Mikuláš Luptáčik

Eco-efficiency analysis of power plants: An extension of data envelopment analysis

Abstract In public discussion on environmental policy, the notion of eco-efficiency is often used. The joint production of goods and undesirable outputs, such as pollutants which may not be freely disposable without costs, causes difficulties to measure the overall performance of the firm. Because of the absence of market prices for the undesirable outputs, we are not able to estimate the environmental costs. Some of the measurement and evaluation difficulties can be overcome by employing data envelopment analysis (DEA) as the efficiency measurement vehicle. We propose the use of two different approaches. In the first approach, we start by decomposing the problem into two parts: (1) the problem of measuring technical efficiency (as the relation of the desirable outputs to the inputs) and (2) the problem of measuring so-called ecological efficiency (as the relation of the desirable outputs to the undesirable outputs) separately. Those two efficiency indicators are then combined. In the second approach, we treat pollutants as the inputs in the sense that we wish to increase desirable outputs and decrease pollutants and inputs. The approaches are applied to the problem of measuring the efficiency of 24 power plants in a European country.

Alternative measures of environmental technology structure in DEA: An application

The nonparametric data envelopment analysis (DEA) literature on environmental efficiency (EE) considers handling undesirable outputs in two alternative ways: either in their original forms with the assumption that these are weakly disposable or in various translated forms with the assumption that these are strongly disposable. Choosing a particular approach implies adoption of a particular, distinct treatment of undesirable outputs, and hence yields a distinct set of EE estimates. To explore the effects of the interplay between choice of EE measure and specific treatment of undesirable outputs, this paper attempts to generate all possible output-oriented EE measures based on these two alternative approaches. Furthermore, guided by the argument that slacks are important in identifying properly the efficiency behavior of firms, it proposes two new alternative, slacks-based formulations of EE: one based on the range directional model, and the other on the generalized proportional distance function model. Using a confected data set of ten firms and a real-life data set of 22 OECD countries, our empirical analysis reveals that: first, EE scores are influenced not only by the choice of disposability assumption for undesirable outputs but also by the way these are treated in various translated forms; second, the choice of any particular treatment of undesirable outputs plays no role in influencing the rankings of firms; and third, our two new alternative EE formulations are, at the least, viable alternatives to existing EE measures in ranking firms according to their eco-efficiency behavior.

Interfaces with Other DisciplinesEco-efficiency and eco-productivity change over time in a multisectoral economic system☆

We measure eco-efficiency of an economy by means of an augmented Leontief input–output model extended by constraints for primary inputs. Using a multi-objective optimisation model the eco-efficiency frontier of the economy is generated. The results of these multi-objective optimisation problems define eco-efficient virtual decision making units (DMUs). The eco-efficiency is obtained as a solution of a data envelopment analysis (DEA) model with virtual DMUs defining the potential and a DMU describing the actual performance of the economy. This procedure is then extended to an intertemporal approach in the spirit of the Luenberger productivity indicator. This indicator permits decomposing eco-productivity change into eco-efficiency change and eco-technical change. The indicator is then further decompounded in a way that enables us to examine the contributions of individual production factors, undesirable as well as desirable outputs to eco-productivity change over time. For illustration purposes the proposed model is applied to investigate eco-productivity growth of the Austrian economy.

Mathematical optimization and economic analysis

Single-Objective Optimization.- Scarcity and Efficiency.- Kuhn#x2013 Tucker Conditions.- Convex Programming.- Linear Programming.- Data Envelopment Analysis.- Geometric Programming.- Multiobjective Optimization.- Fundamentals of Multiobjective Optimization.- Multiobjective Linear Programming.- Multiobjective Geometric Programming.

Optimal price and advertising policy under atomistic competition

Abstract This paper follows that of Phelps and Winter (1970) with an extension made to include advertising. The following question will be discussed: should a firm lower price and/or increase advertising in order to maximize the present profit value? Using the theory of optimal control the rules for optimal price and advertising policy under the assumption of atomistic competition will be derived.

A Consistent Formulation of the Leontief Pollution Model

We consider the environmental Leontief model, which is an input-output model augmented by pollution-generation and pollution-abatement sectors. Two formulations of this model, dating back to Leontiefs work in 1970, can be found in the literature. One formulation treats an exogenously given vector of the tolerated level of pollutants (environmental standards) as a negative variable on the right-hand side of the model. The other formulation supposes that each industry eliminates a given proportion of the pollution that it creates, so that the proportions of gross pollutants which are subject to treatment by each sector enter as given parameters. Even in the case when the levels of production and abatement in the two different model formulations are equal, the solutions of the dual or price model are different for cases where some net pollution is left untreated. First, the analytical relationship between the two price models is established. Secondly, both models formulated in a linear programming framework are extended by imposing emission charges (effluent taxes) for untreated pollution. Finally, it will be shown how to estimate the level of emission charges for both model formulations such that they provide the same levels of production and abatement, as well as the same shadow prices. This is illustrated by a numerical example.

Reconsideration of Non-negative Solutions for the Augmented Leontief Model

We consider the Leontief model augmented with pollution-generation and pollution-abatement sectors. The conditions to ensure the existence of non-negative solutions for the total output and for the vector of abatement activities, depending on the exogenously given final demand and environmental standards, are presented. They are extensions and modifications of the conditions for a single pollutant derived, for example, by Miller and Blair.

Efficiency analysis of a multisectoral economic system

The present paper is concerned with efficiency analysis applied to a single economy represented by the Leontief input–output-model extended by the constraints for primary factors. First, the efficiency frontier is generated using a multi-objective optimization model instead of having to use data from different decision making units. The solutions of the multi-objective optimization problems define efficient virtual decision making units and the efficiency of the given economy is defined as the difference between the potential of an economy and its actual performance and can be obtained as a solution of a DEA model. It can be shown that the solution of the above defined DEA model yields the same efficiency score and the same shadow prices as the models by ten Raa (Linear analysis of competitive economics, LSE handbooks in economics. Harvester Wheatsheaf, New York, 1995; The economics of input–output analysis. Cambridge University Press, Cambridge, 2005) despite the different variables used in both models. Using duality theory of linear programming the equivalence of the approaches permits a clear economic interpretation. In the second part of the paper this approach is extended to the Leontief augmented model including emissions of pollutants and abatement activities. In this way the eco-efficiency of an economy can be analyzed.Recessions are easily recognizable from a decrease in GDP. What really should interest us, however, is the difference between the potential of an economy and its actual performance (J. Stiglitz, 2002).

An environmental input-output model with multiple criteria

It is often claimed that there is a trade-off between economic goals and the quality of the environment. For this reason, an environmental input-output optimization model with multiple objectives is formulated. The criteria are the minimization of factor costs to produce the Gross National Product and the minimization of net pollution for a given level of final demand. Using the LeChatelier-Samuelson principle, we analyze the changes in the production of the sectors and in the prices of the goods (described by the dual model) due to the change in the preferences of the decision makers. It can be shown that higher weights for the environmental objectives imply — in tendency —non-decreasing production of the sectors andnon-decreasing abatement activities. The changes of prices are ambiguous. The condition for increasing prices is given. To some degree, the opposite results can be achieved, if maximization of the value of final demand (or of private consumption) and minimization of net pollution under the constraints for primary input are taken as objective functions. In this case, increasing weights for environmental goals will leadin tendency tonon-increasing final demand and tonon-increasing net pollution. Under given conditions, higher environmental quality will be achieved bynon-increasing gross production and abatement activities.

Lexicographic geometric programming

Abstract The paper presents the Kuhn-Tucker conditions and the duality theory for the lexicographic minimization problem: lex min {F(x) ‖ x ϵ Rn, G(x) ≦ 0m} where F and G are vector valued functions from Rn → Rs and Rn → Rm, respectively. The lexicographic duality is then applied for problems with posynomials in the objectives and in the constraints. The duality theory for lexicographic geometric programming is developed and illustrated by a numerical example.