used his methods to show that the value of five pounds had changed greatly over the course of 260 years. He argued on behalf of the Oxford students and published his findings anonymously in a volume entitled Chronicon Preciosum. 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, does not 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. Paasche and Laspeyres price indices The two most basic formulae used to calculate price indices are the Paasche index (after the economist Hermann Paasche ) and the Laspeyres index (after the economist Etienne Laspeyres ). The Paasche index is computed as while the Laspeyres index is computed as where is the relative index of the price levels in two periods, is the base period (usually the first year), and the period for which the index is computed. Note that the only difference in the formulas is that the former uses period n quantities, whereas the latter uses base period (period 0) quantities. A helpful mnemonic device to remember which index uses which period is that L comes before P in the alphabet so the Laspeyres index uses the earlier base quantities and the Paasche index