Q.Explain, with reasoning, why Laspeyres' Price Index tends to overestimate a genuine rise in the cost of living, while Paasche's Price Index tends to underestimate it.

The bias comes from consumer behaviour that neither formula's fixed weights can capture: people naturally buy less of whatever has become relatively more expensive. …

In real life, when a commodity becomes relatively more expensive, consumers do not keep buying the same quantity of it — they shift some of their spending toward relatively cheaper substitutes. Both Laspeyres' and Paasche's indices freeze quantities at one particular year, so neither can fully reflect this substitution — but they err in opposite directions.

Laspeyres' index ($P_{01}^{L}=\sum p_1q_0/\sum p_0q_0\times100$) keeps using the base-year basket ($q_0$) even at current prices. It effectively asks 'what would it cost to keep buying exactly what we used to buy, at today's prices?' — but real consumers did not keep buying exactly that; they cut back on the goods that rose the most. By pricing a basket that includes 'too much' of the now-expensive goods, Laspeyres' index overstates how much more expensive maintaining the actual, adjusted standard of living has become.

Paasche's index ($P_{01}^{P}=\sum p_1q_1/\sum p_0q_1\times100$) instead uses the current-year basket ($q_1$), which already reflects the consumer having cut back on the goods that got expensive. When this already-reduced basket is priced at the OLD (base-year) prices in the denominator, the effect of the price rise on those particular goods is understated — because the consumer is no longer buying much of them anyway. This makes Paasche's index understate the true rise in cost of maintaining the old standard of living. …

Claiming one index is simply 'more accurate' than the other in every case (the actual numerical comparison depends on the specific data, as Worked Example 4 shows) rather than explaining the direction of bias each formula's weighting scheme tends to produce; and describin …