for base and comparison periods, respectively. Average units volumes, and , and average prices per unit, and , are defined in the obvious way. Also, define the G × 1 vectors of average unit volumes and average prices per unit
Then, the period-to-period trend in total dollar volume is given by
where TN is again the trend in the total HH count, TPq is the trend in average units per HH, and TLp is the trend in average price per unit. The trend in average units is weighted by comparison prices, and thus one might view TPq as a Paasche index of unit volume. Since the trend in average prices is weighted by base units volume, one might thus view TLp as a Laspeyres price index.
An alternative decomposition of the trend is
where TLq is a Laspeyres index of units volume and TPp is a Paasche price index. A second alternative decomposition of the trend is