iii) and (iv), we get â€¦(iv)

# Question-13

Given the following data :
 Year 1995-96 1996-97 1997-98 1998-99 1999-2000 2000-01 2001-02 2002-03 WPI (1993-94) 121.6 127.2 132.8 140.7 145.7 155.7 161.3 166.8

Calculate the inflation rate.

Solution:
Inflation rate for different years are calculated as :

There are many ups and down in the WPI.

# Question-14

Given the following data :
 Year 2000-01 2001-02 2002-03 2003-04 CPI for IW (1992=100) 444 463 482 500

Calculate the inflation rate.

Solution:
Inflation rate for different years are calculated as :

CPI of industrial workers declined in all the years

# Question-15

What is an Index Number ?[MSE (Chandigarh) 2001} Or

Define an Index Number. [NCT 2004]

Solution:
An index number is a statistical device for measuring relative change in the prices of a group of related variables over two or more different times. In other words, an index number is defined as specialised type of average which measure changes in the prices of commodities, industrial production, cost of living index etc.

# Question-16

What is a base Number. [NCT 2000]

Solution:
The base year is the reference year with which the current year is compared. If we measure the changes in prices in 2004 relative to those in 2001, then 2001 is called the base year.

# Question-17

Name few widely used index numbers.

Solution:
Some widely used index numbers are :

(i) Consumer Price Index (CPI)

(ii) The Wholesale Price Index (WPI)

(iii) Index of Industrial Production (IIP) and

(iv) Sensex etc.

# Question-18

How is Weighted Index Number different from a Simple Index Number?

Solution:
In simple (unweighted) index number, all items are treated as having equal importance whereas in weighted index number, relative importance of items is taken care of. Here weights given are quantity weights or value weights.

# Question-19

What is Consumer Price Index Number? Or What does a CPI measure?

Solution:
A consumer price index measures changes in the retail price paid by the ultimate consumers for a specified basket of goods and services over two different time periods.

# Question-20

What is Wholesale Price Index Number? Or What does a WPI measure ?

Solution:
The wholesale price index measures changes in the wholesale prices of a group of commodities traded in wholesale market over two different time periods. In other words, it indicates the change in the general price level.

# Question-21

What is Index of Industrial Production ? [KVS 2005]

Solution:
Index of industrial production is a quantity index. It measures changes in the level of industrial production comprising many industries. This index has been constructed in india annually with base period 1993 - 1994 for the current series.

# Question-22

Mention the formula for the construction of Cost of Living Index using family budget method.

Solution:
Cost of living Index and W = proportion or percentage of expenditure on the items in the total expenditure during the base period.

# Question-23

Give the formula of constructing simple average of price relative.

Solution:
Simple Aggregative Price Index

# Question-24

Give the formula of constructing Index of simple average of price relative.

Solution:
Index of simple Average of Price Relative

# Question-25

Give Laspeyre's formula of constructing Weighted Index Number.

Solution:
(Base year quantities as weights)

# Question-26

Give Paasche's formula of constructing Weighted Index Number.

Solution:
(Current year quantities as weights)

# Question-27

Give the formula of constructing Weighted Index Number by Weighted Average of Relative Method.

Solution:
(Weighted average of price relative index)

# Question-28

Give the formula of constructing Industrial Production Index.

Solution:

It is a weighted average of quantity relatives.

# Question-29

What does a Consumer price Index for industrial workers measure ?

Solution:
A consumer price index for industrial workers measures general inflation.

# Question-30

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

Solution:
A price index measures changes in prices of goods whereas a quantity index measures changes in the volume (or quantity) of goods produced.

# Question-31

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

Solution:
It is essential to have different CPI for different categories of consumers as the cost of living of different categories of consumers differ.

# Question-32

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

Solution:
The CPI for urban non-manual employees do not represent the changes in the cost of living of the president of India.

# Question-33

Name the major groups for whom the consumer price index numbers are constructed in India.

Solution:
Consumer price index numbers are having three types :

(i) The industrial workers,

(ii) The urban non-manual workers and

(iii) The agricultural labourers.

# Question-34

What is Agricultural Price Index ?

Solution:
Index number of agricultural production is a weighted average of quantity relatives. It measures changes in the level of agricultural production of food grains and non-food grains items. Food grains have a weight of 69.52 percent in this index.

# Question-35

What is SENSEX?

Solution:
Sensex is the short form of Bombay Stock Exchange Sensitive Index with 1978-79 as base. It is a useful guide for the investors in the stock market. It deals with 30 stocks represented by 13 sectors of the economy. If the sensex rises, it indicates that the market is doing well and investors expect better earnings on their investments.

# Question-36

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

Solution:
Price Index number does not reflect any type of changes in prices.

# Question-37

Which index number is used to calculate inflation rate ?

Solution:
Wholesale Price Index (WPI) is used to calculate inflation rate.

# Question-38

Write down the formulae of calculating inflation rate.

Solution:
Inflation rate

Where, Xt refers to WPI for the (t)th week.

Xt refers to WPI for the (t - 1)th week.

# Question-39

What is the base year of the new series of wholesale price index numbers published by the Government of India ?

Solution:
The base year of the new series of wholesale price index numbers published by the Government of India is1993-1994

# Question-40

Which index number is used to calculate purchasing power of money and real wages ?

Solution:
Consumer Price Index (CPI)

# Question-41

Write down the formula of calculating purchasing power of one rupee when the cost of living index is given at some base period.

Solution:
Purchasing power of one rupee =

# Question-42

Write down the formula for calculating real wages.

Solution:
Real wages =

# Question-43

What will be the real wage of the consumer if his money wage is Rs. 10,000 and the cost of living index is 526 ?

Solution:
Real wages =