Marshall-Edgeworth Method 🖇️
While Fisher's method is "Ideal", it requires calculating square roots, which can be tedious. The Marshall-Edgeworth Method (or Edge-worth Marshall) is an alternative compromise.
The Concept 💡
Instead of taking the Geometric Mean of the final indices (like Fisher), this method takes the Arithmetic Mean of the Quantities (q0 and q1) as the common weight.
Essentially, it uses the average quantity of the base year and current year to smooth out the bias.
Weight (w):
w = (q0 + q1) / 2
The Formula 📐
P_01 = [ ∑ p1(q0 + q1) / ∑ p0(q0 + q1) ] * 100
Expanded Version:
P_01 = [ (∑ p1 q0 + ∑ p1 q1) / (∑ p0 q0 + ∑ p0 q1) ] * 100
[!TIP] Notice the pattern? It's simply:
[ (Num of Laspeyres) + (Num of Paasche) ] / [ (Denom of Laspeyres) + (Denom of Paasche) ] * 100
Advantages vs Disadvantages ⚖️
| Pros | Cons |
|---|---|
| Simple to Calc: No square roots needed (unlike Fisher). | Less "Ideal": It does not satisfy the Factor Reversal Test. |
| Good Compromise: Uses both year weights, balancing the bias. | Data Needed: Still requires current year quantities (q1), which may be hard to get quickly. |
Which one to choose? 🤷
- Laspeyres: If you only have Base Quantities (Common).
- Paasche: If you want current consumption Impact.
- Fisher: If you want the most accurate, mathematical perfection.
- Marshall-Edgeworth: If you want a good approximation of Fisher without square roots.
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