Weighted Aggregative Index Calculator
भारित समूही सूचकांक कैलकुलेटर
Calculate and compare 6 different weighted aggregative price indices: Laspeyres, Paasche, Fisher’s Ideal, Marshall-Edgeworth, Dorbish-Bowley, and Kelly’s Index
| Commodity | P₀ (Base Price) | P₁ (Current Price) | Q₀ (Base Quantity) | Q₁ (Current Quantity) |
|---|
Laspeyres: \( P_{01}^L = \frac{\Sigma P_1 Q_0}{\Sigma P_0 Q_0} \times 100 \)
Paasche: \( P_{01}^P = \frac{\Sigma P_1 Q_1}{\Sigma P_0 Q_1} \times 100 \)
Fisher’s Ideal: \( P_{01}^F = \sqrt{P_{01}^L \times P_{01}^P} \)
Marshall-Edgeworth: \( P_{01}^{ME} = \frac{\Sigma P_1(Q_0+Q_1)}{\Sigma P_0(Q_0+Q_1)} \times 100 \)
Dorbish-Bowley: \( P_{01}^{DB} = \frac{P_{01}^L + P_{01}^P}{2} \)
Kelly’s: \( P_{01}^{K} = \frac{\Sigma P_1 \bar{Q}}{\Sigma P_0 \bar{Q}} \times 100 \)
| Commodity | P₀ | P₁ | Q₀ | Q₁ | P₀Q₀ | P₁Q₀ | P₀Q₁ | P₁Q₁ |
|---|
Weighted Aggregative Index Methods: Complete Guide
भारित समूही सूचकांक विधियाँ: पूरी मार्गदर्शिका
What are Weighted Aggregative Index Methods?
Weighted Aggregative Index Methods are statistical techniques used to measure price changes over time by aggregating price and quantity data of multiple commodities. These methods assign different weights (quantities) to different commodities based on their importance in the basket.
Complete Formulas for All Methods
1. Laspeyres Price Index (Étienne Laspeyres):
\[ P_{01}^{L} = \frac{\sum P_1 Q_0}{\sum P_0 Q_0} \times 100 \]
2. Paasche Price Index (Hermann Paasche):
\[ P_{01}^{P} = \frac{\sum P_1 Q_1}{\sum P_0 Q_1} \times 100 \]
3. Fisher’s Ideal Index (Irving Fisher) – COMPLETE FORMULA:
\[ P_{01}^{F} = \sqrt{P_{01}^{L} \times P_{01}^{P}} = \sqrt{\frac{\sum P_1 Q_0}{\sum P_0 Q_0} \times \frac{\sum P_1 Q_1}{\sum P_0 Q_1}} \times 100 \]
Or equivalently:
\[ P_{01}^{F} = \sqrt{\frac{(\sum P_1 Q_0)(\sum P_1 Q_1)}{(\sum P_0 Q_0)(\sum P_0 Q_1)}} \times 100 \]
4. Marshall-Edgeworth Index (Alfred Marshall & F.Y. Edgeworth):
\[ P_{01}^{ME} = \frac{\sum P_1 (Q_0 + Q_1)}{\sum P_0 (Q_0 + Q_1)} \times 100 \]
5. Dorbish-Bowley Index (Dorbish & Bowley):
\[ P_{01}^{DB} = \frac{P_{01}^{L} + P_{01}^{P}}{2} \]
6. Kelly’s Index (Kelly):
\[ P_{01}^{K} = \frac{\sum P_1 \bar{Q}}{\sum P_0 \bar{Q}} \times 100 \] where \(\bar{Q} = \frac{Q_0 + Q_1}{2}\)
Key Differences Between Methods
- Laspeyres: Uses base year quantities – tends to overestimate inflation
- Paasche: Uses current year quantities – tends to underestimate inflation
- Fisher’s Ideal: Geometric mean of Laspeyres and Paasche – satisfies time reversal test
- Marshall-Edgeworth: Uses average quantities – compromise approach
- Dorbish-Bowley: Arithmetic mean – simple but doesn’t satisfy time reversal test
- Kelly’s: Similar to Marshall-Edgeworth – uses average quantities