Following table shows the data on energy consumption and expenditure at Badarpur Thermal Power Station, in Delhi region. Construct an aggregative price index for the energy expenditures in year 2015 using Laspeyres’ index.
|
Sector |
Quantity (weights) |
Unit Price (₹/kWh) |
||
|
|
Year 1987 |
Year 2015 |
Year 1987 |
Year 2015 |
|
Commercial |
5416 |
6015 |
1.97 |
10.92 |
|
Residential |
15293 |
20262 |
2.32 |
6.16 |
|
Industrial |
21287 |
17832 |
0.79 |
5.13 |
|
Agriculture |
9473 |
8804 |
2.25 |
8.10 |
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 403
Where:
- $p_0$ = Price in base year ($1987$)
- $p_1$ = Price in current year ($2015$)
- $q_0$ = Quantity in base year ($1987$)
|
Sector |
$q_0$ (1987) |
$p_0$ (1987) |
$p_1$ (2015) |
$p_1q_0$ |
$p_0q_0$ |
|
Commercial |
5416 |
1.97 |
10.92 |
$59,142.72$ |
$10,669.52$ |
|
Residential |
15,293 |
2.32 |
6.16 |
$94,204.88$ |
$35,479.76$ |
|
Industrial |
21,287 |
0.79 |
5.13 |
$109,202.31$ |
$16,816.73$ |
|
Agriculture |
9473 |
2.25 |
8.10 |
$76,731.30$ |
$21,314.25$ |
|
Total |
|
$\sum p_1 q_0 = 339,281.21$ |
$\sum p_0 q_0 = 84,280.26$ |
$\text{(Laspeyres Index) } I_{2015} = \frac{10.92 \times 5416 + 6.16 \times 15293 + 5.13 \times 21287 + 8.10 \times 9473}{1.97 \times 5416 + 2.32 \times 15293 + 0.79 \times 21287 + 2.25 \times 9473} \times 100$
$= \frac{339281.21}{84280.26} \times 100$
$= 403$