Dorbish-Bowley Price Index Calculator
डॉर्बिश-बोले मूल्य सूचकांक कैलकुलेटर
Calculate Dorbish-Bowley Price Index – arithmetic mean of Laspeyres and Paasche indices. Get detailed step-by-step solutions.
| Commodity | P₀ (Base Price) | P₁ (Current Price) | Q₀ (Base Quantity) | Q₁ (Current Quantity) | Action |
|---|
Where:
\( P_{01}^{DB} \) = Dorbish-Bowley Price Index
\( L \) = Laspeyres Price Index = \( \frac{\sum P_1 Q_0}{\sum P_0 Q_0} \times 100 \)
\( P \) = Paasche Price Index = \( \frac{\sum P_1 Q_1}{\sum P_0 Q_1} \times 100 \)
\( P_0 \) = Price in base year, \( P_1 \) = Price in current year
\( Q_0 \) = Quantity in base year, \( Q_1 \) = Quantity in current year
| Commodity | P₀ | P₁ | Q₀ | Q₁ | P₀Q₀ | P₁Q₀ | P₀Q₁ | P₁Q₁ | Price Change % |
|---|
Dorbish-Bowley Price Index: Complete Guide
डॉर्बिश-बोले मूल्य सूचकांक: पूरी मार्गदर्शिका
What is the Dorbish-Bowley Price Index?
The Dorbish-Bowley Price Index, developed by economists J. L. Dorbish and A. L. Bowley, is a simple arithmetic mean of Laspeyres and Paasche price indices. This approach combines the strengths of both indices while mitigating their individual weaknesses.
Complete Formula and Calculation
Dorbish-Bowley Price Index Formula:
\[ P_{01}^{DB} = \frac{L + P}{2} \]
Where:
\[ L = \frac{\sum P_1 Q_0}{\sum P_0 Q_0} \times 100 \quad \text{(Laspeyres Index)} \]
\[ P = \frac{\sum P_1 Q_1}{\sum P_0 Q_1} \times 100 \quad \text{(Paasche Index)} \]
Detailed Formula:
\[ P_{01}^{DB} = \frac{1}{2} \left[ \frac{\sum P_1 Q_0}{\sum P_0 Q_0} + \frac{\sum P_1 Q_1}{\sum P_0 Q_1} \right] \times 100 \]
- \( P_{01}^{DB} \) = Dorbish-Bowley Price Index from period 0 to period 1
- \( P_0 \) = Price of each commodity in the base period
- \( P_1 \) = Price of each commodity in the current period
- \( Q_0 \) = Quantity of each commodity in the base period
- \( Q_1 \) = Quantity of each commodity in the current period
- \( \sum \) = Summation across all commodities
Advantages of Dorbish-Bowley Index
- Simple Calculation: Easy to compute as arithmetic mean
- Balanced Approach: Combines Laspeyres and Paasche
- Reduces Bias: Less biased than using either index alone
- Practical: Useful when both quantity data are available
Comparison with Other Indices
- vs Laspeyres: Uses both base and current quantities instead of only base quantities
- vs Paasche: Uses both base and current quantities instead of only current quantities
- vs Fisher: Dorbish-Bowley uses arithmetic mean while Fisher uses geometric mean
- vs Marshall-Edgeworth: Different mathematical approach but similar balanced perspective
Mathematical Properties
- Always lies between Laspeyres and Paasche indices
- Does not satisfy factor reversal test
- Does not satisfy time reversal test
- Simple to understand and interpret