Question

Find the Laspeyre’s, Paasche’s and Fisher’s index numbers for the year 2015 with the base year 2014 using the following information:

Answer 1

Here, base year is 2014.

∴ p₀ = Price in 2014,

q₀ = Quantity in 2014,

P₁ = Price in 2015,

q₁ = Quantity in 2015.

The units of price and quantity for the items A, B, C and D are not equal. So we compute after making the units of price and quantity.

Explanation :
Item A: The unit of price is 20 kg and the unit of quantity is kg.

∴ In 2014, the price per kg = \(\frac{80}{20}\) = ₹ 4

In 2015, the price per kg = \(\frac{120}{20}\) = ₹ 6

Item B: The unit of price is kg and the unit of quantity is gram.

∴ In 2014, the quantity in kg = \(\frac{2400}{1000}\) = 2.4 kg

In 2015, the quantity in kg = \(\frac{4000}{1000}\) = 4 kg

[Note: 1000 gram = 1 kg]

Item C: The unit of price is quintal and the unit of quantity is kg.

∴ In 2014. the price per kg = \(\frac{2000}{100}\) = ₹ 20

In 2015, the price per kg =\(\frac{2800}{100}\) = ₹ 28

[Note : 1 Quintal = 100 kg]

Item D: The unit of price is dozen and the unit of quantity is a piece.

∴ In 2014, the price per piece = \(\frac{48}{12}\)= ₹ 4

In 2015, the price per piece = \(\frac{72}{12}\)= ₹ 6

[Note : 1 Dozen =12 pieces]]

To compute Laspeyre’s, Paasche’s and Fisher’s index numbers, the table of calculations is prepared as follows :

Laspeyre’s index number:

Paasche’s index number:

Fisher’s index number:

\(I_p=\sqrt{I_L\times I_P}\)

\(=\sqrt{141.13\, \times\,140.15}\)

\(=\sqrt{19779.3695}\)

= 140.64