Price Index - Formal Calculation

Formal Calculation

Given a set of goods and services, the total market value of transactions in in some period would be

where

represents the prevailing price of in period

represents the quantity of sold in period

If, across two periods and, the same quantities of each good or service were sold, but under different prices, then

and

would be a reasonable measure of the price of the set in one period relative to that in the other, and would provide an index measuring relative prices overall, weighted by quantities sold.

Of course, for any practical purpose, quantities purchased are rarely if ever identical across any two periods. As such, this is not a very practical index formula.

One might be tempted to modify the formula slightly to

This new index, however, doesn't do anything to distinguish growth or reduction in quantities sold from price changes. To see that this is so, consider what happens if all the prices double between and while quantities stay the same: will double. Now consider what happens if all the quantities double between and while all the prices stay the same: will double. In either case the change in is identical. As such, is as much a quantity index as it is a price index.

Various indices have been constructed in an attempt to compensate for this difficulty.