A framework is developed for decomposing product price changes into changes in input prices, technical efficiency, and deviations of price from unit cost. This framework facilitates the measurement of productivity growth in noncompetitive industries. The history of American steel rail prices between 1879 and 1910 is analyzed, and it is concluded (in contrast with much recent work) that productivity growth remained rapid until the twentieth century and that the steel industry was sufficiently collusive so that the rail producers received the benefits of that productivity growth as excess profits.

A framework is developed for decomposing product price changes into changes in input prices, technical efficiency, and deviations of price from unit cost. This framework facilitates the measurement of productivity growth in noncompetitive industries. The history of American steel rail prices between 1879 and 1910 is analyzed, and it is concluded (in contrast with much recent work) that productivity growth remained rapid until the twentieth century and that the steel industry was sufficiently collusive so that the rail producers received the benefits of that productivity growth as excess profits.

ECONOMISTS and statisticians who construct estimates of total factor productivity or who estimate production functions or systems of consumer demand functions are often forced to aggregate subsets of their data. In order to perform this aggregation, an index number formula is generally used. A price index P(pO, pl, x?, xI) is defined to be a function P of the prices of the N commodities to be aggregated in periods 0 and 1,p?-(pll, . . . , PNO) and pl (pl,.'.. PN'), respectively, and of the corresponding quantities utilized during periods 0 and 1, x? (xi?, . . .,XNO) andX1 _ (xi', . . .,XN1), respectively. A quantity index Q(p0, pl, x?, xl) is defined to be another function Q of the price and quantity vectors for the two periods. Generally, we assume that P and Q satisfy Fisher's (1922) weak factor reversal test: