Index Numbers

Question 1

Meaning of Index Number

Answer 1

It is a statistical tool which compare the price of commodity at two different periods. (Base year and Current year)

Question 2

How is Index number expressed

Averages used in Construction of Index Number is _________

Answer 2

Index Number expressed in terms of Percentages

1. AM and GM

GM -> Best average for construction of Index Number

Question 3

Formula for Simple Index Number

a. aggregative Price Index
b. Relative Price Index

Answer 3

a. Aggregative Price Index

EP1 /EP0 x 100 , EP1 = Current year price Sum, EP0 = Base Year Sum.

it is dependent on units

b. Relative Price Index

E(P1/P0) x 100 / N , N-> No of commodities

it is independent on units

Question 4

Weighted Index Number

a. Laspeyre’s Index
b. Paasche’s index
c. Bowley index
d. Fisher Index
e. marshall index

Answer 4

a. E(P1Q0) / E(P0Q0) x 100
b. E(P1Q1) / E(P0Q1) x 100
c. AM of laspeyre’s and paasche’s index
-> L+P/ 2
d. GM of Laspeyre’s and Paasche’s Index
-> square root ( Ep1q0/Ep0q0 x Ep1q1/Ep0q1) x 100
e. P1 (q0+q1) / P0 (q0+q1) x 100

Marshall index is approx to Fisher index

Question 5

Consumer Price Index meaning
and formula

Answer 5

Cost of living index
Helps finding Inflation
Measure of average change in Price over a given period of time the consumer pays for the basket of goods and services

CPI = Based on given data use Laspeyre’s/Paasche’s/ other formulas

Sometimes they may use weights
EIW/EW
I -> Group Index
W -> weight

Question 6

Deflated value

Answer 6

When Price of certain goods raises then the seller may reduce the quantity to sell the goods for less Price

deflated Value = Current Value / current year CPI

Question 7

Splicing of Index Number

Formula

Answer 7

Combining two index number series into single continuous index number series with common base

Original Price Index / Price index of year to which it has to be shifted * 100

Question 8

Chain Index Number

Meaning
and Formula

Answer 8

A Chain Index number is an index in which value of any given period is related to the value of immediate preceding period

CIN = Link relative of current year } Price of current year x CIN of previous Year / 100

Question 9

Purchasing power of money

Answer 9

1/ Price Index number

Question 10

Real Wages

Answer 10

Current Year Wages x Base year CPI / Current Year CPI

Base Year Price Index if nothing given assume 100

Question 11

Percentage Increase in Real Wage

Answer 11

[ 1- (1+ % increase in price / 1+ % Increase in Wages) ] x 100

% Increase in Price -> Convert it to Decimal

% Increase in Real Wage will always be Less than difference between % Increase in wage and % Increase in price

Question 12

Test of Adequacy

a. Time reversal test
b. Factor reversal test
c. Circular test

Answer 12

All the index number except Simple aggregate Price Index satisfies Unit test cuz all the other are unit free

Time reversal test
-> Current Yr should be reversed with base year
-> P01 x P10 = 1

Only Fisher and Marshall index satisfies Time reversal test

Factor reversal test
-> factors gets interchanged
P01 x Q01 = V01 = EP1Q1/EP0Q0
-> Only fisher index satisfies Factor reversal test

Circular test
P01 x P12 x P20 =1
Fisher index fails to satisfy circular test

satisfied by Simple GM
of Price relatives and weighted aggregate with fixed weight

Question 13

Current year salary

Dearness allowance

Answer 13

Base Yr Salary x Current year CPI / Base Year CPI

dearness allowance = Current Year salary - Base year salary