Q.Using the same data as Examples 5–7, calculate the price index number by the Weighted Average of Price Relatives Method, using weight w = p0q0, and verify that it equals the Laspeyres index found in Example 5.

Weighting each commodity's own price relative by its base-year value w = p0q0 should reproduce the Laspeyres index exactly, as an algebraic identity. …

Step 1 — Price relatives (already found in Example 4) and weights $w=p_0q_0$ (already found in Example 5).

Step 2 — Apply the weighted-average formula. …

This IS the cross-check. Getting 127.59 here, independently via price relatives and value weights, and 127.59 in Example 5 via raw price-quantity aggregates, verifies the algebraic identity stated in Section 4 — the weighted average of …

Using an arbitrary or unstated weight (e.g., quantity q0 alone, without multiplying by p0) instead of the specific value weight w = p0q0 — the exact equality with Laspeyres holds ONLY when the we …