Index Numbers And The Computation Of Factor Productivity1

For purposes of analyzing the nature and meaning of index number formulas to be used in the calculation of factor productivity, a distinction is made between interetemporal comparison of factor productivity for a single country and contemporaneous comparison of factor productivity in two different countries. In the former case, the country in question is supposed ideally to be realizing fully its production possibilities, and the concern is seen as appraisal of shifts in such possibilities over time due to the advance of technological knowledge. Following Moorsteen such an advance is taken to be represented by the change in capacity to produce a standard mix of outputs per unit of a standard mix of inputs. Any mix might be standard, but those actually realized at the times in question are of particular interest. The index number formulas to be applied then depend on the assumed shape of the functions representing production possibilities. The conventional practice of aggregating output arithmetically and inputs geometrically, for example, is in order where production possibilities are given by an elaborated Cobb‐Douglas function, but achieves only more or less approximate results otherwise. The analysis necessarily bears also on the prices at which inputs and outputs are to be valued. For the case of contemporaneous comparison of different countries, technological knowledge is taken ideally to be the same in the countries considered. Hence the concern is to gauge differences in production efficiency, i.e., realization of production possibilities. With production capacity understood to reflect any shortfall from possibilities, and hence production inefficiency in that sense, the analysis proceeds much as before, but given the fact of inefficiency determination of suitable prices for valuation of inputs and outputs becomes relatively difficult. Alternative expedients, none entirely satisfactory, are explored.