Question

Calculate Fishers Ideal Index from the data given below and show that it satisfies the Time
Reversal and Factor Reversal tests.
Base Year General Year
Commodity Quantity Price Quantity Price
A 12 10 15 12
B 15 7 20 5
C 24 5 20 9
D 5 16 5 14

Answer 1

The answer is stated below:

Explanation:

P01 = √Sum of p1q0 / Sum of p0q0 × Sum of p1q1 / Sum of p0q1

= √ 505/ 425 × 530 / 470

= 1.576

P10 = √Sum of p0q1 / Sum of p1q1 × Sum of p0q0 / Sum of p1q0

= √470/ 530 × 425/ 505

= 0.8638

Time reversal test

P01 × P10 = √505/ 425 × 530 / 470 × 470/ 530 × 425/ 505

= √1

= 1

Factor Reversal Test

P01  × Q01 = Sum of p1q1 / Sum of p0q0

where

Q01 = √ Sum of q1p0 / Sum of q0p0  × Sum of q1p1 / Sum of q0p1

= √470/ 525  ×  530/ 505

= 0.9693

Now, putting the values above:

= √ 505/ 425 × 530 / 470  × 470/ 425  ×  530/ 505

= √530 / 425 × 530 / 425

This equal to Sum of p1q1 / Sum of p0q0

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