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Worked Examples · Example 5
Q.

With reference to example above, what will happen to the index number for year 2000 if the commodities are used in different weights (quantities)?

CommodityQuantity (weights)Unit Price (₹) Year 2000Unit Price (₹) Year 2008
A1003.203.8
B201.702.1
C15148.10149.50
D503445
Sikkim CbseNCERTSubjective· 3mImportance★★★★★est
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With fixed quantity weights QQ, use the weighted aggregative index ∑pnQ∑p0Q×100=4914.54275.5×100≈115\dfrac{\sum p_n Q}{\sum p_0 Q}\times100 = \dfrac{4914.5}{4275.5}\times100 \approx 115, so the manufacturer's raw-material cost rose about 15% from 2000 to 2008.

Weighted aggregative index =∑pnQ∑p0Q×100=\dfrac{\sum p_n Q}{\sum p_0 Q}\times100, where QQ = the fixed quantity (weight) of each commodity, p0p_0 = its base-period (2000) unit price and pnp_n = its current-period (2008) unit price.

  1. Weight each commodity's price by its quantity QQ in both years, then aggregate.
CommodityQQp0p_0 (2000)pnp_n (2008)p0Qp_0 QpnQp_n Q
A1003.203.80320.00320.00380.00380.00
B201.702.1034.0034.0042.0042.00
C15148.10149.502221.502221.502242.502242.50
D5034.0045.001700.001700.002250.002250.00
Total∑p0Q=4275.50\sum p_0 Q = 4275.50∑pnQ=4914.50\sum p_n Q = 4914.50
  1. Sum the base-period values. ∑p0Q=320+34+2221.5+1700=4275.5\sum p_0 Q = 320+34+2221.5+1700 = 4275.5.
  2. Sum the current-period values. ∑pnQ=380+42+2242.5+2250=4914.5\sum p_n Q = 380+42+2242.5+2250 = 4914.5.
  3. Apply the formula. Index =∑pnQ∑p0Q×100=4914.54275.5×100=114.95≈115=\dfrac{\sum p_n Q}{\sum p_0 Q}\times100 = \dfrac{4914.5}{4275.5}\times100 = 114.95 \approx 115. …

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