In this paper we focus on specification of revenue functions in their dual price space. We consider two distance functions, both dual to the revenue function: Shephard output distance function and the directional output distance function, both in price space. The former is multiplicative,...

The purpose of this paper is to develop models with and without potential emissions trading and to compare industry profits under the two regimes. The model in which emissions trading is permitted is a nonparametric industry frontier model in the spirit of Färe et al. (1992). It is relative to...

In this paper we analyze the impact on firm profits of the environmental regulations in the Swedish pulp and paper industry. The approach taken is a non-parametric programming model of the technology. A feature of this industry is that environmental regulations are determined individually for...

This paper develops the theory of economic price and quantity indicators, being the difference analogue of indexes. The properties of indicators and indexes are compared. Observable bounds for the indicators will be derived, as well as two exactness results for Bennet (1920)-type price and...

Inequalities created by relating gauge (distance) functions and their dual support functions have been used in economics and operations research/management science to measure efficiency and productivity. The most familiar example is the Farrell (1957) measure of cost efficiency and its...

This paper introduces a decomposition of the Malmquist productivity index into component indexes. The motivation is to derive an analogue of the decomposition of the Törnqvist index into productivity and quality change provided by Fixler and Zieschang (1992) to the Malmquist index. Since we...

In this paper we introduce a SBM (slacks-based measure) of efficiency based on directional distance functions. This measure is contrasted with the SBM due to Professor Tone [Tone, K., 2001. A slacks-based measure of efficiency in data envelopment analysis. European Journal of Operational...

This study introduces an Environmental Performance Index (EPI) to assess the performance of firms that produce both good and bad outputs. In the one good output one bad output case, the EPI simplifies to the ratio of good–bad output for period t + 1 and period t. After deriving the index,...