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Worked Examples · Example 6
Q.

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

i) Laspeyres' index

ii) Paasche index.

SectorQuantity (weights) Year 1987Quantity (weights) Year 2015Unit Price (₹/kWh) Year 1987Unit Price (₹/kWh) Year 2015
Commercial541660151.9710.92
Residential15293202622.326.16
Industrial21287178320.795.13
Agriculture947388042.258.10
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Energy prices rose roughly four-fold from 1987 to 2015: Laspeyres' index (base-year weights) ≈402.56\approx 402.56 and Paasche index (current-year weights) ≈380.89\approx 380.89.

Laspeyres' price index =∑p1q0∑p0q0×100=\dfrac{\sum p_1q_0}{\sum p_0q_0}\times100 (uses base-year quantities q0q_0); Paasche price index =∑p1q1∑p0q1×100=\dfrac{\sum p_1q_1}{\sum p_0q_1}\times100 (uses current-year quantities q1q_1), where p0,p1p_0,p_1 = prices in 1987 and 2015, q0,q1q_0,q_1 = quantities in 1987 and 2015.

  1. Build the working table (pp in ₹/kWh, qq in weight units).
Sectorq0q_0q1q_1p0p_0p1p_1p1q0p_1q_0p0q0p_0q_0p1q1p_1q_1p0q1p_0q_1
Commercial541660151.9710.9259142.7210669.5265683.8011849.55
Residential15293202622.326.1694204.8835479.76124813.9247007.84
Industrial21287178320.795.13109202.3116816.7391478.1614087.28
Agriculture947388042.258.1076731.3021314.2571312.4019809.00
Total339281.21339281.2184280.2684280.26353288.28353288.2892753.6792753.67
  1. Column sums. ∑p1q0=339281.21\sum p_1q_0=339281.21, ∑p0q0=84280.26\sum p_0q_0=84280.26, ∑p1q1=353288.28\sum p_1q_1=353288.28, ∑p0q1=92753.67\sum p_0q_1=92753.67. …

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