The Problem

The measurement in relative terms of the price development of a single commodity such as granulated sugar from one date to another presents no problem. Of course, we must take care that the prices at the two dates relate to the same commodity, i.e. we must make sure that to all intents and purposes the quality and the packaging have not changed and that the commodity is sold through the same type of retail outlet, etc.1 However, once we are satisfied that indeed we are comparing like with like, all we have to do in order to express the price comparison in relative terms is to determine the ratio between the prices at the two dates. In index-number theory that ratio for a single commodity is called a price relative. When the price of commodity i at date 1, the current date, is compared with its price at date 0, the base date, the price relative, denoted by the symbol p i will be defined as (1.1) p i = P 1 i P 0 i $${p^i} = \frac{{P_1^i}}{{P_0^i}}$$ where P 1 i $$P_1^i$$ and P 0 i $$P_0^i$$ denote the prices of commodity i at dates 1 and 0 expressed in currency units per physical unit (say£s per ton). It is worth noting that p i , unlike P 1 i $$P_{1}^{i}$$ and P 0 i $$P_0^i$$ , is quite independent of the choice of units used in the measurement of prices.