Index Numbers
Index numbers measure relative change in a variable or a basket of goods over time. STPM 950 tests weighted aggregate indices, Laspeyres and Paasche, Fisher's ideal index, base shifting, and deflation.
Formulas
With base-year prices p0 and quantities q0, and current-year p1 and q1:
- Laspeyres price index: L = (Σp1q0 / Σp0q0) × 100.
- Paasche price index: P = (Σp1q1 / Σp0q1) × 100.
- Fisher's ideal index: F = √(L × P).
Laspeyres uses base quantities, Paasche current quantities. Fisher is the geometric mean and is preferred because it passes the time-reversal test. Base shifting: new index = (old index / index of new base) × 100. Deflation: real value = (nominal value / price index) × 100.
Worked example: p0 = (2,4), q0 = (10,5); p1 = (3,5), q1 = (8,6). L = (3×10+5×5)/(2×10+4×5) ×100 = 55/40×100 = 137.5. P = (3×8+5×6)/(2×8+4×6) ×100 = 54/40×100 = 135. Fisher = √(137.5×135) ≈ 136.25.
Traps: using current quantities in Laspeyres; dividing by the current-year base instead of the base-year value; and treating Fisher's index as the arithmetic mean of L and P.