Question

Laspeyres index = 110, Paasche’s Index = 108, then Fisher’s Ideal Index is equal to

Answer 1

Hint: To solve this question, firstly we will see what these indexes are used for and what these indexes are individual. Also, we will see what are the relation between the indices Laspeyre’s index, Paasche’s Index, then Fisher’s Ideal Index. And, using this relation, we will find the value of Fisher’s Ideal Index

Complete step-by-step solution:
Laspeyres’ Index is a methodology to calculate the consumer price index by measuring the change in the price of the basket of goods to the base year. Formula for calculating Lapeyre’s Index is \[{{P}_{L}}=\dfrac{\sum{({{p}_{c}},{{t}_{n}}.{{q}_{c}}{{t}_{0}})}}{\sum{({{p}_{c}},{{t}_{0}}.{{q}_{c}}{{t}_{0}})}}\] , where P is the relative index of the price level in two periods, ${{t}_{0}}$ is the base period usually the first year, and ${{t}_{n}}$ the period for which index is computed.
The Paasche Index is a composite index number of prices arrived at by the weighted sum method. This index number corresponds to the ratio of the sum of the prices of the actual period n and the sum of prices of the reference period 0.
The fisher price index is a consumer price index and is equal to the geometric mean of the Laspeyres index and Paasche’s Index.
So, we have $\text{Fisher }\!\!'\!\!\text{ s Ideal Index = }\sqrt{\text{L}\text{.I }\!\!\times\!\!\text{ P}\text{.I}}$ , where L.I and P.I are Laspeyres’ index and Paasche’s Index respectively.
In question we are given that,
Laspeyres’ index = 110, Paasche’s Index = 108
So, on substituting values we get
$\text{Fisher }\!\!'\!\!\text{ s Ideal Index = }\sqrt{\text{110 }\!\!\times\!\!\text{ 108}}$
On simplifying, we get
$\text{Fisher }\!\!'\!\!\text{ s Ideal Index = }\sqrt{\text{11880}}$
On solving, we get
$\text{Fisher }\!\!'\!\!\text{ s Ideal Index = 108}\text{.995}$
On approximating, we get
$\text{Fisher }\!\!'\!\!\text{ s Ideal Index = 109}$
Hence, Fisher ideal index is 109.

Note: Always remember that the relationship between indices Laspeyres’ index, Paasche’s Index, then Fisher’s Ideal Index is $\text{Fisher }\!\!'\!\!\text{ s Ideal Index = }\sqrt{\text{L}\text{.I }\!\!\times\!\!\text{ P}\text{.I}}$ , where L.I and P.I are Laspeyres’ index and Paasche’s Index respectively. Also, if we have three numbers a, b and c then the geometric mean of a and c which is equal to b is given as $\text{b = }\sqrt{\text{a }\!\!\times\!\!\text{ c}}$. Try not to make any calculation errors.