Answer :
The Laspeyres quantity index for 2019, using 1995 as the base year, is approximately 99.46. The correct option is C. The Laspeyres price index for 2019, using 1995 as the base year, is also approximately 146.34. The correct option is not mentioned.
To evaluate the Laspeyres quantity index for 2019 using 1995 as the base year, we need to compare the quantity of each commodity consumed in 2019 with the quantity consumed in 1995, using the prices from 1995 as weights.
Let's calculate the Laspeyres quantity index for each commodity:
Commodity A:
Quantity in 1995 = 20
Quantity in 2019 = 21
Price in 1995 = 2
Laspeyres quantity index for A = (21/20) * 100 = 105
Commodity B:
Quantity in 1995 = 3
Quantity in 2019 = 2
Price in 1995 = 18
Laspeyres quantity index for B = (2/3) * 100 = 66.67
Commodity C:
Quantity in 1995 = 18
Quantity in 2019 = 23
Price in 1995 = 3
Laspeyres quantity index for C = (23/18) * 100 = 127.78
Now, to calculate the overall Laspeyres quantity index, we take the weighted average of the individual commodity indices:
Laspeyres quantity index = [(weight A * index A) + (weight B * index B) + (weight C * index C)] / (weight A + weight B + weight C)
Using the prices in 1995 as weights, we have:
Weight A = 20 * 2 = 40
Weight B = 3 * 18 = 54
Weight C = 18 * 3 = 54
Laspeyres quantity index = [(40 * 105) + (54 * 66.67) + (54 * 127.78)] / (40 + 54 + 54)
= (4200 + 3600 + 6927.72) / 148
= 14727.72 / 148
≈ 99.46
Therefore, the Laspeyres quantity index for 2019 using 1995 as the base year is approximately 99.46. The correct option is C.
As for the Laspeyres price index, we need to compare the prices of each commodity in 2019 with the prices in 1995, using the quantities from 1995 as weights.
Calculating the Laspeyres price index for each commodity:
Commodity A:
Price in 1995 = 2
Price in 2019 = 3
Quantity in 1995 = 20
Laspeyres price index for A = (3/2) * 100 = 150
Commodity B:
Price in 1995 = 18
Price in 2019 = 36
Quantity in 1995 = 3
Laspeyres price index for B = (36/18) * 100 = 200
Commodity C:
Price in 1995 = 3
Price in 2019 = 4
Quantity in 1995 = 18
Laspeyres price index for C = (4/3) * 100 = 133.33
Calculating the overall Laspeyres price index, using the quantities in 1995 as weights:
Weight A = 20
Weight B = 3
Weight C = 18
Laspeyres price index = [(weight A * index A) + (weight B * index B) + (weight C * index C)] / (weight A + weight B + weight C)
Laspeyres price index = [(20 * 150) + (3 * 200) + (18
* 133.33)] / (20 + 3 + 18)
= (3000 + 600 + 2399.94) / 41
= 5999.94 / 41
≈ 146.34
Therefore, the Laspeyres price index for 2019 using 1995 as the base year is approximately 146.34.
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