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Worked Examples · Example 7
Q.

From the following price and quantity data for three commodities, calculate (a) Laspeyres' Price Index and (b) Paasche's Price Index.

Commodityp0p_0q0q_0p1p_1q1q_1
X510612
Y8596
Z104125
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Concept understanding — Weighted Price Index Numbers

Because commodities differ hugely in how much of them people actually buy, a proper price index weights each commodity by its quantity rather than treating every commodity equally. Laspeyres' Price Index (P01L=∑p1q0/∑p0q0×100P_{01}^{L}=\sum p_1q_0/\sum p_0q_0 \times 100) fixes the weights at base-year quantities, while Paasche's Price Index (P01P=∑p1q1/∑p0q1×100P_{01}^{P}=\sum p_1q_1/\sum p_0q_1 \times 100) uses current-year quantities instead. The choice matters: Laspeyres tends to overstate a genuine cost-of-living rise because it never lets the basket adjust for consumers subs …

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