Fisher’s Ideal Index Calculator
फिशर आदर्श सूचकांक कैलकुलेटर
Calculate Fisher’s Ideal Index – geometric mean of Laspeyres and Paasche indices. Considered the “ideal” index for price measurement.
| Commodity | P₀ (Base Price) | P₁ (Current Price) | Q₀ (Base Quantity) | Q₁ (Current Quantity) | Action |
|---|
Where:
\( P_{01}^{F} \) = Fisher’s Ideal Price Index
\( \sqrt{L \times P} \) = Geometric mean of Laspeyres (L) and Paasche (P) indices
\( P_0 \) = Price in base year, \( P_1 \) = Price in current year
\( Q_0 \) = Quantity in base year, \( Q_1 \) = Quantity in current year
(L + P) ÷ 2
ΣP₁(Q₀+Q₁)/2 ÷ ΣP₀(Q₀+Q₁)/2
Same as Fisher’s
| Commodity | P₀ | P₁ | Q₀ | Q₁ | P₀Q₀ | P₁Q₀ | P₀Q₁ | P₁Q₁ | Price Change % |
|---|
Fisher’s Ideal Index: Complete Guide
फिशर आदर्श सूचकांक: पूरी मार्गदर्शिका
What is Fisher’s Ideal Index?
Fisher’s Ideal Index, developed by American economist Irving Fisher in 1922, is the geometric mean of Laspeyres and Paasche price indices. It is called “ideal” because it satisfies both time reversal and factor reversal tests, which are important mathematical properties for a good index number.
Complete Formula and Calculation
Fisher’s Ideal Index Formula:
\[ P_{01}^{F} = \sqrt{ \frac{\sum P_1 Q_0}{\sum P_0 Q_0} \times \frac{\sum P_1 Q_1}{\sum P_0 Q_1} } \times 100 \]
Alternative Notation:
\[ P_{01}^{F} = \sqrt{L \times P} \]
Where: \( L = \frac{\sum P_1 Q_0}{\sum P_0 Q_0} \times 100 \) (Laspeyres Index)
And: \( P = \frac{\sum P_1 Q_1}{\sum P_0 Q_1} \times 100 \) (Paasche Index)
Where:
- \( P_{01}^{F} \) = Fisher’s Ideal 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
Why is Fisher’s Index Called “Ideal”?
Fisher identified several tests that an ideal index number should satisfy. Fisher’s Ideal Index uniquely satisfies the most important ones:
- Time Reversal Test: \( P_{01} \times P_{10} = 1 \)
- Factor Reversal Test: \( P_{01} \times Q_{01} = \frac{\sum P_1 Q_1}{\sum P_0 Q_0} \)
- Circular Test: \( P_{01} \times P_{12} \times P_{20} = 1 \) (approximately satisfied)
Advantages of Fisher’s Index
- Mathematical Properties: Satisfies time reversal and factor reversal tests
- Balanced Approach: Geometric mean gives equal importance to both periods
- Less Bias: Less biased than Laspeyres or Paasche alone
- Widely Accepted: Considered the best theoretical index
- Consistency: Always lies between Laspeyres and Paasche
Limitations and Practical Issues
- Computational Complexity: Requires geometric mean calculation
- Data Requirements: Needs both base and current quantities
- Interpretation Difficulty: Geometric mean less intuitive than arithmetic mean
- Practical Usage: Less commonly used in official statistics than Laspeyres
Comparison with Other Indices
Mathematical Relationships:
- Fisher’s = √(Laspeyres × Paasche)
- Dorbish-Bowley = (Laspeyres + Paasche) ÷ 2 (Arithmetic mean)
- Kelly’s (with α=β=0.5) = Fisher’s
- Marshall-Edgeworth uses different approach with average quantities
For most practical data: Laspeyres ≥ Fisher’s ≥ Paasche