Why a price index?

The starting point for understanding the utility of a price index is recognizing that there is no need for one if the goal is to compare the price of a single good or service in one period to the price for the same good or service in another period. If \(p_1\) is the price of a good in period 1 and \(p_0\) is the price of that same good in period 0, then the price relative \(p_1/p_0\) unambiguously gives the percent change in price between period 1 and period 0. The need for a price index arises out of a fundamental problem of comparing a collection of two or more prices at two points in time to arrive at an overall change in price.

To illustrate this comparison problem, suppose there are two goods, denoted by \(i\) and \(j\), that sell in periods 0 and 1. If the price of good \(i\) and the price of good \(j\) both increase between period 0 and period 1, then it is uncontroversial to say that prices have increased between period 0 and period 1 (although it is less obvious by how much prices have increased). Similarly, if both prices decrease, then it is natural to say that prices have decreased. However, an issue arises if the price of good \(i\) increases between period 0 and period 1 while the price of good \(j\) decreases. In this case it is unclear if prices have increased or decreased—there is no obvious way to give a single direction to the movement of prices over time.

A solution to this comparison problem is to find a way to aggregate price relatives for many goods and services together to form a single ratio, which is then interpreted as the overall movement in prices over time. This is the job of a price index. Although a price index solves the comparison problem, it introduces a new challenge—how to best combine price relatives to produce a single measure that describes overall change in prices. Consequently, a variety of index-number formulas have been proposed to construct a price index.