Question

Laspeyre's index number formula possesses:

• A. Downward bias
• B. Upward bias
• C. No bias
• D. Nothing can be said

Hint:

Laspeyre uses base year quantities, which stay artificially high for goods that got costlier and were actually consumed less.

Answer 1

The Correct Option is B

Step 1: Laspeyre's price index is \[ P_{0}^{L} = \frac{\sum p_1 q_0}{\sum p_0 q_0} \times 100 \] where the quantities \(q_0\) are fixed at their base year levels.

Step 2: In practice, when the price of a commodity rises, consumers tend to reduce its consumption and substitute cheaper goods. So the true current quantity of a good whose price rose is usually lower than the base year quantity \(q_0\) used in the formula.

Step 3: Because Laspeyre's formula keeps using the higher, unadjusted base year quantity \(q_0\) as weight even for goods whose relative price and consumption pattern has changed unfavourably, it overweights the commodities that got costlier. This systematically inflates the computed index above the true cost of living change.

Step 4: This systematic overstatement is called an upward bias. In contrast, Paasche's index, which uses current year quantities, tends to have a downward bias for the same reason applied in the opposite direction.