Construction of a Price Index — Unweighted Methods

The simplest price index methods give every commodity in the group EQUAL importance, regardless of how much of it is actually bought — this is why they are called unweighted (simple) methods. Throughout this section and the next, the same running notation is used: $p_0$ = base-year price, $p_1$ = current-year price, $q_0$ = base-year quantity, $q_1$ = current-year quantity, for each commodity in the group.

1. Simple Aggregative Method. Add up the current-year prices of all commodities, add up their base-year prices, and take the ratio:

   $P_{01} = \frac{\sum p_1}{\sum p_0}\times 100$

   This method is easy to compute but has a genuine defect: commodities quoted in a HIGH-price unit (say, prices per quintal) dominate the total $\sum p$ far more than commodities quoted in a low-price unit (say, prices per kilogram), purely because of the unit chosen, not because that commodity is actually more important to a consumer's budget. Changing the unit of quotation for even one commodity can swing the whole index.
2. Simple Average of Price Relatives Method. First convert EACH commodity's own price change into a price relative — a small index number for that commodity alone:

   $\text{Price Relative} = \frac{p_1}{p_0}\times 100$

   Then average the price relatives of all $N$ commodities in the group: $P_{01} = \frac{\sum \left(\frac{p_1}{p_0}\times100\right)}{N}$ …