科研之友
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摘要
There are several distance function definitions in a general production framework, including Data Envelopment Analysis, which can be used to describe the production technology and to define corresponding measures of technical efficiency (notably the Shephard and the directional distance functions). This paper introduces a generalisation of the distance function concept based on the idea of minimizing firm%26apos;s opportunity cost. We further state a general dual correspondence between the cost function and this new general distance function, which encompasses all previously published duality results. All our results also hold under the assumption that we work in a Data Envelopment Analysis context. 1. Introduction The theory of duality has acquired great popularity in microeconomics [1每4]. Duality theory has allowed to state the most common alternative ways of representing preferences and technologies, such as indirect utility and expenditure functions, cost and distance functions, and so forth. Having different ways to describe a technology seems very suitable since some types of mathematical arguments are easier to demonstrate by using, for example, a cost function instead of a distance function, that is, a direct representation of the technology [1, page 81]. (A firm produces outputs from a set of inputs. In order to analyze firm choices, it is necessary a convenient way to summarize the production possibilities of the firm, that is, which combinations (vectors) of inputs and outputs are feasible. A technology is the set of all these feasible combinations [1].) Both the cost function and the distance function are, by definition, optimization problems. The theory of duality studies under which conditions these two optimization problems are related. Distance functions are natural representations of multiple-output and multiple-input technologies. Shephard [5] was the first to define a distance function in a production context. In particular, the Shephard input distance function measures the largest radial contraction of an input vector consistent with remaining technically feasible. Additionally, the Shephard input distance function is of common use in production theory and it also has a dual relation to the cost function. Nevertheless, the Shephard input distance function is not the unique known distance function in the literature. During the last two decades, Luenberger [6], Chambers et al. [7], Briec and Lesourd [8] and Briec and Gard豕res [9] have proposed some new achievements with respect to duality theory and distance functions. To be precise,
- 出版日期2011
