Performance: the output/input ratio

This chapter defines the concepts of this Handbook - performance, productivity, efficiency, and profitability - and discusses the interrelations. The most prominent performance measure, total factor productivity growth, is grounded in activity analysis and related to Debreu's coefficient of resource utilization. The performance literature considers Debreu's coefficient a component of the Farrell efficiency measure, but it is the other way round: The sway of Debreu's coefficient is far greater. An important variant, the Debreu-Diewert coefficient of resource utilization, involves a perfect performance aggregation result and admits practical decompositions. Alternative functional forms of performance measures, such as the Malmquist, Törnqvist, and Fisher indices, emerge when instantaneous rates of input and output change are approximated in discrete time in different ways. A recent result by Balk shows that a modification of the Malmquist index stands out, as it is transitive.